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Effects of electric field on the functions of cell membrane proteins

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Effects of electric field on the functions of cell membrane proteins
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Zhang, Zhongsheng
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Channel
Pump
Synchronization
Modulation
Kidney
Dissertations, Academic -- Physics -- Doctoral -- USF   ( lcsh )
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non-fiction   ( marcgt )

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ABSTRACT: The most important and most common channels on cell membrane are voltage-gated Na+ and K+ channels. In so-called "excitable cells" like neurons and muscle cells, these channels open or close in response to changes in potential across the membrane in order to accomplish muscle contraction and transmit signals. By controlling the membrane potential, we observe extraordinary inactivation behaviors of the voltage-gated Na+ channels and the voltage-gated delayed rectifier K+ channels, which shows that electric stimulation pulses can temporarily close the Na+ and K+ channels, just as drugs, like tetrodotoxin (TTX) and tetraethylammonium (ETA), do. The Na/K pump is essential for living system and is expressed in virtually all cell membranes.The ionic transport conducted by Na/K pumps creates both an electrical and a chemical gradient across the plasma membrane, which are required for maintaining membrane potentials, cell volume, and secondary active transport of other solutes, etc. We use a pulsed, symmetric, oscillating membrane potential with a frequency close to the mean physiological turnover rate across the cell membrane to synchronize Na/K pump molecules. The pump molecules can work as a group, pumping at a synchronized pace after a long train of pulses. As a result, the pump functions can be significantly increased. After the pump molecules are synchronized, the applied electric-field frequency can gradually increase in order to resynchronize the molecules to a new, higher frequency. Modulating the pump molecules to a higher frequency leads to a significant increase of pump current. Synchronization and modulation of pump molecules can become a new method to study the function of Na/K pump molecules.This method has huge potential applications in clinic medical treatment. After single-fiber-level study, the final project is on organ level, the rat kidney, by using synchronization and modulation of Na/K pump molecules on the proximal tubule membrane. Because Na+ re-absorption is directly related to the function of the Na/K pump, the more active Na/K pumps are, the more Na+ ions can be absorbed, which results in an increased potential inside the renal proximal tubule. This project is the first step of synchronization and modulation applied on the level of an organ.
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Dissertation (Ph.D.)--University of South Florida, 2008.
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by Zhongsheng Zhang.
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Effects of Electric Field on the Func tions of Cell Membrane Proteins by Zhongsheng Zhang A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Physics College of Arts and Sciences University of South Florida Major Professor: Wei Chen, Ph.D. Dennis K. Killinger, Ph.D. David Rabson, Ph.D. Garrett Mattews, Ph.D. Date of Approval: February 21, 2008 Keywords: channel, pump, synchronization, modulation, kidney Copyright 2008, Zhongsheng Zhang

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Dedication To my wife Hongwei Shang and my son Kevin K. Zhang

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Acknowledgments This dissertation is accomplished under th e supervision of Dr. Wei Chen, without whose instruction, guidance and encouragem ent, many meaningful results would not have been achieved. Special thanks to chairman Dr. Randy Larsen and committee members, Dr. Dennis K. Killinger, Dr. David Rabson and Dr Garrett Matthews, for their support, help and suggestions. NIH and NSF have also supported this work.

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i Table of Contents List of Tables iv List of Figures v Abstract xvii Chapter 1 Introduction 1 Chapter 2 Inactivation of Voltage-D ependent Na+ Channel by Repeated DC and AC Stimulations 10 Introduction 10 Methods and Materials 15 Experimental Results 26 Discussion and Modeling 39 Conclusion 45 Chapter 3 Inactivation of Voltage-G ated Delayed Rectifier K+ Channel by Oscillation Electric Field 46 Introduction 46 Methods and Materials 49 Experimental Results 50 Discussion and Modeling 59 Conclusion 63

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ii Chapter 4 Synchronization of Na/K Pump Molecules by Oscillation Electric Train 64 Introduction 64 Methods and Materials 67 Experimental Results 71 Discussion and Modeling 86 Conclusion 95 Chapter 5 Synchronization of Na/K Pumps under Na/Na and K/K Exchange Modes by Electric Field 96 Introduction 96 Methods and Materials 98 Experimental Results 100 Discussion 105 Conclusion 106 Chapter 6 Modulation of Na/K Pump Proteins by Electric Field 108 Introduction 108 Methods and Materials 109 Experimental Results 110 Discussion 116 Conclusion 117 Chapter 7 Increase Lumen Potential in Rat Proximal Tubule by Synchronization and Modulation of Na/K Pumps 118 Introduction 118

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iii Experiment Setup and Methods 124 Experimental Results 130 Discussion 142 Conclusion 147 Chapter 8 Conclusion and Future Study 148 References 150 List of Publications 170 About the Author End Page

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iv List of Tables Table 1.1 Ion distributions and Nernst pot entials across muscle membrane [1] 4 Table 6.1 Areas and magnitudes of pump currents responding to both positive and negative half-pulse under synchronization-modulation electric stimulation train 114 Table 7.1 Re-absorptions of different matters on different kidney segments including the proximal tubule the loop of Henle, the distal convoluted tubule and the collecting duct [140] 122

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v List of Figures Figure 1.1 Three different views and the basic components of a cell membrane 2 Figure 2.1 Diagram depicting a Na+ channe l protein with four repeating units (domains), each of which consists of eight hydrophobic segments. Six long segments (S1-S6) are helices that span the membrane, and two short segments (SSI and SSII) are inserted in the membrane. The filled circle on the connecting segments between S5 and S6 represents a TTX binding site. An inactivation ball exists between domains III and IV inside of the membrane [25] 11 Figure 2.2 Cross section of Na+ channel protein with an inactivation gate, selectivity filter and TTX binding site [25] 12 Figure 2.3 Activation and inact ivation processes of Na+ ion channel dependent on the membrane potential 14 Figure 2.4 Photograph of the voltage clamp (TEV-200) 17 Figure 2.5 Photograph of the custom-made double Vaseline chamber 19 Figure 2.6 Sketch of the setup for Na+ channel currents measurement including chamber, voltage clamp and controlling computer, etc. 20 Figure 2.7 An example of PClamp software interface used in Na+ channel currents measurement with the top figure showing the actual voltages

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vi which are delivered on the cell membrane and the bottom figure showing the measured Na+ channe l currents after using P/4 method 21 Figure 2.8 An example of P/4 subtraction pr otocol. The main pulse consists of a single depolarizing step function with a magnitude of +40 mV compared to the holding potential of mV. Ther e are four subsweeps with 1/4 of this magnitude (+10 mV), executed before the main pulse with the holdi ng potential at -110 mV 23 Figure 2.9 Measurement of trans-membrane current without using P/4 method 24 Figure 2.10 Na+ channel current after using P/4 method 24 Figure 2.11 Unidirectional stimulation pulse train consisting of 2000 pulses. The duration of each pulse is 8 ms and the magnitude is +50 mV with the holding potential of -90 mV 25 Figure 2.12 Symmetric stimulation pulse train consisting of 2000 pulses. The duration of each pulse is 8 ms and the magnitude is +/-50 mV with the holding potential of -90 mV 26 Figure 2.13 Diagram of a sequence of 28 stim ulating pulses with the duration of 8 ms and the potentials ranging from -70 mV to -2.5 mV. The increase between two consecutive pulses is 2.5 mV. The relaxing time between two consecutive pulses is 2 s 27 Figure 2.14 Na+ channel currents by using P/4 method responding to the pulses shown on Figure 2.13 28 Figure 2.15 Relationship between peak values of currents corresponding to different membrane potentials (Na+ channel I-V curve) 28

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vii Figure 2.16 Na+ channel currents of the indexed pulses as 1st, 10th, 20th th, 200th, 2000th under an unidirectional stimulation pulse train 30 Figure 2.17 Relationship between the peak va lues of Na+ channel currents and the index of the pulses 31 Figure 2.18 Na+ channel currents measured under a symmetric stimulation train. The currents do not show distinct effect when 2000 pulses are applied on the cell membrane 31 Figure 2.19 Measurements of Na+ channe l currents by using a unidirectional stimulation pulse train when this pulse potential is lower than the reversal potential 33 Figure 2.20 Measurements of Na+ channel currents by usi ng a unidirectional stimulation pulse train when this pulse potential is higher than the reversal potential 33 Figure 2.21 Lines connecting Na+ current p eak values of Figure 2.20 and that of Figure 2.21 cross nearly at the same point 34 Figure 2.22 Sketch of unidirectional stim ulation pulse trains with different holding potential durations 35 Figure 2.23 Na+ channel currents responding to the holding potential of -90 mV with duration of 4 ms 35 Figure 2.24 Na+ channel currents responding to the holding potential of -90 mV with duration of 10 ms 36 Figure 2.25 Na+ channel currents responding to the holding potential of -90 mV with duration of 20 ms 36

