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The influence of pH on nucleation, solubility and structure of lysozyme protein crystals

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Title:
The influence of pH on nucleation, solubility and structure of lysozyme protein crystals
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Book
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English
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Apgar, Marc C
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University of South Florida
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Subjects / Keywords:
Light Scattering
Metastable
Supersaturation
Phase Diagram
Tetragonal
Dissertations, Academic -- Physics -- Masters -- USF   ( lcsh )
Genre:
non-fiction   ( marcgt )

Notes

Abstract:
ABSTRACT: X-ray diffraction from protein crystals remains the most reliable way to determine the molecular structure of proteins, and how this structure relates to biological function. However, we still lack the ability to predict solution conditions that support the nucleation and growth of high-quality protein crystals for X-ray diffraction studies. The overall goal of this thesis is two-fold: (a) determine the nucleation behavior and solubilities for lysozyme crystals with two distinct crystal structures (orthorhombic vs. tetragonal) and (b) investigate whether these changes in crystal habit and crystal solubility correlate with any discontinuities in the liquid-liquid phase boundary of lysozyme that occurs under the same solution conditions. We measured lysozyme crystal solubility by nucleating and subsequently dissolving very small lysozyme crystals in highly supersaturated solutions. The presence of crystals in our samples is detected and monitored by measuring the light scattered off the micron-sized crystals. These "turbidity measurements" are repeated across a range of protein concentrations, for pH 4.6 and 5.6, thereby yielding the crystal solubility boundary. Changes in crystal structure are assessed at the end of the experiments by microscopic inspection of the distinct crystal habits.
Thesis:
Thesis (M.S.)--University of South Florida, 2008.
Bibliography:
Includes bibliographical references.
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Mode of access: World Wide Web.
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by Marc C. Apgar.
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Title from PDF of title page.
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ABSTRACT: X-ray diffraction from protein crystals remains the most reliable way to determine the molecular structure of proteins, and how this structure relates to biological function. However, we still lack the ability to predict solution conditions that support the nucleation and growth of high-quality protein crystals for X-ray diffraction studies. The overall goal of this thesis is two-fold: (a) determine the nucleation behavior and solubilities for lysozyme crystals with two distinct crystal structures (orthorhombic vs. tetragonal) and (b) investigate whether these changes in crystal habit and crystal solubility correlate with any discontinuities in the liquid-liquid phase boundary of lysozyme that occurs under the same solution conditions. We measured lysozyme crystal solubility by nucleating and subsequently dissolving very small lysozyme crystals in highly supersaturated solutions. The presence of crystals in our samples is detected and monitored by measuring the light scattered off the micron-sized crystals. These "turbidity measurements" are repeated across a range of protein concentrations, for pH 4.6 and 5.6, thereby yielding the crystal solubility boundary. Changes in crystal structure are assessed at the end of the experiments by microscopic inspection of the distinct crystal habits.
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The Influence of pH on Nucleation, Solubility and Stru cture of Lysozyme Protein Crystals by Marc C. Apgar A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science Department of Physics College of Arts and Sciences University of South Florida Major Professor: Martin Muschol, Ph.D. Chun Min Lo, Ph.D. Dennis Killinger, Ph.D. Date of Approval: April 5, 2008 Keywords: Light Scattering, Metastable, Supersaturation, Phase Diagram, Tetragonal, Orthorhombic, Solubility, Sodium Acetate Copyright 2008, Marc C. Apgar

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i TABLE OF CONTENTS LIST OF TABLES..................................... ................................................... ....................ii LIST OF FIGURES.................................... ................................................... ..................iii ABSTRACT........................................... ................................................... ......................vi 1. INTRODUCTION....................................... ................................................... ............8 1.1. Motivation.......................................... ................................................... ....8 1.2. Hen-Egg White Lysozyme: Interaction Forces in Solution... .....................9 1.3. Protein Phase Diagrams............................... ..........................................10 1.4. Solubility......................................... ................................................... .....12 1.5. Crystal Nucleation and Growth......................... ......................................14 2. MATERIALS AND METHODS.............................. ..................................................1 6 2.1. General Approach.................................... ..............................................16 2.2. Illumination and Detection.......................... ............................................18 2.3. Temperature Control................................ ..............................................19 2.4. Preparation of Stock Solutions....................... ........................................21 2.5. Preparation of Measurement Samples................. ..................................22 2.6. IGOR Software...................................... .................................................24 2.7. Liquid-Liquid Phase Separation...................... ........................................26 2.8. Crystal Nucleation and Solubility Determination........ .............................27 2.9. Dilution Used to Measure Solubility at Low Concentrati ons....................28 2.10. Freezing Point of a Typical Sample................... .....................................29 2.11. Denaturing Temperature of Lysozyme..................... ...............................29 2.12. Temperature Gradients inside the Sample Cuvette..... ...........................31 2.13. Temperature Dependence of the pH for the 100 mM NaAc Buffer..........32 3. RESULTS AND DISCUSSION............................. ..................................................3 5 3.1. Enhanced Crystal Nucleation in Response to Solution Agi tation............35 3.2. Crystal Structure and Habit........................... ..........................................36 3.3. Crystal Solubility................................... ..................................................3 9 3.4. Liquid-Liquid Phase Separation...................... ........................................45 3.5. Hysteresis in Liquid-Liquid Phase Separation............ .............................47 4. CONCLUSION......................................... ................................................... ...........49 REFERENCES......................................... ................................................... ..................50

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ii LIST OF TABLES Table 1 – Temperature at four depths inside the Large Starna cell (9F-Q-10-MS). The top temperature column corresponds to the set te mperature of the controller.......................................... ................................................... ...............31 Table 2 – Temperature at four depths inside the Small Starna cell (Starna,3-3.45Q-3) and aluminum carrier. Each column corresponds to a setting on the temperature controller............................. ................................................... ........32 Table 3 – Output of a pH probe (Fisher 13-620-185) when measuring identical reference buffers that are maintained at 23C and 60 C....................................33 Table 4 pH of four different stock solutions that wer e used for many of the trials reported in this work............................... ................................................... .........34 Table 5 Enthalpies calculated from solubility fitti ng coefficients...................................43 Table 6 Solubility temperatures of tetragonal crysta ls (0.1M NaAc, pH = 4.0). (From Pusey 24 figure 1)........................................ .............................................44 Table 7 Solubility temperatures of lysozyme (0.1M NaAc, pH=4.0) orthorhombic crystals (From Pusey, figure 4.)........................ .................................................44 Table 8 Solubility compared with what has been foun d by other authors. Values from Pusey 24 are obtained from fits to reported data. Values from Schall 21 are directly from reported data...................... ................................................... ..45

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iii LIST OF FIGURES Figure 1 – Three dimensional model of Lysozyme with acid and base residues indicated with red and green respectively (Source: 2LYZ from pdb.org)...............9 Figure 2 Illustration of the interaction potentials of Lysozyme at three ranges...............9 Figure 3 Schematic temperature-density phase diagrams f or hard spheres of diameter s with Yukawa attraction of range d Left: Standard phase diagram with a stable G+L coexistence region below the critical point (CP) Right: Phase diagram for short attraction ( d s /7) which results in G+L coexistence that is metastable with respect to G+S. (Base d on Muschol 22 )........11 Figure 4 – (A)Liquid-liquid phase separations of bovi ne g E crystalline in sodium phosphate for a sample at 22C for a few minutes. (B) Liquid-liquid phase separation of thaumatin at -9C. The initial protein concentration was 229 mg/ml (source: Asherie).............................. ................................................... ....12 Figure 5 – van’t Hoff plots for typical values of enth alpy. From equation 4 C 1 =5.16mg/ml, T 1 =25C.............................................. .......................................14 Figure 6 Illustration showing that scattering increases when proteins aggregate into larger particles. Left: Diffuse protein (G) scatt ers weakly according to Raleigh’s law. Right: Aggregates (L or S) are larger than incident light wavelength, so that mie scattering and refraction occurs a nd scattering increases............................................ ................................................... ............16 Figure 7 Phase diagram with a typical experimental t rial shown as a vertical line and steps shown as numbers. Xs denote liquid-liquid coexi stence and squares denote crystallization.......................... ..................................................1 8 Figure 8 –Block diagram of the temperature-controlled light scattering instrument used for determination of lysozyme phase diagram bounda ries.........................19 Figure 9 – Temperature controlled cuvette holder with water ports indicated.................21 Figure 10 – Protein Concentration vs. Concentration of NaCl with a typical crystal solubility region shaded. Arrows indicate pathways for solution preparation........................................ ................................................... ..............23 Figure 11 – Custom-written graphical interface used f or controlling the light scattering experiments............................... ................................................... .....25 Figure 12 Record of the solution temperature (red) and scattering intensity (blue) vs time for a lysozyme solution (Clys = 97mg/ml, 4% NaCl, pH = 4.6) undergoing temperature-induced phase separatio n. At t =~ 15 min

