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Probing interactions and phase separations of proteins, colloids and polymers with light scattering

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Title:
Probing interactions and phase separations of proteins, colloids and polymers with light scattering
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Book
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English
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Parmar, Avanish Singh
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University of South Florida
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Subjects / Keywords:
Lysozyme
Nucleation
Microrheology
Viscosity
Nanoparticles
Dissertations, Academic -- Physics -- Doctoral -- USF   ( lcsh )
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non-fiction   ( marcgt )

Notes

Summary:
ABSTRACT: The broad objective of my research is to investigate the physical characteristics and interactions of macromolecules and nanoparticles, and the corresponding effects on their phase separation behavior using static and dynamic light scattering (SLS & DLS). Light scattering provides a non-invasive technique for monitoring the in-situ behavior of solutes in solution, including solute interactions, sizes, shapes, aggregation kinetics and even rheological properties of condensed phases. Initially, we investigated lysozyme solutions for the presence of preformed aggregates and clusters that can distort the kinetics of protein crystal nucleation studies in this important model system for protein crystallization. We found that both undersaturated and supersaturated lysozyme solutions contained population of large, pre-existing protein aggregate.Separating these clusters and analyzing their composition with gel chromatography indicated that these clusters represented pre-formed lysozyme aggregates, and not extrinsic protein contamination. We investigated the effect of chaotropic versus kosmotropic ions (water structure breakers vs. structure makers) on the hydration layer and hydrodynamic interactions of hen egg white lysozyme. Surprisingly, neither chaotropic nor kosmotropic ions affected the protein hydration layer. Salt-effects on direct and hydrodynamic protein interactions were determined as function of the solutions ionic strength and temperature. Using both static and dynamic light scattering, we investigated the nucleation of gold nanoparticles forming from supersaturated gold sols. We observed that two well separated populations of nuclei formed essentially simultaneously, with sizes of 3nm vs. several tens of nanometer, respectively.We explore the use of lysozyme as tracer particle for diffusion-base measurements of electrolyte solutions. We showed that the unusual stability of lysozyme and its enhanced colloidal stability enable viscosity measurement of salts solutions at high salt concentration, over a wide range of pH values and temperatures for the common tracer particle polystyrene flocculates. We applied dynamic light scattering to measure the viscoelastic responses of polystyrene probe particles embedded in solutions and gels of two different polymers: polyacrylamide (PAAm) and poly-N-isopropylacrylamide (poly-NiPAAm).
Thesis:
Dissertation (Ph.D.)--University of South Florida, 2009.
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Includes bibliographical references.
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by Avanish Singh Parmar.
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Title from PDF of title page.
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Document formatted into pages; contains 103 pages.
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Includes vita.

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Probing Interactions and Phase Separations of Proteins, Colloids, and Polymers with Light Scattering by Avanish Singh Parmar A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosphy Department of Physics College of Arts and Sciences University of South Florida Major Professor: Ma rtin Muschol, Ph.D. Garrett Matthews, Ph.D. Dennis Killinger, Ph.D. Chun Min Lo, Ph.D. Date of Approval: June 9, 2009 Keywords: Lysozyme, Nucleation, Micr orheology, Viscosity, Nanoparticles Copyright 2009, Avanish Singh Parmar

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Acknowledgements I would like to take this opportunity to express my gratitude to all those who helped me during my research work to finish this thesis. I am deeply indebted to my advisor Dr Martin Musc hol, Associate Professor Department of Physics, for his help, inva luable suggestions, encouragement and his patience, during my research and writing of this thesis. He taught me how to ask questions and express my ideas I will always be grateful to him for his constructive criticisms during our group meeting. His rele ntless pursuit of perfection has made me a better researcher. I will alwa ys be grateful for his ki nd support even during personal crisis. I am also thankful to my com mittee members Dr Ryan Tomy, Dr Garret Matthews, Dr Dennis Killinger and Dr Lo for stimulating discussions and general advice. I am also very grateful to Dr Pritish Mukherjee, Chai r of Department of Physics and Dr. Johnson for their help and advice. I would also like to give special thanks to Shanon H ill, my fellow lab member for her stimulating discussions and support. I would like to thank the rest of my fellow lab members (both past and present), for their coop eration and all the fun we had in the last five years. I am also thankful to my friends (Anurag, Avis, and Himanshu) for their emotional support, camaraderie and help they provided. I would also like to thank my pare nts and family for thei r constant support and inspiration. Last but not least, I woul d also give thanks to my wonderful wife Jayeeta Lahiri for her constant support and encouragement.

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Table of Contents List of Tables ..................................................................................................................... vi List of Figures ................................................................................................................... vii Abstract ............................................................................................................................... x Chapter 1 : Motivation/Introduction ................................................................................... 1 Chapter 2 : Light Scattering ................................................................................................ 4 2.1 Wave Description of Light ................................................................................... 4 2.2 Scattering by an Isolated Polarizable Particle ....................................................... 4 2.3 Scattering by Macrom olecules in Solution ........................................................... 8 2.4 Light Scattering Techniques ............................................................................... 13 2.4.1 Static Light Scattering (SLS) ...................................................................... 13 2.4.2 Dynamic Light Scattering (DLS) ................................................................ 14 2.5 Dynamic Light Scattering Analysis for Viscoelasticity ..................................... 17 2.6 Diagram for Dynamic Light Scattering Set-up ................................................... 19 2.7 References ........................................................................................................... 20 Chapter 3 : Effect of Lysozyme Cluster on Nucl eation Kinetics of Supersaturated Solution ............................................................................................................................. 22 3.1 Introduction ......................................................................................................... 22 3.2 Materials and Methods ........................................................................................ 23 3.2.1 Chemicals .................................................................................................... 23 3.2.2 Preparation of Lysozyme Solutions ............................................................ 24 3.2.3 Dynamic Light Scattering (DLS) Measurements ....................................... 24 3.2.4 Thermal Changes in Solution Viscosity ..................................................... 25 3.2.5 Separation of Pre-existing Clusters ............................................................. 25 3.2.6 SDS Gel Electrophoresis ............................................................................ 25 3.2.7 Growth of Macroscopic Crystals ................................................................ 26 iii

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3.3 Results ................................................................................................................. 26 3.3.1 Detection and Characterization of Sub-micron Clusters in Solutions. ....... 26 3.3.2 Analysis of Cluster Composition ................................................................ 29 3.3.3 Physical Characterizati on of Pre-existing Clusters ..................................... 30 3.3.4 Effects of Sub-micron Lysozyme Clusters on Crystal Nucleation ............. 33 3.3.5 Effects of Pre-assembled Lysozyme Clusters on Lysozyme Crystals ........ 37 3.4 Discussion ............................................................................................................ 38 3.5 References ............................................................................................................ 42 Chapter 4 : Effect of Chaotropic & Kosmotr opic Ions on Hydration & Hydrodynamic Interaction of Lysozyme ................................................................................................... 45 4.1 Introduction ......................................................................................................... 45 4.2 Materials and Methods ........................................................................................ 46 4.2.1 Chemicals .................................................................................................... 46 4.2.2 Preparation of Lysozyme Solutions ............................................................ 46 4.2.3 Static (SLS) and Dynamic (DLS ) Light Scattering Measurements ............ 47 4.2.4 Dynamic (DLS) and Static (S LS) Light Scattering Analysis ..................... 47 4.2.5 Growth of Macroscopic Crystals ................................................................ 48 4.3 Results ................................................................................................................. 48 4.3.1 Chaotropic & Kosmotropic Salts and Water Viscosity .............................. 49 4.3.2 Measuring protein hydration and hydrodynamic protein interactions ........ 52 4.3.2.1 Direct and hydrodynamic interac tion of lysozyme in solutions ...... 53 4.3.2.2 Effects of Kosmo vs. Chao ions on lysozyme hydrations ............... 55 4.3.2.3 Salt specific effects on dire ct and hydrodynamic interaction .......... 58 4.4 Discussion ............................................................................................................ 61 4.5 References ............................................................................................................ 63 Chapter 5 : Nucleation and Growth of Gold Nanoparticles .............................................. 65 5.1. Introduction ........................................................................................................ 65 5.2 Materials and Methods ........................................................................................ 67 5.2.1 Synthesis of Gold Nanoparticles ................................................................. 67 5.2.2 Dynamic light scatteri ng (DLS) measurement ........................................... 68 5.3 Results and Discussion ...................................................................................... 69 5.4 References .......................................................................................................... 75 iv

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Chapter 6 : Lysozyme as Tracer for Measuri ng Viscosity of Aqueous Solutions ............ 77 6.1 Introduction ......................................................................................................... 77 6.2 Materials and Methods ........................................................................................ 78 6.2.1 Chemicals .................................................................................................... 78 6.2.2 Lysozyme Stock Solutions .......................................................................... 78 6.2.3 Dynamic Light Scattering (DLS) ................................................................ 79 6.2.4 Tracer Particle Measurements .................................................................... 79 6.2.5 Analysis of Tracer Diffusivity .................................................................... 79 6.3 Results and Discussion ....................................................................................... 79 6.3.1 Viscosity Measurement Using Polystyrene Nanobeads ............................. 79 6.3.2 Viscosity Measurements Using Lysozyme ................................................. 82 6.4 Conclusion .......................................................................................................... 88 6.5 References ........................................................................................................... 90 Chapter 7 : Probing Viscoelastic Behavior of poly-N-isopropylacrylamide During Thermally Induced Gel Collapse ...................................................................................... 92 7.1 Introduction ......................................................................................................... 92 7.2 Materials and Methods ........................................................................................ 93 6.2.1 Preparation of Polyacrylamide (PAAm) Sample ........................................ 93 6.2.2 Preparation of poly-N-isopropylacrylamide sample ................................... 94 6.2.3 Dynamic Light Scattering Measurements ................................................... 94 7.3 Results ................................................................................................................. 95 7.3.1 Viscosity of Water using Polystyrene Beads .............................................. 95 7.3.2 Microrhelogical Measurement for Polyacrylamide (PAAm) ..................... 96 7.3.3 Poly-N-Isopropylacrylamid e (poly-NIPAAm) System .............................. 97 7.3.3.1 Gel Phase Transitions ...................................................................... 97 7.3.3.2 Microrheological Measurement with Poly-NiPAAm ...................... 98 7.4 References ......................................................................................................... 101 Chapter 8 : Conclusion ................................................................................................... 102 About the Author ................................................................................................... End Page v

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List of Tables Table 4.1 Summary of fitting parameters for viscosity water-salt mixtures at various solution te mperatures. 51 Table 4.2 Summary of Jone s-Dole viscosity B coeffici ents for the salt ions in this study. 52 Table 6.1 Temperature and concentration dependence on the viscosity values of three different salts (NaCl, MgCl2, and CsCl) 87 vi

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List of Figures Figure 2.1 Scattering geometry 5 Figure 2.2 Overview of static li ght Scattering measurements 13 Figure 2.3 Overview of dynamic light scattering meas urements 15 Figure 2.4 Field correlation functio n for polystyrene sphere 16 Figure 2.5 Malvern instrument DLS setup 19 Figure 3.1 DLS of lysozyme stock so lutions prepared with different suppliers 27 Figure 3.2 Effect of filt ration on contamination of Seikagakau lysozyme 28 Figure 3.3 Analysis and composition of lysozyme clusters by SDS Gel Electrophoresis 30 Figure 3.4 Dependence of cluster peak amplitude on lysozyme concentration 31 Figure 3.5 Thermal collapse of lysozyme clusters 32 Figure 3.6 Cluster distribution in lysozyme /salt solution prior to quenching 34 Figure 3.7 DLS from supersaturated lysozyme solutions 36 Figure 3.8 Lysozyme crystals containing different levels of lysozyme clusters 37 Figure 4.1 Plot of the visc osity of water at T = 20 C as function of dissolved salt concentration 50 Figure 4.2 Salt-Specific Effects on Debye Ratios KClys/R and Mutual Diffusivities Dm of Lysozyme 54 Figure 4.3 Effects of Ch aotropic and Kosmotropic Salt Ions on Lysozyme hydration. 57 vii

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Figure 4.4 Dependence of Direct and Hydrodynamic Interaction Parameters on Salt Type, Salt Concentration and Solution Temperature 59 Figure 4.5 Protein crysta ls grown from lysozyme solutions in the presence of Chaotropic vs. kosmotropic Cations 60 Figure 5.1 Normalized temporal correla tions of the intensity of scattered light vs.delay time of colloidal gold pa rticles at different time intervals. 69 Figure 5.2 Intercepts of the intensity correlation function of scattered light and the overall intensity of scat tered light vs. the incubation time of the sample 70 Figure 5.3 Particle size distributions obtained duri ng the early phases of the synthe sis of gold colloids in the presence of cephalexin 71 Figure 5.4 Changes in the mean pa rticle size for both the small and large gold co lloids as function of inc ubation period and solution temperature. 72 Figure 5.5 Changes in the total inte nsity of scattered light during the synthesis of colloidal gold particles at T = 15 C and 25 C. 73 Figure 5.6 Percentage of total light scattered by either population of colloidal gold particles during synthesis at T = 15 C 74 Figure 6.1 Viscosity of water as a function of temperature using polystyrene as a probe 80 Figure 6.2 Viscosity of 100mM Na Ac using different probes 81 Figure 6.3 Dependence of pH and te mperature on hydrodynamic radius 82 Figure 6.4 Effect of temperature and salt concentration on Diffusion coefficient of lysozyme 84 Figure 6.5 Measured viscosity of CsCl, NaCl, and MgCl2 as a function of temperature and concentration using lysozyme as a probe for DLS measurement 86 Figure 7.1 Absorbance of the polymer solution at 260nm as a function of time 94 viii

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Figure 7.2 Viscous modulus a nd viscosity of water at T=20 C as a function of fre quency derived by microrheological measurements using beads. 95 Figure 7.3 Microrheological measurem ent for polyacrylamide (PAAm) 96 Figure 7.4 Changes in the total scat tering intensity of (poly-NiPAAm) as a function of temperature 98 Figure 7.5 Microrheological meas urement for (poly-NiPAAm) 99 Figure 7.6 Comaprison of elastic modul us, viscous modulus and viscosity as a function of frequency at thr ee different temperatures 100 ix

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Probing Interactions and Phas e Separations of Proteins, Colloids and Polymers with Light Scattering Avanish S. Parmar ABSTRACT The broad objective of my research is to investigate the physical characteristics and interactions of macrom olecules and nanoparticles, a nd the corresponding effects on their phase separation behavior using static and dynamic light scattering (SLS & DLS). Light scattering provides a non-inva sive technique for monitoring the in-situ behavior of solutes in solution, including so lute interactions, sizes, shap es, aggregation kinetics and even rheological properties of condensed phases. Initially, we investigated lysozyme so lutions for the pres ence of preformed aggregates and clusters that can distort the ki netics of protein crysta l nucleation studies in this important model system for protein crystallization. We found that both undersaturated and supersaturated lysozyme solutions contained population of large, preexisting protein aggregate. Separating thes e clusters and analyzing their composition with gel chromatography indicated that thes e clusters represented pre-formed lysozyme aggregates, and not extrinsi c protein contamination. We investigated the effect of chaotropic versus kosmotropic ions (water structure breakers vs. structure makers) on the hydrati on layer and hydrodynamic interactions of hen egg white lysozyme. Surprisingly, neither chaotropic nor kosmo tropic ions affected the protein hydration layer. Salt-effects on direct and hydrodynamic protein interactions were determined as function of the solu tions ionic strength and temperature. Using both static and dynamic light sca ttering, we investigated the nucleation of gold nanoparticles forming from supersaturat ed gold sols. We observed that two well separated populations of nucle i formed essentially simultane ously, with sizes of 3nm vs. several tens of nanome ter, respectively. x

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xi We explore the use of lysozyme as tracer particle for diffusion-base measurements of electrolyte solutions. We s howed that the unusual stability of lysozyme and its enhanced colloidal stability enable viscosity measurement of salts solutions at high salt concentration, over a wide range of pH values and temperatures for the common tracer particle polystyrene flocculates. We applied dynamic light scattering to measure the viscoela stic responses of polystyrene probe particles embedded in solu tions and gels of tw o different polymers: polyacrylamide (PAAm) and poly-N-isopropylacrylamide (poly-NiPAAm).

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Chapter 1 Motivation/Introduction The broad objective of this thesis is to investigate the phys ical characteristics and interactions of macromolecules and nanopart icles, their effect on phase separation behavior and to characterize the rheological properties of their condensed phases. Using ]static (SLS) and dynamic (DLS ) light scattering provides a uniquely suited set of experimental technique to perform these ta sks: light scattering in intrinsically noninvasive and can be used to measure a very wide range of material characteristics, including solute interaction, particle size distributions an d aggregation kinetics, and rheological properties of soft condensed pha ses. My overall research program was divided between two different projects. The first project investigated the interaction effects and nucleation behavior of proteins and gold sol during solid phase formation. The second set of projects focused on opt ical, non-invasive approaches towards characterizing rheological prop erties of aqueous solutions and hydrogels. In the following I will motivate the specific research proj ects we performed within this broader framework. X-ray diffraction from high-quali ty protein crystals remains the most reliable approach for obtaining detailed information about the 3-dimensional stru cture of proteins. This information is critical for understandi ng how the spatial structure of these ordered polypeptide polymers supports their biological function. Attempts at high-throughput protein structure determinations, however, have been frustrated by the difficulties of establishing suitable solution conditions fo r promoting the nucleation and subsequent growth of high-quality crystals. Frequently, th e main bottleneck is the initial step of crystal nucleation itself. The kinetics of protein crystal nucleation and the morphology of aggregates were among the earliest targ ets of fundamental studies in protein crystallization. However, fundamental studi es of crystal nuclea tion, using the common model protein small hen egg white lysozyme produced inconsistent and contradictory 1

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results. Using dynamic light scattering (DLS ), we investigated whether intrinsic heterogeneities in commonly used stock mate rials of lysozyme might contribute to the observed inconsistencies. Chapter 3 summarizes our research efforts in characterizing different commercial sources of lyophilized lysozyme stock and the effect their preexisting heterogeneities have on prot ein crystal nucleation and growth. Another persistent challenge in protein crystallization is to understand how the choice of precipitant affects the subsequent kineti cs of protein crystal nucleation and growth. The specific questions we investigated were whether and how different salt ions affect the protein hydration layer and the hydrodynami c interactions of the protein. The hydration layer is commonly considered an important kinetic barrier toward protein aggregation. Similarly, the kinetics of crysta l nucleation and crystal growth could also be affected by the effects of hydrodynamic interac tions among the protein molecules. Using a combination of static and dynamic light scattering, we investigated th e effect of either chaotropic or kosmotropis ions (i.e. ions that either break or reinforce local water structure) on the hydration layer and hydrodynamic interactions of hen egg white lysozyme under conditions supportive of protein crystallization (Chapter 4). The nucleation and growth mechanisms of colloid gold partic les synthesized from solution is of broad interest to the rapidl y growing field of nanoparticle chemistry and physics. However, to fully understand the forma tion of particles at various levels, it is essential to capture and investigate the early stages of nucleation of these nanoparticles, their growth kinetics and the effect of various solution para meters on this process. We applied static and dynamic light scattering to investigate the unusual nucleation and growth kinetics of gold nanoparticles synthesi zed from the solution phase in the presence of the antibiotic Cepha lexin (Chapter 5). Local measurements of solution viscosity as function of various solution parameters (temperature, pH, solute type and concentration) is often critical for characterizing solute transport in solution. Many commonly used viscosity measurements require bulk samples, can be time consumi ng, require considerable heating power and thermal equilibration times due to the large thermal capacity of common liquids, and often require independent measurements of so lution density in order to obtain viscosity values. As an alternative and nonintrusive method, we used diffusion measurements of 2

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nanoscopic tracer particles toob tain the viscosity of saline solutions as function of salt type, salt concentration and solution temperat ure. We compared the performance of two different types of tracer particles to accomp lish this task: uniformly sized polystyrene beads versus the protein hen egg white lysozyme. The results of this comparison are summarized in chapter 6. Local measurements of tracer particle diffusivity with optical techniques can be further extended for characterizing the viscoela stic properties of soft materials such as gels and polymer solutions. These materials typically have comple x structures spanning multiple length and time scales. The response of these complex materials to shear strain is an important step towards characterizing and understanding their internal structure. Using dynamic light scattering off polystyrene beads embedded in gels, we characterized the viscoelastic behavior of two different types of polymers: cross linked polymer polyacrylamide (PAAm) and poly N-isoprop ylacrylamide (pNiPAAm). The latter system is particularly intriguing sin ce NiPAAm gels undergo a thermally driven dehydration transition. Results of these experiments are presented in chapter 7. 3

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Chapter 2 Light Scattering 2.1 Wave Description of Light Light is a minimally invasive probe that can be used to obt ained information about the structure and dynamics of molecules. Maxwells equation forms the basic of the description of all electromagnetic phenomena. These equations identify the light as a transverse electromagnetic wave with the dir ection of the oscillating E and B-field is perpendicular to the direction of propagation to each other. The electric field associated with a plane wave at location r and time t is given by tiexpr.ikexpEt,rE0 (2.1) )t,r(Ewhere is the spatial orienta tion of the oscillation (pol arization) for a field strength of magnitude E0 0 is the wavelength of light, k is the wavevector ( = 2 / 0), and is angular frequency ( = 2 0 = 2 c / 0) 2.2 Scattering by an Isolated Polarizable Particle The following discussion reproduces in larg e part the theoretical description of light scattering by Johnson & Gabriel2. In fig.2.1, a plane electromagnetic wave propagates in the +x direction, and the x and y axes define the scattering plane. We assumed that the incident light is linearly pol arized along the z-direction. kxcos( oz E i E )t This electric field interacts with electrons tom or molecule (located at the origin) to (2.2) in an a induce an electric dipole moment, which oscillate at an angular frequency The expression for the induced dipole moment is p = Ei (2.3) 4