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viii Figure 2.26 Na+ channel currents responding to the holding potential of -90 mV with duration of 200 ms 37 Figure 2.27 Relationship between the peak va lues of Na+ channel currents and the index of pulses. The curves repr esent holding durations of T=4 ms, T=10 ms, T=20 ms and T=200 ms from the top to the bottom 37 Figure 2.28 Three Na+ channel I-V curves. On e is pre-train (triangle), one is 0.5ms-later-of-train (diamond), and one is 2-min-later-of-train (circle). This figure proves that the stimul ation pulses can just temporarily keep Na+ channel proteins in an un-conductive state 38 Figure 2.29 Two curves fitting, with one be ing the real data from Na+ channel currents measurement and the othe r is the fitting data of single exponential decay 40 Figure 2.30 The recovery times after ch annels are opened. When the restore voltage is negative (left side) compar ed to the holding potential (right side), the recovery process is faster than that using the holding potential 42 Figure 2.31 Single exponential curve to fit experimental data 43 Figure 2.32 Double exponential curves to fit experimental data 43 Figure 3.1 A stimulation pulse train that includes 200 pul ses. All pulses have the same magnitude (-10 mV) and duration (10 ms) 50 Figure 3.2 A sequence of 28 stimulation pulses with a 25 ms duration with the membrane potential changing from -70 mV to -14 mV is applied on the cell membrane to measur e K+ ion channel currents 51

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ix Figure 3.3 K+ channel currents corresponding to different membrane potentials. It shows the major characteristic of th e so-called delayed rectifier K+ channel, which is that the channel needs about 10-15 ms to complete the opening process, and all curre nts are outward currents with unobservable inactivation process 52 Figure 3.4 K+ channel satura tion currents are plotte d as a function of the membrane potentials. A fitting straight line is plotted also. The line slope represents the channel conducta nce, and the crossing point with the X-axis is the theoretical turning point, K+ channel open door threshold 53 Figure 3.5 Measured voltage signal that is applied on the cell membrane during the experiment (The first 1000 ms), which is similar to the designed potential 54 Figure 3.6 Recorded K+ channel currents (The first 1000 ms) 55 Figure 3.7 Recorded K+ channel currents (all 200 pulses) viewed from another perspective compared to Figure 3.6 55 Figure 3.8 Demonstration of the relations hip between the number of pulses and K+ channel saturation currents under each pulse 56 Figure 3.9 Three different internal soluti ons with 20, 40, 70 mM concentrations of K+ ions are used in three fibers through the same experiment procedures. The top curve represents a K+ ions concentration of 70 mM, the middle 40 mM and the bottom 20 mM, respectively 57

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x Figure 3.10 Three curves (Figure 3.9) closely match each other after normalization 57 Figure 3.11 K+ channel currents measur ement (same muscle fiber) under two electric stimulation trains, with the top curve having twice resting time than the bottom curve 58 Figure 3.12 Inactivation curv e is fitted to a single exponential decay 61 Figure 3.13 Inactivation curve can be approximated by the sum of two exponential decay curves with time constants differing by almost an order 62 Figure 4.1 A step function is used to m easure Na/K pump current. The membrane potential jumps to -30 mV with a duration of 30 ms 68 Figure 4.2 A sequence of 15 stimulating pulses with 10 ms duration holding the membrane potentials from -120 mV to +20 mV. The time difference between two continuant pulses is 1 min. 68 Figure 4.3 A stimulation elec tric train which includes a 100 pre-pulses followed by three data acquisition pulses, with all pulses having equal magnitudes and durations. The positiv e pulse potential is -30 mV, and the negative pulse potential is 150 mV, which are symmetric to the membrane holding potential of -90 mV The duration of each pulse is 12 ms 70 Figure 4.4 A Na/K pump current elicit ed by a single 30 ms step pulse depolarizing the membrane potential to -30 mV (Figure 4.1). Na/K pump current shows only an outward current component 72

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xi Figure 4.5 Na/K pump currents responding to different membrane potential pulses according to Figure 4.3 73 Figure 4.6 A pump current generated by cu rrent T0_C (without Ouabain) minus current of T0_ O (with Ouabain), which is the traditional method to measure Na/K pump currents 74 Figure 4.7 A pump current resulted fro m the difference between two data acquisition pulses with pre-trai n pulses (T100_C minus T100_O), which indicates the influence of the external electric field on pump proteins 75 Figure 4.8 Pump currents elicited by the fi rst 20 synchronization pulses. Initially, the inward pump currents responding to the negative half-pulse are very small. After a few oscillating pulses, the inward currents start to be distinguishable and increase w ith the number of pulses. Both inward and outward pump currents become larger and larger 76 Figure 4.9 Pump currents elicited by the last 20 synchronization pulses become saturated and the magnitude ratio between the outward and the inward pump currents is close 3:2 77 Figure 4.10 Outward pump currents as a func tion of a number of train pulses, which indicates that 100 pulses ar e needed to synchronize pump molecules with an oscillating memb rane potential from 30 mV to -150 mV and 10 ms duration 78 Figure 4.11 Outward parts of Na/K pump cu rrents are plotted as a function of the stimulation train pulse durations. When the pulse duration is 10 ms

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xii (50 Hz), close to the mean physiological turnover rate the oscillation field has the highest effect. When the oscillating frequency is away from the physiological mean frequency, less effect is observed on the pump currents. This figure show s the dependence of synchronization on the external electric frequencies 80 Figure 4.12 New stimulation protocol: a 100pulse train with a duration of 6 ms followed by a membrane potential of mV for another 50 ms before return to -90 mV 81 Figure 4.13 After 3 data acquisition pulses, without stimulation pulses, Na/K pump current drops to zero during 6 ms 82 Figure 4.14 The stimulation train is the same as that in Figure 4.12 except that the duration is 12 ms instead of 6 ms 82 Figure 4.15 New stimulation protocol: the membrane potential is changed from mV to mV instead of from mV to mV for the last two data acquisition pulses after three data acquisition pulses 85 Figure 4.16 Na/K pump currents measurem ent by using Figure 4.15 stimulation protocol. The positive part of th e pump current increases a little because not all pump molecules are synchronized and the pump current generated by the remaining pump molecules still depends on the membrane potential. The negative part of the currents does not change at all, which represents the total number of the synchronized pump molecules 85

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xiii Figure 4.17 Left: Na/K pump currents from random pump molecules in response to a single pulse; Right: the sync hronized pump currents in response to an oscillating pulse train 87 Figure 4.18 Albers-Post model: This figure shows the stages of conformational changes (E1 E2): ion binding, release and occlusion, and ATP hydrolysis. The circle of arrows indicates the forward pump cycle 89 Figure 4.19 Six-state model of Na/K pump cycle [110] 90 Figure 4.20 Calculated Na/K pumping flux as a function of the membrane potential from sixstate mode [110] 91 Figure 4.21 Calculated Na/K pumping flux under the infl uence of an oscillating electric field is increas es dramatically [110] 93 Figure 4.22 The figure on the left side re presents the normal configuration of Na/K pump proteins; the figure on the right side represents the synchronized configuration of Na/K pump proteins 94 Figure 5.1 A single step pulse is used on th e muscle fiber to measure Na/K pump currents under the Na/Na exchange mode 100 Figure 5.2 When Na/K pump proteins are working under the Na/Na exchange mode, for each loop of Na/K pumps, the same amount of Na+ ions is transported in and out through the ce ll membrane. This process is no longer electrogenic. Under a single pulse (Figure 5.1), Na/K pump current equals zero 101 Figure 5.3 Pump currents under the Na/Na ex change mode during the first 300 ms of the oscillation pulse train 102

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xiv Figure 5.4 Pump currents under the Na/Na exchange mode during the last 300ms of the oscillation pulse train 103 Figure 5.5 The X-axis represents the number of pulses, the Y+ axis represents the positive pulse pump currents and the Yaxis represents the negative pulse pump currents. The ratio betw een the positive currents and the negative currents is close to 1:1 103 Figure 5.6 Pump currents during the first 300 ms of the oscillation pulse train under the K/K exchange mode 104 Figure 5.7 Pump currents during the last 300 ms of the oscillation pulse train under the K/K exchange mode. Compared to Figure 5.6, there is no significant difference between those two figures 105 Figure 6.1 Synchronization-modulation pulse tr ain, the duration of the first part of which is 15 ms, followed by 10 ms, 6ms, 4 ms and 3ms consecutively. The magnitude of potential is +/60 mV 110 Figure 6.2 Pump currents when the pulse duration is 15 ms (synchronization) 111 Figure 6.3 Pump currents when the pulse duration is 10 ms (first modulation) 112 Figure 6.4 Pump currents when the pulse duration is 6 ms (second modulation) 112 Figure 6.5 Pump currents when the pulse duration is 4 ms (third modulation) 113 Figure 6.6 Pump currents when the pulse duration is 3 ms (fourth modulation) 113 Figure 6.7 All Na/K pump current traces s uperimposed together shows that both outwards and inwards pump currents are continuously increasing when the field frequency is gradually in creased. The areas underneath either