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iv (T = 11C) the solution undergoes liquid-liquid phase separation which persists until the solution is rewarmed to 12.25C. At t = 60 minutes, the stirring rod is turned on which immediately induces crystal nucleation. Crystals persisted in solution until the temperature was r aised to 47C. (Source: trial #330)............................... ................................................... ..........26 Figure 13 – Lysozyme solution after liquid-liquid phase separation. Photo was taken during the intensity peak at 40 minutes in (Sou rce: trial 488)...................27 Figure 14 Record of the solution temperature (red) and scattering intensity (blue) vs time for a lysozyme solution (Clys = 42mg/ml, 4% NaCl, pH = 5.6) undergoing temperature-induced phase separatio n. There are three intensity peaks which correspond (from left to right) to three phases: liquid-liquid phase separation, tetragonal crystals and orthorhombic crystals. At this concentration, orthorhombic crystals could not be melted without denaturing lysozyme. (Source: trial # 539)...... .......................................28 Figure 15 – Two different diluting methods for crystal s in solution represented by two arrows from the open circle to the filled circle. D 1 occurs when diluting first then cooling. D2 occurs when cooling first .......................................29 Figure 16 Scattering and temperature versus time fo r 61.4 mg/ml lysozyme in 4% NaCl. Sample denatured at 65C (trial # 458).... ..........................................30 Figure 17 – Record for a concentrated lysozyme solution ( Clys=252mg/ml, 4% NaCl, pH=4.6) that undergoes aggregation early in the trial. Raising the temperature to 60C did not reduce scattering which m ade solubility determination impossible. (Source: Trial 444)......... ...........................................31 Figure 18 Temperature dependent pH changes of four buffer/salt solutions................34 Figure 19 – Portion of a trial record (Clys=78mg/ml, 4% NaCl, pH=5.5) emphasizing the effect of the stirring rod. Immediatel y after stirring starts, crystals nucleate and scattering increases. (Source: trial 4 85)...........................35 Figure 20 -Temperature (red) and scattering intensity ( blue) versus time for a lysozyme solution (Clys = 54mg/ml, 4% NaCl, pH = 5.6) und ergoing liquid-liquid phase separation at 40 minutes, tetrago nal crystal growth at 130 minutes and orthorhombic crystal growth at 220 min utes. (Source: trial #488)........................................ ................................................... ................36 Figure 21 – Photo of lysozyme after cycling through the L L phase and stirring for 30 minutes at a temperature slightly above this phase. No te numerous aggregated crystallites. (Source: Photo 1500, trial # 488, 165 minutes)..............37 Figure 22 – Photo of lysozyme that has been slowly warme d to 42C taken just before melting. Note two distinct shapes: squares and prisms that resemble Figure 23 and Figure 24. (Source: Photo 151 1, trial #488, 206 minutes)............................................ ................................................... ..............38 Figure 23 – Photo of tetragonal lysozyme crystals from oth er research. Left: lysozyme (Clys=100mg/ml, NaCl=4%, 0.1M NaAc, pH=5.0) held at 18.5C for 30-45 minutes. (Source: Gorti fig 7) Righ t: lysozyme

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v (Clys=100-150mg/ml, NaCl=2.5%,0.05M NaAc, pH=4.6) at 2 0C. (Source: Yoshizaki fig 4)............................ ................................................... .....38 Figure 24 – Growth habit of tetragonal lysozyme with i ndices of axis and faces indicated. (Source: Monaco).......................... ................................................... .38 Figure 25 Photo of lysozyme (Clys = 54mg/ml, 4% NaCl, pH = 5.6) held at 42C for ~30 minutes. Tetragonal crystals melted 18 minutes p rior to this photograph. (Source: Photo 1518, trial #488, 220 min utes)...............................39 Figure 26 Sketch of the crystal photographed in Figu re 25..........................................39 Figure 27 – Phase diagram of lysozyme (100mM NaAc buffer 4% NaCl, pH=4.6). Squares: solubility measurements, Solid line: least squares fit to a van’t Hoff law (eq. 4), Circles: LL phase measurement s plotted for comparison. No orthorhombic phase was observed at this pH ...........................40 Figure 28 Semi-log plot of Figure 27............. ................................................... ............40 Figure 29 Phase diagram of lysozyme (0.1M NaAc, pH=5.6 4% NaCl). Diamonds: orthorhombic, Squares: tetragonal, Circles: LL phase, Lines: least squares fits to a van’t Hoff law (eq. 5)........ ................................................41 Figure 30 – Semilog plot of Figure 29. Note the two solublities are equal at approximately 2 mg/ml................................ ................................................... ....41 Figure 31 – Solubility of lysozyme (100mM NaAc, 4% NaCl) tetragonal crystals. Open squares: pH=4.6, solid squares: pH=5.6, Lines: le ast squares fits to a van’t Hoff law (eq. 5)............................ ................................................... ........42 Figure 32 Phase diagram previously presented in Figur e 3 with the orthorhombic phase added (dotted curve). The orthorho mbic phase and tetragonal phase are equally soluble where the curves cross (ES). ES is at a concentration lower than the liquid-liquid phas e (dashed curve)..................43 Figure 33 Tetragonal solubilities for this work plot ted against that of Pusey 24 ..............44 Figure 34 Solubilities for this work plotted agains t that of Pusey 24 ...............................45 Figure 35 – Liquid-Liquid phase clearing temperature s for lysozyme in 4%NaCl solution at 4.6 and 5.6 pH.......................... ................................................... .....46 Figure 36 Intensity plotted against temperature that clearly shows hysteresis of liquid-liquid phase separation in lysozyme solution (Clys = 42mg/ml, 4% NaCl, pH = 5.6). The trial began at 30C and was slo wly cooled until it clouded at 8C. As the sample was rewarmed, it cleared a fter temperature rose above 11C. (Source: trial #539)..... .......................................47 Figure 37 Temperature difference as measured by ther mocouple probe between clouding and clearing, (4% NaCl, pH = 5.6). T he solid line is a best fit: T=-2.27Ln(C)+12.25 which intersects with the T =0 axis at 219 mg/ml.............................................. ................................................... ................48

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vi THE INFLUENCE OF PH ON NUCLEATION, SOLUBILITY AND C RYSTAL STRUCTURE OF LYSOZYME PROTEIN CRYSTALS Marc Apgar ABSTRACT X-ray diffraction from protein crystals remains the most re liable way to determine the molecular structure of proteins, and how this structure relates to biological function. However, we still lack the abilit y to predict solution conditions that support the nucleation and growth of high-qualit y protein crystals for X-ray diffraction studies. The overall goal of this thesis is t wo-fold: (a) determine the nucleation behavior and solubilities for lysozyme crystals wi th two distinct crystal structures (orthorhombic vs. tetragonal) and (b) investiga te whether these changes in crystal habit and crystal solubility correlate wit h any discontinuities in the liquid-liquid phase boundary of lysozyme that occurs u nder the same solution conditions. We measured lysozyme crystal solubility by nucleating and subsequently dissolving very small lysozyme crystals in highly supersaturated solutions. The presence of crystals in our samples is detected and monitore d by measuring the light scattered off the micron-sized crystals. These "turb idity measurements" are repeated across a range of protein concentrations, for pH 4.6 and 5.6, thereby

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vii yielding the crystal solubility boundary. Changes in crystal structure are assessed at the end of the experiments by microscopic inspection o f the distinct crystal habits. Attractive protein interactions in solution also induce liquid-liquid phase separation. Similar to the crystal solubility measuremen t, we use the turbidity increase associated with liquid-liquid phase separation t o map out this phase boundary. Since both crystal formation and liquid-liqui d phase separation are driven by attractive protein interactions, we investigat ed whether the dramatic changes in crystal solubility associated with different prote in crystal structures lead to any discernable “discontinuities” in the liquidliquid phase boundaries.