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where, p is the induced dipole moment, and is the polarizability ten sor. ig.2.1: Scattering Geometry or optically isotropic scatterers, is a constant and independent of orientation and ) tkxcos( z0 E z E z p F F equation (2.3) becomes p (2.4) tromagnetic theory that an ac We know from elec celerating charge generates electromagnetic radiation. Hence, an oscillating dipole produces radiation19,20 and its oscillating electric moments pz provides the source of scatte red radiation. The solution for the scattered field of an oscillating dipole in the far-field (R >> 0) becomes19,20 R 1 p 2 p 2 d E 2 dt s (2.5) o, if we solve the above equations the expression for Es at R resulting from a dipole at the origin in Fig.2.1 is (see Griffith section 11.1.2)19 S Y X Z E B P 5

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) sin( R 2 c)4( p 2 s E 0 (2.6) p and R. tric field E are given by (2.7) Thus, the incident radiation Ii where is the angle between The intensities corresponding to the elec E.EcI 0 2 Z0 E 0 c /2 0 dt)t( 2 cos) 2 ( 2 0 E 0 c i I (2.8) It is more common to use complex variables oz ei(kxt) (2.9) E = E So, Ii can be written as1 2 i E 2 0 c Ii (2.10) From equation (2.7) the intensity of scattered light is given by s> = c0Es 2 (2.11) denoted the average of the quantity. Now, using equation (2.4) and equation (2.8), we get i 2I 2 pc 0 (2.13) 6

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Substituting equation (2.13) int we get o equation (2.12) 2 sin 2 R 4 0 2 ) 0 4( 2 R 4 c 2 ) 0 4( 4 Ii (2.14) y to rewrite the equation (2.14) in terms of change in re concentration C instead of polarizability p as they are the experimentally determined uantities. Expanding the refractive i ndex n in a Taylors series gives 24 16 2 sin 0 IsNow, I will tr fractive index n with q C c n 1n (2.15) and then squaring it gives C c n 21 2 n (2.16) n2 is also written as2,21 ) 0 (N1 2 n So, from equation (2.16) a nd equation (2.17) we get (2.17) n C m 0 2C C n N 0 2 (2.18) where m is the scattering mass per particle. So, inserting equation (2.18) into equati on (2.14) and then multiply it by N=NAC/M, the as of particles can be written as intensity of scattered light per volume fo r a g 2 sin C n 2 4 CM 2 4 I I2 s A NR 0i (2.19) scatterers per unit volume and M where N is the number of is the molecular weight. 7

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2.3 Scattering by Macromolecules in Solution The scattering intensity for condensed phases is less than predic ted by equation (2.14) ence of the scatte red light waves. When of scattered light to these optical homogenities. For this we will consider that the solution of scatterers is composed of N and equation (2.19) due to the destructive in terfer a monochromatic light is inci dent onto a dilute macromol ecule solution, due to the difference in refractive index of solvent and so lute, the incident light is scattered by each illuminated macromolecules into all directions7,11. The scattered light waves from different macromolecules interfere at the detector to produce a net scattering intensity I(t). If all the macromolecules were stationary then the scattered light intensity would be constant. However, macromolecules in th e solution undergo Brownian motion, which constantly changes the opti cal inhomogenities and, th erefore, the corresponding fluctuations in scattering intensity in the solutions. In the following, I will relate the intensity in small volume element ( V) with V << Connection to the scat tering theory developed in section 2.2 is made by realizing that fluc tuation in concentrati on or density leads to fluctuation in polarizability. Fluctuation in polarizability by one volume element is defined as vvv where, is the fluctuations I the polarizability, (2.20) v v is the instantaneous polarizability, and v the time average of v is Fequation (2.14) we see t th rom hate intensity of scattered ra diation is proportional to e square of the polarizability. Thus, th 22 2 vv vv (2.21) oss term cancels because v is zero. Similarly, the contribution of the On the right hand side of equation, the cr the time average of v cancels as it is always possible to 8

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pair two scattering volumes such that destru ctive interference occurs. The net scattering will depend on 2 .Now, using equation (2.21) into equation (2.14) and multiplying by N=1/ V, we get v 2 4 16 I 2 R 4 0 2 ) 0 4( v i I s (2.22) s in polarization for a gi the mean square fluctuations in concentration as Now, mean square fluctuation ven volume element are related to 2 C 2 C 2 ) V ( V,T (2.23) ex of the so lution is related Similarly, the refractive ind to the polarizability by 0 V 2 o n 2 n (2.24) 0Differentiating equation (2.24) with re spect to solute concentration gives Where, n is the index of refraction of solute and n is the index of refraction of solvent. V,T C 0 V 1 n V,T C n2 (2.25) nd (2.25), we get Using equations (2.23) a 2 C 2 V,T C n 2 2 (2.26) quation (2.26) into equation (2.22), we terms of the mean concentration fluctuation 0 Vn2 v Finally, substituting e get the scattering intensity in 9

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2 R 4 0 V,T C i I s I (2.27) 2 C 2 n V 2 n 2 4 The energy required to produce the concentrati on fluctuation is the Helmholtz free energy s are small, we can expand F in te F. Since the fluctuation rms of Taylors series ....... 2 C 2 C F 2 !2 1 C V,T C F F V,T (2.28) ill be zero because the system is in equilib concentration fluctuations is equal to exp (F/kBT). So, it will be The first term w rium. The probability of 2 C V,T 2 C F 2 F T B k exp T B k exp (2.29) The ensemble average of ( C)2 is given by 0 Cd T B k F exp T B k F exp 2 0 C 2 C (2.30) Solving the given integral, we get V,T 2 C F 2 T B k 2 C (2.31) 10

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Putting equation (2.31) into equation (2.27) we is conventional to write th sion in powers of par ticle get the concentration dependence of the terms of a virial expan concentration C. In the following I will se two very important relations whose derivation can be found anywhere else2,21 scattering intensity. However, it e concentration dependence in u V,T C 1 1 VC V8 V,T 2 C F 2 (2.32) ..... 2 C 3 B3C 2 B2 M 1 A N V,T C 1 1 VT B k 1 (2.33) Using equations (2.31), (2.32), & (2 .33) and equation (2.27), we get ........ 2 p c 3 B3 p c 2 B2 1 M A N 2 R 4 i 2 p dc dn p c 2 n 2 4 I s I (2.34) In scattering experiments, Ii and R are fixed and we measure Is. These measured quatities ed into one quantity called Rayleigh ratio R can be combin 2 R i I s I R (2.35) We also define an optical consta nt K which only depends on the solvent properties, The advantage is that it is independent of th e incident light intens ity and the distance to the scattered light detector. and but not solute parameters. 2 p 4 A 2dC dn N n4 K (2.36) 11

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where n0 is the solvent's refrac s number, the wavelength of inp lysozyme (dn/dC ) = 0.185 for = 633nm 15. Equation (2.36) is tr ue for incident light tive index, NA Avogadro' the refractive inde cident light, and (dn/dC ) is x incr ement due to the solute. For p polarized in the z-direction. For unpolarized incident light we can make corrections by decomposing the intensity into equal parts of incident light polarized in both the zdirection and the y-direction. Then K is defined as 2 p 4 A 2dC dn N n2 K (2.37) s of K and R, we So, defining equation (2.34) in term get .... 2 p C 3 B3 p C 2 B2 M 1 R p kC (2.38) e have neglected the in traparticle inte particles. Therefore, this equation applies fo r small solute particles with major dimension less than /10. When the size of the particle is greater than /10 the light scattered from R = [(ItotIsol)/Itol] [n/ntol]2 R ,tol (2.39) oluene standard, respectively. R ,tol is the Rayleigh ratio Rtol In equation (2.38) w rference effects between the two points within the particle will reach the detector at di fferent time which will produce an additional phase difference (due to the path difference for the light scattered from two points) and thus will cause angular depe ndence of the scattered light intensity. In practice, R is obtained by comparison agains t a standard of known scattering cross section (in our case, toluene). where Itot, Isol and Itol are the measured scattering intensity of the protein solution, the salt/buffer background and of the t for toluene at = 633. For our set-up, the manufa cturer quotes a Rayleigh ratio of = 13.52 10-6 cm-1.22. For interacting particles, this normalized Rayleigh ratio R is related to the properties of the protein solution via KCp/R = M-1 [1 + ks M-1 + 2B22Cp 12

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where M is the molecular weight of the protein, Cp is the protein concentration (in mg/ml), ks is the direct interaction parameter, and = Cp is the protein's volume frtion in ac. The constant K in equation (2.40) is given by equation (2.37). For our set-up, verse of the scattering wavenumber q-1 38 nm and lysozyme's hydrodynamic radius is Rh = 1.9 nm. Since Rh q << 1, lysozyme is a Rayleigh scatterer thereby eliminating the need for scattering intensity measurements at multiple angles 2.4 Light Scattering Techniques 2.4.1 Static Light Scattering (SLS) Signal Fig.2.2: Overview of Static Light Scattering Measurements As shown in fig.2.2, during a ty t scattering experi ment, incident light Ii pinges on a macromolecular solution, and the scattered light Is is detected at some the signa l is noisy due to pica l ligh im angle and distance R. As shown on the LHS of fig. 2.2 thermal fluctuation in the local concentration of scatterers. In static light scattering we measure the time-averaged intensity of this scattered light. In general, the scattering intensity of macromolecula r solutions is given by 5 )q(S)q( P dC dn NR MCn4 I I2 p A 24 p 22 i s (2.41) 13

PAGE 25

where, P (q) and S (q) are the form structure factor of the molecules, which nd in effec refractive index, M is the molecular weight of rotein), dn/dCp the refractive and static te rparticle interference account for intraparticle a ts respectively, n is the solvent the solute (p index increment of the solu tion due to the protein, Cp is the proteins mass density, NA is Avogadros constant, R is the distance between the origin of the scattering volume and the detector, is the wavelength of the incident light., and q is the scattering wave number given by sin n4 q (2.42) 2 Equation (2.41) is a generalized versi on of equation (2.38) derived above. e is a Rayleigh scatterer as its radius (R 2nm) is much smaller than the = 632.8 nm). Therefore P (q) = 1. Since, the mean protein spacing escribed by a virial expansion in the solute concentration. The corresponding scattering Lysozym wavelength of light ( (d) is much less than the wavelength of the light, structure factor S (q=0) can be d intensity cab therefore be written as given in equation (2.38). To first order approximation in Cp, equation (2.38) becomes 5 p2 pCB2 M 1 R kC (2.43) where we have neglected all hi gher order terms. A plot of KCp/R vs. protein concentration Cp varies linearly with protein concen tration. The molecular weight of the oefficients B2 is equal to the slope of KCp/R. Positive values of B2 indicate net 6ime as shown in fig.2.3. These fluctuations arise from the fact that the particles undergo random protein can be derived from the y-intercept at Cp=0 and values of the second virial c repulsion whereas negative values of B2 indicate net attraction between proteins 2.4.2 Dynamic Light Scattering (DLS ) Unlike static light scattering which measures the time-averaged scattered intensity, dynamic light scattering measures the fluctuati on in the scattered inte nsity with t 14

PAGE 26

thermal (Brownian) motion. Therefore, the distance between them is constantly varying. at the detector is due to the constructive The fluctuation in the intensity of scatter light and destructive interference of light scattered by the rando mly moving particles within the illuminated sample volume. The time dependent changes in intensity contain information about this Brownian motion. DL S measures the temporal correlations of theses statistical fluctuations in light scattering intensity. Fig.2.3: Overview of Dynamic Light Scattering Analysis Experimentally, a single photon detector records the number of scattered photons arriving within a short sample time interval ( 10-6 s). A multichannel digital correlator uses this digitized record of photon counts vs. time to calculate the intensity-intensity autocorrelation function g2( )7 dttItI dttItI g2 (2.44) In dynamic light scattering, particle size distributions are derive d from the measured intensity autocorrelation function g2( ) in a three step process. First, the intensity correlation function g2( ) is converted into the field correlation function g1( ) via the Siegert relation 7,8. 1 )(2 1gg. (2.45) 15

PAGE 27

An example of the field correlation function is shown in Fig. 2.4. The field correlation function, in turn, is the Laplace transfor0 (2.46) where pa rticles of a given s decay rates derived from the di stribution of particle sizes7. Each decay rate can be where D is the particle diffusion constant and q is the scattering vector given by equation (22) e Boltzmann constant, T the absolute temperature, the Hm of the decay rates of local concentration fluctuation for the different-sized particles present in the solution7-9 deGg1, denotes the decay rate for ize and G( ) is the distribution of related to the particle's diffusivity and the scattering geometry of the measurements via = D q2 (2.47) .4. Finally, the Einstein-Stokes17 relation is used to convert diffusion constants into particle sizes D0 = kBT / (6 RH) (2.48) Here k represent thB(temperature-dependent) solution viscosity and R the hydrodynamic radius of the diffusing particles. Fig.2.4: Field Correlation Function obtained fo r the polystyrene sphere in water 16

PAGE 28

The interaction effc vary both with salt concentration and salt identity otein concentrations, contributions from interactions to collec tive diffusivity increase in di rect proportion to the protein concentration. To this a pproximation, the corresponding co llective diffusion coefficient Dc is related to the single particle diffusivity D0 via5 Dc = D0 [1 + kD ] = D0 [1 + (kS + kH) (2.49) where kD = kS + kH is the sum of the direct and hydrodynamic protein interactions kS and iven by the Stokes-Einstein relation [see equation (1.48)]. Measuring the protein de tly fr om measurements of the static light scattering intensity vs. pr otein and salt concentration. .5 Dynamic Light Scattering Analysis for Viscoelastic Measurements ects on mutual protein diffusivity D 5,14. At moderate pr kH, is the protein volume fraction and D0 is the single-particle di ffusivity of the protein g pendence of the collective diffusion coefficient Dc, while simultaneously accounting for the contributions from di rect protein interactions kS and changes in solution viscosity (Cs,T), we can derive values for both the hydrodynamic radius RH and the hydrodynamic interaction parameter kH of the protein. Values for the direct protein interaction parameter kS can be obtained independen 2 We used Dynamic Light Scattering (DLS) to do microrheological measurements to obtain the viscoelastic properties of the polym er solutions for sol and gel phase. In this dynamics of probe particles are measured by DLS which is embedded in the solution. For a purely viscous medium, the beads embedded in the solution will diffuse through it and will have viscouslike behavior. For an elastic medium the motion of the probe particle will be constrained. Soft materials such as pol ymers are viscoelastic in nature i.e. they store and dissipate energy. In general th e full frequency dependence is given by the generalized Stokes-Einste in equation given by )( 2 raif T B k )f(* G (2.50) 17

PAGE 29

)(r2 is the where, G*(f) is the frequency dependent complex shear modulus, Fourier transform of the mean square displacement, a is the radius the beads. To get the mean square displacement, th e field correlation function g1( ), in turn, is obtained from the experimentally measured intensity correlation function g2( ) via the Siegert relation given by equation (2.45).The field correlation function g1( ) was normalized to get the intercept 1. For DLS, the electric field autocorrelation is given by11 6rqexpg22 1 (2.51) where q is the magnitude of scattering vect or which is given by equation (2.42). The r2( )> is calculated from Mason et. al 16 method to estimate algebraically the complex shear modulus. In this ent of the beads in the complex fluid. Assuming power law form for < r ( )> leads to el astic G(f) and here mean square displacement < equa tion (2.51) as above. Using method we use local power law to describe th e mean square displacem2viscous G(f) modulli, which are given by16 G(f) = G (f) cos[ (f)/2] (2.52) G(f) = G (f) sin[ (f)/2] (2.53) w ]f1[ f Here, a is the radius of the bead, 1 ra Tk fG2 B (2.54) f 1 r2 is the magnitude of < r2( )> evaluated at = 1/f. is the gamma function The local power law (f) is given by17 2rln f/1 ln he relationship between dynamic viscosity and viscous moduli G (f) is given by18 T 18

PAGE 30

f The ratio of elastic and viscous modulus is the loss tangent f"G (2.55) which is given by18 f'G f"G tan (2.56) 2.6 Diagram for Dynamic Light Scattering Set-up igure 2.5: Diagram of Dynamic Light Scattering Set-up from Malvern Instruments. As e laser illuminates the sample, back scattere d light is measured by the detector at an ngle of = 173 The digital correlator generates the intensity-intensity correlation nction g2( ). Software algorithms then invert g2( ) to obtain the size distribution.1 Laser Fth a fu Digital Signal Processor Correlator Cell Detector Attenuato 17 3 0 19

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2.7 References Loudon R.; (1973) The Quantum Theory of Light, Clarendon Press, Oxford, Johnson C.S., Gabriel D.A.; (1981) Laser Light Scattering, Dover Publications, Inc. Y Thomson J.A., Schurtenberger P .,Thurston G.M, Benedek G.B.; (1987) Proceedings of Muschol M., Rosenberger F. (1996) Journal of Chemical Physics 167, 738 Chu, B. (1991) Laser Light Scattering: Basic Principles and Practice, 2nd ed.; cademic Press: San Diego Cummins, H. Z.; Pike, R. (1973) Photon correlation and light beating spectroscopy; ew York plications; alvern Instruments. DLS technical note MRK656-01. United Kingdom. 1-3224. 645-3650. logica Acta 39, 371 rd ermodynamics, 7 edn., New York, McGraw-Hill 1 2 N 3the National Academy of Scie nces United States of America, 84, 7079 4. George A., Wilson W.W.; (1994) Acta Crystallographica D 50 361 Muschol M., Rosenberger F. (1995) Journal of Chemical Physics 107, 1953 5 6 7 A 8 Plenum Press: N 9. Brown W, (1993) Dynamic light scattering: the method and some apClarendon Press: Oxford 10. M 11. Berne, B. J. and R. Pecora (1976). Dynamic light scattering: with applications to chemistry, biology and physics. New York, Wiley. 12. Kuehner, D. E., C. Heyer, et al. (1997). Biophysical Journal 73: 321 13. Neal, D. G., D. Purich, et al. (1984). J. Chem. Phys. 80(7): 3469-3477. 14. Grigsby, J. J., H. W. Blanch, (2000). Journal of Physical Chemistry 104: 3 15. Ball, V. and J. J. Ramsden (1998). Biopolymers 46: 489-492. 16. Mason T.G., (2000) Rheo17. Dasgupta B.R., Tee S., Crocker J.C., Frisken B.J., Weitz D.A. (2002), Physical Review E 65, 051505 18. Adeyeye M.C., Jain A.C., Ghorab M.K.M., Reiley W.J. (2002) AAPS PharmaSciTech 3 (2): article 8 19. Griffith, D.J. Introduction to Electrodynamics, 3 edn., Patience-Hall Indiard20. Jackson J.D., Classical Electrodynamics, 3 edn., New York, Willey 21. Zemansky M.W., Dittman R.H., Heat and Thth 20

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22. Malvern Instruments T echnical Support Library, UK 21

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Chapter 3 Effect of Lysozyme Cluster on Nucleation Kinetics of Supersaturated Solution .1 Introduction Knowing the native, 3-dimensional struct ure of proteins provides important insights to the molecular mechanisms unde rlying their cellular functions 1, the origins of many ebilitating disorders 2-4 and supports the design of ne w drugs that target those very me disorders 5. X-ray diffraction from protein crystals still remains the primary tool for btaining high-resolution 3-D protein structures. Attemp ts at high throughput protein ructure determinations, however, have been fr ustrated by the difficulties of establishing itable solution conditions to promote the nucleation and subsequent growth of highuality protein crystals. These difficulties arise, in part, from the large number of djustable material and solution parameters th at affect the nucleation and growth kinetics f protein crystals and, with them, th ffraction resolu tion. The long-term object is to improve our unders tanding of the physical chem istry governing protein phase p m 3 in d sa o st su q a o e re sulting di se aration in order to develop an approach toward protein crystallization derived fro first principles. Often, the most difficult step in protein crystallization is to induce and control the very first stage of crysta l growth: crystal nucleation 6. The kinetics of protein crystal nucleation and the morphology of aggreg ates leading to crystallization vs. precipitation, therefore, were among the first targets of fundamental studies in protein crystallization 7. A variety of experimental techniques have been used to explore protein crystal nucleation, including neutron 8 and x-ray scattering 9, video microscopy 10, calorimetry 11, static light scattering 12-14 and, most prominently, dynamic light scattering 7, 15-20. The results of these and other studies, however, have often remained ambiguous or contradictory. Even for the well characteri zed and frequently used model protein hen egg-white lysozyme under comparable soluti on conditions, the exis ting data don't agree on the induction times for nucleation, the si ze, the number, or the morphology of the 22

PAGE 34

critical nuclei. An analysis of three recen t experiments on nucleation in lysozyme using microscopy 21, m icrocalorimetry 11 and static light scattering 14 yielded nucleation rates th dif defect density of lysozyme crtals at lyophilized lysozy me stocks contain significant poulat atfered by as much as twenty orders of magnitude 22. Similar disagreement exists regarding th e structure of protei n crystal nuclei. Using dynamic light scatte ring, Georgalis et al.23-26 reported large populations of amorphous lysozyme clusters in supersatur ated solutions. Measurements by other investigators have been unabl e to detect large cluster populations under comparable solution conditions 9, 27, 28. In addition, the population densities of sub-micron clusters is orders of magnitude above the number of macroscopically observed crystals 10 seen under comparable growth conditions. Observations of nucleation kinetics in supersaturated lysozyme solution with dynamic light scattering in our laboratory showed significa nt discrepancies depending on the source of the stock materials. Previous reports have investigated the contamination of lysozyme stocks by protein impurities, and thei r effects on lysozyme crystal growth and crystal quality 29-31. Lorber et al. 30 correlated protein impurities (ovalbumin, BSA) in lysozyme solutions with changes in the tota l number and ys. Protein impurities have been impli cated in changes of growth rates on the 101 facet of tetragonal lysozyme crystals 32, the density of optical def ects in lysozyme crystals 33 and limitations of X-ray diffraction resolution 34, 35. Even in the absence of contaminating impurities, structural microheterogeneities of lysozyme monomers have been linked to altered crystal habits and crystal quality 36. These report, however, implicitly assumed that the contaminating proteins were either monomeric or small oligomers. In this paper, we report th pions of sub-micron clusters. We investigated the composition and physical properties of these clusters, and went on to characterize their impact on the kinetics of lysozyme crystal nucleation in supersaturated solutions. 3.2 Materials and Methods 3.2.1 Chemicals We used three different stock mate rials of lyophilized lysozyme: 3x recrystallized, dialyzed and lyophilized stock from Seikag aku America (cat# 100910-3, Lot LF 1121) or 23