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xv the outwards or the inwards pump cu rrents remain the same regardless of the pulse durations. 116 Figure 7.1 The basic structure of kidney 119 Figure 7.2 The basic structure of naphron 121 Figure 7.3 The electric potential differen ce across the renal t ubular cell and the direction of net Na+ ions re -absorption in the tubule 123 Figure 7.4 Photograph of a micropipette tip (microelectrode), which is filled with tiny Sudan black mixed castor oil and measurement solution 126 Figure 7.5 Schematic diagram of a microelectrode and a connector setup 127 Figure 7.6 Photograph of a microele ctrode and a c onnector setup 127 Figure 7.7 After micropuncture and oil injec tion, a tiny solution is also injected into the tubule. Through this way, an independent tubular segment is created and the tubule feel back system is cut off 129 Figure 7.8 The potential inside the tubule in normal functional condition does not change with time 130 Figure 7.9 With reabsorption of ions and wa ter, the lumen potential is increased until it reaches the satu ration state after the tubule is blocked. The time to reach the saturation state is about 297+/-41 s 131 Figure 7.10 After the lumen potential reaches a constant value, the stimulation electric field train (synchronizatio n-modulation) is applied to the kidney. The new build-up potential is increased about 3-7 mV 133 Figure 7.11 Same as Figure 7.10 except that th e potential of the last pulse of the stimulation train changes from -1 V to 0 V instead of from 1 V to 0 V 134

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xvi Figure 7.12 Detailed information of the last pulse in Figure 7.10 135 Figure 7.13 Detailed information of the last pulse in Figure 7.11 136 Figure 7.14 When high concentration Ouabain is resolved in the injected solution, the lumen potential does not show significant change after stimulation train 137 Figure 7.15 The top of the Figure shows two electric stimulation pulses which are applied to the kidney. The bottom of the Figure s hows the lumen potential responding to the pulses 138 Figure 7.16 Same as 7.15 except that the poten tial of the last pulse changes from 1 V to 0 V instead of from -1 V to 0 V 139 Figure 7.17 Solution Two (without HCO3ions) is used instead of Solution One. After electric stimulation train, the lumen potential can still be increased, but with less value compared to Figure 7.10 140 Figure 7.18 After the stimulation train is fi nished, the lumen potential gradually decreases to the original value when the tubule is not blocked by oil 142 Figure 7.19 A sketch of Na+ H+ HCO3ions transport system in the proximal tubule segment 145 Figure 7.20 A sketch of Na+ Cl HCO3ions transport system in the proximal tubule segment 147

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xvii Effects of Electric Field on the F unctions of Cell Membrane Proteins Zhongsheng Zhang Abstract The most important and most common channels on cell membrane are voltagegated Na+ and K+ channels. In so-called exci table cells like neurons and muscle cells, these channels open or close in response to changes in potential across the membrane in order to accomplish muscle contraction and transmit signals. By controlling the membrane potential, we observe extraordinary inactivation behaviors of the voltage-gated Na+ channels and the voltage-gated delayed rectifier K+ channels, which shows that electric stimulation pulses can temporarily cl ose the Na+ and K+ channels, just as drugs, like tetrodotoxin (TTX) and tetraethylammonium (ETA), do. The Na/K pump is essential for living system and is expressed in virtually all cell membranes. The ionic transport conducted by Na /K pumps creates both an electrical and a chemical gradient across the plasma me mbrane, which are required for maintaining membrane potentials, cell volume, and secondary active transport of other solutes, etc. We use a pulsed, symmetric, oscillating membrane potential with a frequency close to the mean physiological turnover ra te across the cell membrane to synchronize Na/K pump molecules. The pump molecules can work as a group, pumping at a synchronized pace after a long train of pulses. As a result, th e pump functions can be significantly increased. After the pump molecules are synchronized, the applied electric-field frequency can

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xviii gradually increase in order to resynchronize the molecules to a new, higher frequency. Modulating the pump molecules to a higher freq uency leads to a sign ificant increase of pump current. Synchronization and modulation of pump molecule s can become a new method to study the function of Na/K pump molecules. This method has huge potential applications in clinic medical treatment. After single-fiber-level study, the final proj ect is on organ level, the rat kidney, by using synchronization and m odulation of Na/K pump mol ecules on the proximal tubule membrane. Because Na+ re-absorption is dire ctly related to the function of the Na/K pump, the more active Na/K pumps are, the more Na+ ions can be absorbed, which results in an increased potentia l inside the renal proximal tubul e. This project is the first step of synchronization and modulati on applied on the level of an organ.

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1 Chapter 1 Introduction A living cell is an extraordinarily complex, dynamic, and physicochemical system which maintains in or near the steady state by continual entry and exit of materials and energy to finish self-assembling and self-re plicating process. Th e cell boundaries are formed by a dynamic membrane which is consisting of phospholipids, cholesterols, proteins, and carbohydrates, etc. The typical thickness of cell membrane is about 2-6 nanometers, which physically and chemically isolates cells (cytoplasm) from their environments. Cell membrane is essential for the integrity and functions of the cell. The main functions of cell membrane include: (1 ) Protect the cell from environments (2) Regulate the transport materials in and out of the cell by such methods as pumps, channels, and exchangers, etc. (3) Provide st able binding sites for the enzymes catalysis (4) Allow cells to recognize each other (5 ) Provide anchoring sites for cytoskeletal filaments and components to group cells toge ther to form tissues [1, 3, 4]. Figure 1.1 shows three different views on cell membrane and basic components of cell membrane [2]. Part (A) is a human red blood cell membrane of electron micrograph in cross-section. Part (B) and (C) are schematic drawings of two-dimensional and three-dimensional views of a cell membrane and its basic components.

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Figure 1.1 Three different views and the basic components of a cell membrane [2]. All cell membranes contain lipid bi-layers and proteins: lipid bi-layers provide the basic compartmentalization f unction of the cell membranes, whereas proteins invest membranes with their specialized functions: signaling, transport, and catalysis, etc. [3, 4]. Membrane proteins are very important to th e regulation of cell behaviors. For example, some proteins in cell membrane are recepto r proteins, which deal with communication and recognition between cells [12]; and some are transport proteins that regulate the movement of ions and soluble molecules th rough the cell membrane, like sodium (Na+) and potassium (K+) ions channels [4]. Each type of cell membranes contains specific proteins and lipid bi-layers components that en able them to perform their unique roles for cells functions [1, 4]. The concentration of ions inside the cell is different from that of outside in order to maintain cell living conditions. For example, the cytoplasm of animal cells contains a 2

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concentration of K+ ions as much as 20-40 times higher than that in the extra-cellular fluid. Conversely, the extra-cellula r fluid contains a concentration of Na+ ions as much as 10 times greater than that with in the cell (Table 1.1) [1]. At equilibrium state, each kind of ion with the concentration difference ge nerates a voltage across the cell membrane. This potential can be calculated by Nernst equation [1], which is derived from basic principles of physical chemistry. For exampl e, the electric potential generated by Na+ ions (Na+ ions equi librium potential) across the memb rane can be calculated by the following equation: E(Na)=(RT/ZF)Ln([Na]I/[Na]O) where R is the universal gas constant, T is the absolute temperature in degrees Kelvin, z is the charge number of th e electrode reaction, and F is the Faraday constant. If [Na]I/[Na]O = 0.12 (the rate of Na+ ions concentrati on inside of the cell to that outside of the cell), then E(Na) = 67 mV, which shows that the inside is negative with respect to the outside (Table 1.1). In living cells, all different ion types are simultaneously present and contribute to the resting potential across the cell membrane, and the presence of pumps maintains these concentration differences [1]. It is found that the resting potential of the cell membrane is about -70 mV to -100 mV for most animal cells [1]. The direct effect of changing membrane potential is to modulate the transport properties of charged particles across the membrane and af fect cell mechanical properties. 3

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4 Ion Intracellular Concentration Extracellular Concentration Nernst Potential Na+ 12 mM 145 mM -67 mV K+ 155 mM 4 mM +98 mV Ca+2 0.001 mM 1.5 mM -129 mV Cl4 mM 123 mM +90 mV Table 1.1 Ion distributions and Nernst potentials acr oss skeletal muscle membrane [1]. Most ions, like Na+, K+, H+, Ca+2, Cl-, SO4 -2 are transported through the cell membranes by transport proteins [1, 3, 4], and each type of protein mainly transports a unique substance in order to maintain the cell compositions, volume and membrane potential. Depending on the transport proteins transport occurs by different mechanisms those that do not consume energy in the form of ATP form channels (passive transport) and those that do consume ATP fo rm pumps (active transport) [1]. In order to understand how concentration gradient and membrane potential are formed through the cell membrane by channels and pumps, we have to know which ion is transported across the cell membrane, how the ions are transported and what the different mechanisms between different transport systems are.