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8 1. INTRODUCTION 1.1. Motivation The objective of this thesis is to contribute to our under standing of conditions that promote or interfere with the nucleation and gr owth of high-quality protein crystals from solution. Study of the solution conditions th at influence protein crystal growth leads to further understanding of the nucl eation and growth process. In this study, crystals are nucleated and subsequentl y dissolved by respective cooling and warming samples of hen egg whit e lysozyme. A static light scattering apparatus is used to detect the presen ce of crystals or liquid droplets that form in samples that initially contain lyso zyme monomers. The measurements are repeated across a range of protein conce ntrations, and for two separate pH values (pH = 4.6 and 5.6) to obtain p hase diagrams. The specific measurement protocol had to be adjusted to acc ommodate differences in the phase nucleation and equilibration behavior of th e liquid-liquid phase boundary, tetragonal crystal solubility, and orthorhombic crystal solubility.

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9 1.2. Hen-Egg White Lysozyme: Interaction Forces in S olution Figure 1 – Three dimensional model of Lysozyme with acid and base residues indicated with red and green respectively (Source: 2LYZ f rom pdb.org). Hen egg white lysozyme is a globular protein with a mol ecular weight of 14,388 g/mol. Lysozyme is comprised of a single chain of 129 amino acids 20 that, because of hydrophobicity, compacts into an ellipso idal shape approximately 45 across 1 The net charge of Lysozyme depends on solution pH and will carry a 10-12 positive charges 2 at pH 4.6. It is important to recognize, however, that proteins are “zwitterionic” by nature, i.e. they will carry a combination of both positive and negative charges at any given pH. This bipolar charge distribution gives rise to a permanent dipole mo ment (and higher charge distribution moments) that contribute to the attractive protein-protein interactions. Figure 2 Illustration of the interaction potentials of Lysozyme at three ranges.

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10 1.3. Protein Phase Diagrams Proteins can undergo a variety of phase transitions in solution, including the formation of crystalline phases and liquid-liquid phase separation, i.e. the separation of the solution into two liquid phases at va stly different concentrations. These transitions can occur when the long-range repulsi on between the charged protein molecules is reduced by the presence of salt ion s. Negative ions from dissociated salts attract to a positively charged protein to create an ion cloud with a net charge that is lower than the protein alone. The electrostatic fields become screened from neighboring proteins and short-ranged at tractive forces become noticeable. Molecular dynamics calculations of particles interacting via such short-range interactions have provided important insights into the expected shape of protein phase diagrams 3 In these models, globular proteins under crystallizatio n conditions are represented as spherical particles interact ing via attractive, short ranged forces between them 5,11 These short range attractions can be approximated with a Yukawa interaction potential 3 () < = ) ( / ) ( ) (s s e ss dr r e r r u r (1) where s is the diameter of the hard core sphere, while d and e characterize the range and well-depth for the attractive interactio n, respectively. The infinite potential produced when coming in contact with one an other (r = s ) is the nature of hard spheres, and a reasonable assumption for lysozyme 3,4 For atoms or small molecules, Monte Carlo simulation with this inter action potential generate a phase diagram comparable to typical van-der Waals gases (Figure 3, left

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11 panel) 22 At low concentrations and high temperatures, the syste m is in the gas phase. Upon lowering the temperature, the gas condens es and enters the gasliquid coexistence region (G+L), with the gas-phase an d liquid-phase concentrations in that region given by the left and rig ht branch of the parabolic coexistence curve. These two branches merge at the critical point (CP). At higher concentrations, we cross the sublimation phase b oundary into the gassolid coexistence region, with the sublimation and gas-li quid coexistence curves merging at the triple point (TP). Figure 3 Schematic temperature-density phase diagrams f or hard spheres of diameter s with Yukawa attraction of range d. Left: Standard phase diagram with a stable G+L coexistence region below the critical point ( CP) Right: Phase diagram for short attraction (ds/7) which results in G+L coexistence that is metastable with respect to G+S. (Based on Muschol 22 ) The shape of this “traditional” phase diagram changes dramatically as the size of the molecule is increased beyond approximately seve n times the range of the attractive force. Large molecules exhibit a sublima tion curve that “hops over” the G+L coexistence curve (dashed), and results in a me tastable phase boundary below a sublimation curve that is more thermod ynamically stable 3 To interpret these results for particles interacting i n the gas phase to proteins suspended in solution, we need to define the gas-phase a s protein uniformly

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12 dispersed in solution. The gas-liquid coexistence, in t urn, represents the separation of the protein solution into two liquid p hases with very different protein concentration. Proteins will tend to coalesce into den se liquid droplets, as shown in the liquid-liquid phase separation photograph in F igure 4 below. Crystal solubility, i.e. the coexistence curves of protein crystals i n equilibrium with proteins dispersed in solution, should be identified w ith the G+S coexistence curve (sublimation curve) in the above model. Several i nvestigators have shown that this simplified model predicts the phase separation boundaries seen with supersaturated protein solutions 4,22,23 Figure 4 – (A)Liquid-liquid phase separations of bovine gE crystalline in sodium phosphate for a sample at 22C for a few minutes. (B)L iquid-liquid phase separation of thaumatin at -9C. The initial protein concentration was 229 mg/ml (source: Asherie 5 ) 1.4. Solubility Consider a system of solid protein crystals in solution. Prot ein crystals in a protein-free solvent will lose protein molecules to th e surroundings and will increase the protein concentration of the solution. Alt ernatively, a protein-rich solvent will act as a source of protein molecules that w ill be consumed during crystal growth. As long as the crystals don’t entirely melt the system will reach an equilibrium concentration at which crystals lose prot ein molecules at the same

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13 rate as they are gained. The concentration of protein s in the solution at equilibrium is the solubility 5 The van’t Hoff law is a general thermodynamic relation ship that can be used to relate the equilibrium solubility concentration to the solubility temperature. Suppose a solution containing crystals that is kept at temp erature T 1 reaches an equilibrium concentration C 1 As the solution temperature is changed to T 2 a new equilibrium is reached at C 2 Two equilibrium points are related by the van’t Hof f expression for solubility 6,7 : n D = n 1 2 1 2 1 1 ln T T R H C C (2) Where D H is the enthalpy of crystallization and R is the gas const ant. The relationship can be used to predict all other equilib rium points along the solubility curve. To plot a solubility curve, C 1 and T 1 are fixed to a single point and all other points C 2 are calculated by plugging in different temperature s T 2 To simplify the evaluation, equation (2) is rearranged like so: n n D = 2 1 1 2 1 2 exp T T T T R H C C (3) Assuming T 2 is not too far from the reference temperature T 1 the denominator inside the exponential can be approximate d as T 1 T 2 T 1 2 which allows further simplification, ( ) ( ) 1 2 1 2 exp T T C C =a (4)