PAGE 35

Sigma-Aldrich (cat# L-7651, Lot 016K11891), and 2x recrystallized, dialyzed and lyophilized stock from Worthi ngton (cat#2933, Lot 35E8060). All other chemicals were obtained from Fisher Scientific a nd were reagent grade or better. 3.2.2 Preparation of Lysozyme Solutions Lyophilized lysozyme was dissolved directly into 0.1 M sodium acetate/ acetic acid (NaAc) buffer at pH = 4.5. For crystalliz ation experiments (supersaturated solutions), lysozyme/buffer solutions were mixed 1:1 with salt/buffer stock solution, each at twice the final concentration of protein or salt, re spectively. Prior to mixing, both solutions e solubility temperature applicable to the final solution the 40 mg/ml lysozyme/ 4% NaCl solutions most frequently used for samples: (A) Seikagaku lysozyme containing sub-micron clusters (220 nm syringe filtration), (B) Seikagaku ster (20 nm syringe filtration), and (C) were warmed above the lysozym composition. For our nucleation studies, the solubility temperature was determined to be 39 C following the method of Rosenberger et al. 37. Solutions were then tran sferred to preheated cuvettes and placed into the thermostated holder of our light scattering unit. Supersaturation was induced by quenching the solution temperature to 9 C. Nucleation and growth of clusters in supersaturated solutions was investigated with three different lysozyme after removing sub-micron clu Worthington lysozyme which was free of sub-micron clusters (therefore, 220 nm filtration was sufficient). Prior to light scattering measurements all samples were centrifuged in a Fisher accuSpin1R centrifuge at 9,5000 g for 15 min at 25 C and filtered through either (A) a 220 nm pore size PVDF Fisherbrand or (B) a 20 nm pore size Anotop syringe filter. Actual lysozyme co ncentrations were determined from UV absorption measured at = 280 nm ( 280 = 2.64 ml mg-1 cm-1 38) with a Thermo Electron Corporation UV1 spectrophotometer. 3.2.3 Dynamic Light Scattering (DLS) Measurements DLS measurements were performed with a Zetasizer Nano S (Malvern Instruments Ltd., UK) with a 3mW He-Ne laser at = 633 nm. The unit dete cts the back-scattered light at an angle of = 173 Sample temperature was controlled by the built-in peltier cooling device. After thermal equilibration of the samples, autocorrelation functions were 24

PAGE 36

collected continuously using acq uisition times of 30 s to 60 s per correlation function. Using the "narrow modes" algorithm provi ded with the Zetasizer Nano software, autocorrelation functions were converted to particle size distributions. Results with alternative inversion algorithms yielded comp arable results. A more detailed description of the analysis of DLS data is given in chapter 2. 3.2.4 Thermal Changes in Solution Viscosity Measurements of solution viscos ity as function of temper ature are discussed in ere derived from measurements trifuge filters (N anoSep 100K, Pall Corporation). After each filtration, the cluster fraction on the filter surface was reseparation of the non-dissociated clusters gel electrophoresis. Aliquots of pre-assembled clusters isolated from Seikagaku and Sigma ic light scattering, we confirmed that SDS detail in chapter 5. Briefly, changes in bu ffer viscosity w of temperature-related change s in apparent lysozyme diffusivity for undersaturated solutions in the range from 5 to 55 C. Several precautions were taken to assure the observed changes in solution viscosity deri ved from lysozyme diffusivity were not contaminated by diffusivity change s caused by protein interactions 39 or aggregation. 3.2.5 Separation of Pre-existing Clusters Pre-existing sub-micron clusters in lysozyme stocks were separated from monomeric lysozyme or small protein aggregates by filtering lysozyme/buffer solutions three times through 100,000 MW cutoff cen dissolved into 0.5 ml NaAc buffer. Successful from the low molecular weight protein b ackground was confirmed using dynamic light scattering. 3.2.6 SDS Gel Electrophoresis Aliquots of lysozyme for all three st ock materials (Worthington, Seikagaku, Sigma) were analyzed either after 220 nm or 20 nm filtration with SDS PAGE stock were analyzed separate ly. Using dynam did dissociate pre-assembled clusters into their low molecular weight components. Protein concentrations for the aliquots containi ng the isolated cluster peak were below the sensitivity of our UV spectrometer (< 5 g/ml). For SDS gel electrophoresis, 15 l of 25

PAGE 37

sample was mixed with 15 l of reducing sample buffer and heated at 95 C for 4 min, cooled and loaded onto the gel. The gel was a 12% Bis-Tris gel (Invitrogen, Carlsbad, CA) run in 3-(N-morpholino) propanesulfoni c acid (MOPS) running buffer according to the manufacturers instructions. To avoid spill over from lanes with high protein a cluster aliquots were loaded onto lanes separated ol ecular weights of markers used were as in overnight (16 hrs) before their sizes, numbers and quality were assessed. Soconcentrations, Seikagaku and Sigm y blanks from their neighbors. The m b dicated in Fig. 3B. Gels we re stained using a high-sensitiv ity silver stain (Silver Snap II, Pierce). 3.2.7 Growth of Macroscopic Crystals Macroscopic crystals were grown from each of the three types of lysozyme samples (Seikagaku 220 nm; Seikagaku 20 nm; Worthingt on 220 nm) used in our light scattering studies of cluster formation. To minimi ze differences in solution conditions, solution volume, and solution-container or solutionair interfaces, macroscopic crystals were grown in the same sample cuvettes used dur ing the DLS measurements. To keep the total number of macroscopic crystals at a reas onable level, though, the temperature-time profile of the samples had to be slightly modified: As in the dyna mic light scattering experiments, sample temperatures were initially quenched from 45 C to 9 C, but solutions were kept there for only 15 minutes before warming them back up to room temperature (22 C). Macroscopic crystal were th en allowed to grow at room temperature3.3 Results 3 3.1 Detection and Characterization of Sub-micron Clusters in Undersaturated lutions. Fig. 3.1A shows the field correlation functions of light scattered from solutions from each of the three stock materials. E ach of the three autoco rrelation functions has a rapid decay component, but also a discernable slower tail or "s houlder" extending to longer decay times. These slower decay times i ndicate the presence of larger aggregates. The corresponding particle size distributions of the unfiltered stock so lutions reveal three well-separated peaks (Fig. 3.1B). 26

PAGE 38

Fig. 3.1: Dynamic light scattering from lysozyme solutions pr epared with lyophilized stock from different suppliers All solutions contained C = 40 mg/ml (2.8 mM) of lysozyme dissolved in 100 mM sod lysium acet ate (NaAc) buffer at pH = 4.5, T = 20 C (A) ield correlation function g1( ) vs. delay time for light scattered by (1) Worthington sozyme; 2x cryst., dialyzed () (2) Seikagaku lysozyme; 3x crystallized, dialyzed () nd (3) Sigma lysozyme; 3x crystallized, dialyzed (). (B) Distribution of particle sizes the correlation functions shown in (A). For clarity, the distributions for eikagaku lysozyme and Sigma lysozyme were offset from the origin. inant monomer peak is centered at an apparent radius of r = (1.8 0.2) nm, consistent with the diffusivity of monomeric lysozyme under these conditions. Seikagaku nd Sigma lysozyme solutions also yield significant cluster peaks centered around 60-90 m. The amplitude of the cluster peak was typically larger for Sigma lysozyme, while its enter was located 10-20 nm below the peak position for Seikagaku clusters. The amplitude and position of this second peak, however, varied somewhat with the lot umber of the lysozyme stock. No such peak was detected for this batch of Worthington F ly a derived from S The dom a n c n lysozyme. All samples also displayed a sm all, third peak located around r = (2.3 0.2) m, which we ascribed to air bubbles induc ed during sample preparation. Sample filtration through 220 nm syringe filters and/or centrifugation readily removed this third peak. 27

PAGE 39

Fig. 3 .2: Effects of sample filtration on cont amination of Seikagaku lysozyme by subicron clusters. (A) Log-log plot of field correlation function g1( ) for 50 mg/ml eikagaku lysozyme in 100 mM NaAc buffer at pH = 4.5 without filtration ( ) and after rough a syringe f ilter with 220 nm pore size ( ) or 20 nm pore size ( ). Notice e decline in the pronounced "shoulder" of th e autocorrelation functi ons with decreasing ore size. (B) Distribution of protein clusters derived from the correlation functions in ). The effects of sample filtrations on the aggregate peak support the size distributions dynamic light scattering. For clar ity, the distributions for Seikagaku before nd after filtration were offset from one another. The subsequent experiments focused on identifying the composition of the clusters rming the second peak in lyophilized lysozy me stock, and on characterizing some of the physical properties of these clusters. We selected the Seikagaku and Worthington ocks for further characterization. To confir m the size distributions of the second peak erived from dynamic light scattering we f iltered both the Worthington and Seikagaku lutions through 220 nm syringe filters an d measured the resulting autocorrelation nctions. As mentioned above, the small popul ation of micron-sized bubbles (third peak ver D = 10.9 cm /s (220 nm filter) to D light scattering closely matched the physical aggregate sizes in the stock solutions. m S filtration th th p (A derived from a fo st d so fu in Fig. 3.1B) disappeared from all solutions. The shoulder of the correlation function (Fig. 3.2A) and its asso ciated cluster peak (Fig. 3.2B) found in the Seik agaku solutions, however, were only modestly reduced by this filtration step. Filtering the Seikagaku stock material through a 20 nm syringe filter instead, eliminated the shoulder in the correlation function (Fig. 3.2A ), increasing the average diffusivity of the Seikagaku samples from D = 9.5 cm2/s (unfiltered sample) o2= 12.2 cm2/s (20 nm filter). Concomitantly, the clus ter peak associated with the shoulder in the correlation function disappeared after 20 nm filtration (Fig 3.2 B). The effects of sample filtration, therefore, confirmed that the size distributions derived from dynamic 28

PAGE 40

3.3.2 Analysis of Cluster Composition Multiple investigators have reported contamination of lysozyme stock solution by various low molecular weight (< 100 kD) protein impurities 29, 31, 36. We set out to determine whether (a) the clusters found in our lysozyme stock were indeed composed of protein and (b) whether these clusters were formed by lysozyme or by one of the miscellaneous impurities previously found in lysozyme stocks. As described in the Materials and Methods sections, we used 100 kD MW cut-off centrifuge filters to separate the cluster peak of Seikagaku and Sigma stock material from the low-molecular weight protein components. As confirmed by dynamic light scattering (Fig. 2.3A), three consecutive filtrations and re-suspensions clearly separated the cluster peak from the low molecular weight background. The size di stributions obtained with dynamic light scattering also indicated that the majority of the clusters remained intact after repeated centrifugation and filtration, with only a mi nor "fragment peak" appearing around 18 nm. Aliquots containing either lysozyme stock material after filtration through syringe filters or the separated cluster peak were analyzed by SDS PAGE gel electrophoresis, llowed by high-sensitivity silver staining (Fig. 3.3B). The left hand side of the SDS gel sh filtratio clter fo ows the analysis of Worthington stock material after 220 nm filtration (lane A), Seikagaku lysozyme after 220 nm filtration (l ane B) and 20 nmn (lane C), and Sigma lysozyme after 220 nm filtration (lan e D) and 20 nm filtration (lane E). All lysozyme stocks contain at least three diffe rent contaminants with estimated molecular weights of 6, 18 and 29 kD respectively. The 18 and 29 kD impurity bands closely match previous results by Thomas et al 29 of an unidentified impurity (18.2 kD) and of an SDSresistant lysozyme dimer population (28 kD). The smallest molecular weight band (6 kD) has not been reported before and could po tentially represent a proteolytic fragment of lysozyme. The analysis of the cluster peaks for Seikagaku and Sigma lysozyme are shown in lane F and G of Fig. 3.3B. Within the resolution limit of the silver staining, the cluster peaks are entirely composed of lyso zyme, with no discernabl e contributions from the protein impurities seen in the stock material. These observations establish that the uspeak is composed predominately of ly sozyme itself. Notice, also, that the SDS resistant lysozyme dimers (29 kD band) do not tend to associate with the lysozyme clusters. Lysozyme stock solu tions, therefore, contain at least two different types of 29

PAGE 41

contaminants: protein impurities and non-dissoci ated lysozyme clusters. Notice that the latter would not be detected by SDS PAGE gel analysis of the stock material. Fig. 3.3: Isolation and Analysis of Lyso zyme Clusters by SDS PAGE Gel Electrophoresis. (A) Confirmation of cluster separation: part icle size distribution derived from dynamic light scattering from solution of clusters re-suspended in NaAc buffer after separation (for details, se e Material and Methods). (B) SDS PAGE gel electrophoresis of lysozyme stock materials and cluster fractions Lanes: (A) Worthington lyso 220 nm filtration; Seikagaku lysozyme after (B) 220 nm filtr ation and (C) 20 n zyme after m filtration; Sigma lysozyme af ter (D) 220 nm filtration and (E) peak separated from (F) Seikagaku lysozyme material at 1 mg/ml was loaded. Concentratio sensitivity of our UV spectrophotometer (~ 5 are indicated in the margin. 3.3.3 Physical Characterization of Pre-existing Clusters We investigated whether the observed prot monomer population or if they are pre-assemb that end we determined whether the fraction of was altered by changes in protein concentratio buffer solution without further purification. he protein concentration of a given sample the protein cluster peak was unaff ected by protein concentration. 20 nm filtration. Clusters and (G) Sigma lysozyme. 15 l of stock n of isolated cluster peak was below the g/ml). Molecular weights of marker lanes ein clusters exist in equilibrium with the led, non-equilib rium structures. Towards protein aggregates in Seikagaku solutions n. Seikagaku lysozyme was dissolved in T was sequentially reduced from 40 mg/ml down to 5 mg/ml. As shown in Fig 3.4, the ratio of the area under the cluster peak to the area under the monomer peak was essentially independent of lysozyme concentra tion. Similarly, the location and shape of 30

PAGE 42

Fig. 3.4: Dependence of cluster peak amplitude on lysozyme concentration. Ratio of cluster-to-monomer peak area for unfiltered Seikagaku lysozyme in 100 mM NaAc buffer (pH = 4.5) derived from dynamic light scattering data measured at concentrations between 5 to 40 mg/ml. We had noticed that the locati on of the cluster peak was sensitive to solution temperature. Charactering the dependence of cluster size on solution temperature using dynamic light scattering require s knowledge of the temperat ure dependence of the buffer viscosity see Eqn. 2.49 in chapter 2). To determine (T) we measured the changes in the collective diffusivity Dc of monomeric lysozyme as a function of lysozyme concentration. The Dc vs Clys data were extrapolated to obtain D0, i.e. the diffusivity in the limit of vanishing protein interactions. Using the Einstein Stokes relation ( Eqn. 2.49 in chapter 2), values for D0 at different temperatures wher e then converted into changes of buffer viscosity (T). Details of these experiments and their data analysis will be presented in chapter 6. Values for the visc osity of 100 mM sodium acetate buffer thus determined fell within 3% for those of water at the sa me temperature and agreed with independent measurements of the dynamic vi scosity of sodium acetate buffer at T = 20 39C 31

PAGE 43

Fig. 3.5: Thermal collapse of lysozyme clusters. Peak size of lysozyme clusters vs. solutio mg/l n temperature ( ) in undersaturated solutions of Seikagaku lysozyme (Clys = 40 m, 100 mM NaAc, pH = 4.5) As indicated by the width of the error bars (N = 4), sample to sample variations in aggregate size decreased systematically with temperature. Upon cooling (T = 20 C) lysozyme clusters did not regain their original size prior to heating even during extended measurements over 12 hrs ( ). We next measured the response of the lysozyme cluster peak in undersaturated solutions to increases in solution temperat ure. After accounting for the temperaturedependence of the viscosity, (T), the residual change in cluster size distribution was determined in the temperature range of 20C to 55 C. As shown in Fig. 3.6, the position of the cluster peak systematically decreased with increasing sample temperature from (93 5) nm at 20 C down to (72 1) nm at 55 C, with little change to the overall shape of the size distribution. Th e error bars in Fig. 3.5 indicate that this beha vior was highly reproducible from run to run. When returning the sample temperature from 55 C down sozyme clusters are permanent, non-equilibriu m structures. This conclusion is further su to 20 C, clusters retained the reduced size and distributions established at 55 C, even during extended observations for 12 hours. The lack of concentration depende nce in relative aggregate population and the irreversible changes in aggregate size w ith temperature cycli ng indicate that these ly pported by the behavior of the lysozyme cl usters after filtration: lysozyme cluster removed after 20 nm filtration did not grow back. Given that these clusters are present in 32

PAGE 44

different concentrations and sizes in most st ock materials, we suppose that they represent tightly bound lysozyme clusters formed to different degrees duri ng the supplier-specific purification / lyophi lization process. 3.3.4 Effects of Sub-micron Lysozyme Clusters on Crystal Nucleation in Supersaturated Lysozyme Solutions The characterization of pre-assemble d lysozyme clusters detailed so far had been performed in undersaturated conditions, i.e. in solutions without sufficient concentrations of added salt required for lyso er 220 nm or 20 nm syringe filters. Distributions of pre-existing cl usters were measured at 45 C, i.e. in undersaturated ed to 9 C, perature of 38 C. The temperature of 9 C was zyme crystallization. Next we investigated how these preassembled lysozyme clusters affected the cr ystal nucleation proces s in supersaturated solutions. We dissolved 40 mg/ml of lysozyme directly into 4% NaCl / buffer solutions at a temperature of 45 C. Using a static light scatteri ng set-up similar to Rosenberger et al. 37, we independently determined the solub ility temperature of lysozyme for this combination of solute/solution parameters to be 39 C. After dissolving the protein, Worthington lysozyme solutions were filt ered through 220 nm syringe filters and Seikagaku lysozyme solutions through eith solution conditions (see Fig. 3.6). Soluti on temperature was then quench hich is well below the solubility tem w chosen to accelerate crystal nucleation while keep ing the solutions above the liquid-liquid phase separation boundary located around 7 C (data not shown). Theoretical models 43 and experimental observations 21 have suggested that crystal nucleation rates are enhanced near this phase separation boundary. 33

PAGE 45

Fig. 3.6: Cluster distribution in lysozyme/salt solutions prior to thermal quenching. Solutions containing either Worthingt on lysozyme after 220 nm filtration ( ), or Seikagaku lysozyme after 220 nm filtration ( ) or 20 nm filtration ( ). Clys = 40 mg/ml in 4% NaCl, 100 mM NaAc at pH = 4.5, T = 45 C. For clarity, clus ter distributions for the different samples have been offset from the origin. Autocorrelation functions and clus ter distributions prior to supersaturation (see r than the polydis persity index of th e and move toard Fig. 3.6) were comparable to those observe d in undersaturated so lutions without added salt (Fig. 3.5). After 20 nm filtrations, neither the Worthington nor the Seikagaku solutions displayed discernable cluster peak s. The polydispersity of the Seikagaku monomer peak ( = 0.09), however, was slightly highe e Worthington samples ( = 0.05). In contrast, Seikagaku solutions after 220 nm filtration displayed a well developed pr otein cluster peak centered at 80 nm. The growth of new protein clusters afte r quenching the protein solutions into the supersaturated region is refl ected in the time-dependent ch anges of the autocorrelation functions shown in Fig. 3.7. Within minutes after thermal quenchi ng, the "shoulder" of the autocorrelation function measured for Se ikagaku samples after 220 nm filtration (Fig. 3.7A) and after 20 nm filtration (Fig. 3.7 B) started to grow in amplitud ws increasingly longer decay times. Both features are indicato rs for the growth of significant populations of large (> 50nm) cluste rs in these solutions. In contrast, within the optical observation volume of our instrument (~ 5 nL), no growth of new protein clusters was discernable in the Worthington samples (F ig 3.7C). After approx. 110 34

PAGE 46

minutes, however, a drop in the zero-interc ept of these autocorrelation functions developed. In all samples, such a drop coin cided with the appearance of visible protein crystals at the surface of the glass cuvette. This change is consistent with enhanced contributions of static scattering to the auto correlation function as the laser beam reflects off surface-attached crystals. Particularly in triguing is the persistent difference in the nucleation behavior between Seikagaku samples following 20 nm filtration and the Worthington sample after 220 nm filtration. Neither sample showed a discernable cluster peak prior to supersaturation (Fig 3.6). The larger polydispersity of the Seikagaku samples prior to supersaturation, however, suggests that the pronounced difference in nucleation-related cluster forma tion of these samples is rela ted to a population of smalldiameter aggregates (< 10-20 nm) not resolved as a separate peak by dynamic light scattering. 35

PAGE 47

Fig. 3.7: Dynamic light scattering from supersat urated lysozyme solutions. Temporal evolution of the field correlation function for light scattered from supersaturated lysozyme solutions. Data for the same solu tions shown in Fig. 6, but after quenching solution temperature down to 9 C, i.e. well below the saturation temperature of 38 C. Seikagaku lysozyme solutions subjected to e ither (A) 220 nm filtration or (B) 20 nm filtration. (C) Worthington lysozyme solution subjected to 220 nm filtration. 36