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5 Ion channels are pore like proteins spanning the cell membrane [1, 4]. Ion channels can open simultaneously at both side s of the membrane, and ions move through these channels. Transport through channels is always down electr ochemical potential gradient (electric potential and chemical gradients), so membrane potential can change the channel functions and behavi ors. Transport properties of a particular ion channel are the result of summation of hundreds and thousands of single channels over time (different ion channels have different dens ity on different cell membrane). There are a lot of kind of channels among the cell membrane with diffe rent functions and different open and close mechanisms. The conformational change between closed and open states is called gating system. Ion channels can be classified according to which chemical or physical modulator controls their gating activities. Thus, we have different groups of channels as voltage-gated channels, ligand-gated channe ls, and second-messenger-gated channels, etc [1]. The most important and most common channels are voltage-gated Na+ and K+ channels [1, 7] (voltage-gat ed means the probability of a channel opening or closing purely depends on the membrane potential). In so-called excitable cells like neuron and muscle cells, those channels ope n or close in response to cha nge in action potential across the cell membrane. All ion channels show sel ectivity prefer certain ions while rejecting others, but none of ion channels have an absolute selectiv ity for a single ion species [1]. It has been proved that channels, though selectively perm eable, could pass many ionic species. Thus, Na+ channel is a channel that Na+ ions nor mally permeates, but other ions still can go through with much lower permeability than Na+ ions. Similarly, the K+ channel also allows ions other than K+ ions to pass [49] The sequence of ions to which a channel is

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6 permeable is according to the permeability (the selectivity sequence), which is a characteristic property of channel [1]. A large number of pharmacological agents (neurotoxins) have been identified which can affect ionic channels of electrically excitable cells, called channel blocker. The most important and common agents are Te trodotoxin (TTX) [5] and Teraethylammonium (TEA) [6], which selectively block Na+ and K+ channels, respectively. Only nano-molar concentration of TTX is required to bl ock 100% Na+ channels, and micro-molar concentration of TEA is required to block most K+ channels. These agents enable investigators to block either Na+ channels or K+ channels in a reversible manner. Therefore, it is possible to study th e individual kind of ionic channel. Channels can reduce the ionic gradient s across the membrane because the ions always move from high concentration to lo wer concentration when channels are opened. The concentration gradients across the membrane are established and maintained mainly by active transport system [13, 14, 130, 131], which process generally requires chemical reactions of binding the transpor ted substances to a protein, th en pumping the ions in or out of the cell through the cell membrane. The reason that this kind of protein is called pump is that the ions are transported agains t concentration gradient or electric field. For example, Na/K pump proteins, for each loop, extrudes three Na+ ions and intrudes two K+ ions, both from low concentration side to high concentration side [8]. This is one reason why active transp ort needs a lot of energy from th e hydrolysis process of ATP to finish this loop [8, 9, 10]. It has been estimated that r oughly 20-30% of all ATP is hydrolyzed by Na/K pumps in a resting human being [11, 13].

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7 There are a lot of kinds of pump proteins with different mechanisms and transporting different substances on the cell membrane. Na/K pump protein is the most important and basic active transport protein whic h is found in different kinds of cells with a slightly different structure but almost the same functions [9, 10]. Na/K pump can create and maintain trans-membrane ions concentr ation gradients of Na+ and K+ ions, which then form energy source that is used by cells for a variety of tasks, including several vital functions [1, 9, 13]: (1) It he lps establish a potential acro ss the cell membrane with the interior of cell being negatively charged in re spect to the exterior. This resting potential prepares for the propagation of action potenti als leading to nerve impulse and muscle contraction. (2) The accumulati on of Na+ ions outside of ce ll draws water out of cell and, thus, enables the cell to maintain osmotic balan ce. (3) In steady state, the passive flows of Na+ ions and K+ ions from high concentration side to low concentra tion side of the cell membrane are mainly balanced by active Na/K pump transport. The stoichiometry of Na/K pump appears that one mol ecule of ATP is hydrolyzed to one molecule of ADP and one molecule of phosphate, three molecules of Na+ are transported outward and two molecules of K+ are transported inward [8, 9, 10]. Under these circumstances, Na/K pump is electroge nic [10, 14], producing a net current that will result in membrane hyper-polarization. Sin ce Na/K pump requires both Na+ and K+ ions and catalyzes hydrolysis of ATP, it has been called Na/K-ATPase. Contrary to ionic channels operation, (1) Na/K pump proteins are never open to both sides of the membrane simultaneously. (2 ) Na/K pump proteins are working all the times over the physiological membrane potential till this potential is lower than Na/K pump equilibrium potential which is about -300 mV [1, 80]. Na /K pump proteins

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8 movement can be explained by a relatively si mple chemical cycle that includes several steps: binding ions, conformational change, a nd releasing ions, etc. Na/K pump protein apparently has two primary conformational st ates called E1 and E2 [1, 23, 105]. These two conformational states have different affinities for Na+, K+ and ATP. In each cycle of reaction sequence, E1 and E2 alternat ely bind and release Na+ and K+ ions and catalyze hydrolysis of ATP. The E1 conformation has an ion-binding site that faces cytoplasm and binds Na+ ions, whereas E2 conformation has an ion-binding site that faces extracellularly and binds K+ ions. As of today, the sequence of Na/K pump transport events can be summarized as follows: (1) Pump at E1 conformation state, binding ATP and 3 intracellular Na+ ions; (2 ) ATP hydrolyzed to ADP and P, with ADP released resulting in an occluded state, E1-P -[3Na+]; (3) Conformational change of Na/K pump to expose the Na+ ions to the outside of the cell membrane, where they are released, resulting in E1-P state. The release of Na+ ions may be a release of individual ions through intermediate reactions [15]; (4) Conformation of E1-P state converts to conformation of E2-P state; (5) Conformation of E2-P binding 2 extra-cellular K + ions; (6) Na/K pump reoriented. Two K+ ions are re leased in the cytoplasm side; and (7) Na/K pump in E1 conformation state again and ready for next cycle. Step 3 and step 6 are ratelimiting steps [1, 16, 103]. Because the ions move against the electric potential and concentration gradient by using the energy released from ATP, the time of these two rated-limiting steps takes up the majority of the entire motion time. Changing ratelimiting steps will change the whole cycle time [16, 84, 90, 103]. Na/K pump proteins can be blocked by car diac glycosides, such as Ouabain [1, 18, 22], applied in extra-cellular solution with micro-molar c oncentration. Active efflux of

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9 Na+ ions and influx of K+ ions are blocked in a matter of minutes for muscle cells [1]. Because of its specificity of action, Ouabai n has been enormously used to study Na/K pump proteins. In fact, the blockage of th e flux components by Ouabain is taken as strong evidence that this component is transported by Na/K pump proteins. The pump current is also called Ouabain-sensitive current. As described above, membrane potential plays a very importa nt role in the functions of channels and pu mps. External electric fiel ds can produce a variety of profound biochemical and physiological change s on the cell membrane proteins [17, 19, 20, 21]. My research focuses on how oscillation electric fields influe nce the functions of Na+ channel, K+ channel and Na/K pump proteins by changing the membrane potential according to well-designed potential protocols.

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10 Chapter 2 Inactivation of Voltage-Depende nt Na+ Channel by Repeated DC and AC Stimulations Introduction The macromolecule of Na+ channel protei n is the first voltage-gated ion channel which is isolated and sequenced from electric organs of electric eel [24], and later from a number of other tissues including rat skeletal muscle, rabb it skeletal muscle, and human brain, etc [26, 27, 28, 33]. Isolation of Na+ cha nnel macromolecule allows researchers to determine, using methods of molecular biology, the nucleotide sequence of genes encoding the primary structure of Na+ cha nnel proteins amino acid residues sequence [29, 30, 31]. Na+ channel proteins of different cells have different number of amino acid residues. For example, analysis of Na+ ch annel sequence of electrophorus electricus electroplax indicates that th is Na+ channel protein consists of 1,820 amino acid residues [24]; while the amino acid sequence of a Na+ channel from squid loligo bleekeri contains 1,522 amino acid residues [32]. However, all Na+ channel proteins consist of four domains, I-IV [1], with each domain cons isting of eight hydrophobic segments (Figure 2.1) [25]. Six long segments (S1-S6) are helices that span th e cell membrane, and two short segments (SSI and SSII) are inserted in the membrane (face outside of the membrane). The filled circles on the connecti ng segments between S5 and S6 represent a