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14 where C 1 is the solubility concentration at the reference temp erature T 1 and the constant a is given by 2 1 RT H D =a (5) Figure 5 – van’t Hoff plots for typical values of enthal py. From equation 4 C 1 =5.16mg/ml, T 1 =25C Solubility curves are typically two-dimensional graphs that plot concentration against temperature, with all other conditions held co nstant. Protein solubilities can be plotted against temperature 8,22 salt concentration 22 pH 8 or ionic strength of the buffer 9,10 Various experimental conditions can be presented with multiple plots on a single temperature versus concentration graph Protein pointmutations can be studied by measuring changes in solubi lity and some mutations have been shown to shift or invert the solubility lin e 11 1.5. Crystal Nucleation and Growth Crystals will grow at conditions below the solubility cu rve and will melt at conditions above. Solutions more concentrated than the solubility are said to be supersaturated and the degree of supersaturation can be expressed as fractional difference from C sat In principle, all supersaturated solutions (C>C sat ) should

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15 nucleate crystals. In general, nucleation of crystals requir es some additional driving force because there is an energy barrier associate d with the surface free energy for small crystalline clusters 12 Protein crystals will hardly ever nucleate unless concentration exceeds solubility by a factor of leas t three 5 (C>3C sat ). Once protein crystals have nucleated, they will grow at a rate proportional to the square of supersaturation 20 but have been found to not grow at all if supersatur ation is too low (C<2C sat ) 20 For concentrations in the range 2-3 C sat crystals grow readily 13,20 and become large enough to be seen with optical microsco pe in a few hours. Highly concentrated (>3C sat ) solutions grow too quickly and new protein molecules attach anywhere instead of the energetically fa vorable sites resulting in poorly formed crystals with numerous defects 14 Extremely high supersaturation can result in aggregation of protein into amorphous liquid droplets that lack any long-range order, i.e. liquid-l iquid phase separation. Nucleation is assumed to begin when two monomers bind to create a dimer 15 The second aggregation step will either be binding o f an additional monomer to the dimer of binding of dimer to dimer. Subsequent steps could occur via additional aggregation pathways because of the increase d variety of particle populations in solution. Some crystal growth has been fo und to proceed by addition of higher order aggregates that have preform ed in the bulk solution prior to attachment 15 There is some evidence that nucleation begins with l ow-order liquid droplets until it reaches a critical size and rear ranges into a crystal 12

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16 2. MATERIALS AND METHODS 2.1. General Approach Our approach to measure protein phase separation is to take advantage of the strong temperature dependence of protein solubilit y and of the dramatic changes in light scattering intensity associated with phas e separation. During our experiments, we quench the temperature of protein solutions while measuring changes in light scattering intensity caused by phase separation 16,22 Figure 6 Illustration showing that scattering increase s when proteins aggregate into larger particles. Left: Diffuse protein (G) scatters weakly according to Raleigh’s law. Right: Aggreg ates (L or S) are larger than incident light wavelength, so th at mie scattering and refraction occurs and scattering increases. The basic principle of the measurement is readily explain ed by looking at the theoretical phase diagram of proteins in solutions (see Figure 7). The starting point (point 1) of our measurements is the uniform sol ution phase, equivalent to the gas phase (G). The sample is then cooled to point 2 which is below the gas-

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17 liquid phase boundary (dashed curve) and two coexisting li quid phases form (Xs). The phase change can be detected as a rapid incre ase of light scattering and confirmed by re-warming the sample above the phas e boundary. The sample is slowly warmed toward point 3 until scattering reduces and the temperature at which this occurs is recorded. The temperature is maintained at point 3 until scatte ring increases again which is attributed to a phase change into crystals (square s in Figure 7). Protein crystals can form in the G+S coexistence region, and these cr ystals will also contribute to scattering. For crystal solubilities, we ha d to proceed cautiously with our measurements since (a) crystal nucleation require s very high values of supersaturation and (b) crystals, once formed, have to be given long time periods to equilibrate with their surrounding solutions. Hen ce temperature changes were performed in small steps, and subsequent step increases were not taken until the temperature and scattering intensity during the previous step had stabi lized. Orthorhombic crystals grow and melt slower than tetrago nal crystals so these can be differentiated by the rate of change of scatterin g intensity. Finally, the crystals are melted as the sample is slowly warmed from po int 3 to point 1, and the solubility temperature is recorded.

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18 Figure 7 Phase diagram with a typical experimental tr ial shown as a vertical line and steps shown as numbers. Xs denote liquid-liquid coexi stence and squares denote crystallization. 2.2. Illumination and Detection To implement these measurements, we modified and impr oved a temperature controlled light scattering instrument pr eviously built in our laboratory 17 A schematic overview of the hardware used for the dete ction of temperature-induced phase separation in protein solut ions is shown in Figure 8. The light source was a high intensity, AlGaInP light em itting diode (superbrightleds.com, model RL5-RD1560) which had a cen ter wavelength l = 638nm, and power output of about 1mW. The LED was po wered by a 6 volt DC battery in series with an R = 330 W resistor to deliver an operating voltage of 1.84 V. A power meter measured the light output at P = 1 mW and confirmed that it was stable and noise-free. The light was focused with an f = 15cm lens on the center of the sample cuvette. Light scattered from the samples was collected with an f = 30mm lens at a right angle to the inciden t illumination and was focused onto a silicon photodiode (UDT sensors, model 11 -05-001-1).

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19 Figure 8 –Block diagram of the temperature-controlled light scattering instrument used for determination of lysozyme phase diagram boun daries The LED, temperature controller and photodiode detec tor were covered with a box to prevent ambient room light from entering th e photodetector. The photo current, which is proportional to the incident light i ntensity, was converted into a voltage using a high-impedance (R = 100M W ) current-to-voltage amplifier (Femto, model DLCPA-200). The amplifier gain was set to 10 8 and an internal 10 Hz low-pass filter was enabled. The output voltage from the amplifier was digitized with a data acquisition board (National Inst ruments, model PCI6221 and BNC2090 breakout box). Voltage was sampled 100 times pe r second, and the average voltage for each one second interval was calculat ed to create another filter in software, that was low-pass below 1Hz. 2.3. Temperature Control The temperature of the protein solutions was controll ed by placing the sample cuvette inside a temperature controller (Quantum North west, model TLC50F).

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20 The temperature controller has a water-cooled peltier element connected to an electronic control module that adjusts the current to provide the proper rate of cooling/heating for a chosen sample temperature. Measu rements of the protein phase separation required that (a) the sample tempera ture could be changed under computer control (b) scattering intensities coul d be acquired and correlated to actual sample temperatures and (c) sample temperatur e could be automatically readjusted in response to changes in ligh t scattering intensity indicating phase separation. Tap water was run throu gh the peltier cooler for heat transfer from the controller to maintain tempe rature of the cuvette holder to within 0.1 C. A calibrated thermocouple probe was inserted into the top of the cuvette to measure sample temperature throughout the en tire experiment. These readings were typically 0.1-0.5 C different fro m the temperature reported by the controller and lagged behind the set temperatu re due the thermal equilibration time required. The quartz cuvette (Starna, model 9F-Q-10-MS) held 0. 8 to 1.7 ml of sample solution in a rectangular column. It also had a conica l cavity at the bottom to allow a stirring rod to rotate freely. The stirring r od (Fisher 14-512-152) was actuated with a magnet located at the bottom of the cu vette holder and could be turned on or off via software. The stirring rod was found to become stuck when samples became excessively viscous so the drive magnets were u pgraded by the manufacturer early in the experiments. Trials requ iring temperatures below 10C were performed while flushing dry nitrogen gas th rough the holder to prevent condensate from forming on the cuvette.