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3.3.5 Effects of Pre-assembled Lysozyme Clusters on Macroscopic Lysozyme Crystals Fig. 3.8: Protein crystals grown with lysozy me containing different levels of nondissociated lysozyme clusters. Solutions contained Clys = 40 mg/ml of lysozyme, 4% NaCl, 100 mM NaAc (pH = 4.5) Lysozyme was dissolved at 45 C, i.e. above the solubility temperature for lysozyme under these conditions. Solu tion temperature was then quenched for 15 min to 9 C. After warming solutions back up, samples were kept at room temperature for 16 hrs. First column: Image of the total number of crystals present in glass cuvette containing (A) Seikagaku lysozy me (220 nm filtration), (B) Seikagaku lysozyme (20 nm filtration) and (C) Worthington lysozyme (220 nm filtration). Second column: Magnified image of tetragona l lysozyme crystals grown in the three cuvettes above. Notice the changes in the total number and sizes of crystals going from top to bottom. Optical defect de nsities and the number of twinned crystals decreases in the same order. 37

PAGE 49

Fig. 3.8 show typical images of crystals grown from all three types of solutions (Seikagaku 220 nm, Seikagaku 20 nm and Worthington 20 nm) using a temperature-time profile close to that used during dynamic li ght scattering measurements (see Materials and Methods). Supersaturated solutions of Seikagaku lysozyme after 220 nm filtration yielded large numbers of relativ ely small, frequently twinne d crystals. Supersaturated solutions of Seikagaku lysozyme after 20 nm filtration generated far fewer macroscopic crystals of larger size (~ 1mm), but still with noticeable fractions of twinned and optically defective crystals. Worthington lysozyme pr oduced yet fewer crystals with the highest quality of crystals, as ascertained by visual inspection. Since we grew crystals under the same conditions (temperature profile, containers and sample volume) used in our light scattering measurements, we were unable to numerically quantify the differences in crystal numbers and defect de nsities between these samples. Nevertheless, the results clearly indicate that the nucl eation and cluster growth beha vior seen with dynamic light scattering directly corresponds to the outco me of macroscopic growth experiments under the same conditions: Pre-assembled lysozyme clusters dramatically increase the number of submicron and macroscopic protein crysta ls and enhance crystal defects such as twinning and optical heterogeneities. 3.4 Discussion Lysozyme is a well characterized protein that is frequently employed in fundamental studies of protein crystal nucleation and growth kinetics. Our analysis of lyophilized lysozyme indicates that commercial source s of this important model protein are consistently contaminated by sign ificant populations of submicron ( 200 nm) clusters (Fig. 2.1B). SDS PAGE gel chromatography of the isolated cluster fr action confirms that these clusters are composed of lysozyme. The fraction of lysozyme clusters does not change with protein concentration (Fig. 3. 4). Filtration through 20 nm syringe filters permanently removes these clusters from solutio n (e.g. Fig. 3.2B). Furthermore, clusters sizes shrink irreversibly with increasing sample temperature (Fig. 3.5). In contrast to recent reports of equilibrium lysozyme clus ters at high lysozyme and very low ion concentrations 45, the above characteristics identify the clusters described here as non38

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dissociated, non-equilibrium lysozyme aggreg ates already presen t in the lyophilized stock. Several laboratories have characterized protein impurities in lyophilized lysozyme stocks, and their impact on subsequent protein crystal growth 29, 31. Similarly, the role of structural micro-heterogeneities of lysozyme monomers was raised as possible culprit for changes in crystal growth behavior 36. The presence of such sample heterogeneities was typically identified using SDS PAGE gel chromatograph, size exclusion chromatography or affinity chromatography. Hence, it might seem surprising that the significant sample heterogeneity due to non-dissociated lysozy me clusters reported here had not been detected previously. These clusters, however are likely to evade detection by the above techniques. In SDS gel chromatography, the clusters are dissociated by SDS and make a negligible contribution to the dominant lysozyme monomer band. In column chromatography, in turn, pre-existing cluste rs will evade standard UV detection due to their low overall concentration. We were una ble to obtain UV absorption readings on the aliquots containing isolated lysozyme cluste rs, even though they yielded a well-defined light scattering peak (Fig. 3.3A ) and were readily detected after separation using SDS PAGE gel chromatography with silv er staining (Fig. 3.3B). Our light scattering experiments in supersaturated lysozyme solutions indicate that these non-dissociated lysozyme clusters have a pronounced effect on the crystal nucleation and growth process. The amplit ude of submicron cluster populations (Fig. 3.7A) and the number of macroscopic lysozy me crystals (Fig. 3.8A) was significantly enhanced by the presence of pre-existing clus ters. In the absence of these clusters (Worthington 220 nm), no submicron lysozyme cl usters were detected in supersaturated solutions (Fig. 3.7C) even though macroscopi c crystals formed on the container walls (Fig. 3.8C). Non-dissociated lysozyme clusters evidently ac t as heterogeneous nucleation centers, promoting cluster formation in supe rsaturated lysozyme solutions. Given the affinity of lysozyme monomers for aggrega tion with these non-dissociated clusters and given their typical sizes (40-200 nm), non-disso ciated clusters should readily incorporate into lysozyme crystals and contribute to defect formation in macroscopic crystal. This expectation is born out by the high densit ies of optical defects and twin boundaries 39

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observed in crystals from cluster-contaminated solutions (Fig 3.8A). Both of these macroscopic defect features are bound to degrade X-ray resolution. Filtration of Seikagaku stock materi al through 20 nm filters removed the nonequilibrium clusters peak centered around 100 nm completely (Fig. 3.2B). Hence, one might expect that the Worthington sample s after 220 nm filtrati on and the Seikagaku samples after 20 nm filtration should display equivalent nucleation behavior. However, the 20 nm filtered Seikagaku solutions had indu ctions times for cluster formation closer to 220 nm filtered Seikagaku solutions th an Worthington solutions at identical supersaturation (see Fig. 3.7). Dynamic light scattering from undersaturated solutions of Seikagaku lysozyme (20 nm filtration) yielded polydispersities 0.09 which were consistently higher than the polydispersity of 0.05 measured for Worthington lysozyme (220 nm filtration). Polydispers ity implies the presen ce of small (< 20 nm) unresolved clusters in either solution. Th e higher polydispersity of "cluster-free" Seikagaku lysozyme over Worthington lysozyme could be related to two factors. SDS PAGE gel chromatography of the two samples (l ane A and C in Fig. 3.4) indicates that Seikagaku lysozyme contains slightly higher levels of protein impurities than Worthington lysozyme. Furthermore 20 nm f iltration could break up the larger lysozyme clusters in Seikagaku lysozyme into smaller fragments. Cluster fr agments generated by filtration through 20nm filters ar e likely to enhance the polydispersity of the "monomer peak". This latter interpre tation is supported by the effects of repeated filtration during isolation of the cluster peak from the mono mer background. Dynamic light scattering from isolated lysozyme clusters yielded a small secondary peak centered at 18 nm, indicating the generation of such cluster fragments (first peak, Fig 3.3A). In either case, the enhanced polydispersity is apparently suffi cient to lead to a significant acceleration of cluster nucleation and growth kinetics in supers aturated solutions. The apparent lack of discernable cluster formation in supersaturat ed solutions with Worthington lysozyme is noteworthy. The formation of macroscopic lysozyme crystals from the same solutions clearly indicates that crystals do nucleate and grow under these conditions (Fig. 3.8C). These two observations could be seen to impl y that the formation of large (fractal?) protein clusters in lysozyme solutio ns frequently described by others 24, and seen here in the contaminated Seikagaku samples, is just related to the existence of contaminating 40

PAGE 52

lysozyme clusters. This conclusion, however would be premature. First of all, the majority of macroscopic crystals obtained from supersaturated Worthington solutions grew on the cuvette walls, apparently via heterogeneous surface nucleation (see Fig. 3.8C). Furthermore, dynamic light scattering only monitors a very small fraction (in our instrument: 5 nL) of the bulk volume of the sa mple. Therefore, the absence of larger clusters reported by dynamic li ght scattering might just indi cate the dominance of surface over bulk nucleation rates in supersaturated solutions of Worthington lysozyme. In addition, supersaturated lysozyme solutions can form gel phases 14, 46. Gelation clearly has to be preceded by the formation of gel clusters Therefore, pre-assembled lysozyme clusters might just enhance the rates of cl uster nucleation and growth in the bulk over heterogeneous nucleation rates at the solution interfaces. Overall, understanding the mechanisms that c ontrol protein crystal nucleation in supersaturated protein soluti ons and that determine the morphology of nucleation clusters and macroscopic new phases is critical for improving our control ove r phase separation in macromolecular and colloidal systems. While conceptually straightforward, measurements of crystal nucleation rates fo r crystals are fraught with experimental obstacles that are difficult to assess and co ntrol. Our data on lysozyme nucleation and cluster growth raise yet another experimental concern that, thus far, has received little attention: sample heterogeneity due to pre-assembled protein clusters present in lyophilized stock material. Tw o specific features of the nucleation behavior in the presence of these non-dissociated clusters are of particular concern. First, filtration through standard 0.22 m syringe filters or centrifugation up to 15,000 g do little to remove the existing non-equilibrium lysozyme cl usters from solution. The presence of such non-dissociated clusters, in turn, drama tically shortens induction times and increases the population densities of sub-micron protein clusters nucleating from supersaturated solutions two parameters that are frequen tly assessed for comparison with theoretical models of crystal nucleati on. Hence, contamination of lysozyme solutions by nondissociated, non-equilibrium lysozyme clusters is a likely candidate for explaining some of the large discrepancies in nucleati on rates reported in the literature 22. 41

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3.5 References 1. Berman, H. M.; Westbrook, J.; Feng, Z.; Gilliland, G.; Bhat, T. N.; Weissig, H.; Shindyalov, I. N.; Bourne, P. E.(2000) Nucleic Acids Research 28, 235-242. 2. Eaton, W. A.; Hofrichter, J. (1990) Advances in Protein Chemistry 40, 63-279. 3. Annunziata, O.; Pande, A.; Pande, J.; O gun, O.; Lubsen, N. H.; Benedek, G. B.(2005) Biochemistry 44, (4), 1316-1328. 4. Koo, E. H.; Landsbury, P. T. J.; Kelly, J. W. (1999) Proceedings of the National Academy of Sciences United States of America 96, 9989-9990. 5. Anderson, A. C.(2003) Chemistry & Biology 10, 787-797. 6. McPherson, A.(1999) Crystallization of Biological Macromolecules. Cold Spring Harbor Press: Cold Spring Harbor, NY 7. Kam, Z.; Shore, H. B.; Feher, G. (1978) Journal of Molecular Biology 123, 539555. 8. Niimura, N.; Minezaki, Y.; Ataka, M.; Katsura, T.(1995) Journal of Crystal Growth 154, (1-2), 136-144. 9. Finet, S.; Bonnete, F.; Frouin, J.; Provost, K.; Tardieu, A.(1998) European Biophysics Journal with Biophysics Letters 27, 263-271. 10. Galkin, O.; Vekilov, P. G.(2001) Journal of Crystal Growth 232, (1-4), 63-76. 11. Darcy, P. A.; Wiencek, J. M. (1999) Journal of Crystal Growth 196, 243-249. 12. Kulkarni, A.; Zukoski, C. F.(2002) Langmuir 18, 3090-3099. 13. Wilson, J. L.; Pusey, M. L.(1992) Journal of Crystal Growth 122, 8-13. 14. Kulkarni, A. M.; Dixit, N. M.; Zukoski, C. F.(2003) Faraday Discussions 123, 37-50. 15. Kadima, W.; McPherson, A.; Dunn, M. F.; Jurnak, F. A. (1990) Biophysical Journal 57, 125-132. 16. Malkin, A. J.; McPherson, A.(1993) Journal of Crystal Growth 133, (29), 12321235. 17. Wilson, W. W.(1990) Method 1, (1), 110-117. 18. Mikol, V.; Hirsch, E.; Giege, R.(1989) FEBS Letters 258, 63-66. 19. Georgalis, Y.; Saenger, W. (1993) Advances in Colloid and Interface Science 46, 165-183. 42

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20. Georgalis, Y.; Umbach, P.; Soumpasis, D. M.; Saenger, W.(1998) Journal of the American Chemical Society 120, (22), 5539-5548. 21. Galkin, O.; Vekilov, P. G. (2000) Journal of the Americ an Chemical Society 122, (1), 156-163. 22. Dixit, N. M.; Kulkarni, A. M.; Zukoski, C. F. (2001) Colloids and Surfaces aPhysicochemical and Engineering Aspects 190, (1-2), 47-60. 23. Poznanski, J.; Georgalis, Y.; Wehr, L.; Saenger, W.; Zielenkiewicz, P.(2003) Biophysical Chemistry 104, (3), 605-616. 24. Georgalis, Y.; Umbach, P.; Saenger, W. ; Ihmels, B.; Soumpasis, D. M. (1999) Journal of the American Chemical Society 121, (8), 1627-1635. 25. Georgalis, Y.; Umbach, P.; Raptis, J.; Saenger, W. (1997) Acta Crystallographica Section D-Biological Crystallography 53, 691-702. 26. Schaper, A.; Georgalis, Y.; Umbach P.; Raptis, J.; Saenger, W. (1997) Journal of Chemical Physics 106, (20), 8587-8594. 27. Piazza, R.; Peyre, V.; Degiorgio, V. (1998) Physical Review E 58, (3), R2733. 28. Muschol, M.; Rosenberger, F.(1996) Journal of Crystal Growth 167, (3-4), 738747. 29. Thomas, B. R.; Vekilov, P. G.; Rosenberger, F. (1996) Acta Crystallographica Section D-Biological Crystallography 52, 776-784. 30. Lorber, B.; Skouri, M.; Munch, J.-P.; Giege, R. (1993) Journal of Crystal Growth 128, 1203-1211. 31. Skouri, M.; Lorber, B.; Giege, R.; Munch, J.-P.; Candau, J. S. (1995) Journal of Crystal Growth 152, 209-220. 32. Thomas, B. R.; Vekilov, P. G.; Rosenberger, F. (1998) Acta Crystallographica Section D-Biological Crystallography 54, 226-236. 33. Caylor, C. L.; Dobrianov, I.; Kimmer, C.; Thorne, R. E.; Zipfel, W.; Webb, W. W. (1999) Physical Review E 52, R3831-3834. 34. Robert, M. C.; Capellea, B.; Lorber, B.; R., G. (2001) Journal of Crystal Growth 232, (1-4), 489-497. 43

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35. Caylor, C. L.; Dobrianov, I.; Lemay, S. G.; Kimmer, C.; Kriminski, S.; Finkelstein, K. D.; Zipfel, W. ; Webb, W. W.; Thomas, B. R. ; Chernov, A. A.; Thorne, R. E. (1999) Proteins-Structure Function and Genetics 36, 270-281. 36. Ewing, F. L.; Forsythe, E. L.; van der Woerd, M.; Pusey, M. L. (1996) Journal of Crystal Growth 160, 389-397. 37. Rosenberger, F.; Howard, S. B.; Sowers, J. W.; Nyce, T. A. (1993) Journal of Crystal Growth 129, 1-12. 38. Roxby, R.; Tanford, C. (1971) Biochemistry 10, (18), 3348-&. 39. Muschol, M.; Rosenberger, F.(1995) Journal of Chemical Physics 103, (24), 10424-10432. 40. Mandel, L. (1963) Review of Modern Physics 37, 231. 41. Chu, B. (1991) Laser Light Scattering. Basic Principles and Practice. 2nd. ed. ed.; Academic Press: San Diego 42. Berne, B.; Pecora, R. (1976) Dynamic Light Scattering. Wiley: New York 43. tenWolde, P. R.; Frenkel, D. (1997) Science 277, (5334), 1975-1978. 44. Tanaka, S.; Yamamoto, M.; Kawashima, K.; Ito, K.; Hayakawa, R.; Ataka, M. (1996) Journal of Crystal Growth 168, 44-49. 45. Stradner, A.; Sedgwick, H.; Cardinaux, F. ; Poon, W. C. K.; Stefan U. Egelhaaf, S. U.; Schurtenberger, P. (2004) Science 435, 492-495. 46. Muschol, M.; Rosenberger, F. (1997) Journal of Chemical Physics 107, (6), 19531962. 44

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Chapter 4 Effect of Chaotropic and Kosmotropic Ions on the Hydration and Hydrodynamic Interaction of Lysozyme 4.1 Introduction Water molecules bound to the surface and incorporated into the core of protein molecules are considered to play a critical in regulating the bi ological functions of proteins and their phase separation behavior 13,14. Yet the structure and dynamics of hydration water remain the topic of ongoing expe rimental and theoreti cal research efforts 19. Neutron scattering and x-ray diffraction from protein crystals indicate that water density near the surface is increased by about 10-15 % beyond the bulk density 36, with similar results obtained from molecular dynamics simulations 27. NMR, time-resolved fluorescence, and dielectric relaxation spec troscopy have all been used to probe relaxation of water on sub-nanosecond time scales revealing an overall retardation of the rotational relaxation dynamics of water molecules near protein surfaces 12,24,31. Similarly, the ability of salt ions to either disrupt or enhance hydrogen bonding networks is well established 6,9. Salt ions are categorized as either water-structure makers (kosmotropic) or breakers (chaotropic). The efficacy of sp ecific salt ions at enhancing or disrupting water structure is similar in many different sy stems. This rank ordering of salt ions was originally established by Hofmeister's st udies of salt-specific effects on protein precipitation 21. However, just as the case of wate r at interfaces itself, no universally accepted model has been put forth to explain the mechanisms mediating the salt-specific effects of the Hofmeister series. We investigated whether addition of either chaotropic or kos motropic salt ions at concentrations up to 1 M would alter lysozyme hydration or the hydrodynamic interaction among the lysozyme molecules. Lysozyme is a small globular protein frequently used in studies of protein hydration 6,9 and protein diffusion 17,28. While saltspecific effects on direct protein-protein in teractions have been studied repeatedly 15,17,28, 45

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much less is known about salt-specific eff ects on hydrodynamic interactions and protein hydration. We used five different salts (MgCl2, NaCl, CsCl, NaI, and NaHPO4) to investigate ion-specific effects on hydration or hydrodynamic interactions. These salts contained ions varying fr om strongly kosmotropic (PO4 3-, Mg2+) to strongly chaotropic (Cs-, I-) character, and contained at least one negative a nd positive ion among either group of ions. This allowed us to keep either the co-ion (Na+) or counter ion (Cl-) to the positively charge lysozyme molecule constant. The overall goal was to gain insights into the effects of chaotropic or kosmotropic ions on the water structure around lysozyme, and on solvent-mediated hydrodynamic interactions among multiple lysozyme molecules. Both questions can be addressed simultane ously by measuring static and dynamic light scattering from lysozyme in salt-water solutions. 4.2 Materials and Methods 4.2.1 Chemicals Dialyzed, 2 recrystallized and lyophilized lysozyme stock from Worthington Biochemicals (cat#2933) was used for all experiments. As shown in chapter 3 Worthington stock material was least likel y to be contaminated by pre-existing submicron lysozyme clusters that interfere with light scattering and/or nucleation studies 32 All other chemicals were obtained from Fish er Scientific and were reagent grade or better. 4.2.2 Preparation of Lysozyme Solutions Lyophilized lysozyme was dissolved directly into 25 mM sodium acetate/ acetic acid (NaAc) buffer at pH = 4.5. Stock solutions for MgCl2, NaCl, NaH2PO4 and CsCl were prepared by dissolving each into the same 25 mM NaAc buffer at pH = 4.5 at a final salt concentration of 2 M. To avoid complex formation, NaI stock solutions had to be prepared fresh on the day of the experiment and the highest stock c oncentration used was 0.2M. The pH of all stock solutions was re-adjusted after the addition of salt, if necessary. Lysozyme solutions for light scat tering measurements were prepared by 1:1 mixing of lysozyme/buffer with salt/buffer stock solutions, each at twice their final concentrations. Prior to mixing, lysozyme solutions were filtered through 20 nm pore 46

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size Anotop syringe filters while salt solu tions were filtered through 220 nm syringe filters. At the higher salt concentrations ( 600 mM), lysozyme solutions become supersaturated at room temper ature or below and can form crystals. Therefore, after mixing, lysozyme solutions were heated to 45 C in order to reduce the risk of inducing crystal seeds. Solutions were then transf erred to glass cuvettes and placed into the thermostated holder of the light scattering unit. Actual lysozyme concentrations of solutions were determined from uv absorption measured at = 280 nm using 280 = 2.64 ml / (mg cm) 35. 4.2.3 Static (SLS) and Dynamic (DLS) Light Scattering Measurements Both SLS and DLS measure-ments were perf ormed using a Zetasizer Nano S (Malvern Instruments Ltd., UK) with a 3mW He-Ne laser at = 633 nm. The unit collects back-scattered light at an angle of = 173 Sample temperature during measurements was controlled to within 0.1 C by the built-in Peltier element. Correlation functions were determined from the average of 5 measurements, with a typical acquisition time of 60 seconds per corr elation function. Scattering intensities for SLS analysis were obtained from the aver age count rate of th e samples and were calibrated against toluene, using the Rayleigh ratio of RT = 13.52 10-6 cm-1 quoted by the manufacturer 37. For DLS measurements, a ny correlations function with polydispersity values greater than 0.08 was rejected. For the three salts (MgCl2, NaCl, CsCl) for which temperature-dependent viscosity data were available, light scattering measurements were performed at six di fferent temperatures starting from 40 C down to 15 C in steps of 5 C. After each temperature step, solu tions were allowed to equilibrate thermally for 5 min. 4.2.4 Dynamic (DLS) and Static (SLS) Light Scattering Analysis Dynamic Light Scattering Analysis: The autocorrelation function of scattered light measured in DLS yield the decay rates of local concentration fluctuations for macromolecules in solution 2,5,11. A more detailed description of data analysis of DLS is given in section 2.4.2 of chapter 2. 47