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TTX binding site. An inactivation ball exists between domains III and IV (inside of the membrane). Initial determination of the ami no acid sequence reveals that the segment S4 [40, 50] contains four amino acids with pos itively charged residue s (Figure 2.1), which are responsible for sensing the membrane potential. Figure 2.1 Diagram depicting a Na+ channel prot ein with four repeating units (domains), each of which consists of eight hydrophobic segments. Six long segments (S1S6) are helices that span the membrane, and two short segments (SSI and SSII) are inserted in the membrane. The filled circle on the connecting segments between S5 and S6 represen ts a TTX binding site. An inactivation ball exists between domains III and IV inside of the membrane [25]. Na+ channel is formed as a tetramer where each domain from I to IV forms a quarter of the channel. The ionic pore has a la rge aqueous cavity, with a gate close to the 11

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interior and a selectivity filter on the outer ves tibule (Figure 2.2) [25]. The mouth of ion channel is found to be about 1.2 nm, narro wing to 0.3-0.5 nm. This narrowing of the channel forms a selectivity filter [33]. Figure 2.2 Cross section of Na+ channel protei n with an inactivati on gate, selectivity filter and TTX binding site [25]. Voltage-gated Na+ channel is normally closed at resting potential. However, in response to the membrane potential depolariz ation, channel can change from closed state to open state (Figure 2.3). Then, Na+ channel tr ansits to inactive st ate automatically [34, 35, 36, 37], followed by a close state after the cell membrane potential becomes re12

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13 polarized. Inactivation is a distinct and majo r property of voltage-gated Na+ channel, which has a fast decay phase [36]. The time of inactivation is within millisecond range. The reason that Na+ channel can be inactive automatically is that there is a special structure responsible for inactivation of th e channel between domain III and domain IV. Once channel is opened, even though depolar ization potential is still maintained, conduction stops. This is thought to be the result of docking the region (ball) of protein into internal mouth of the channel. Inactiv ation process is coupled with the opening of channel; that is, those two events are not independent (Figure 2.3). What will happen when depolarization is terminated and memb rane potential returns to normal values? Channel can not function fully until the ball exit from the mouth of the channel. For example, when the membrane potential is retu rned to -90 mV, it takes an average of 2-3 ms [36] for all balls to exit from the inte rnal mouths of channels. This time has an important consequence because if membrane potential is depolarized again during 2 or 3 ms, not all channels are able to conduct as so me balls are still in or partially in the inactivation position (channel stays in the refr actory period [1]). This is one of the reasons why an action potential can not be fo llowed too closely by another in excitable cells.

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-90 mV Res t Activation Inactivation Refractor y Ball Doo r Res t Figure 2.3 Activation and inactiv ation processes of Na+ i on channel dependent on the membrane potential. Although most attention is initially focused on refining knowledge of ionic current, investigations of capacitance current give important new insights into channel mechanisms [38, 39, 40, 44]. The capacitance cu rrent is also called gating current or displacement current, which is generated by the motion and redistribution of charges inside membrane that accompanies opening or cl osing of an ionic channel. Since the gate is in molecular scale, it is subject to the thermal effects. Hence, the gate opening and closing are random; however, its probability of being in open state is increased as membrane potential increases (non-linear relatio nship) [41]. When the gate is opened, the positive gating charges move from inner surface of membrane to outer surface, which signals conformational change of channel macromolecule. In response to a step of membrane potential, the total gating charges, Q (on), estimated by integrating the gating 14

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15 current from the onset of membrane potential pulse, are equal to th e total gating charges, Q (off), estimated from the offset of the pulse [1]. This result indicates that the redistribution of charges in membrane is reversible [1, 39]. Af ter gating charges are moved, the gate opens, and Na+ ions flow thr ough the channel. So th e inactivation ball and gating charges are working together to control Na+ channel opening and closing behaviors. Pharmacological manipulation can not onl y block conduction of channels (TTX is used to block Na+ channel currents), but al so manipulate channel kinetics. For example, proteolytic enzyme pronase, applied at intracel lular, removes the ball structure that is responsible to inactivation fr om Na+ channel macromolecule without affecting the part that is responsible for activation of the cha nnel [42]. This result s uggests a segregation of function within Na+ channel macromolecule. Methods and Materials The experimental techniques a nd recipes of the solutions used in this research are developed previously [43] and widely used in our lab. (1) Solutions (mM) [43]: Normal Ringer: 120 NaCl 2.5 KCl 2.15 Na2HPO4 0.85 NaH2PO4. H2O 1.8 CaCl2.H2O Relaxing Solution: 120 K-glutamate

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16 1 MgSO4.7H2O 0.1 EGTA 5 PIPES External Solution: 120 NaCl 5.4 KCl 4 MOPS 1.8 MgCl2 2 BaCl2 0.2 CdCl2 1 CsCl 3 3, 4 Diminopyridine (DAP), Internal Solution: 45.5 Cs-glutamate 5 Cs2-PIPES 20 Cs2-EGTA 6.8 MgSO4 5 Glucose 5.5 Na2-ATP 20 Tris-Creatine Phosphate (2) Voltage clamp TEV-200 (Two-Electrode-Voltage-Clamp ) has been designed as a general purpose voltage clamp with two electrodes fo r control (Channel 1 and Channel 2) and one electrode for grounding (Figure 2.4). Channe l 1 continuously reco rds the actual cell membrane potential and that value is comp ared to the command potential, which is

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generated from either PClamp software or LabView program according to different experiments. When the membrane potential n eed be clamped, other electrode (Channel 2) continuously passes current to maintain th e membrane at the command potential through a feedback loop. In addition, TEV-200 features a virtual current monitor/bath clamp (VCM/BC) head-stage which monitors th e sum of channel currents flowing through preparation and simultaneously maintains th e bath at zero po tential (Grounding). Figure 2.4 Photograph of the voltage clamp (TEV-200). 17

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18 (3) Skeletal muscle fi ber preparation [43] Frogs (rana pipiens) are k illed by rapid neck disartic ulation, in accordance with the protocol approved by Inst itutional Animal Care and Us e Committee at University of South Florida. Skeletal twitch muscles, semitendinosus and illus, are dissected and removed from frog hindlimb, then put into a dish with Normal Ringer solution. This treatment is necessary to depolarize the musc le fiber and prevent ce lls from contraction during dissection and experimental preparation. After muscle is put into a dish filled with Normal Ringer solution and pinned down, ch ange relaxing solution and wait about 10 min before single fiber dissection. A single mu scle fiber with good qua lity (clear, about 50-150 um diameter and 3-6 mm long) is hand -dissected and transferred to a custommade chamber [44, 45, 46] (Figure 2.5) filled w ith the relaxing solution. After that, the fiber is clamped by two plastic clips at both en ds. Adjusting the clips allows fiber to be stretched properly to avoid fi ber contraction during chemical treatment and electric stimulation. The width of two partitions is about 100 um and the widt h of central pool is about 300 um. Thin Vaseline and two plastic gl ass cover slips are us ed to electrically isolate the three pools from each other. The fiber segments in two end pools are treated by a solution with 0.1% Saponin for two minutes [43] (it makes the two fiber segments electrically and ionically pe rmeable within the two end pool s.) and washed out with the internal solution by 3 times. Finally, the central pool solution then is changed with the external solution by 3 times. The whole process time is about an hour.

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Figure 2.5 Photograph of the custom-made double Vaseline chamber. (4) Experiment setup Three agar bridges connect three pools (one central pool and two end pools) to three small ponds filled with 3M KCl. The agar bridges are glass tubes with inner diameter of 1 mm filled with agar gel made by 3M KCl solution. Three intermediate ponds are then connected to voltage clamps by three Ag/AgCl pallets to make the pass way resistances as low as possible. Figure 2.6 shows the sketch of whole experiment setup including chamber, voltage clamp and controlling computer. 19

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Voltage Clamp TEV-200 V I G Center pool Computer Fiber Clip Chamber Figure 2.6 Sketch of the setup for Na+ channe l currents measurement including chamber, voltage clamp and controlling computer, etc. (5) Data acquisition Both stimulation pulse generation and signa l recording are either carried out with a DAQ multifunction system (National Inst ruments PCI6036E) controlled by LabView programs or PClamp software. PCI6036E is low-cost 16-bit DAQ to deliver reliable performance in a wide range of applications. The advantage of this system is to allow researchers to make differe nt LabView programs according to different purposes of experiments with different parameters. PClamp is a commercialized software package for 20

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voltage clamp and patch clamp, which is very easy to use but has a lot of limitations for our research. An example of interface of PClamp software for Na+ channel currents measurement is shown in Fi gure 2.7: top panel is the actual voltages which are delivered on the cell membrane and bottom panel is the actual measured Na+ channel currents using the P/4 method. Figure 2.7 An example of PClamp software interface used in Na+ channel currents measurement with the top figure showing the actual voltages which are delivered on the cell membra ne and the bottom figure. (6) P/4 method When membrane potential is depolarize d, the recorded trans-membrane current generally consists of three major components: (1) Linear leakage current, which is the 21