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21 Figure 9 – Temperature controlled cuvette holder with water ports indicated 2.4. Preparation of Stock Solutions All stock solutions were made with deionized water obta ined from a fourstage water filtration system (Barnstead E-Pure model D4641). We typically used two stock solutions for any given trial: a buffer solution adjusted to the appropriate pH and a buffer/salt solution with salt con centration at twice its final value. Solutions for measurements were generated by disso lving the protein at twice its final concentration in the buffer stock solution and mixing it in equal proportions with the twice-concentrated salt/buffer solu tion. To make a 100mM sodium acetate buffer, an appropriat e amount of dry sodium acetate (Fisher cat# BP333-500, purity > 99%) was weighed and dissolved into water. The pH was adjusted with glacial a cetic acid (Fisher cat# BP1185-500, purity > 99.9%). Solution pH was measured with a calibrated and temperature compensated pH probe (Fisher model 13-62 0-185) and pH meter (Fisher model AR15) until the desired pH was reached. Stocks solutions were stored in sealed glass bottles that were refrigerated at 5C. A stock of buffer with 8% w/v NaCl was prepared by dissol ving 80 mg of NaCl (Fisher cat# BP358-212, purity 99.5%) in 1 ml deionized water and heating it

PAGE 23

22 above 80C to ensure the salt is thoroughly dissociated. Then the solution was cooled and 100mM of NaAc is added. The pH was set in a similar manner as the buffer stock. Setting the pH of the salt solution sepa rately ensured that any effect the salt has on the pH or the pH probe was elimi nated. 2.5. Preparation of Measurement Samples Lyophilized lysozyme protein (Worthington Biochemical, Lake wood, NJ, cat# LYSF) was weighed out on a scale, gently combined with 1 ml of buffer stock and warmed to 45C for at least 15 minutes. Then the solu tion was filtered through a 0.22 m m syringe filter (Fisher cat# 09-720-3) and transferred to sealed centrifuge tubes and stored at 45C prior to the trial. The actual protein concentration of the sample was meas ured from the uvabsorption of the sample. A small portion of the sampl e (typically 10 m l) was diluted 150-fold into the buffer stock. A spectrophotom eter (Thermo Electron, model UV1) was used to measure the optical absorption o f the sample at l = 280 nm, where the absorption coefficient for lysozyme is know n 4,22 to be a 280 = 2.64 ml/mg cm. Prior to the concentration measurement, th e spectrophotometer was zeroed with a lysozyme-free buffer solution. The absorpt ion measurement was multiplied by the dilution factor and divided by the absorption coefficient to obtain the actual lysozyme concentration in mg/ml. The dilution and concentration measurement was performed at least twice to improve accur acy and to detect mistakes if and when they occurred. The accurately measured lysozyme solution was combined, in equal parts, with the buffer stock containing 8% NaCl to achieve fi nal solution containing half the measured concentration of lysozyme at 4% NaCl. 400 -1000 m l of sample

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23 was transferred into the quartz measurement cuvette t hat was placed into the peltier temperature controller. The sample was allo wed to equilibrate to temperature for several minutes while turning the stir ring bar to ensure thorough mixing of the solution. The specific sequence chosen for sample preparation was n ot accidental. Figure 10 below depicts alternative sample preparatio n pathways within a typical protein vs. salt concentration phase diagram. Line A1 (vertical line) represents adding solid-phase lysozyme directly to a 4% NaCl/buffer so lution. Method A1 is not desirable because the sample will pass through the s olid-phase region briefly which might risk crystal nucleation prior to the onset of measurements. Lines B1 and B2 represent the method employed for these experi ments. Note that the sample is much less likely to cross into the solid-phase reg ion. B1 represents the 8% NaCl stock solution and B2 represents the lysozyme at twice the final target concentration. Figure 10 – Protein Concentration vs. Concentration of NaCl with a typical crystal solubility region shaded. Arrows indicate pathways for sol ution preparation.

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24 2.6. IGOR Software Automated computer control was achieved with IGOR Pro 5. 03 mathematical software that was purchased from www.wavemetrics.com. Cu stom written IGOR routines communicate with the temperature controller, with the data acquisition card and with the user via a small graphical user interf ace (GUI). A second-bysecond log was kept for measured scattering intensity, cont roller temperature and thermocouple temperature. The program initiall y determines the scattering intensity of the homogeneous sample solution while the sample is kept above the crystal solubility temperature for the given sample composi tion. This scattering intensity is considered the minimal scattering intensity, or V Clear The IGOR macro “start new trial” is invoked to bring up a small GUI wi ndow which is used to set the specific parameters for the trial. Figure 11 below is an image of the GUI at the beginning of a typical trial. The settings shown in Figure 11 were for trial 539 w hich resulted in the data shown in Figure 14 below. Trial 539 was typical for m ost trials performed but specific settings vary from trial to trial. The clouding ste p is skipped for conditions where these measurements are not possible, i.e. low prot ein concentrations. The crystal growth and the melting steps are usually possible if the cloud point measurements are possible.

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25 Figure 11 – Custom-written graphical interface used for controlling the light scattering experiments The trial is started by clicking “start” in the GUI and al l the steps that the user has checked are performed sequentially from top to bott om. In this example, the first step is to preheat the sample for 5-10 minutes at 45C, while stirring to ensure that the sample is homogeneous. Then, the stirri ng rod is turned off and temperature is lowered to 30C which is still above t he temperature where liquidliquid phase separation is expected to occur. When stabi lized, background intensity, V Clear is measured and recorded as baseline intensity for the remainder of the trial. The value of V Clear will be used as the basis for thresholds in subsequent steps in the trial.

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26 Figure 12 Record of the solution temperature (red) and scattering intensity (blue) vs time for a lysozyme solution (Clys = 97mg/ml, 4% NaCl, pH = 4.6) undergoing temperature-induced phase separation. At t =~ 15 min (T = 11C) the solution undergoes liquid-liquid phase separation w hich persists until the solution is rewarmed to 12.25C. At t = 60 minutes, t he stirring rod is turned on which immediately induces crystal nucleation. Crystals persist ed in solution until the temperature was raised to 47C. (Source: trial #3 30) 2.7. Liquid-Liquid Phase Separation Liquid-liquid phase separation is induced by stepping the temperature down until a rapid increase in scattering is detected, which o ccurred at 15 minutes in Figure 12 above. The temperature that induced the scattering increase is recorded as T cloud After clouding, T Clear is determined by slowly stepping the temperature back up until the scattering returns close to the baseline intensity, V clear A photo of a lysozyme solution that has undergone liqui d-liquid phase separation is shown in Figure 13. The separated soluti on reveals small droplets of fluid at highly elevated protein concentration obse rved during the clouded phase of trial 539, between 40-50 minutes in Figure 1 4. The droplets are large relative to wavelength so that incident light undergo es multiple-scattering and

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27 refraction/reflections at the interfaces of the two so lution phases. As a result, the solution displays a turbid, milky-white color. Figure 13 – Lysozyme solution after liquid-liquid phase separation. Photo was taken during the intensity peak at 40 minutes in (Sour ce: trial 488) 2.8. Crystal Nucleation and Solubility Determinatio n After the sample clears, a constant temperature is main tained while crystals are allowed to nucleate. The stirrer is turned on beca use, in previous trials, the stirrer was found to enhance the crystal nucleation rate. At that point, the solution is below the expected crystal solubility temperat ure but above the cloud temperature for liquid-liquid phase separation (poin t 3 in Figure 3). Thus, any dramatic intensity increase can be attributed to the nu cleation of many small crystals. The instrument simply waits at this temperature un til there is an adequate intensity increase, usually 10 times V Clear Next, the temperature is stepped up slowly while the resulting scattering intensity is monitored. The temperature is raised until the sample scattering reduce s to the background scattering intensity, indicating that all crystals have mel ted. This point is recorded as the solubility temperature T Sol

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28 Figure 14 Record of the solution temperature (red) and scattering intensity (blue) vs time for a lysozyme solution (Clys = 42mg/ml, 4% NaCl, pH = 5.6) undergoing temperature-induced phase separation. Ther e are three intensity peaks which correspond (from left to right) to three pha ses: liquid-liquid phase separation, tetragonal crystals and orthorhombic crystals. At this concentration, orthorhombic crystals could not be melted without denatu ring lysozyme. (Source: trial # 539) 2.9. Dilution Used to Measure Solubility at Low Con centrations For lower protein concentrations, crystal nucleation requ ires excessively long time periods. To obtain crystal solubilities at low pro tein concentrations, crystals are nucleated at higher lysozyme concentrations, then sampl es are diluted with 4% NaCl buffer solution and the experiment is resumed. Figure 15 below illustrates two alternatives for diluting these solutio ns. The open circle represents the starting point where high concentration crystals are n ucleated and the solid circle represents the target condition after dilution. Method D1 involves diluting first and then cooling which is not desirable because th e sample will pass outside the solid-liquid coexistence region and the crystals will melt. Method D2 was used in these experiments because cooling the sample fi rst ensures that the crystals do not melt during dilution.