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Collective diffusion coefficient Dc is related to the single particle diffusivity D0 via as given by equation (2.49) in chapter 2. Dc = D0 [1 + kD ] = D0 [1 + (kS + kH) (4.1) where kD = kS + kH is the sum of the direct and hydrodynamic protein interactions kS and kH, is the protein volume fraction. Static Light Analysis: A more detailed description of da ta analysis of SLS is given in chapter 2. For interacting particles, the normalized Rayleigh ratio R is related to the properties of the protein solution via as given by equation (2.40) in chapter 2 KCp/R = M-1 [1 + ks where M is the molecular weight of the protein, Cp is the protein concentration (in mg/ml), ks is the direct interaction parameter, and = Cp is the protein's volume fraction. 4.2.5 Growth of Macroscopic Crystals Macroscopic lysozyme crystals were grown at lysozyme concentrations of 20 mg/ml using all three salts at concentrations of 0. 6 M and 1M, respectively. Solutions were placed in sealed crystalli zation wells and incubated overnight (16 hrs) at 4 C. 4.3 Results The overall goals of this study were tw o-fold: to ascertain whether strong chaotropic or kosmotropic ions alter the ex tent of hydration around individual lysozyme molecules; and to determine whether and how chaotropic or kosmotropic ions selectively alter the water-mediated hydrodynamic interact ions among lysozyme molecules. Using measurements of lysozyme diffusion, we tr acked changes to the hydrodynamic radius of lysozyme and to its hydrodynamic interactions in the presence of various chaotropic or kosmotropic salt ions. 48

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4.3.1 Chaotropic & Kosmotropic Salts and Water Viscosity The selection of salts used for this st udy was driven by several considerations. First, we used salt for which reliable viscosity data vs. salt concentration and, when available, vs. solution temperature. These data are critical both for careful determinations of the hydrodynamic radius of lysozyme (see equation 2.49 in chapter 2) and for quantifying the chaotropic/kosmotr opic character of the ions that make up the salts. We chose the following five salts for our study: MgCl2, NaCl, CsCl, NaH2PO4 and NaI. This way we either kept the anion (Cl-) or cation (Na+) of the salts constant, while selecting corresponding cations/anions rang ing from strongly Kosmotropi c to strongly chaotropic (see Table 4.2). Na+ and Clthemselves are weakly kosmotropic and chaotropic, respectively. Published values for salt-indu ced changes to the visc osity of water at 25 C for each salt are summarized in Fig. 4.1. Since experimental data poi nts are sparse, we used Kaminsky's extension to the empirical Jones-Dole equation 23 (cs) = 0 ( 1 + K1 Cs + K2 Cs + K3 Cs 2) (4.3) to derive viscosity values for the specific salt concentrations used in our experiments. Here 0(T) is the water viscosity at a given solution temperature and K1 through K3 are empirical fitting coefficients. The resulting fi ts through the experimental data for T = 25 C are displayed as dashed curves in Fig.4.1. Fitting coefficients for each salt, and at all temperatures for which data were available, are summarized in Table 4.1. Values of the linear K2-term or Jones-Dole B coefficient, measured for multiple combinations of ions, can be used to quantify the kosmotropic or ch aotropic character of specific ions, and are summarized in Table 4.2. We use these valu es only to characteri ze the relative strength of the chaotropic/kosmotropic characte r for the six ions in our study. 49

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Fig. 4.1: Plot of the viscosity of water/salt solutions at T = 20 C as function of dissolved salt concentration. The slope of the initial increase (NaH2PO4, MgCl2, NaCl) or decrease (NaI, CsCl) is indicative of the pred ominant kosmotropic (full symbols) or chaotropic (open symbols) character of the cation/ani on combination for a given salt. Symbols represent measured viscosity values for NaH2PO4, MgCl2, NaCl, NaI and CsCl 26, while the dotted lines represent fits through the viscosity data using the Kaminsky equation 23. Extrapolated viscosity values were used for all salt concen trations for which measured viscosities were unavailable. 50

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Table 4.1: Summary of fitting parameters for viscosity water-salt mixtures at various solution temperatures. Salt Temperature (C) K1 [mM]-1 / 2 ( 10-4) K2 [mM]-1 ( 10-5) K3 [mM]-2 ( 10-8) NaCl 15 -6.20 9.22 -0.27 20 -8.47 10.96 -0.563 25 -7.11 11.39 -0.651 30 -3.54 10.60 -0.266 35 -5.49 11.89 -0.549 MgCl2 15 8.82 34.02 6.66 20 8.80 33.96 6.22 25 8.87 35.34 6.09 30 7.29 36.46 5.64 35 9.07 36.13 5.91 CsCl 15 -2.11 -7.33 1.96 20 -12.72 -1.14 -0.028 25 3.56 -6.10 1.73 30 8.49 -7.05 2.36 35 7.91 -5.77 2.15 NaH2PO4 25 -5.36 34.17 14.62 NaI 25 1.27 0.86 1.57 51

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Table 4.2: Summary of Jones-Dole viscosit y B coefficients for the salt ions in this study. Positive values indicate kosmotropic and negative values chaotropic ions. Data adapted from Table 3.1 8. Ion Jones-Dole B-coefficient PO4 30.590 Mg2+ 0.385 Na+ 0.086 ClCs+ -0.007 -0.045 I-0.068 4.3.2 Measuring protein hydration and hy drodynamic protein interactions Combining static and dynamic light scattering, we determined salt-specific effects on lysozyme hydration and on the mutual hydrodynamic interactions among the lysozyme molecules. A detailed analysis of DLS data is given in chapter 2. The diffusive behavior of macromolecules in solution is altered by the presence of direct and solvent mediated hydrodynamic interactions. These interaction effects on mutual protein diffusivities Dc are significant and depend both on sa lt concentration and salt identity 17,28,30. For moderate protein concentrations, direct and hydrodynamic interaction increase linearly with protei n concentration (equation 4.1). Depending on the dominance of net attractive or repulsive interactions, the protein's collective diffusivity Dc can be either higher (net repulsion) or lower (net attraction) than the corresponding singleparticle diffusivity (equation 2.49 of chapter 2). By measuring the protein dependence of the collective diffusion coefficient Dc(CLys), while accounting for th e contributions from direct protein interactions kS and changes in solution viscosity (Cs,T), we can derive values for both the single-mo lecule hydrodynamic radius RH and the mutual hydrodynamic interaction parameter kH. Values for the direct protein interaction 52

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parameter kS are determined independently from the protein-dependence of the static light scattering inte nsity (equation 4.2). 4.3.2.1 Direct and hydrodynamic interaction of lysozyme in solutions Figure 4.2 summarizes the changes in light scattering intensity (SLS) with lysozyme concentration Clys at T = 20 C, for a series of increasing salt concentrations and for three (MgCl2, NaCl and CsCl) of the five salts consid ered in our study. Scattering intensities are displayed as normalized Debye ratios KCLys/R (equation 2.43 in chapter 2). Debye plots provide a particularly st raightforward interpretation of SLS data: The y-intercept of the KCLys/R vs. CLys data is the inverse of the protein's molecular weight Mw, while the sign of their slope indicates whether proteins experience net repulsive (positive slope) or attractive (negative slope) interactions at the given solution conditions 15,18. The change from positive to negative slopes with incr easing salt concentra tion results from the transition of charge-mediate d protein-protein re pulsion at low salt concentration to attraction due to short-range protein inter actions (van der Waal s, hydrophobic, etc). Several previous studies have matched th e transition from repulsive to attractive interactions using colloidal DLVO theory 17,25,28. While successful for any given salt, DLVO theory can not account for the ion-specif ic differences in protein interactions at the same ionic strengths (i.e. e ffective charge screening). 53

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Fig. 4.2: Salt-Specific Effects on Debye Ratios KClys/R and Mutual Diffusivities Dc of Lysozyme: Plot of (Top Row) the Debye ratios KClys/R and (Bottom Row) mutual diffusivities Dc of lysozyme as function of lysozyme concentration Clys, in the presence of (A) MgCl2, (B) NaCl or (C) CsCl, at increasing salt conc entrations (50 mM, 250 mM, 625 mM and 1 M). The y-axis intercepts of the Debye plots yields the inverse of the molecular weight (1/M) of lysozyme, while the sign of the slop e indicates whether interactions among the lysozyme molecules ar e either net repulsive (positive slope) or attractive (negative slope). For the plots of mutual diffusivities, the y-axis intercepts yield the free particle diffusivity D0 while the slope indicates the magnitude and sign of the combined effects of direct and hydrodynami c interactions on lyso zyme molecules. All measurements shown were taken at T = 25 C. The bottom row of Fig. 4.2 displays the ch anges in the coolectiv e diffusion constant Dc of lysozyme under the same conditions used fo r the SLS measurements in the top row. For all DLS data in Fig. 3.2B the measured size polydispersity was less than 0.08, indicating that changes in Dc are not contaminated by aggregate formation in solution. Any measurements at high sa lt concentrations suggesting potential aggregate/cluster 54

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formation (high polydispersity, temporal drifts in scattering intensity or Dc) were excluded from the analysis. The presence of positive slopes in both DLS and SLS data, together with the strictly linear behavior of both data sets with pr otein concentration are fu either protein hydrati on or in the solution-mediated hydrodynamic protein interactions. .t These differences are well below the thickne ss for a single monolayer of water extending rther indicators that potential contributions due to protein aggreg ation are negligible 29. The plots of mutual diffusivity Dc vs. lysozyme concentration are very similar in appearance to the Debye plots in the top row. Mutual lysozyme diffusivities Dc vary linearly with lysozyme concentration, with the slopes changing from positive to negative values as salt concentration increases. As indicated in equation (4.1), the slopes of Dc vs. CLys measured with DLS are the superposition of both direct and hydrodynamic interactions among the protein molecules. Subtracting the ks values obtained with SLS, therefore, we determined the magnitude of the hydrodynamic interaction parameter kH for solution-mediated interactions among the lysozyme molecules. Using this approach enabled us to determine whether the presence of chaotropic vs. kosmotropic ions similar to the already well-established effects on direct protein interact ionscan induce saltspecific changes in 4 3.2.2 Effecs of Kosmotropicvs. Chaotro pic ions on lysozyme hydrations Based on the significant influence of salt ions on local water structure, it seems natural to wonder whether chaotropic or kosmotropic ions can alter the extent of the ordered water layer around proteins. Using DL S, we determined whether different salts lead to discernable swelling or contraction in lysozyme's hydration layer. We can obtain the single-particle diffusivity D0 of lysozyme by extrapolating the mutual diffusivity Dc to its y-axis intercept at Clys = 0. Using the Stokes-Einstein relation (see equation 1.49 in chapter 1), the radius of hydrated lysozyme can be obtained from the single-particle diffusivity D0 (Fig. 4.2) and values of the solution viscosity (Cs,T). Figure 4.3 displays the resulting values for lysozyme's hydrodynamic radius for each of the five salts. These data are notable in several ways. First of all, when accounting for saltand temperature dependent solution viscosity and for protein interaction effects on diffusivity, the hydration radii of lysozyme unde r any conditions are within 0.25 of one another. 55

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to about 2.6-2.8 7. Hence, our experimental resolu tion permits us to resolve changes down to 1/10 the thickness of a single water layer. Equally remarkable, while the effects of chaotropic vs. kosmotropic salt ions on the local structure of water are significant, there is no discernable swelling or disruption of the lysozyme hydration layer due to the presence of either kosmotropic or chaotropic ions. This remains true up to salt concen trations of 1M and over the entire range of temperatures in our experiments. This is shown in Fig. 4.3B for the case of MgCl2, which is representative for the behavior of all the other salts. These re sults imply that the overall extent of lysozyme's hydration laye r is very stable. The question remained whether the net charge of the prot ein itself might determine whether chaotropic/kosmotropic ions can disrupt the pr otein's hydration layer. It has been shown before that the Hofmeister series for the solubility of lysozyme was inverted 33, presumably due to the net positive charge of lysozyme at pH=4.5 34. According to Debye-Hckel theory, the concentration of ca tions near the positively protein surface will be reduced from their bulk concentrations 22. To investigate this possibility, we included NaH2PO4 and NaI in our measurements, salts with either a highly chaotropic (I-) or kosmotropic (PO4 3-) co-ion. Yet, neither of these two negative ions altered the hydrodynamic radius of lysozyme (Fig. 4A). 56

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Fig. 4.3: Effects of Chaotropic and Kosm otropic Salt Ions on Lysozyme Hydration. (A) Meand hydrodynamic radius Rh of lysozyme in the presence of various salts with predominately chaotropic or kosmotropic salt ions and for salt c oncentrations varying from 50 mM to 1 M. Rh values for different concentr ations of the same salt were averaged since they displayed no discernabl e systematic variations (see 4.3B). (B) Hydrodynamic radius Rh of lysozyme in the presence of MgCl2 at different solution temperatures T, and for MgCl2 concentrations ranging fr om 50 mM to 1 M. It is well known that water becomes progressively disordered with increasing temperature 14. We therefore determined whethe r there were temperature-dependent variations in the hydrodynamic radius of lysozyme in the presence of chaotropic vs. kosmotropic ions. Fig. 4.3B shows the re sults of a typical measurement with MgCl2 over the temperature range of 15-40 C. The range of temperature values was limited due to problems with bubble formation (high T) and the onset of phase separation (low T). Within these limitations there are, again, no indications for any salt-specific effects on 57

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protein hydration with solution temperature. The lack of any discernable effects on the hydrodynamic radius of lysozyme with salt co ncentration and salt type simultaneously indicates that there is also no salt-induced swelling of the protein itself (which might be otherwise difficult to discriminate from changes to the protein's hydration layer. 4.3.2.3 Salt specific effects on direct and hy drodynamic protein-protein interaction To convert the slopes of our static and dynamic light scattering data (Fig. 4.2A and B) into direct and hydrodynamic interaction paramete rs (defined in equation (4.1) and (4.2)), we use the value = 0.703 ml/g for the specific volume of lysozyme 35. Figure 4.4 displays the resulting values for the dire ct and hydrodynamic interaction parameters ks and kh, as function of solution temperature a nd salt concentration. The systematic variations become more apparent when di splayed against solution temperature (shown here for MgCl2, NaCl and CsCl, and for increasing salt concentrations). At the lowest salt concentrations (50 mM), the direct protein interactions parameter ks remains positive at all temperatures. For the same salt concen tration, repulsive prot ein interactions are more prominent in the 1:1 salt solu tions (NaCl, CsCl) than the 2:1 MgCl2 solutions. Both observations are consistent with the Debye theo ry of diffusive charge screening. At low salt concentrations, protein interactions w ill be dominated by protein-protein charge repulsion, with the 2:1 salt MgCl2 more effective than NaCl and CsCl in screening out this charge repulsion 22. With increasing salt concentration char ge repulsion progressively diminished and net protein repulsion (positive ks) turns into net attraction (negative ks). While the saltinduced decrease in net re pulsion, at least qualitatively, fo llows the logic expected for salt screening of protein charges, salt specific effects rapidly emerge even at moderate salt concentrations. In particular, NaCl at or a bove 250 mM is significantly more effective in promoting attractive lysozyme interactions than either MgCl2 or CsCl. The dashed horrizonatl lines in Fig. 4.4A indicate the range of interaction parameters kS (or, equivalently, second virial coefficients B22) considered favorable for protein crystal growth 18. As shown in Fig. 4.5, we were able to obtain lysozyme crystals with all three salts when incubating solutions at low temperature and at sufficiently high salt concentrations to reach the "crystallization band" in Fig. 4.4A. Lysozyme solutions 58

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incubated with 1M NaCl yielded larger numbers of smaller crystals, consistent with the enhanced attraction among lysozyme monom ers and, therefore, the increased supersaturation of the solutions under ot herwise identical growth conditions. Fig. 4.4: Dependence of Direct and Hydrodynamic Interaction Parameters on Salt Type, Salt Concentration and Solution Temperature. Plot of the net strength of (top row) direct lysozyme interactions KS, (bottom row) corresponding hydrodynamic interactions KH = KD KS as a function of solution temperature T, and for four different salt concentration Cs. Data are shown for (left column) MgCl2, (middle column) NaCl and (right column) CsCl. KS and KD are derived from the slopes of the SLS and DLS data respectively. The band of negative Ks va lues indicated by the two horizontal dashed lines in the top row is considered favorable for protein crystallization growth 18 59

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Fig. 4.5: Protein crystals grown from lysozyme solutions in the presence of chaotropic vs. kosmotropic cations. Microscope images of tetragona l lysozyme crysta ls grown with (left column) 0.6 M or (right column) 1M of (top row) MgCl2, (middle row) NaCl or (bottom row) CsCl. All solutions containe d 20 mg/ml of lysozyme in 25 mM NaAc buffer (pH = 4.5) and were inc ubated overnight (16 hrs) at 4 C. The lysozyme crystals grown at [NaCl] = 1 M show a mixture of tetragonal crystals and (sea urchinlike) spheres of needle crystals. The latter ar e most likely orthorhombic crystals. 60

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4.4 Discussion Lysozyme's hydrodynamic radius of (1.89 0.025) nm remained unaltered by the presence of salts containing e ither strong chaotropic or kosmo tropic ions. This remained true up to salt concen trations of 1 M (NaH2PO4, MgCl2, NaCl, CsCl) or up to the onset of lysozyme precipitation (NaI). Previous meas urements had noted the lack of changes in lysozyme hydration in the presence of NaCl up to 0.4 M or sodium acetate up to 2.5 M 28 and MgCl2 up to 1 M 17. Our measurements extend these observations to a series of salts with either predominately chaotropic or kos motropic character and put a much tighter limit (0.25 or less than 1/10th of a monolayer of water ) on residual changes that might evade detection. The data also indicate th at it did not matter whether the chaotropic or kosmotropic ion carried the same (Mg2+, Cs+, Na+) or opposite charge (PO4 3-, Cl-, I-) as the net charge of lysozyme. Hence, the elev ation (negative ions) or depression (positive ions) of local salt concentrations beyond th eir bulk concentrations near the positively charge lysozyme surface did not alter these re sults. Variations in solution temperature did not produce any discernable changes in lysozyme hydrati on in the presence of various salts, either. The lack of any discernable changes in lysozyme hydration by either chaotropic or kosmotropic salts seem surprising give n the pronounced salt-s pecific effects on viscous dissipation in bulk wa ter (see Fig. 4.1). Appare ntly, neither chaotropic nor kosmotropic ions are able to alter the exte nt of the hydration layer around lysozyme. This could imply that the protein surface re sidues and surface structure is much more effective at ordering water than either chaotr opic or kosmotropic ions. Alternatively, ionspecific effects onto surface water might only change the fast relaxation dynamics of water occurring at or below picoseconds, much faster th an the microsecond relaxation times probed in translational diffusion of lysozyme. This later viewpoint seems somewhat difficult to reconcile with the obvious salt-specific effects on bulk water viscosity which do need to be accounted for. Hence, specific effects on water relaxation even at a much faster time scale should tr anslate into increased viscosity near the protein's surface 20. We prefer the interpretation that neither chaotropic nor kosmotropic ions will perturb the structure and dynamics of surface water, but that ion-specific effects are 61

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mediated via direct inter actions with the protein 4. This is supported by the clear ionspecific effects on direct protei n-protein interactions obtained with static light scattering (Fig. 4.2A). However even there, the or dering of specific ion effects on attractive lysozyme interactions (Na+ > Mg2+ > Cs+) is at odds with consider ations of either charge screening (MgCl2 > NaCl, CsCl) or the typical order of these cations within the Hofmeister series (Mg2+ > Na+ > Cs+) 8. It is hard to image th at the two-fold higher bulk concentrations of (weakly) chaotropic Clions in MgCl2 vs. NaCl solutions should be able to compensate for the strong kosmotropic character of Mg2+ compared to the moderately kosmotropic Na+ ions. This implies that there are other ion-specific effects on protein interactions beyond the sc ope of the Hofmeister series. As with protein hydration, ther e are no indications that hydrodynamic protein interactions are directly modified by i on-specific effects. However, hydrodynamic interactions are strongly anti-c orrelated to direct protein in teractions thereby coupling them indirectly to salt-specific effects on direct protein interactions. With increasing salt concentration, hydrodynamic inte ractions transition from net attraction to repulsion while direct protein interactions move in the opposite direction (Fig. 4.4). We have previously noted that trend in lysozyme solutions at fixed temperature for both NaCl and sodium acetate 28. This anti-correlation is not dependent on any specific salt ion and persists as a function of temperature. Experiments on hydrodynamic interactions with pairs of colloidal spheres can provide guidance in th e interpretation of this observed coupling 10,16. Specifically, direct attractiv e interactions are likely to bias diffusion in favor of colinear motion towards one another. Hydrodyna mic momentum transfer will oppose such motion, resulting in enhanced hydrodynamic repulsion. Similarly, with proteins experiencing net repulsion, the direct inter action will tend to push other proteins out of the way, thereby decreasing solution-mediated momentum transfer when compared to non-interacting particles. Hence, enhanced attraction or repulsion among the lysozyme molecules would be accompanied by corresponding increases or decreases in hydrodynamic interactions, as obs erved in our experiments. 62