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22 current that flows through membrane resist ances and membrane capacitances. Ideally, this current scales linearly with the value of depolarization potentia l. (2) Nonlinear gating current, which is the displacement current associated with the movements of gating charges inside of the membrane [38, 39]. (3) Nonlinear, voltage-ac tivated current [1], which is the current that flows through ion cha nnels when channels open due to change in the membrane potential. The channel curren t does not linearly depend on the membrane potential. In order to easily study nonlinear, vol tage-activated current component, it is essential to remove the linear leakage current from the record current (gating current is too small in comparison to the channel current) Briefly, a series of scaled-down replicas (sub-sweep) of the stimulation pulses are applied to the cell membrane prior to or after actual stimulation pulses. Then, the accumulated sub-sweep response current is subtracted from actual stimulation response cu rrent. The remaining current is nonlinear voltage-activated current. This technique is called P/N subtraction, where N is the number of sub-sweeps that each has 1/Nth of the magnitude of main stimulation pulse (usually, N equals to 4, thus called P/4 met hod). An example of P/4 subtraction protocol is shown below. In Figure 2.8, the main stimulation pulse consists of a single depolarizing step function with the magnitude of +40 mV compared to the holding potential of mV. There are four sub-sweeps with 1/4 of this magnitude (+10 mV), executed before the main pulse. Sub-sweeps ar e executed at their own holding level. In this example, the normal holding potential level is mV. It is desirable to execute the sub-sweeps at mV because in this potentia l the ionic channels can not be opened. After the normal holding potential is change d to sub-sweep holding level, the program

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waits a specified setting time at sub-sweep holding level before sending sub-sweeps. After the sub-sweeps are completed, membrane potential returns to the normal holding level (-90 mV) to accomplish the main step pulse function. Figure 2.8 An example of P/4 subtraction prot ocol. The main pulse consists of a single depolarizing step function with a magn itude of +40 mV compared to the holding potential of mV. There are f our sub-sweeps with 1/4 of this magnitude (+10 mV), executed before the main pulse with the holding potential at -110 mV. 23

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-400 -300 -200 -100 0 100 200 300 400 02468101Time (ms)Current (nA)2 Figure 2.9 Measurement of trans-membra ne current without using P/4 method. -500 -400 -300 -200 -100 0 100 200 02468101Time (ms)Current (nA)2 Figure 2.10 Na+ channel current after using P/4 method. 24

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Figure 2.9 and 2.10 show the measured cu rrent before subtraction (without P4 method, Figure 2.9) and the current after the subtraction of sub-sweeps (P/4 method). The remaining current (Figure 2.10) is the nonlinea r voltage-activated cu rrent Na+ channel current. (7) Electric stimulation pulse trains In this experiment, two main stimulati on pulses are used: on e is unidirectional stimulation pulse train with 2000 pulses as Fi gure 2.11 shows. The duration of pulse is 8 ms and the magnitude of each pulse is +50 mV; the other is symmetric stimulation pulse train as Figure 2.12 shows. The reason to use two different trains is mainly because Na+ channel proteins have different behaviors under the influe nce of those two kinds of electric stimulation trains. Figure 2.11 Unidirectional stimulation pulse tr ain consisting of 2000 pulses. The duration of each pulse is 8 ms and the magnitude is +50 mV with the holding potential of -90 mV. 25

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Figure 2.12 Symmetric stimulati on pulse train consisting of 2000 pulses. The duration of each pulse is 8 ms and the magnitude is +/-50 mV with the holding potential of -90 mV. (8) All the experiments are c onducted at room temperature including those explained in the following chapters unless otherwise indicated. Experimental Results When the cell membrane is depolarized, the combination currents, mainly Na+ ions and K+ ions channel currents, can be m easured. The early transient current is carried by Na+ ions and later the persistent current is carried by K+ ions. As mentioned before, TEA can block the later current component which is normally carried by K+ ions without affecting the early Na+ current component. In this experiment, in order to identify voltage-gated Na+ channel current, K+ ions in side the cell are substituted by Cs+ ions to reduce outward K+ current. 3 mM of 3, 4 di minopyridine (DAP), which is another K+ 26

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channel blocker, is added to the external solution (TEA already in the solution). Since the kinetics of Na+ channel current are much fa ster than those of K+ channel current, the remaining small K+ channel current does not affect the accuracy of Na+ channel current measurement. A sequence of 28 stimulating pulses with 8 ms duration holding the membrane potential at a range from 70 mV to -2.5 mV is first applied on the cell membrane (membrane holding potential is -90 mV, which is very close to resting potential in physiological condition). The difference of the potential between two consecutive pulses is 2.5 mV (Figure 2.13). The relaxing time betw een two consecutive pulses is 2 s. The trans-membrane currents responding to each stimulation pulse are recorded. After subtracting the linear leakage current (P/4 method), Na+ channel currents responding to different membrane potentials are plotted in Figure 2.14. Figure 2.13 Diagram of a sequence of 28 stimula ting pulses with the duration of 8 ms and the potentials ranging from -70 mV to -2.5 mV. The increase between two consecutive pulses is 2.5 mV. The re laxing time between two consecutive pulses is 2 s. 27

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Figure 2.14 Na+ channel current s by using P/4 method responding to the pulses shown on Figure 2.13 Figure 2.15 Relationship between peak values of currents corresponding to different membrane potentials (Na+ channel I-V curve). 28

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29 In Figure 2.15, the triangles represent the peak values of each Na+ channel current corresponding to different potent ials from Figure 2.14. The crossing point (channel current equal to zero) of Na+ cha nnel I-V curve with X-axis represents the reversal potential. At this potential, the chemical force due to ionic concentr ation gradient and the electric driving force due to the appl ied membrane potential are balanced to each other, so there is no Na+ channel current at this potential. In our experiments, both external and internal solutions are designed to reduce reversal pot ential, which normally is 60 mV for frog skeletal muscle fiber. The result of reversal pot ential from Figure 2.15 is very close to the estimated number (-15 mV). The slope of Na+ channel I-V curves represents channel conductance. After Na+ channel I-V curve measurement, the membrane potential is changed according to the designed protocol (Figure 2.11), which is a train of unidirectional stimulation pulses. Potentia l and responding trans-membrane current are simultaneously recorded during the whole s timulation period. Using P/4 method, the linear leakage current is removed from the raw data. For each pulse, an increasing percentage of channel proteins remain in the un-conduc tive state (inactivation state or closed state). After 2000 of unidirectional stimulation pul ses, almost all individual channel proteins remain in the un-conductive state. This indica tes that Na+ channel currents can be blocked by electric method (Figure 2.16).

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Figure 2.16 Na+ channel currents of the indexed pulses as 1st, 10th, 20th th, 200th, 2000th under an unidirectional stimulation pulse train. To illustrate the result mo re clearly, Figure 2.16 just s hows some of Na+ channel currents within 2000 pulses (1st, 10th, 20th th, 200th, 2000th). The result indicates Na+ channel currents gradually decease with the increase of pulses, until almost all the channels reach the un-conductiv e state. All Na+ channel cu rrents have the same rising phase, falling phase and peak position. Figure 2.17 shows the relationship between the peak values of each Na+ channel current and the index of the pulse. It is cl ear that, after 2000 pulses Na+ channel currents gradually reach zero (< 5%). 30

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Figure 2.17 Relationship between the peak values of Na+ channel currents and the index of the pulses. Figure 2.18 Na+ channel currents measured under a symmetric stimulation train. The currents do not show distinct effect when 2000 pulses are applied on the cell membrane. 31

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32 We change the stimulation train to a new protocol (Figure 2.12), which is a symmetric pulse train as compared to the previous protocol. The new train has the same positive magnitude (+50 mV relative to -90 mV) and negative magnitude (-50 mV relative to -90 mV) w ith 8 ms pulse duration. Interest ingly, Na+ channel currents do not show distinguishable effects during the pe riod when 2000 pulses are applied on the cell membrane. Figure 2.18 (1st, 10th, 20th th, 200th, 2000th ) shows some of Na+ channel currents during symmetric stimulation train. Other experiments are performed to c onfirm that those phenomena result from Na+ channel function change, not because of the change of local ionic concentration around Na+ channels, which concentration b ecomes lower and lower with continuous flow of Na+ ions into the cel l. We use two different poten tial trains (like Figure 2.11) on the same fiber: one potential is lower than the reversal potentia l (-40 mV) and another potential is higher than the re versal potential (-10 mV). In both experiments, the peak current absolute values (Figure 2.19 and Fi gure 2.20) gradually decease, the results similar to the results that we get before. The crossing points for the same order of two Na+ currents are almost the same in Figure 2.21 (1st, 10th, 20th th, 200th, 2000th). This result proves that the concentrations of Na+ ions inside and outside of the cell are the same as original values no matter how many pulses are applied on the cell membrane. Quick diffusion of Na+ ions in the extern al solution provides e nough ions flow through Na+ channels for each pulse.