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29 Note that crystals will grow at the filled circle in the figure but kinetic factors result in very slow nucleation rates. Growing crystals in th ese regions was attempted but abandoned after several hours of waitin g for nucleation. Figure 15 – Two different diluting methods for crystals in solution represented by two arrows from the open circle to the filled circle. D1 occurs when diluting first then cooling. D2 occurs when cooling first. 2.10. Freezing Point of a Typical Sample A typical sample (Clys = 22.2mg/ml, 4%NaCl, pH = 4.6) was used for determination of the freezing point. The freezing poi nt is important for establishing a lower measurement limit for the SLS exp eriments. The sample was frozen inside the cell until a thermocouple probe w as firmly entrenched and could not be removed. The temperature was slowly increase d until the probe was freed. The probe temperature at this point was -5.4C 2.11. Denaturing Temperature of Lysozyme The denaturing temperature of lysozyme was measured by st eadily increasing temperature until scattering increased. The ass umption is that the increased scattering is a result of lysozyme uncoiling and aggregating. Scattering increased slightly at 63C and significantly at 65C as s hown in Figure 16 below. Broide 4 obtained similar results and reports that lysozyme irre versibly precipitates

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30 at 65C. The denaturing temperature is important be cause it sets the upper temperature limit for these experiments. Figure 16 Scattering and temperature versus time for 61.4 mg/ml lysozyme in 4% NaCl. Sample denatured at 65C (trial # 458). The upper temperature limit results in an upper concen tration limit because a portion of the solubility curve exceeds the denaturing t emperature. Denatured proteins scatter light in a way that cannot be differe ntiated from light scattered from crystals. So if crystals do not melt when temperatu re is raised to ~62C, solubility measurement is impossible, as exemplified in Figure 17 below. Liquid-liquid phase measurements are also difficult a t high concentration because of the tendency of nucleate crystals before the me asurement can be made. The presence of “unmeltable” crystals acts as back ground scatterering that cannot be differentiated from liquid droplets, a s can be seen in the elevated intensity at 50 minutes in Figure 17, which occurred bef ore liquid-liquid separation. When highly-concentrated trials nucleated to o many unmeltable

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31 crystals before liquid-liquid separation, the trial was aborted because no valid data points could be obtained. Figure 17 – Record for a concentrated lysozyme solution ( Clys=252mg/ml, 4% NaCl, pH=4.6) that undergoes aggregation early in the trial. Raising the temperature to 60C did not reduce scattering which ma de solubility determination impossible. (Source: Trial 444) 2.12. Temperature Gradients inside the Sample Cuvet te The vertical temperature gradients inside two types of sample cuvette were measured by inserting a thermocouple probe into the cuve ttes containing water. The cell holder was set to a constant temperature and a llowed to equilibrate before measuring. An Extech 421305 thermocouple mete r was used for these measurements. Temperature variations in the large cell (Starna 9F-Q-10-MS) were measured with a small stirring rod at the bottom set to medium speed. Table 1 – Temperature at four depths inside the Large Starna cell (9F-Q-10-MS). The top temperature column correspo nds to the set temperature of the controller. Depth Temperature (C) (mm) 45.0 30.0 15.0 5.0 10 44.0 31.2 17.2 7.0

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32 20 44.4 30.8 16.6 6.3 30 44.6 30.7 16.3 6.1 40 45.0 30.7 15.7 5.8 Table 2 – Temperature at four depths inside the Small Starna cell (Starna,3-3.45-Q-3) and aluminum carrier. Each col umn corresponds to a setting on the temperature controller. Depth Temperature (C) (mm) 45.0 30.0 15.0 5.0 10 44.6 30.1 16.3 6.9 20 45.2 30.5 16.1 6.5 30 45.3 30.5 16.1 6.4 40 45.4 30.5 16.0 6.3 Typical thermocouple probe depth during phase separatio n experiments was chosen to be 30 mm; a position close to but slightly above the light beam passing through the sample. 2.13. Temperature Dependence of the pH for the 100 mM NaAc Buffer The pH of four batches of stock solutions was measured at four temperatures to determine whether and how much solution temperat ure altered buffer pH. The NaAc buffer was stabilized to 4.6 or 5.6 pH, stored in glass bottles at 5C for days-weeks before measurements. A temperature compensated pH probe (Fisher 13-620-185) was used for all of the pH measurem ents in this trial. The first concern when making this type of measurement was to ensure that the pH changes observed are not simply thermal drift of the pH probe. We used two NIST traceable buffers with known temperature-dependen ce (Fisher SB107-500 and SB101-500) to calibrate the probe before measurem ent at a given temperature. The instructions that are supplied wit h the probe say that the

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33 calibration for elevated pH measurement can be achieve d by cycling the probe from hot and cold samples while monitoring the probe voltage. When the voltage measured in the cold bath differs by +/2mV or less, the probe is claimed to be calibrated for elevated temperatures. This was perfo rmed using two separate vials of pH=4 buffer standard, at 23C and 60C respect ively. The measurements are in Table 3 below. Table 3 – Output of a pH probe (Fisher 13-620-185) w hen measuring identical reference buffers that are maintain ed at 23C and 60C Measurement 23C 60C 1 190 mV 2 198 mV 3 188.7 mV 4 198.9 mV 5 189.4 mV Notice that the reading at the low temperature devia tes less than 2mV. After completing this calibration, both buffer standards were measured at 60C. The standards are labeled to be 4.09 pH and 6.95 pH at th ese temperatures but the meter measured 3.81 and 6.98. A pH error of 0.38 w as observed after calibrating the probe with this technique. We opted for a more conservative calibration technique, by re-calibrating the probe at the exact temperature where pH measurements w ere required. To do this, two vials containing pH standards were placed in a 2 00 mL water bath. Four measurement samples were put into the same beak er to ensure temperature match between calibrations and measurements. The pH probe was calibrated with the two standards using temperature-speci fic pH values as indicated on the label. This calibration was repeated for each temperature prior to

PAGE 35

34 measuring the four stock solutions. The pH of the stock sol utions deviated from the target pH by at most 0.18 pH units. Table 4 pH of four different stock solutions that wer e used for many of the trials reported in this work Stock A B C D Target pH 4.5 5.5 5.5 5.5 NaCl % 12 0 8 0 Prep. Date 2/26/07 10/18/07 12/4/07 12/4/07 pH at 60 4.60 5.60 5.62 5.64 pH at 40 4.62 5.61 5.60 5.61 pH at 20 4.53 5.68 5.53 5.66 pH at 10 4.59 5.55 5.65 5.61 pH at 7 4.58 5.54 5.59 5.62 4.00 4.50 5.00 5.50 6.00 020406080Temperature (C)pH 0% NaCl pH 5.5 8% NaCl pH 5.5 0% NaCl pH 5.5 12% NaCl pH 4.5 Figure 18 Temperature dependent pH changes of four buffer/salt solutions