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4.5 References 1. Ball, V. and J. J. Ramsden (1998). Biopolymers 46: 489-492. 2. Berne, B. J. and R. Pecora (1976). Dynamic light scattering: with applications to chemistry, biology and physics. New York, Wiley. 3. Blake, C. C. F., D. F. Koenig, et al. (1965). Nature 206: 757-761. 4. Bostrm, M., D. R. M. Williams et al. (2003). Biophysical Journal 85(2): 686-694. 5. Brown, W., Ed. (1993). D ynamic light scattering: th e method and some applications. New York, Oxford University Press. 6. Cacace, M. G., E. M. Landau, et al. (1997). Quarterly Reviews of Biophysics 30(03): 241-277. 7. Cheng, L., P. Fenter, et al. (2001). Physical Review Letters 87(15): 156103:1-4. 8. Collins, K. D. (2004). Methods 34(3): 300-311. 9. Collins, K. D. and M. W. Washabaugh (1985). Quarterly Reviews of Biophysics 18: 323-422. 10. Crocker, J. C. (1997). The Journal of Chemical Physics 106(7): 2837-2840. 11. Cummins, H. Z. and R. Pike (1973). Photon correlation and light beating spectroscopy. Nato Advanced Studies Institute Capri, Italy, Plenum Press. 12. Desinov, V. P. and B. Halle (1996). Faraday Discussions 103: 227-244. 13. Deyoung, L. R., A. L. Fink, et al. (1993). Accounts of Chemical Research 26(12): 614-620. 14. Dill, K. A., T. M. Truskett, et al. (2005). Annual Review of Biophysics and Biomolecular Structure 34(1): 173-199. 15. George, A. and W. W. Wilson (1994). Acta Crystallographica Section D-Biological Crystallography 50: 361. 16. Grier, D. G. and S. H. Behrens (2001). Interactions in Colloidal Suspensions: Electrostatics, Hydrodynamics and their Interplay. Electrostatic Effects in Biophysics and Soft Matter. C. Holm, P. Kekicheff and R. Podgornik. Dordrecht, Kluwer. 17. Grigsby, J. J., H. W. Blanch, et al. (2000). Journal of Physical Chemistry 104: 36453650. 18. Guo, B., S. Kao, et al. (1999). Journal of Crystal Growth 196: 424-433. 63

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19. Halle, B. (2004). Philosophical Transactions of Royal Society of London B 359: 1207-1224. 20. Halle, B. and M. Davidovic (2003). Proceedings of National Academy of Sciences United States of America 100(21): 12135-12140. 21. Hofmeister, F. (1888). Arch. Exp. Pathol. Pharmakol. 24: 247-260. 22. Hunter, R. J. (1987). Foundations of Colloidal Science. Oxford, Clarendon Press. 23. Kaminsky, M. (1957). Zeitschrift fr Physikalische Chemie 12: 206. 24. Knocks, A. and H. Weingartner (2001). Journal of Physical Chemistry B 105(17): 3635-3638. 25. Kuehner, D. E., C. Heyer, et al. (1997). Biophysical Journal 73: 3211-3224. 26. Lobo, V. M. M. (1989). Handbook of electrolyte solutions. New York, Elsevier. 27. Merzel, F. and J. C. Smith (2002). Proceedings of National Academy of Sciences United States of America 99: 5378-5383. 28. Muschol, M. and F. Rosenberger (1995). Journal of Chemical Physics 103(24): 10424-10432. 29. Muschol, M. and F. Rosenberger (1996). Journal of Crystal Growth 167(3-4): 738747. 30. Neal, D. G., D. Purich, et al. (1984). Journal of Chemical Physics 80(7): 3469-3477. 31. Pal, S. K., J. Peon, et al. (2002). Proceedings of National Academy of Sciences United States of America 99(4): 1763-1768. 32. Parmar, A. S., P. E. Gottschall, et al. (2007). Biophysical Chemistry 129: 224-234. 33. Ries-Kautt, M. M. and A. F. Ducruix (1989). Journal of Biological Chemistry 264(2): 745-748. 34. Roxby, R. and C. Tanford (1971). Biochemistry 10: 1-12. 35. Sophianopoulos, A. J., C. K. Rhodes, et al. (1962). Journal of Biological Chemistry 237(4): 1107-1112. 36. Svergun, D. I., S. Richard, et al. (1998). Proceedings of National Academy of Sciences United States of America 95(5): 2267-2272. 37. Malvern Instruments Technical Support Library, UK 64

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Chapter 5 Nucleation and Growth of Gold Nanoparticles 5.1. Introduction The properties of colloidal gold, silver and other such similar metal colloids have been of interest for centuries with an extens ive scientific research going back to Michael Faraday in 1857 1. In 1908, Mie presented a soluti on to Maxwells equations that describes the extinction (absorp tion and scattering) of spherica l particles of arbitrary sizes 2. Ever since, various models and appr oximations have been develoed to study nanoparticles systems 3,4. Over the years, it has been re alized that the morphology and the growth-rate of these nanostructu res in the solution phase can be controlled and designed by tuning the reaction parameters. The wet chemical synthesis of nanomaterials has advanced to the level where it is possible to tailor make particle shapes, sizes and their distributions by manipulating various pa rameters during the growth process 5,6. However, to achieve control over the synthesis, it is important to unders tand the process of nucleation and growth of crysta llites from the cluster level upward, includes the specific roles played by various physical and chemi cal parameters such as temperature, concentration, pH, stirring, osmotic potenti al, incubation time etc. The mechanisms involved in the growth of nanopa rticles follow different rules than those applicable to bulk materials. Over the last several decad es, the mechanism of nucleation and growth processes of colloidal partic les synthesized by various met hods has been researched in detail. The initial swell in nucleation studi es began predominantly with condensation 7,8 and crystallization 9,10 studies during the early twentieth century. However, mechanistic studies of colloid and cluster formation began when LaMer and Dinegar 11 synthesized sulfur hydrosols nucleating from supersaturated solutions. Uniform particle size was achieved by short nucleation a nd relatively long growth pe riods. Studies on kinetics and mechanisms of particle formation showed in compatibility with Lamers supersaturation theory 12. Models and statistical th eories began to be developed for understanding the 65

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formation of the critical nucleus and spontaneous growth which gives rise to particular sizes 13,14. Overbeek 15 did extensive studies on the particle growth rate and the particle size distribution citing the possi ble rate-determining steps. Analysis of the activation barrier in the nucleation process, studies on the parameters relevant for kinetic or thermodynamic control, and factors controll ing the growth process have improved our understanding of the overall process. Howe ver, the nucleation event itself is quite complicated and difficult to study experiment ally. It depends on numerous factors like nucleation rates, cluster mobility, maximum cluster density, spatial and size distribution of clusters, and modes of growth. To fully understand the formation of particles at various levels, it is essential to capture and investigate the early stages of nucleation of the nanoparticles, their growth kinetics and the effect of various parameters. Henceforth, the study of mechanisms of crystal growth is currently attracting in creasing interest and recent advancements in the instrumental techniques have made it feasible for in-situ experimental investigation of the process with higher resolution and precision. Among the experimental techniques us ed to study and understand the kinetic and thermodynamic nature of nanocrystal nucleation and growth are small angle X-ray scattering (SAXS)16, UV-visible spectroscopy, X-ra y absorption spectroscopy 17, time dependent TEM 18, and DLS 19. Though these techniques ar e highly efficient for the in-situ measurements of particle size and shape determination, the ma in problem with all methods is that they obtain information about larger clusters (around >1-2nm). The limitation on the time scale of the measurements is yet another issue since nucleation and growth of the nanoparticles during laboratory syntheses proceeds quite fast. The nucleation events, in particular, are difficult to re solve since they represent a transient, metastable state. Additionally, complications due to the reactio n set-up (multi step synthesis processes, high temperature/pressure etc.) prevent co mbination of light scattering with X-ray scattering for simultaneous in-situ measurements. Therefore, a careful investigation of nucleation and growth of nanoc rystallites in the solution phase demands a synthesis protocol that is (1) single st ep (2) can be coupled with sta ndard light/X-ray scattering setups (3) and has a slow-enough reaction rate to capture the growth process. Recently, Ramya Jagannathan et al reported a novel synthesis route where they used the antibiotic cephalexin to reduce chloroauric acid 20. In this method colloidal gold 66

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capped by antibiotic in aqueous solution is read ily prepared by a facile one-step protocol. Their NMR and X-ray photoelectron spectrosc opy (XPS) results have shown that the sulphur moiety present in the beta lactam is responsible for the dua l role of reducing and capping (stabilizing) the gold nanoparticles20. Interestingly, in this method, they could control the morphology of the gold nanoparticles from quasi-spherical to flat triangular flakes and finally to truncated triangles a nd hexagons by increasing the concentration of gold ions correspondingly. Their transmi ssion electron micrograph also showed the presence of a large number of smaller 1-3 nm particles. This one-step synthesis-route is a pr omising model system for studying the growth of the gold nanoparticles. The rationale behind choosing this particular synthesis method over several other established methods was due to the following reasons: a) the reaction is sufficiently slow (approx. 1.5 hour at 28 deg C), b) establishes the mechanism of colloidal gold synthesis by a biomolecule, sp ecifically an antibiotic c) scattering and absorption studies can be performed using a si mple system with no auxiliary chemicals or processes needed. Here we report our results on in situ dynamic light scattering studies at various incubation temperatures to understand th e nucleation and growth mechanism. 5.2 Materials and Methods 5.2.1 Synthesis of Gold Nanoparticles We followed with slight modifica tion the one-step synthesi s protocol developed by Jagannathan et al 20 to synthesize the an tibiotic functionalized go ld nanoparticles. In short, 10-4 M chloroauric acid was reduced by 10-5 M of the antibioticcephalexin. Both the antibiotic and chloroauric acid were firs t diluted to twice thei r final concentrations into the distilled water before mixing them to induce the formation of nanoparticles. For the DLS studies, we passed both stock soluti ons through 0.22 m syringe filters to filterout any performed aggregates. Using DLS, bot h the stock solutions were checked for the presence of such pre-existing pa rticle clusters (or dust particles) that might interfere with subsequent nucleation studies21. The 2x stock solutions were cooled to 5 C, mixed in equal proportion to their final concentration and then placed in to a quartz cuvette for light scattering measurements. The pH of the so lution was monitored by using a digital pH 67

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meter. The pH was stable around ~ 3.7. Following the particle synthesis, the resulting colloidal gold nanoparticle suspensions remained stable without aggregation or precipitation. 5.2.2 Dynamic light scattering (DLS) measurement Dynamic light scatte ring (DLS) measurements were performed using a Zetasizer Nano S (Malvern Instruments Ltd., UK) w ith a 3 mW He-Ne laser operating at a = 633nm. For details see chapter 1. Glass cuvettes containing the mixed chloroauric acid/ cephalexin solutions were placed inside the thermostated sample holder of the DLS unit and were allowed to equilibrate to their set temperature (15 C, 25 C or 35 C) for five minutes. Intensity autocorrelation functi ons of scattered li ght were collected continuously using acquisition times of 60 seconds per correlation function. Throughout the experiment, the total intensity of scattered light changed dramatically due to the incessant nucleation and growth of strongly scattering gold colloid s. Therefore, the measurement software protocol was set up to first measure the total scattering intensity and to adjust a variable neutral density filter in the detection arm accordingly, in order to keep the avalanche photodiode count well below saturation. Relative scattering intensities were corrected for this variable attenuation. The complete analysis of Dynamic Li ght Scattering (DLS) measurements for particle size distribution is described in Chap ter 2. For our system parameters, q = 2.64 nm-1 hence, particles wi th hydrodynamic radii rh close to or below q-1 38 nm could be treated simply as isotropic Rayleigh scatte rers. Finally, the distribution of diffusion coefficients can be converted into particle si ze distributions using the Stokes-Einstein as given by equation (2.49) in chapter 2. During the nucleation studies, the amplitude of the autocorrelation functions steadily increased as nucleation and aggregatio n of the gold sol prog ressed. Correlation functions with intercepts at t 0 smaller than 0.2 were excluded from our analysis due to their intrinsic noisiness. Otherwise, correl ation functions were converted into particle size distributions using the "general purpos e" inversion algorithm provided with the Zetasizer Nano S software. Particle size distributions obtained from alternative inversion algorithms yielded comparable results. 68

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5.3 Results and Discussion In Figure 5.1, we show the temporal evol ution of the intensity correlation function of light scattered from the solution under going the synthesis of gold colloids at 15 C. Due to the reduced synthesis rate, the early stages of the nucleation and growth of the colloidal gold particles are more readily resolved at T = 15 C. Initially, no correlations are detected since the concentr ation fluctuations of the gold solution alone are too fast to be resolved by DLS. Fig. 5.2 displays the temporal evolution of the intercept of the intensity correlation function g2( ) vs. the incubation time of the sample. There is a significant latency period of approx. 30 min be fore the onset of nucleation and growth of gold particles as detected by DLS. This latency period decreases significantly as the solution temperature is raised to 25 C or to 35 C. After a period of rapid increase, the g2 ( ) intercept eventually levels off around 0.78, below the theoretical limit of 1. The lower plateau value of 0.78 arises from c ontributions to the dyna mic signal from purely static scattering off the various interfaces (air /glass/solution) Fig: 5.1. Normalized temporal correlations of the intensity of scattered light, g2( )-1, vs. delay time obtained at different time points (see label on curve) during the synthesis of colloidal gold particles from chloroauric acid solutions (10-4 M) in the presence of the antibiotic cephalexin (10-5 M), incubated at 15 C. With increasing incubation period, the correlations of the scattered light arising fr om the gold colloids nucleating and diffusing in the aqueous suspension increases significantly. Together with the zero intercepts of the intensity correlation functions, Fig. 5.2 also shows the total intensity of scattered lig ht during the synthesis of the gold colloids. 69

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Obviously, the rapid increase in the temporal correlations of scattered light (~ 30 min) significantly precedes the upswing in overall scattering intensity (~ 80 min), both of which are associated with the nucleation and growth of the gold colloid particles. This is an intriguing observation since in creases in static scattering intensity are frequently used as indicators for the onset of nucleati on events in supers aturated solutions 22,23. Our observations suggest that the correlation amp litude of dynamically scattered light is a much more sensitive and reliable indicator fo r nucleation events than "kinks" in static light scattering data. Nevertheless, DLS is unlikely to capture the actual nucleation event due to at least two complicating factors. Fi rst, the dynamic signal during the very early phases of nucleation is contaminated by contributions from residual dust and air inclusions. In addition, the shot noise of the photon detect or limits resolution of very small populations of particles. Fig. 5.2 Intercepts of the intensity correla tion function of scattered light ( ) and the overall intensity of scattered light () as vs the incubation time of the sample. The solid squares highlight the time points for most of the correlation functions displayed in Fig. 5.1, and their corresponding particle size distri butions shown in Fig. 5.4. A fit through the intercepts of g2( ) -1 vs. incubation time with a simple sigmoidal functions faithfully reproduces the experimentally observed behavior as expected for an "activated process" such as nucleation. Notice also the significant lag of the total scattering intensity compared to the upswing in the amplitude of the correlation function. This implies that dynamic light scattering is a much more sens itive indicator of the nucleation event than static light scattering. Figure 5.3 displays the particle size distributi ons obtained from the autocorrelation functions during the early stages of the nucleation and aggregation 70

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process (see also open squares in Fig. 5.2). Noticeably, the larger particle peak around 20-30 nm emerges ahead of the smaller aggreg ates near 1-2 nm. However, caution is required when interpreting this result. First, as indicated by the St okes-Einstein relation (equation. 2.49 in chapter 2) and equation 2.42 in chapter 2, the autocorrelation of light scattered by small 1-2 nm aggregates d ecays at rates of onl y few microseconds.. Unfortunately, the correlation functions g2( )-1 remain rather noisy, particularly at these short delay times, until the amplitude of the zer o-intercept is well above 0.5. In addition, the scattering intensity of the particles increases approximately quadratic with particle volume. As a result, a single particle of ra dius 25 nm will scatter one million times more light than a 2 nm particle. As is apparent from Fig. 5.2, the overall scattering intensity from the solutions remains rather weak prior to approx. 85 minutes into the experiment. In addition, the contribution to the scattering intensity from the small particles never exceeds 20% of the total scattering intensity (see Fig. 5.6). All these factors might collude to minimize the contributions of sma ller particles to the dynamic light scattering signal during the very earl y stages of nucleation. Fig. 5.3 Examples of particle size distributions obtained duri ng the early phases of the synthesis of gold colloids in the presence of cephalexin during incubation at 15 C. Fig. 5.2 indicates at what point in the nucleation pr ocess these particle size distributions where obtained. The particle distri butions at all temperatures eventually showed two wellresolved particle peaks centered around 25 nm and 1 nm, respectively. At higher temperatures, the apparent delay between the emergence of the larger and smaller peak was much less pronounced. 71

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Figure 5.4 summarizes the tem poral evolution of the two pe aks in the particle size distribution vs. the incubation time for samples at 15 C, 25 C and 35 C, respectively. Most strikingly, the particle distribution is bimodal with two narrow peaks located around 25 nm and 0.5-1.5 nm. Following a brief latency period, the two well-separated populations of gold nanoparticles emerge from the supersaturated solutions nearly simultaneously, with the larger particles slightly preceding the smaller particles particularly at the lowest reaction temperature of 15 C. As discussed above, it is not obvious whether this apparent difference in late ncy of nucleation is just a consequence of the limited detection sensitivity for the smaller aggregates. We are therefore, cautiously, concluding that both populations of gol d nanoparticles nucleate essentially simultaneously. The observations of two differ ent particle populations of distinct mean size are consistent with earlier obser vations made by Jagannathan et. al 20 in a separate study (as discussion above) where the TEM micr ographs showed the presence of larger particles surrounded by a large number of smaller particles20. Fig. 5.4 Changes in the mean particle size for both the small and large gold colloids as function of incubation period and solution te mperature. Two well separated populations of gold colloids with surprisingly tight limits on their particle distributions emerged at all incubation temperatures. The radius for the peak of either population of gold colloids remained essentially unchanged throughout the entire observation period of several hours. 72

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Figure 5.5 summarizes the tempor al evolution of the relative scattering intensity from the solutions at T = 15 C and 25 C, respectively. Following the initial lag-time for nucleation, the overall scatteri ng intensity from these soluti ons rapidly increases with time, closely following a power law with exponents around 1.7. Fig. 5.5 Changes in the total intensity of scattered light during the synthesis of colloidal gold particles at T = 15 C and 25 C. In c ontrast to the relative distribution of gold colloids (Fig. 5.5) the total number of co lloidal gold particles rapidly increases throughout the incubation period. In addition, the synthesis clearly proceeds significantly faster at T = 25 C than at T = 15 C. Intens ity data shown here have been corrected to account for neutral density filters inserted in front of the detector in order to prevent saturation. Figure 5.6 shows the corr esponding changes in relative scattering intensity for the small vs. the large colloidal particles over the same time period. In stark contrast to the rapid increase in total scattering intensity, the relative contributions to the scattering intensity from either particle population remain nearly fixed at a ratio of approximately 20% for the small colloids vs. 80% for the larger colloids. Again, this suggests the remarkable feature that both populations are nucleating and growing at identical rates throughout the synthesis process. The chemical origin of the co-exist ence of two different size ranges with tight control over particle size, nucleation and growth rates is not obvious to us, but does suggest that all thr ee components of the synthesis are somehow 73

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tightly coupled to one another. We believe that this is the first report of simultaneous nucleation and growth of two size ranges. It seems that va rious functional groups on the antibiotic molecule (cephalaxin) might be pl aying a significant role in this process. Fig. 5.6 Percentage of total light scattered by either population of colloidal gold particles during synthesis at T = 15 C. Similar to the overall sizes of the two colloidal gold particles, the relative populat ions for either peak does not appear to change throughout the nucleation and growth period shown in our data. The results at T = 25 C and 35 C are comparable but have been omitted here for clarity. Our DLS data exhibit, a highly unusual and surprising nucleation and growth process for gold nanoparticles mediated by the pres ence of cephalexin. In addition, these two nanoparticle populations reach their respecti ve final sizes very rapidly and then cease growth altogether. At the same time, the total number of gold colloid continues to grow rapidly, and their rate of formation is a sens itive function of incubati on temperature. It is intriguing to note that, at all temperatures, we observe bimodal distri bution of particles in a homogenous system. These observations rais e important fundamental questions relating to the nucleation and growth mechanisms resulting in the observed behavior. What causes the apparent simultaneous nucleation of two distinct gold nanoparticles from an essentially homogenous solution ? What distinguishes thes e two particle populations? What causes the rapid cessation of growth not ju st for one but both of these particles, and why does it occur at such different sizes? Why do these two populations not "compete" 74

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for nutrient but continue to nuc leate and increase in numbers essentially in lock-step with one another? 5.4 References 1. Faraday, M. (1857) Philosophical Transactions of the Royal Society 147, 145. 2. Mie, G. (1908) Annals of Physics 25, 377. 3. Lance Kelly, K.; Coronado, E.; Lin Zhao, L.; Schatz, G. C. (2003) Journal of Physical Chemistry B 107, 668. 4. Finney, E. E.; Finke, R. G. (2008) Journal of Colloid Interface Science 317, 351. 5. Wang, T. S.; Henglein, Z. L.; El-Sayed, M. A. (1996) Chemistry of Materials 8, 1161. 6. Sun, Y.; Xia. (2002) Science 298, 2176. 7. Becker, R.; Doring, W. (1935) Annals of Physics 24, 719. 8. Volmer, M.; Weber. (1926) A. Zeitschrift fr Physikalische Chemie 119, 277. 9. Turnbull, D. (1950) Journal of Applied Physics 21, 1022. 10. Turnbull, D.; Fisher, J. C. (1949) Journal of Chemical Physics 17, 71. 11. LaMer, V K.; Dinegar, R. H. (1950) Journal of the American Chemical Society 72, 4847. 12. Turkevich, J.; Stevenson, P. C.; Hillier. (1951) J. Discussions of the Faraday Society 11, 55. 13. La Mer, V. K. (1952) Industrial and Enginnering Chemistry Research 44, 1270. 14. Granqvist, C. G.; Buhrman, R. A. (1976) Journal of Applied Physics 47, 2200. 15. Overbeek, J. Th. G. (1982) Advances in Colloid and Interface Science 15, 251. 16. Abe cassis, B.; Testard, F.; Spalla, O.; Barboux, P. (2007) Nano Letters 7, 1723. 17. Ingham, B.; Illy, B. N.; Ryan, M. P. (2008) Journal of Physical Chemistry C 112, 2820. 18. Shankar, S. S.; Rai, A.; Ankamwar, N.; Singh, A.; Ahmad, A.; Sastry, M. (2004) Nature Materials 3, 482. 19. Holoubek, J. (2007) Journal of Quantitative Spectroscopy & Radiative Transfer 106, 104. 20. Jagannathan, R.; Poddar, P.; Prabhune, A. (2007) Journal of Physical Chemistry C 111, 6933. 75