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-80 -60 -40 -20 0 20 012345678Time (ms)Na Channel Current (nA) Figure 2.19 Measurements of Na+ channel curre nts by using a unidir ectional stimulation pulse train when this pulse potential is lower than the reversal potential. -20 0 20 40 012345678Time (ms)Na Channel Current (nA) 33 Figure 2.20 Measurements of Na+ channel curre nts by using a unidir ectional stimulation pulse train when this pulse potential is higher than the reversal potential.

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34 -80 -60 -40 -20 0 20 40 -50 -10 0Membrane potential (mV)Na Channel Current (nA)40 -30 -20 Figure 2.21 Lines connecting Na+ current peak values of Figure 2.20 and that of Figure 2.21 cross nearly at the same point. In previous experiments, the duration of pulse potential and the duration of holding potential are both 8 ms. To further illustrate the re lationship between the duration of pulse and the duration of holding potential we finished a series of experiments by using one single fiber with different holding potential time trains. Figure 2.22 shows the stimulation pulse train. We change the durat ion of T for each experiments (T = 4 ms, 10 ms, 20 ms and 200 ms). Figure 2.23 to Figur e 2.26 show the responding results under different holding potential dura tion trains respectively. With the increase of the holding time, it becomes more difficult to force Na+ i on channel proteins to remain in the unconductive states. In those figures, the same selected currents (1st, 10th, 20th th, 200th, 2000th) as before are used.

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Figure 2.22 Sketch of unidirectional stimula tion pulse trains w ith different holding potential durations. -600 -500 -400 -300 -200 -100 0 100 0123456Time (ms)Current (nA) Figure 2.23 Na+ channel currents responding to the holding potential of -90 mV with duration of 4 ms. 35

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-600 -500 -400 -300 -200 -100 0 100 0123456Time (ms)Current (nA) Figure 2.24 Na+ channel currents responding to the holding potential of -90 mV with duration of 10 ms. -600 -500 -400 -300 -200 -100 0 100 012345Time (ms)Current (nA)6 Figure 2.25 Na+ channel currents responding to the holding potential of -90 mV with duration of 20 ms. 36

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-600 -500 -400 -300 -200 -100 0 100 012345Time (ms)Current (nA)6 Figure 2.26 Na+ channel currents responding to the holding potential of -90 mV with duration of 200 ms. Figure 2.27 Relationship between the peak values of Na+ channel currents and the index of pulses. The curves represent hold ing durations of T=4 ms, T=10 ms, T=20 ms and T=200 ms from the top to the bottom. 37

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In Figure 2.27, X-axis represents the index of each pulse. Y-axis represents the peak values of each Na+ channel current. The curves represent a holding duration equal to 4 ms, 10 ms, 20 ms, and 200 ms from the top to the bottom. This result shows that the longer the holding time becomes, the more likel y that Na+ ion channel proteins return to normal configuration before the next pulse. -250 -200 -150 -100 -50 0 50 100 -80-60-40-200 Membrane potential (mV)Na Channel Current (nA) Figure 2.28 Three Na+ channel I-V curves. One is pre-train (triangle), one is 0.5-mslater-of-train (diamond), and one is 2-mi n-later-of-train (circle). This figure proves that the stimulati on pulses can just tempor arily keep Na+ channel proteins in an un-conductive state. Finally, another three Na+ channel IV curve measurements are conducted by applying the same step pulses (Figure 2.13) to the cell membrane before and after 2000 pulse train stimulation. There are two I-V cu rves after the train stimulation with two different relaxation times (0.5ms and 2 min.) The three Na+ channel I-V curves are shown in Figure 2.28. One is pre-train (tria ngle) curve, one is 0.5-ms-later-of-train 38

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39 (diamond) curve and one is 2-min-later-of-train (circle) curve. The 2-min-later-of-train IV curve is almost identical to the pre-train I-V curve, which proves that indeed electric stimulation pulses can just temporarily make the Na+ channels stay in the un-conductive state. Discussion and Modeling There are two possible explan ations for this research results. The first theory is based on the influence between the charge movement and the ball movement. The second theory is based on the gating charges tir edness under the electr ic stimulation pulse train. (1) Under a single pulse (F igure 2.3), Na+ channel prot eins will open due to the gating charge movement, which takes about 1-2 millisecond. After the channels are open, the inactivation balls will move into the m outh of the channels to block Na+ channels automatically and the channels stay in inactive state. Na+ channels inactivation process follows a single exponential decay [48] because only one parameter determines the whole process the balls movement. The time consta nt of this single e xponential curve is the mean time for balls to move from resting positions to inactive positions, which is within millisecond range. Figure 2.29 shows the result tw o curves fit as expected (one is data from Na+ channel current measurement; one is a single exponential fitting curve). The time constant is about 0.5 ms in this measur ement. One important th ing to point out is that there is a delay betw een the charge movement ( opening door) and the balls movement (inactivation), so those two even ts are hard to influence each other.

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-700 -600 -500 -400 -300 -200 -100 0 100 012345Time (ms)Na Channel Current (nA)6 Figure 2.29 Two curves fitting, with one being the real data from Na+ channel currents measurement and the other is the fitting data of single exponential decay. When the cell membrane potential retu rns to the normal holding potential, Na+ channel deactivates and the balls will exit fr om the internal mouths of channels to the resting positions and the gating charges will m ove back to the closing positions at the same time. Will the balls movement still fit the same single exponential decay curve with the same time constant? Now the two movements will influence each other because in this condition there is no delay between the charges movement and the balls movement. The balls movement may not fo llow the same single exponential curve when leaving the inactive positions. Just like the ch arges movement current, on and off are not the same curves, despite the total ga ting charges, Q (on) is equal to the total 40

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41 gating charges, Q (off) [39]. The open door char ges movement curve is totally different from the closed door charges movement curve [39]. Because there is no direct way to meas ure the curve of refractory period, an indirect method is applied. We use two c onsecutive pulses (conditioning depolarization) on the cell membrane to measure channel cu rrents. When conditioning depolarization is applied, after first pulse most of channels stay in inact ivated state, and membrane potential must return to normal (-90 mV) or negative value (<-90 mV) to restore their ability to conduct again. We use variable intervals be tween those two pulses. Na+ channel current measured from the second pulse indicates the percentage of channels that can still conduct or the percent of balls that still stay in the mouths of Na+ channel proteins. The recovery result shows that if the restore vo ltage is negative (Figure 2.30 Left), it is a very fast recovery process compared to the recovery using the holding potential (Figure 2.30 Right). From this resu lt, we can explain why the symmetric pulse train just has a little effect or no eff ect on Na+ channel protein functions. For unidirectional pulse train, the recovery time is relatively longer. When continual unidirectional pulse train is a pplied on the cell membrane, afte r the first pulse, some balls leave the mouths of the channels. When the se cond pulse arrives, some balls are still in the inaction positions, which results in the s econd Na+ channel current smaller than the first channel current. The same situation occu rs on the third, fourth, fifth currents, so on and so forth until finally almost all channels stay in un-conductive state. The process involves two exponential curves : one is the movement of charges and the other is the movement of balls (as we mentioned before, charges movement and balls movement have different time constant). Figure 2.32 shows the sum of two exponential

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curves matching the experimental data, a fit ting result much better than that in Figure 2.31 (a single exponential current fitting). Two time constants from Figure 2.32 have a difference of one order (Figure 2.32). 0 0.2 0.4 0.6 0.8 1 1.2 012345678910Time (ms)Recovery Figure 2.30 The recovery times after channels are opened. When the restore voltage is negative (left side) compared to the holding potential (right side), the recovery process is faster than that using the holding potential. 42

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Figure 2.31 Single exponential cu rve fit experimental data. Figure 2.32 Double exponential curv es fit experimental data. 43

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44 (2) The second possible theory to explai n this result is the immobilization and mobilization of the gating char ges. We know for each pulse the gating charges (mobilized part) will physically move from the inside of the membrane to the outside of the membrane to control Na+ channels opening and closing. In Armstrong and Bezanillas paper [47], they point out that there are two kinds of charge groups existing on the cell membrane. (1) The charge that is mobilized in inactivation process forming the fast component which is presumably related to th e gating activation process. (2) The charge that is immobilized in inactivation pro cess forming the major part of the slow component. If before the full recovery of the charges movement from the opening position to the closing position, the second pul se is applied on the membra ne, resulting in part of mobilized charges becoming immobilized. The same occurrence appears for subsequent pulses. As a result, less and less Na+ channe l proteins can conduct with the increase of the number of pulses. Under the train stimulation, most of the charges are immobilized temporarily. We call it tiredness of gating char ge. In the same paper [47], th e authors also point out if the holding potential returned to the negative potential, it is easy to detect that the mobilized charges go back to the initial posit ion. This is why it is hard to block Na+ channels under symmetric oscillation train st imulation. Because the movement of charges controls the door behaviors, the tiredness of gating charges means the door will not conduct any ions under a continual pulse trai n. This explanation just deals with the charge movement under the influence of elect ric field rather than the ball movement.