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35 3. RESULTS AND DISCUSSION 3.1. Enhanced Crystal Nucleation in Response to Sol ution Agitation Figure 19 – Portion of a trial record (Clys=78mg/ml, 4 % NaCl, pH=5.5) emphasizing the effect of the stirring rod. Im mediately after stirring starts, crystals nucleate and scattering incr eases. (Source: trial 485) Crystal nucleation is dramatically accelerated when a stirri ng rod is used to agitate the solutions. Lysozyme samples at a temperatu re 1-2C above the liquid-liquid coexistence curve would form crystals nearl y immediately after starting the rotation of the stirring rod. One examp le is shown in Figure 19 above where light scattering remains low until the stirring rod starts. The scattering can be attributed to crystal nucleation because of crystals were observed by microscopic inspection and because scattering reduced when the crystals are melted by warming. At low protein concentration, cry stals would not nucleate after waiting 2-3 hours without a stirring rod but wo uld nucleate minutes after

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36 starting the stirring. At extremely low concentration s (< 5 mg/ml), crystals could not be nucleated with or without a stirring rod. Hen ce the stirring rod in our experiments serves two purposes: it prevents the small mi crocrystals we nucleate from settling out and we find that it dramat ically enhances nucleation rates. 3.2. Crystal Structure and Habit Crystal structures are derived from observations of the crysta l habits, which are distinctly different from tetragonal vs. orthorhom bic crystals. Crystal habit is checked by briefly pausing the trial and removing 10 m l of sample from the cuvette. The removed sample volume is placed onto a mi croscope slide so that it can be viewed with an Olympus IX-70 inverted microscope Figure 20 -Temperature (red) and scattering intensity ( blue) versus time for a lysozyme solution (Clys = 54mg/ml, 4% NaCl, pH = 5.6) und ergoing liquid-liquid phase separation at 40 minutes, tetragonal crystal growt h at 130 minutes and orthorhombic crystal growth at 220 minutes. (Source: tria l #488) shows one of the earlier trials (Trial 488) perform ed at pH 5.6. This trial utilizes a method similar to the preceding trials to gro w and then melt the

PAGE 38

37 tetragonal crystals. At the 200 minute point, the tetr agonal crystals are completely melted and the scattering intensity has retur ned to the baseline observed at the beginning of the trial. But after 2 00 minutes, the scattering intensity increased again despite a temperature that co nsistently melted crystals in previous trials. It is clear that a new crystal type wa s growing, at a slower rate, but with a higher solubility temperature. The high solubility temperature appears to correspond to orthorhombic crystals that grow slower, but are more difficult to melt. Photos taken at various stopping points through out the trial reveal significant changes in crystal appearance as the trial prog ressed. Before beginning the trial, the sample was inspected under the microscope and it was confirmed to be clear of any crystals or aggregates. At seve ral points during the trial in aliquots of the sample were photographed a nd are included in Figure 13, Figure 21, Figure 22 and Figure 25. The photograph s can be compared with other authors that have associated macroscopic crystal habit s with crystal structure. Figure 21 – Photo of lysozyme after cycling through the L L phase and stirring for 30 minutes at a temperature slightly above this phase. No te numerous aggregated crystallites. (Source: Photo 1500, trial #488 165 minutes)

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38 Figure 22 – Photo of lysozyme that has been slowly warme d to 42C taken just before melting. Note two distinct shapes: squares and pri sms that resemble Figure 23 and Figure 24. (Source: Photo 1511, trial #488, 206 minutes) Figure 23 – Photo of tetragonal lysozyme crystals from oth er research. Left: lysozyme (Clys=100mg/ml, NaCl=4%, 0.1M NaAc, pH=5.0) hel d at 18.5C for 3045 minutes. (Source: Gorti 18 fig 7) Right: lysozyme (Clys=100-150mg/ml, NaCl=2.5%,0.05M NaAc, pH=4.6) at 20C. (Source: Yoshi zaki 19 fig 4) Figure 24 – Growth habit of tetragonal lysozyme with i ndices of axis and faces indicated. (Source: Monaco 20 )

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39 Figure 25 Photo of lysozyme (Clys = 54mg/ml, 4% NaCl, pH = 5.6) held at 42C for ~30 minutes. Tetragonal crystals melted 18 minutes prior to this photograph. (Source: Photo 1518, trial #488, 220 minutes) Figure 26 Sketch of the crystal photographed in Figur e 25 3.3. Crystal Solubility The solubility measurements are fit to the van’t Hoff equation (equation 4) with a determined by a least squares fit. The IGOR fitting routines perform best when fitting to data that lie along a decaying exponential. Before fitting, temperatures were first multiplied by -1 so that the te mperature axis was “flipped” and a decaying exponential was produced (C vs. -T). The fit was performed and temperature was again multiplied by -1 before plotti ng the fits that are shown in the figures below.

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40 Figure 27 – Phase diagram of lysozyme (100mM NaAc buffer 4% NaCl, pH=4.6). Squares: solubility measurements, Solid line: least squares fit to a van’t Hoff law (eq. 4), Circles: LL phase measurements plott ed for comparison. No orthorhombic phase was observed at this pH. Figure 28 Semi-log plot of Figure 27. At pH 5.6, both tetragonal and orthorhombic crystals occ urred and two different solubilities were measured and fit to separ ate curves (Figure 29). The nucleation rate for orthorhombic crystals increases with i ncreasing protein concentrations which made measurements of tetragonal solu bilities impossible above 60 mg/ml. As shown in Figure 31 below, tetrago nal crystal solubility at pH 5.6 follows almost exactly the same curve as pH 4.6.

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41 Figure 29 Phase diagram of lysozyme (0.1M NaAc, pH=5.6 4% NaCl). Diamonds: orthorhombic, Squares: tetragonal, Circles: LL phase, Lines: least squares fits to a van’t Hoff law (eq. 5). Figure 30 – Semilog plot of Figure 29. Note the two solublities are equal at approximately 2 mg/ml.

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42 Figure 31 – Solubility of lysozyme (100mM NaAc, 4% NaCl) tetragonal crystals. Open squares: pH=4.6, solid squares: pH=5.6, Lines: least squares fits to a van’t Hoff law (eq. 5). The solubility data obtained from these experiments sug gests that the notional phase diagram presented in Figure 3 should be modified by adding an orthorhombic solubility curve as shown in Figure 32. The orthorhombic curve crosses the tetragonal curve at a point of equivalent sol ubility (ES) where the growth of both crystal types reduces free energy equally. At concentrations above ES, orthorhombic crystals are more energetically fa vored and more stable than tetragonal crystals.

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43 Figure 32 Phase diagram previously presented in Figure 3 with the orthorhombic phase added (dotted curve). The orthorhomb ic phase and tetragonal phase are equally soluble where the curves cross (ES). ES is at a concentration lower than the liquid-liquid phase (dashe d curve). To relate the solubility curves to enthalpy of crystal for mation, equation 4 can be solved for D H: 2 1 RT Ha= D (6) Enthalpy is calculated using the solubility fitting coeff icients and are presented in Table 5 below. Table 5 Enthalpies calculated from solubility fitting coefficients pHNaCl C1a aa a T1D DD D H 4.64%tetra5.16-0.139298-24.5kcal/mol5.64%tetra4.96-0.146298-25.7kcal/mol5.64%ortho2.51-0.052298-9.3kcal/mol For comparison to other work in this field, data points were obtained from Pusey’s 24 figure 1, for tetragonal solubility. The Pusey exper iments were also performed with 100 mM Acetate buffer, set to a slight ly lower pH = 4.0. The figure below shows good agreement with data collecte d in this study.