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21. Parmar, A. S.; Gottschall, P. E.; Muschol, M. (2007) Biophysical Chemistry 129, 224. (22) Muschol, M.; Rosenberger, F. (1997) Journal of Chemical Physics 107, 1953. (23) Arnaudov, L. N.; De Vries, R. (2005) Biophysical Journal 88, 515. 76

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Chapter 6 Lysozyme as Tracer for Measuring Viscosity of Aqueous Solutions 6.1 Introduction Solution viscosity is a fundamental para meter controlling powe r dissipation over many length scales, ranging from flow of ma croscopic objects down to the diffusive motion of nanopartcles. A wide variety of methods is in use for measuring the bulk viscosity of fluids, including cap illary viscometers, falling ball viscometers, vibrational viscometers, rotating disk viscometers 1-3 and, more recently, piezoelectric or magnetostrictive resonators 4, 5. However, due to the thermal capacity of common liquids, viscosity measurements can be time c onsuming and often require independent measurements of solution density to convert ki nematic into dynamic viscosity values. In addition, bulk measurements are not applicable for mapping out spatial variations in viscosity in such diverse sy stems as biological blood flow 6 or during phase transitions in glassy systems 7. Monitoring diffusive motion of s ub-micron tracer particles provides a convenient way to obtain sp atially resolved data on solution viscosity, with good temporal resolution, and no need for additi onal density measurements when changing solution conditions (e.g. solution temperature or solute concentration). Tracer diffusion also permits remote-sensing of viscosity change s for solutions at extremes of temperature or pressure 2, 3 Viscosity data are critical for evalua ting dynamic light scattering measurements on how solution conditions affect colloidal diffusivity. Changes in colloidal diffusivity with solution conditions typically contai n contributions from both altered solution viscosity and from solution-spec ific changes in colloidal interactions and/or aggregation behavior, and their corresponding effects on solute diffusivity 8-11. Ideally, one would like to measure solution viscosity and solu tion specific effects on diffusive solute transport independently, and without the n eed for reverting to time-consuming bulk viscosity measurements. Using a suitable trace r particle, dynamic light scattering can be 77

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used to perform both tasks. In practice, how ever, saline solutions readily induce a loss of colloidal stability and subsequent aggregation of the most commonly us ed tracer particle: uniform populations of polystyrene beads. Even surface coatings can extend the range of stability of polystyrene beads only moderately Here we report that the small protein hen-egg white lysozyme provides an attractive alternative as tracer particle for dynamic light scattering measurements of the viscosity of saline solutions. 6.2 Materials and Methods 6.2.1 Chemicals As tracer particles we used either monodisperse polystyrene nanobeads (Polysciences Inc., cat # 64006) or two times recrystalliz ed, dialyzed and lyophilized lysozyme (Worthington Enzyme, cat # 2932, Lot: X6J8946). Using DLS, we obtained hydrodynamic radii of Rh = (32.0 0.6) nm for the microbeads and Rh = (1.89 0.03) nm for lysozyme. All chemicals were obtained fr om Fisher Scientific and were reagent grade or better. 6.2.2 Lysozyme Stock Solutions Lyophilized lysozyme was dissolved directly into 25 mM sodium acetate/acetic acid (NaAc) buffer at pH = 4.5. Stock solutions of MgCl2, NaCl, and CsCl were prepared by dissolving each salt directly into 25mM NaAc bu ffer at pH = 4.5 to a stock concentration of 2M. The pH of all stock solutions was readjusted after addition of the salt, if necessary. Prior to mixing lysozyme stock so lutions were filtered through 20 nm Anotop syringe filters and salt /buffer stock solutio ns were filtered through 220 nm syringe filter to remove any particulate impurities. After mixi ng the protein and salt stock solutions at a ratio of 1:1, the mixtures were incubated at 45 C for 5 min. This reduced the risk of inducing crystal seeds at high salt concentrations. Solutions were transferred to glass cuvettes and placed into the thermostated cuvette holder of a dynamic light scattering unit (Zetasizer Nano, Malvern Instruments Ltd., UK) Actual lysozyme concentrations of all solutions were determined from uv absorption measured at = 280nm using 280 = 2.64 ml / (mg cm) 12. 78

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6.2.3 Dynamic Light Scattering (DLS) All dynamic light scattering (DLS) measurements were performed with a Zetasizer Nano S (Malvern Instruments Ltd., UK) with a 3mW He-Ne laser at = 633nm. For details see chapter 1. 6.2.4 Tracer Particle Measurements For measurements with polystyrene beads, 300 l of the polystyrene standard (1% w/v) was dissolved either into 12 ml of wate r, with an added 10 mM of NaCl, or into 100 mM NaAc solution. Both solutio ns were filtered through a 0.22 m pore size PVDF syringe filter. For water or NaAc solu tions, the temperature-dependence of their viscosity was measured from 50 C down to 5 C in 5 C steps, allowing 10 minutes of thermal equilibration after each temperature change. For the three saline solutions in this study (MgCl2, NaCl, and CsCl), DLS measurements were performed at six different temperatures between 40 C and 15 C, again in steps of 5 C, and at four different salt concentrations (50 mM, 250 mM, 625 mM and 1M ). Analysis of co rrelation data used the average of three (for polys tyrene) or five (for lysozyme ) correlation functions, with a typical acquisition time of 180 and 60 seconds, respectively. 6.2.5 Analysis of Tracer Diffusivity Tracer diffusivities were derived from the decay rates of measured intensity autocorrelation functions g2( ). A detailed description of the analysis is given in chapter 2. 6.3 Results and Discussion 6.3.1 Viscosity Measurement Using Polystyrene Nanobeads DLS-based measurement of solution vi scosity is essentially a two-step process: (a) determine the hydrodynamic radius of the tracer particle in a solutio n of known viscosity (e.g. water at 20 C); (b) convert changes in tracer diffusivity under different solution conditions (temperature, composition, pH, etc) back into changes in solution viscosity using the Stokes-Einstein relation [given by equa tion (2.49) in chapter 2]. This approach 79

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imposes two constraints: First, the hydrodynami c radius of the trac er particles remains constant (e.g. no swelling or aggregation). Second, effects of interactions among the tracer particles on the diffusive relaxati on dynamics are properly accounted for [see equation (2.49) in chapter 2]. Fig.6.1: Viscosity of Water: (A) Plot of the viscosity of water as a function of temperature measured by Dynamic Light Sc attering (DLS) using polystyrene latex (RH = 31.9 nm) as a probe. Connecting lines are added as visual guides only.(B) Plot of relative viscosity of measured water viscosity usi ng lysozyme to the tabulated value in the literature12. The dashed line represents .5% error. Using dynamic light scattering, we measured the diffusivity D0 of polystyrene nanobeads as function of solution temperature. To convert tracer diffusivities into solution viscosity using the Einstein Stokes relation [equation (2.49) in chapter 2], we need to determine the hydrodynamic radius of the tracer particles under known solution conditions. For polystyrene b eads in water solutions at 20C ( = 1.002 mPa s) 12 we obtained D0 = 4.20 x 10 -12 m2/s. This yields a hydrodynami c radius for the polystyrene 80

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beads of Rh = 32.0 nm, which compares favorably with the manufacturers quoted dry diameter of 64.8 nm. Using this value for Rh, we determine polystyrene diffusivity in water as function of temperature between 5 and 50 C and derived the underlying changes in water viscosity (T). As shown in Fig. 6.1, water viscosities obtain using polystyrene tracer diffusivity were within 2.5 % of tabulated values for water viscosity 15. We repeated temperature-dependent vi scosity measurements using 100 mM and 250 mM NaAc buffer at pH = 4.5. While m easurements at 100 mM NaAc buffer provided reliable data (see Fig.4.2A), at 250 mM NaAc concentration polystyrene beads had lost their colloidal stability and flocculated. Fig.6.2: Viscosity of 100mM NaAc using different probes: (A) Plot of viscosity of 100mM NaAc measured by Dynamic Light Sca ttering using lysozyme (open circle), and polystyrene latex (dark circle). Measured viscosity values compared with tabulated8 (dark square) viscosity values at T = 20 C. (B) Relative viscosity of 100mM NaAc using lysozyme as tracer particle to the polystyren e latex as a tracer particle. The dashed line represents 2.5% difference in va lues using two different probes. 81

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6.3.2 Viscosity Measurements Using Lysozyme To address the problem of polystyrene fl occulation even at very modest ionic strengths we explored the use of the protein lysozyme as alternative tracer particle. Henegg white lysozyme is a small (14.3 kD) enzy me whose 3-dimensional structure has been carefully characterized 16. Depending on salt identity, at moderate concentrations lysozyme will remain soluble for salt concentrations up to 1 M or more 17, 18. Due to the four disulfide bonds in its native struct ure, lysozyme does not unfold up to 74 C 19. More specifically, we have shown (see Fi g. 6.3) that the hydrodynamic radius of lysozyme is essentially unchanged over a wide range of solution conditions, and irrespective of the chaotropic or kosmotropic charac ter of salt ions added to the solution 20. Fig.6.3: Dependence of pH and temperature on hydrodynamic radius: (A) Plot of ratio of mutual diffusion coefficient (Dc) and free particle diffusivity (D0) i.e. (Dc/D0) as function of lysozyme concentration CLys for pH = 3 at T = 20 C & 50 C and for pH = 4.5 for T = 20 C. (B) Mean hydrodynamic radius RH of lysozyme for part (A) derived from the measured free particle diffusivity D0 and corrected for th e salt and temperaturedependent changes in water viscosity. 82

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One additional concern requiri ng attention is the effects of particle interactions on diffusion measurements. Dynamic light scat tering measures the diffusive relaxation kinetics of thermally induced fluctuations in local tracer concentrations 13, 21. The StokesEinstein relation [equation (2.49) in chapte r 2] only applies to thermally agitated diffusion, without contributi ons from (direct or hydrodynami c) particle interactions. Polystyrene beads can be used at sufficiently high dilution to fulfill this requirement. Protein interactions in solution, however, significantly alter the diffusivity measured at the finite protein concentrations needed for sufficient scattering intensities 8, 22. These changes in Dc are due to the potential of net for ce between lysozyme at different salt concentrations. For low sa lt concentrations residual ch arge repulsion among lysozyme molecules is only partially screened, causing a net increase in the relaxation rate and, therefore, mutual diffusivity (see e.g. Fig. 6.4A). At higher salt concentrations, shortranged attractive forces dominate which slow down mutual diffusion. Over the range of lysozyme concentrations used in our study lysozyme's mutual diffusivity Dc changes linearly with concentration (see Fi g. 6.4). Extrapolating Dc (CLys) to its infinite dilution limit (CLys = 0) yields the corresponding free particle diffusivity D0 appearing in Eqn. [(2.49) in chapter 2]. Extrapolation of the diffusion data to infinite dilution also guards against the potential effects of (concentra tion-dependent) protein oligomerization on measured diffusivities. As additional precautio n against contamination of diffusivity data from temperature-induced oligomeriza tion or precipitation we rejected any autocorrelation functions whose polydispersity exceeded 0.08. 83

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Fig.6.4: Effect of temperature and salt conc entration on Diffusion coefficient Dc of lysozyme: Plot of diffusion coefficients Dc as a function of lysozyme concentration Clys (A) for 50mM CsCl as a function of increasing temperature for the temperature range of 15 C 40 C. (B) for CsCl at increasing salt conc entrations (50mM, 250mM, 625mM and 1M). The sign of slopes indicate whether in teractions among the lysozyme molecules are either net repulsive (positive) or net attractive (negative). The y-axis intercepts at Clys = 0 yields the free particle diffusivity D0. To compare the performance of polyst yrene with lysozyme, we repeated the viscosity measurements vs. temperature in 100 mM NaAc buffer. From the extrapolated free-particle diffusivity of D0 = 11.02 x 10-11 m2/s and a viscosity value of = 1.029 mPa s for NaAC buffer at 20 C 8, we obtained RH = 1.89 nm for the hydrated lysozyme monomer. Mutual diffusivities Dc of lysozyme vs. temperature were then repeated for the same series of NaAc solution temperature. The extrapolated free-particle diffusivity values D0 were converted into corresponding changes in buffer viscosity using the 84

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Stokes-Einstein relation [equation (2.49) in chapter 2]. NaAc buffer viscosity values obtained with either polystyrene beads or lysozyme as tracer particles fall within 2% of previous measurements using a Cannon-Ubbelohde viscometer 8. We extended lysozyme-based viscosity measurements to an extended range of salt concentrations (50 mM to 1 M) and to three salts with ranging from kosmotropic (MgCl2) to weakly kosmotropic (NaCl) to predominat ely chaotropic (CsCl). Fig.6A displays the changes in the mutual diffusivity Dc of lysozyme in 50mM CsCl/ 25 mM NaAc buffer solutions at pH = 4.5 as function of so lution temperature. Fig. 6.4B shows the corresponding changes in mutual diffusivity Dm for a fixed temperature of T= 25 C at four different concentrations of CsCl. As discussed above, changes in the potential of net force from repulsion (low salt concentration) to attraction (high salt concentration) causes the slope of the mutual diffusivity Dc vs. lysozyme concentration Clys to change from positive to negative values (Fig. 6.4B). Fig. 6.5 summarizes the temperatureand concentration dependent viscosity changes for CsCl, NaCl and MgCl2 solutions. The dashed lines in Fig. 6.5A represent fits through the viscosity values assuming that the temperature dependence arises solely from an Arrhenius-type activation process, i.e. = A exp( G/RT). Over the limited range of temperatures, the corresponding fits show reasonable agreement, but systematic deviations are apparent. We did not explore these deviations further since they are not the focus of the current work. Fig. 5.5B displays the depe ndence of soluti on viscosity on salt concentrations for a fixed temperature (T = 20 C). For the case of MgCl2 and NaCl, solution viscosity increases with increasing salt concentration, consistent with the dominant kosmotropic character of its cations (Mg2+, Na+). Similarly, the viscosity of CsCl solutions decreases since both its constituent ions are chaotropic. The dashed lines are fits through the data with the Kaminsky equation23 (Cs) = 0 (1 + K1 Cs 1/2 + K2 Cs + K3 Cs 2) (6.1) This equation is an extension to the more commonly used Dole-Jones equation, with the C1/2 term accounting for ionic screening effect s (Debye-Hckel theory) and the higherorder terms representing empirical extensions to match experimental data at intermediate (linear) and higher (quadratic) salt concentrations. 85

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Fig.6.5: Measured viscosity of CsCl, NaCl, and MgCl2 as function of temperature and concentration using lysozyme as a probe for DLS measurement: Plot of viscosity vs. temperature for Cs Cl, NaCl, and MgCl2 at various concentrations. Dashed lines are added as visual guides only. For, MgCl2 measured values are compared with tabulated values using Kaminsky equation 17 (dark lines values). (B) Plot of the relative viscosity of measured viscosity using lysozyme as tracer particle to the tabulated value17. The dashed line represents % error. 86

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Table 6.1: Temperature and concentration dependence of the viscosity for NaCl, MgCl2, and CsCl solutions in 25mM sodium acet ate buffer at pH = 4.5 obtained from measurements of lysozyme diffusivity. NaCl T (C) (mPa-s) 100mM 250mM 625mM 1000mM 15 1.138 1.169 1.187 1.224 20 0.996 1.028 1.058 1.079 25 0.881 0.924 0.955 0.983 30 0.804 0.829 0.860 0.888 35 0.721 0.747 0.782 0.810 40 0.668 0.691 0.741 0.764 MgCl 2 T (C) (mPa-s) 100mM 250mM 625mM 1000mM 15 1.145 1.255 1.433 1.591 20 1.024 1.101 1.269 1.411 25 0.896 0.997 1.132 1.222 30 0.800 0.891 1.023 1.107 35 0.720 0.801 0.905 1.003 40 0.672 0.734 0.844 0.928 87

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Table 6.1 (Continued) CsCl T (C) (mPa-s) 100mM 250mM 625mM 1000mM 15 1.144 1.116 1.087 1.056 20 1.011 0.985 0.962 0.933 25 0.892 0.877 0.862 0.856 30 0.793 0.792 0.778 0.779 35 0.726 0.712 0.710 0.708 40 0.678 0.652 0.646 0.652 6.4 Conclusion We have compared polystyrene beads vs the small protein lysozyme for use as tracer particles for light-scattering based viscosity measurements of aqueous saline solutions. Compared to traditional techniques, dynamic light scattering measurements of tracer diffusivity requires mi nimal solution volumes (< 100 l), can be used to measure spatial or temporal variations in viscosity, determine th e effects of extreme solution conditions (high pressure, high temperature) an d can be applied to confined geometries (microfluidics). One of the main draw-b acks of commonly used polystyrene beads as tracer particles, however, is their limited co lloidal stability, which renders them prone to flocculation at or below phys iological concentrations ( 150 mM) of electrolytes. As indicated in the above results secti on, lysozyme provides a stable and robust alternative to polystyrene beads, remaini ng soluble for many different salts up to concentrations of 1M or more. There are several reasons why lysozyme is a good choice as a tracer particle for viscosity measurements in saline solutions. First of all lysozyme is a small, globular protein with a well-defined molecular weight. Therefore, variations in tracer size arising from particle synthesi s are negligible. As globular protein, 88

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lysozyme's shape is sufficiently compact to be considered a uniform sphere for the purpose of translational diffu sion measurements. Furthermore, lyophilized lysozyme stock with low levels of impurity and contamin ation of disordered aggregates is readily available. Therefore, with some care to avoid contamination from non-specific lysozyme clusters 14, lysozyme solutions with a very low de gree of polydispersity can be readily prepared. Lysozyme is also a protein with an unusua lly high degree of structural stability. Due to the presence of four disulfide bridges in its structure, lysozyme is resists thermal unfolding up to temperatures of 74 C 24. Furthermore, we have shown that lysozyme retains its hydrodynamic radius of 1.9 nm within very tight limits over a wide range of pH values (pH 2-8) and temperatures (5-50 C). In addition neither strongly kosmotropic nor chaotropic salt ions, at concentrations at or below 1M, we re able to disrupt lysozyme's hydration layer 20. Despite the common use of lysozyme in light-scattering studies of protein phase separation and crystallization 25-28, lysozyme actually tends to remain soluble over a wide range of soluti on conditions, as well, particularly when compared to polystyrene beads. This stability is closely related to the combination of a large net charge of lysozyme particularly at acidic pH values29, with its overall small radius and modest short-range attraction 8. These advantages of lysozyme are tempered by the salt-specific effects on its solubility 17 and the loss of net charge upon appro aching of its isoele ctric poin t around pH = 11 29. The net charge repulsion, which promotes lysozyme's colloidal stability at intermediate salt concentrations, does aff ect the diffusive relaxation dynamics of the concentration fluctuations measured in dynamic light scattering. This necessitates the use of dilution curves (see Fig. 5A) in order to extract the single-particle diffusivity appearing in the Einstein-Stokes relation in equation (1 .49) in chapter 1. However, this latter complication is specific to DLS measurements which require sufficient protein concentrations in order to resolve the dynamic concentrati on fluctuations against the static scattering background. The latter lim itation can be readily addressed and the use of lysozyme as tracer partic le further extended by us ing fluorescence correlation spectroscopy in conjunction with low concentrations of fluorescently labeled lysozyme. 89

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In short, lysozyme provides an attractiv e and readily feasible choice as tracker particle to monitor the viscosities of ionic solutions over a wide ra nge of parameters and with many advantages compared to typical viscosity measurement in bulk samples. 6.5 References 1. H. Saad, Y.C. Bae, E. Gulari, (1988) Langmuir 4 63. 2. F. Audonnet, A.A.H. Padua, (2001) Fluid Phase Equilibria 181 147. 3. I.M. Abdulagatov, N.D. Azizov, (2006) Fluid Phase Equilibria 240 204. 4. P.G. Stoyanov, C.A. Grimes, (2000) Sensors and Actuators 80 8. 5. B.A. Martin, S.W. Wenzel, R.W. White, (1989) Sensors and Actuators A-Physical 22 704. 6. D.S. Long, M.L. Smith, A.R. Pries, K. Ley, E.R. Damiano, (2004) Proceedings of the National Academy of Sciences United States of America 101 10060. 7. R. Zondervan, F. Kulzer, G.C.G. Berkhout, M. Orrit, (2007) Proceedings of the National Academy of Sciences United States of America 104 12628. 8. M. Muschol, F. Rosenberger, (1995) Journal of Chemical Physics 103 10424. 9. W. Liu, T. Cellmer, D. Keerl, J.M. Prausnitz, H.W. Blanch, (2005) Biotechnology and Bioengineering 90 482. 10. J.J. Grigsby, H.W. Blanch, J.M. Prausnitz, (2000) Journal of Physical Chemistry 104 3645. 11. D.F. Rosenbaum, C.F. Zukoski, (1996) Journal of Crystal Growth 169 752. 12. A.J. Sophianopoulos, C.K. Rhodes, D. N. Holcomb, K.E. Van Holde, (1962) Journal of Biological Chemistry 237 1107. 13. B.J. Berne, R. Pecora, (1976) Dynamic light scattering: with applications to chemistry, biology and physics. Wiley, New York. 14. Parmar A.S., Gottschall P.E., Muschol M. (2007) Biophysical Chemistry 129 224-234 15. R.C. Weast, M.J. Astle, (1978) CRC Handbook of Chemistry and Physics. 59 ed., CRC Press, West Palm Beach, Fla. 16. H.M. Berman, J. Westbrook, Z. Feng, G. Gilliland, T.N. Bhat, H. Weissig, I.N. Shindyalov, P.E. Bourne, (2000) Nucleic Acids Research 28 235. 17. M.M. Ries-Kautt, A.F. Ducruix, (1989) Journal of Biological Chemistry 264 745. 90

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18. M. Muschol, F. Rosenberger, (1997) Journal of Chemical Physics 107 1953. 19. R. Wetzel, L.J. Perry, W.A. Baase, W.J. Becktel, (1988) Proceedings of the National Academy of Sciences Un ited States of America 85 401. 20. A.S. Parmar, M. Muschol, (2009) Biophysical Journal accepted. 21. H.Z. Cummins, R. Pike, (1973) Nato Advanced Studies Institute; Plenum Press, New York,. 22. A.M. Kulkarni, N.M. Dixit, C.F. Zukoski, (2003) Faraday Discussions 123 37. 23. M. Kaminsky, (1957) Zeitschrift fr Physikalische Chemie 12 206. 24. T. Knobovets, J.J. Osterhout, P.J. Conolly, A.M. Klibanov, (1999) Proceedings of the National Academy of Sciences United States of America 96 1262. 25. B. Guo, S. Kao, H. McDonald, A. Asanov, L.L. Combs, W.W. William Wilson, (1999) Journal of Crystal Growth 196 424. 26. J.J. Grigsby, H.W. Blanch, J.M. Prausnitz, (2001) Biophysical Chemistry 91 231. 27. R. Piazza, M. Pierno, (2000) Journal of Physics-Condensed Matter 12 A443. 28. N.M. Dixit, C.F. Zukoski, (2002) Physical Review E 66. 29. R. Roxby, C. Tanford, (1971) Biochemistry 10 1. 91

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Chapter 7 Probing the Viscoelastic Behavior of po ly-N-isopropylacrylamide (poly-NiPAAm) During Thermally Induced Gel Collapse 7.1 Introduction Soft materials such as polymers, gels, and many biomaterials are viscoelastic in nature 1,2 i.e. they store as well as dissipate en ergy when an external stress is applied. Solids are elastic in na ture and can store energy upon appl ication of shear strain. Liquids are viscous in nature and dissipate energy. Soft materials exhibit both of these properties and are viscoelastic in nature. Generally, the vi scoelasticity of soft materials i.e. elastic and viscous modulus is measured using rh eometer. Rheometer measures the stress response upon application of a well defined strain 3. The viscoelastic behavior of soft materials is typically condens ed into the complex shear modulus G*(f) where the real part measures the in-phase elastic response of the medium G(f) a nd the imaginary part measures the out-of-phase viscous response G(f). More recently a complimentary technique called microrheology 4-9 has been developed to measure such viscoelastic behavior of soft materials. In microrheology a microscopic probe particle is embedded in the soft medium and its local displacement as function of an external force is measured to determine its viscoelastic properties. Th ere are many different techniques used for measuring the displacement of probe particles, including pa rticle tracking measurements 10, Diffusion wave spectroscopy (DWS) 11 and quasielastic light scattering (QELS) 12. In our experiments, the external force is random thermal motion of the probe particles. This motion can be very different from those in purely visc ous fluids. It can be either subdiffusive motion or can be loca lly bound. Hence, we need to establish a relationship between the average microscopic mo tion of a colloidal probe particles to the macroscopic viscoelastic response of the complex medium. There are many advantages of this technique over conventional rheometer. First, of all only a very small amount of sample is required around 100 l compared to conventional rheometers which require 92

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millilitres of sample. This is important for biol ogical materials which are not available in large quantity or are intrinsically small (si ngle cells). Secondly, no external stress is applied the as probe particles are thermally dr iven at all frequencies. Again, this is advantageous for many biological relevant materials as larger external stress can restructure then irreversibly. Thirdly, since these probe particles are very small, their inertia can be neglected and the viscoelastic properties of materials can be measured at higher frequencies. In this chapter, we will use the dynamic light scattering (DLS) to measure the viscoelastic properties of various soft materials in the sol as well as in the gel regime, and also probed a thermally induced gel collapse near and far from the phase transition temperature. 7.2 Materials and Methods 7.2.1 Preparation of Polyacry lamide (PAAm) Sample The polyacrylamide (PAAm) solution is prepared in distilled water with 2.2 wt % of acrylamide monomers are mixed with 0.1 wt % of tetramethylenediamine, which acts as catalyst. For the formation of a sol phase, 0.03 wt % of the cross linker Methyylenebisacrylamide are added. Adding 0. 2 wt % of Methyylenebisacrylamide leads to the formation of a gel phase, instead. A mmonium persulfate 0.5 wt % is added as initiator to the solution. Finally, 0.005 wt % of polystyrene beads (RH = 450 nm) is added to the solution. Fig. 6.1 shows the absorp tion of a PAAm solution undergoing gelation at 260nm as a function of time. The plateau in absorption around 50 minutes indicates that the polymerization reaction is completed.13,14 To achieve the formation of a gel phase, the solution is kept under N2 for 40 minutes. 93

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Fig.7.1: Absorbance of the polymer solution at 2 60nm as a function of time. The onset of plateau around 50 minutes is indication of completion of polymerization reaction. 7.2.2 Preparation of Poly-N-isopropyl acrylamide (polyNIPAAm) Sample The poly-N-isopropylacrylamide (p oly-NIPAAm) gels are pr epared in distilled water with 4.86 wt % NiPAAm mixed with 0.019 wt % amm onium persulfate which is the initiator, 0.49 wt % TEMED as the activator and 0.113 wt % of BisAAm as crosslinker. For microrheological measurements 0.005 wt % of polystyrene beads (RH = 450nm) are used are added in the solutions as probe particles. To achieve gel formation, the solution is exposed to UV irradiation at = 360nm for 40 minutes. 7.2.3 Dynamic Light Scattering Measurements For DLS studies, we filtered the solution without beads through 0.02 m syringe filters to filter out any pre-assembled clusters 15. DLS measurements performed with beads in solution yielded bead sizes of 454 5 nm, confirming that the beads do not aggregate in solution. The 0.005 wt % beads co ncentration was chosen to ensure that the scattering signal dominated by scattering fr om beads dominates (vs. the polymer in solution). However, the concentration also has to remain small enough to prevent the multiple scattering. Glass cuvettes containing the gel with beads as probe particles were placed inside the thermostated sample hol der of the DLS unit and were allowed to equilibrate to their set temperatures (20 C for PAAm sol and gel and 5, 31, or 33 C for poly-NiPAAm gel) for 5 minutes. Autocorrela tion functions were obtained from averages 94

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of 5 measurements at each temperature. A detailed analysis of DLS data is given in chapter 2. 7.3 Results 7.3.1 Viscosity of Water using Polystyrene Beads As first test we used the gene ralized Stokes-Einstein e quation (equation 2.50 in chapter 2) 6 to measure the viscosity of water at T = 20 C. From the field correlation function g1( ) we derived mean square displacement < r2( )> [(equation (2.51)]. Using the analysis as given in chapter 2 we cal culated the full frequency dependence of the viscous modulus of polystyrene beads diffusing in water as shown in Fig. 7.2. As the motion of the beads in water is purely diffusive the viscous modulus va ries linearly with frequency (Fig.7.2). Using equation (2.55) we calculated the viscosity of water as function of frequency as shown in Fig.7.2. As expected, the viscosity of water at all frequency was found be 1.00cp, in agreement with tabulated values 16. We also calculated the viscosity of wate r using the Stokes-Einstein equati on given by equation (2.49) yield the same value. We therefore had confirmed th e reliability of our analysis for a purely viscous medium. Fig.7.2: Viscous modulus G(f) and viscosity (f) of water at T =20 C as a function of frequency derived by microrheol ogical measurement using pol ystyrene beads. Viscosity of water was constant and match tabulated values.16 95

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7.3.2 Microrhelogical Mea surement for Polyacrylamide (PAAm) We used dynamic light scattering measurements to measure the viscoelastic properties of cross-linked polyacrylamide (PAAm ) using polystyrene as probe particle in the sol and gel regimes. The aim was to reproduce existing result in order to confirm that we have command at this technique.13 Fig.7.3: (A) Correlation functions for the sol (o pen square) and gel (dark square) phase for the polyacrylamide (PAAm) sample with embedded polystyrene beads (RH = 450nm) at 20 C, (B) Plot of the mean square displacemen t of probe particle for PAAm sample for sol (open square) and gel phase (dark square), (C) local slope of sol (open square) and gel phase (dark square) (D) Elastic modulus G (f ) (dark circle) and viscous modulus G(f) (open circle) and corresponding viscosity (f) of sol phase as a function of frequency. The horrizontal line shows the corresponding wate r viscosity at that temperature, and (E) same as in (D), but for gel phase. Fig. 7.3A shows the field correl ation function for polystyrene beads dispersed in either the sol or gel phases. We can see that a bead in the sol phase displays a much faster 96

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decay than in the gel phase. The correlation f unctions in Fig. 7.3A are converted into mean square displacement [see equation (2.51)], plotted in Fig. 7.3B. The slope of the mean square displacement for sol phase is ar ound 0.8 to 0.9, for all time scales. A slope closer to 1 shows the dominance of viscous be havior. As expected for the sol phase, the viscous modulus G(f) is greater than the elastic modulus G(f) fo r the entire frequency range shown in Fig. 7.3C. For gel phase, th e mean square displacement has a slope near 0.9 at short time scales, indicating predomin ately viscous behavior. At longer time scales it approaches 0.3 which shows the elastic behavi or expected for gel samples (Fig. 7.3B). In this case the elastic modulus dominates over the viscous modulus in the low frequency range and become comparable to each othe r at high frequency. Our result reproduces previous work by Dasgupta et al. 13. We conclude therefore, that we have control over this method. In the following, we are goi ng to use this method to study the thermal dehydration transition in poly-N-isopropylacrylamide (poly-NiPAAm). 7.3.3 Poly-N-Isopropylacrylamide (poly-NIPAAm) System 7.3.3.1 Gel Phase Transitions Poly-NiPAAm undergoes a therma lly controlled volume phase transition. During this transition the number and placement of crosslinks doesnt change but the gel conformation and density changes. This is esse ntially a first-order phase transition with a sharp temperature onset (see Fig. 7.4) When the phase transition occurs, the polymer network collapses, the chains become more densely packed and the solvent water is expelled from the network. It was firs t predicted by Dusek and Patterson in 1968 17. Tanaka was the first one to describe it for ionize acrylamide gel 18. There are many factors which can trigger this phase transiti ons including pH, temperature, high pressure, uv light, etc. In this section we are goi ng to discuss the temperature induced phase transition of poly-N-isopropylacrylamide (poly-NIPAAm). A more detailed discussion of polymer gels and phase transitions of gels can be found elsewhere 19,20. Light scattering experi ments are performed on th e poly-NIPAAm gel with beads embedded inside the gel network. Scatteri ng intensity data is shown in Fig.7.4. The sudden jump in the scattering intensity indica tes that the phase transition occurs at 34 C. 97

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At this point thegel becomes turbid (white) and it is not possible to use DLS to analyze bead motion. Fig.7.4: Changes in the total scattering intensity of poly-N-isopropylacrylamide (polyNIPAAm as a function of temperature. Intensity data shown here have been corrected to account for neutral density filters inserted in front of the detector in order to prevent detector saturation. 7.3.3.2 Microrheological Measurement with Poly-N-isopropylacrylamide (polyNIPAAm) As DLS measurement of microrheological behavior can not been performed for turbid sample, we limited our DLS measurements to the temperature range of 5 C (far from the transition temperature), to 33 C (very near to phase tr ansition temperature). We made sure that the solution remains transpar ent during the measurement. Fig.7.5A shows the correlation functions for bead movement at 5 and 33 C. It shows that at 33 C the decay rate is faster than at 5 C. We also notice a double decay mode at 33 C. The mean square displacement was derived from the corr elation functions shown in Fig. 7.5B. [A detailed analysis of DLS data for measuring th e viscoelastic behavior of polymer gels is given in Chapter 2]. At both temperatures the elastic modulus dominates over the viscous modulus at low frequency range and they b ecome comparable at high frequency range (Fig. 7.5C and D). 98

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(A) (B) (C) (D) (E) Fig.7.5: (A) Correlation functions for 450 nm polystyrene beads embedded in poly-Nisopropylacrylamide (poly-NIPAAm) gel at 5 C (open square) and 33 C (dark square) (B) Plot of the mean square displacement of the probe particle for poly-NIPAAm gel sample at 5 C (open square) and 33 C (dark square) (C) local slope of gel at 5 C (open square) and 33 C (dark square) (D) Elastic modulus G (f) (dark circle), and viscous modulus G(f) (open circle) a nd corresponding gel viscosity (f) as a function of frequency at 5 C. The dark line shows the corre sponding water viscosity at that temperature, and (E) same as (D) for gel at 33 C. Fig.7.6 shows the microrheological measuremen ts of the polymer gels at three different temperatures (5, 31, and 33 C). It can be seen that the elas tic modulus values at the lower frequency are comparable for all three temp eratures. At higher frequencies the elastic modulus decreases as the temp erature increases. The viscous modulus is constant at lower frequency range and increases linear ly at high frequencies. Like the elastic modulus, the viscous modulus also decreases as the temperature increases. At all temperatures the elastic modulus domina tes over the viscous modulus at lower temperatures and frequencies, and is comparable or dominated by the viscous modulus at high frequencies. Viscosity values decreas es as the frequency increases for all temperatures and level off towards water viscosity. It should be noted that at 5 C the viscosity value reaches the water viscosity for frequency around 8kHz, whereas for 31 99

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and 33 C it level off to water viscosity value around 5kHz and 2kHz respectively as shown in fig.7.6. Fig.7.6: Comparison of elastic modulus G(f), viscous modulus G(f), and viscosity (f) as function of frequency at three (5, 31, and 33 C) different temperat ures. The dark line shows the corresponding water visc osity at that temperature. Note the dip of (f) below the water viscosity at T = 33 C. We are not yet certain whether this is due to an artifact in our da ta analysis or the presence of yet another relaxation process not properly accounted for in our data analysis. This work is in progress and will try to finish it before leaving. 100

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7.4 References 1. Macosko C.W. (1994) Rheology: Prin ciples, Measurements and Applications, VCH, New York. 2. Larson R.G. (1999) The Structur e and Rhelology of Complex Fluids, Oxford University Press, New York 3. Ferry J.D. (1980) Viscoela sticity Properties of Polymers, Wiley, New York 4. Ziemann F., Raddler J., and Sackmann E. (1994) Biophysical Journal, 66, 2210 5. Mason T.G. and Weitz D.A. (1995) Physical Review Letter, 74, 1250 6. Mason T.G. (2000) Rheologica Acta, 39, 371-378 7. Crocker J.C., Valentine M.T., Weeks E.R. Gisler T., Kaplan P.D., Yodh A.G., and Weitz D.A. (2000) Physical Review Letter 85, 888 8. Dasgupta B.R., Tee S.Y.,Crocker J.C ., Frisken B.J., and Weitz D.A. (2002) Physical Review E 65, 051505 9. Garel M.L., Valentine M.T., Crocker J. C., Bausch A.R., and Weitz D.A. (2003) Physical Review Letter 91, 158302 10. Crocker J.C., and Grier D.G. (1996) Journal of Colloids and Interface Science 179, 298 11. Pine D.J., Weitz D.A., Chaiki n P.M., and Herbolzheimer (1988) Physical Review Letter 60, 1134 12. Berne B.J. and Pecora R. (1976) Dynamic Light Scattering: With Applications to Chemistry, Biology and Physics, Wiley, New York 13. Dasgupta B.R. and Weitz D.A. (2005) Physical Review E 71 021504 14.Bio-Rad Laboratories Bulletin 1156 (unpublished) 15. Parmar A.S., Gottschall P.E., and Muschol M. (2007) Biophysical Chemistry 129 224 16. R.C. Weast, M.J. Astle, (1978) CRC Handbook of Chemistry and Physics. 59th ed., CRC Press, West Palm Beach, Fla. 17. Dusek, K. and Patterson, D. (1968) Journal of Polymer Science Part A-2, 6, 1209. 18. Tanaka, T. (1978) Physical Review Letter 40, 820 19. Li, Y. and Tanaka, T. (1992) Annual Review of Materials Science 22, 243-277 20. Tanaka, T., Annaka, M., Ilmain, F., Ishii, K., Kokofuta, E., Suzuki, A. and Tokita, M. (1992) NATO ASI Series, H64 683-70 101

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Chapter 8 Conclusion Using static and dynamic light scattering (SLS & DLS) we investigated a series of fundamental problems concerning phase separation kinetics of macromolecules and polymers, and the resulting rheological properties of their condensed phase. We have characterized the interactions of proteins in solution and their effects on their aggregation behavior under conditions that promote protein crysta llization. We have shown that it is necessary for nucleation and growth studies in prot ein crystallization to carefully characterize whether the starting materials is a homogenous collection of monomers or contains substantial populatio ns of pre-formed large aggregates. The clusters present in the stock materials of hen-egg white lysozyme, a frequently used protein in crystallization studi es, will distort the nucleation kinetics and increase crystal defect formation. These clusters might well be the reason for the pers istent contradiction in existing nucleation data on the size of crys tal nuclei, their induction time or the total number of nuclei generated under comparable conditions. Using DLS and SLS, we have also de termined the (non-)effects of chaotropic (water structure breaking) versus kosmotropic (water structure making) ions on the hydration layer and the hydrodynamic interactions of lysozyme. Our results show that neither protein hydration nor solvent-mediated hydrody namic interactions displays any obvious salt-specific effects, while salt-specific effects on direct prot ein interaction were prominent. DLS has been used to monitor the si multaneous nucleation and growth of gold nanoparticles synthesized from solution in the presence of the antibio tic cephalexin. Their nucleation kinetics were measured at three di fferent incubation temper atures (15, 25, and 35 C). It seems that two populations of nucle i with distinctly different sizes formed simultaneously. Equally intriguing, the sizes of these two nuclei populations remained 102

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103 essentially fixed, only their numbers incr eased over time. Decreasing the temperature only slowed down the in duction period prior to nucleation. We also used DLS to measure the viscos ity of aqueous solution with lysozyme as a tracer particle. We find that lysozyme provides an advantageous tracer particle for viscosity measurement of saline solution up to 1 M where other probe particles like polystyrene beads flocculate. Due to its inhere ntly high structural a nd colloidal stability, lysozyme provides a useful tracer particle for high salt concentrationa and a wide pH and temperature range, which are relevant for bi ological solutions and sample processing in aqueous environments. Finally we extended tracer particle m easurements with DLS to characterize the microrheological properties of polymers in thei r gel or sol phase. Th e viscoelasticity of the medium i.e. the elastic as well as visc ous modulus, were determined over a range of "force frequencies" spanning five decad es. We also succeeded in performing microrheological measurements for PAAm in the sol and gel regime. For polyNiPAAm we measured the viscoelastic behavior near and far from th e phase transition temperature in the gel regime.

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About the Author Avanish Singh Parmar has completed his Bachelors and Maste rs degree in Physics from Banaras Hindu Uinersity, India. He came to USA in August 2003 in University of Cincinnati as a graduate stude nt. He joined Department of Physics, University of South Florida in spring 2005 and star ted working with Dr. Martin Muschol with specialization in Biophysics. He won prestigious Duckwall and Th arp Fellowship as a graduate student in department of physics for hi s outstanding research work He completed his summer internship in Bristol-Myers Squibb in New Jersey. He is going to join UMDNJ-Robert Woods Medical Hospita l as a post doc in Biochemistry department under Dr. Barbara Brodsky. He really enjoyed his stay in Tampa and University of South Florida.


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ABSTRACT: The broad objective of my research is to investigate the physical characteristics and interactions of macromolecules and nanoparticles, and the corresponding effects on their phase separation behavior using static and dynamic light scattering (SLS & DLS). Light scattering provides a non-invasive technique for monitoring the in-situ behavior of solutes in solution, including solute interactions, sizes, shapes, aggregation kinetics and even rheological properties of condensed phases. Initially, we investigated lysozyme solutions for the presence of preformed aggregates and clusters that can distort the kinetics of protein crystal nucleation studies in this important model system for protein crystallization. We found that both undersaturated and supersaturated lysozyme solutions contained population of large, pre-existing protein aggregate.Separating these clusters and analyzing their composition with gel chromatography indicated that these clusters represented pre-formed lysozyme aggregates, and not extrinsic protein contamination. We investigated the effect of chaotropic versus kosmotropic ions (water structure breakers vs. structure makers) on the hydration layer and hydrodynamic interactions of hen egg white lysozyme. Surprisingly, neither chaotropic nor kosmotropic ions affected the protein hydration layer. Salt-effects on direct and hydrodynamic protein interactions were determined as function of the solutions ionic strength and temperature. Using both static and dynamic light scattering, we investigated the nucleation of gold nanoparticles forming from supersaturated gold sols. We observed that two well separated populations of nuclei formed essentially simultaneously, with sizes of 3nm vs. several tens of nanometer, respectively.We explore the use of lysozyme as tracer particle for diffusion-base measurements of electrolyte solutions. We showed that the unusual stability of lysozyme and its enhanced colloidal stability enable viscosity measurement of salts solutions at high salt concentration, over a wide range of pH values and temperatures for the common tracer particle polystyrene flocculates. We applied dynamic light scattering to measure the viscoelastic responses of polystyrene probe particles embedded in solutions and gels of two different polymers: polyacrylamide (PAAm) and poly-N-isopropylacrylamide (poly-NiPAAm).
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