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44 Table 6 Solubility temperatures of tetragonal crysta ls (0.1M NaAc, pH = 4.0). (From Pusey 24 figure 1) C (mg/ml) Tsol 3 17 6 24 9 28 12 30 Figure 33 Tetragonal solubilities for this work plott ed against that of Pusey 24 Reported data for orthorhombic crystals are also compared with data collected here. Orthorhombic solubility reported in th is paper is a steep function of temperature and the crystal enthalpy is 8.5 kcal/mol while data Pusey 24 12.6 kcal/mol. Table 7 Solubility temperatures of lysozyme (0.1M NaA c, pH=4.0) orthorhombic crystals (From Pusey, figure 4.) C (mg/ml) Tsol 10 28 13 31 15 36 18 39 20 41 23 43 25 45

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45 Figure 34 Solubilities for this work plotted against that of Pusey 24 Schall 21 used calorimetry to obtain tetragonal phase diagra m information for lysozyme in 50 mM acetate buffer at pH = 4.5. Crystal ent halpies where found for 3% and 5% NaCl concentrations. Schall reports sig nificantly lower enthalpy than this work or Pusey 24 which might be attributed to the technique or the lower ionic strength of the buffer. Table 8 Solubility compared with what has been found by other authors. Values from Pusey 24 are obtained from fits to reported data. Values from Schall 21 are directly from reported data. SourcepHNaCl C1a aa aD DD D H Apgar4.64%tetra5.16-0.139-24.5kcal/molApgar5.64%tetra4.96-0.146-25.7kcal/molPusey4.04%tetra6.73-0.111-19.6kcal/molSchall5.23%tetra-10.5kcal/molSchall4.65%tetra-17.1kcal/molApgar5.64%ortho2.51-0.052-9.3kcal/molPusey4.04%ortho8.79-0.052-9.2kcal/mol 3.4. Liquid-Liquid Phase Separation Liquid-liquid phase separation was induced as described in the methods section above for a range of protein concentrations. Th e phase boundary plotted

PAGE 47

46 in Figure 35 resembles a portion of the theoretically p redicted coexistence curve 3,23 in Figure 3. Attempts to measure the liquid-liquid (G+L) phase at high concentrations were hampered by the proclivity to nucleat e crystals. The few data points above 200 mg/ml were successful only because t he trials were performed quickly after sample preparation before the onset of crystals. Muschol 22 reports that the liquid-liquid phase will reach a ma xima at a critical concentration (~25530 mg/ml), and that this curve fol lows a mathematical expression for the bimodal of critical phenomena. It i s not possible to fit the data in this thesis to a mathematical expression because the re are insufficient measurement points near or above the critical concentratio n. The liquid-liquid phase measurements at pH 5.6 followe d a similar curve, although it appears translated 5-10 C higher in temp erature (Figure 35). The trend to shift the coexistence curve upward with increased pH agrees with simulations 23 At pH 5.6, the proclivity for crystal growth was very st rong, and it was not possible to measure the liquid-liquid phase ch ange above 150 mg/ml. Figure 35 – Liquid-Liquid phase clearing temperatures for lysozyme in 4%NaCl solution at 4.6 and 5.6 pH

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47 3.5. Hysteresis in Liquid-Liquid Phase Separation Using the data recorded by the thermocouple probe, te mperature was plotted against scattering intensity as shown in Figure 36 below. The temperature required to induce separation (clouding) is several degr ees lower than the temperature for clearing hysteresis. The same hysteresis can be repeated when temperature cycles are repeated. Figure 36 Intensity plotted against temperature that clearly shows hysteresis of liquid-liquid phase separation in lysozyme solution (Clys = 42mg/ml, 4% NaCl, pH = 5.6). The trial began at 30C and was slowly coole d until it clouded at 8C. As the sample was rewarmed, it cleared after temperatu re rose above 11C. (Source: trial #539) Using the analysis employed by Asherie 5 a series of clouding temperatures are subtracted from the clearing temperatures and are plotted in Figure 37 below. The temperature difference between T clear and T cloud decreases as the solution concentration approaches the critical concentration 5 An exponential fit to these points is extrapolated to the T=0 axis which can be used to estimate critical concentration. Using this approach, the critical point(CP in Figure 3) is estimated to be C crit = 219 mg/ml, approximately correct 22,24

PAGE 49

48 Figure 37 Temperature difference as measured by ther mocouple probe between clouding and clearing, (4% NaCl, pH = 5.6). T he solid line is a best fit: T=-2.27Ln(C)+12.25 which intersects with the T=0 axis at 219 mg/ml.

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49 4. CONCLUSION The phase diagram of lysozyme can be traced out using a co nceptually straight forward light scattering arrangement. When t he data include an adequate range of concentrations, it is possible to fit the data to the van’t Hoff expression and fitting parameters yield the enthalpy of crystallization. The enthalpy of crystallization of tetragonal crystals does not a ppear to be effected by pH and the solubility curve is unchanged. However, at pH = 5.6 orthorhombic crystals can also occur with significantly different solubi lity and enthalpy. There were not enough liquid-liquid phase separation data points to perform a fit to the theoretically expected coexistence curve. At pH=5.6, liquid-liquid phase separation occurred at higher temperatures which is expected because of the reduced net charge on Lysozyme. There were no obvious indications that changes in crystal structure correlate to changes in the coe xistence curve for liquid-liquid phase separation. A discontinuity in th e coexistence curve might occur at the concentration of equivalent solubility (ES in Figure 32) which is too low in this study to make a determination. The pronounced effect of the stirring rod on crystal n ucleation rates is highly intriguing. Investigation of this mechanism, however, i s beyond the scope of this thesis.

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50 REFERENCES 1 C. Ishmoto, T. Tanaka, Phy. Rev. Letters 39 8 (1977) 2 F. Rosenberger, J. Crystal Growth 166 (1996) 40-54 3 M. Hagen, D. Frenkel, J. Chem. Phys. 101 5 (1994) 4 M. Broide, T. Tominc, M. Saxowsky, Phys. Rev. E 53 6 (1996) 5 N. Asherie, Methods 34 266 (2004) 6 Dill, Bromberg, Molecular driving forces: statistical thermodynamics in ch emistry and biology Garland, New York, 2002 7 M. Jackson, Molecular and Cellular Biophysics Cambridge, New York, 2006 8 E. Cacioppo, M. Pusey, J. Crystal Growth 114 (1991) 286-292 9 E. Forsythe, M. Pusey, J. Crystal Growth 168 (1996) 112-117 10 P. Retailleau, A. Ducruix, M. Ris-Kautt, Acta Cryst. D58 (2002) 1576-1581 11 J. McManus, A. Lomakin, O. Ogun, A. Pande, M. Basan, J. Pande, G. Benedek, PNAS 104 43 (2007) 16856-16861 12 P. Vekilov, J. Crystal Growth 275 (2005) 65-76 13 P. Darcy, J. Weincek, Acta. Cryst. D54 (1998) 1387-1394 14 I. Yoshizaki, T. Sato, N. Igarashi, M. Natsuisaka, N. Tanaka, H. Komatsu, S. Yoda, Acta. Cryst. D57 1621-1629 (2001) 15 M. Pusey, J. Crystal Growth 110 (1991) 60-65 16 F. Rosenberger, S. Howard, J. Sowers, T. Nyce, J. Crysta l Growth 129 (1993) 17 S. Hill, (2005), Design of light scattering unit to measure protein phase transitions, USF undergraduate honors thesis 18 S. Gorti, E. Forsythe, M. Pusey, Crystal Growth & Des. 5 473-482 (2005) 19 I. Yoshizaki, S. Fukuyama, H. Koizumi, M. Tachibana, K Kojima, Y. Matsuura, M. Tanaka, N. Igarashi, A. Kadowaki, L. Rong, S. Ada chi, S. Yoda, H. Komatsu, J. Crystal Growth 290 185-191 (2006) 20 L. Monaco, F. Rosenberger, J. Crystal Growth 129 (1993) 465-484 21 C. A. Schall, E. Arnold, J. Wiencek, J. Crystal Growth 165 293 (1996) 22 M. Muschol, F. Rosenberger, J. Chem. Phys. 107 6 (1997) 23 M. Malfois, F. Bonnete, L. Belloni, A. Tardieu, J. C hem. Phys. 105 8 (1996) 24 E. Cacioppo, S. Munson, M. Pusey, J. Crystal Growth 110 (1991) 66-71