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45 Conclusion Na+ channels are trans-membrane proteins that allow Na+ ions flow in or out of cell due to different membrane potential. In our present work, we observe some extraordinary behaviors (un-c onductive state) of voltage-gated Na+ channel proteins, which show that unidirectional electric s timulation pulses can temporarily close Na+ channels.

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46 Chapter 3 Inactivation of Voltage-Gated Del ayed Rectifier K+ Channel by Oscillation Electric Field Introduction The voltage-gated K+ channel has different mechanisms of activation and inactivation from those of the Na+ channel because of the differe nt configuration of protein structure [51, 52]. Several K+ channel genes have been cloned and sequenced [52, 53, 54, 55]. The different amino acid sequencing of different K+ channels can explain the differences in behaviors (i.e. kinetics) of these K+ channels. Voltage-gated K+ channels [52] comprise of a family of at least 50 different isoforms ranging from delayed rectifier [53] (slow activation, very slow inactivation) to A-type K+ channel [54] (fast activation, fast inactivation). In this chapter we will focus on voltage-gated delayed rectifier K+ channel proteins [55] behavior s under the influence of osci llating electric field (all K+ channels below are considered voltage-ga ted delayed rectifier K+ channels unless otherwise indicated). Like the Na+ ion channel, the K+ ion ch annel also consists of four homologous domains, each of which has six membrane spanning regions and some of those regions have been identified with sp ecific channel functions [60] Four domains form a pore through which K+ ions can permeate across th e cell membrane. K+ channel protein is also tetrameric symmetry like Na+ channe l protein. Thus the subunits are arranged

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47 around a central four-fold axis th at is coincident with the ax is of the central pore [60]. The extra-cellular mouth leads into a narrow selectivity filter. Beyond this there is a central water-filled cav ity that can accommodate a single K+ ion. There is then a narrow hydrophobic region, which forms the main channel gate [60, 63]. The region of amino acid sequence associated with the selectivity filter is highly conserved between different K+ channels. All K+ channels are thought to share the same main structure. They are different in presence/absence of additional helices, non-membrane domains or subunits that control their gating behaviors. The structure of K+ channel main domain is revealed by x-ray diffraction studies of a b acterial K+ channel, KcsA [62]. Each segment 4 (S4) contains a sequence of 5 to 8 positively charged amino acids. Experimental evidences [50, 61] prove that this region is invol ved in sensing the membrane potential and therefore controlli ng channel opening and closing. When any of four S4 segments still stays in resting position (inside the membrane), the pathway for K+ ion conduction is still blocked. The only way to make K+ channel conductive is to move out all the four S4 segments toward outsid e of the membrane. In the resting potential, most of time S4 segments are in resting position (closing door) and very infrequently all four S4 segments may be, for a brief period of time, in active position due to a thermal effect which produces a brief ionic current through the K+ channel. If the membrane potential is suddenly depolarize d, there is a period of time before all four S4 segments move into active position (opening door); this will produce an initial delay in the opening of the channel. K+ ions always flow from high concentration region (inside cell) to low concentration region (outside cell). The K+ channel usually will function till the

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48 membrane potential falls back to the resting pot ential. This is why people call this kind of K+ channel voltage-gated dela yed rectifier K+ channel. One of the common properties of voltage -gated channels is their ability to inactivate in response to the membrane potential depolarization. Two general mechanisms of inactivation have been characterized. The first mechanism is usually characterized by relatively fast inactivati on during a sustained membrane potential depolarization, effected at molecular level by th e ball. Molecular mechanisms of this type of inactivation, called N-type in activation [64, 65, 66], have been studied in detail in Na+ and K+ channels. The ball part responsible for th is type of inactivation is localized at the cytoplasmic side of channel. For example, in Shaker K+ channel, the N-terminal region of the channel plays the role of the ball, which occludes the inner pa rt of the pore after channel activation and thus closes the channel. This kind of inactivation mechanism includes Na+ channels discussed in chapter tw o. The second type of inactivation process, usually with significantly slow er kinetics, has been observed in a number of channels. This type of inactivation is called C-type [67, 68, 69] or slow inactivation. Although the detailed mechanisms of slow inactivation processes are incomple tely understood, there exist two explanations: one is th e rearrangement of the pore; th e other involves relatively localized charges in conformation of the residues near the external mouth of the permeation pathway, rather than motion of a region (the ball) of the channel. Most commonly, membrane depolarization opens these channels and closes automatically very long time later. Voltage-gated delayed rect ifier K+ channel belongs to this group. Researchers thought at first that this kind of voltage-gated K+ channel did not have the inactive process, but later found out it does, but just very slow inactivation process.

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49 Methods and Materials (1) Skeletal muscle fiber pr eparation (see chapter two) (2) Solutions (Unit mM): Normal Ringer: (see chapter two) Relaxing Solution: (see chapter two) External Solution: 120 NaCl 4.25 KCl 2.15 Na2HPO4 0.85 NaH2SO4 1.8 CaCl2 1.5 RbCl2 1.5 BaCl Internal Solution: 45.5 K-glutamate 5 PIPES 20 EGTA 6.8 MgSO4 5.5 Na2-ATP 20 Tris-Creatine Phosphate 5 Gluocse (3) Voltage clamp (see chapter two) (4) Data acquisition (see chapter two) (5) Electric stimulation pulses

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Figure 3.1 shows the unidirectional stimulation train which includes 200 pulses. All pulses have same magnitude (-10 mV ) and duration (10 ms). The symmetric stimulation pulse train with 200 pulses (like Figure 2.13 in chapter two) has a magnitude of -10 mV/-170 mV (holding poten tial is -90 mV as usual) and pulse duration of 10 ms. Figure 3.1 A stimulation train includes 200 pulses. All pulses have the same magnitude (10 mV) and duration (10 ms). Experimental Results First, a sequence of 28 stimulation pulses with 25 ms duration holding membrane potential at a range from -70 mV to 14 mV is applied on the cell membrane. The increasing potential of two consecutive pulses is 2 mV (Figure 3.2). The relaxation time between two successive pulses is 10 s, which as sures that the fiber can relax back to the initial condition before next pulse. The tran s-membrane currents responding to each 50

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stimulating pulses are recorded. After subtracting the linear cu rrents, K+ channel currents corresponding to different potentials are plotte d in Figure 3.3. It shows the main characteristic of the so-called delayed rectifier K+ channel, which is that the channel needs about 10-15 ms to complete opening processes, and all currents are outward currents with unobservable inactivation. So unl ike Na+ channel current measurement, the duration of stimulation pulse for K+ channel currents measurement is relatively longer, which permits K+ ions currents to reach saturation state (Figure 3.2). Figure 3.2 A sequence of 28 stimulation pulses with a 25 ms duration with the membrane potential changing from -70 mV to -14 mV is applied on the cell membrane to measure K+ ion channel currents. 51

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Figure 3.3 K+ channel currents corresponding to different membrane potentials. It shows the major characteristic of the so-called delayed rectifier K+ channel, which is that the channel needs about 10-15 ms to complete the opening process, and all currents are outward currents with unobservable inactiv ation process. The values of K+ channel saturation cu rrents are plotted as a function of the membrane potentials (shown on Figure 3.4) The triangles represent K+ channel saturation currents and the solid line is a fitting straight line for last ten data points. The line slope represents channel conductance a nd the crossing point with X-axis is the theoretical turning point, the open-door threshold. When the membrane potential is higher than this threshold, (t here is not a real threshold in K+ channels due to thermal effect) theoretically K+ channel conductivity is constant just like a normal resistor. In this experiment, the conductance of this K+ channel is about 6.7 uS. When the channel is opened, K+ ions are transported from the high electrochemical potential side to the low 52

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electrochemical potential side and channel currents depend on membrane potential and concentration of ions (this is why it is a st raight fitting line on K+ channel I-V curve). Below this threshold, there is still a small amount of K+ currents. Due to the thermal effect, there is still a small probability that K+ channel can open no matter what the cell membrane potential is. Figure 3.4 K+ channel saturati on currents are plotted as a function of the membrane potentials. A fitting straight line is plotted also. The line slope represents the channel conductance, and the crossing poi nt with the X-axis is the theoretical turning point, K+ channe l open door threshold. 53 After measuring the K+ ch annel I-V curve, the stimul ation train (Figure 3.1) is delivered on the cell membrane by using a La bView program. Two signals of voltage and current are recorded and shown in Figure 3.5 and Figure 3.6. Figure 3.5 shows the real

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voltage signal that is applied on the cell me mbrane during experiment, which has a very good comparison to Figure 3.1 except the ed ge. Figure 3.6 shows K+ channel current signal. It is clear that K+ currents decrease with the number of pulses increased. Both figures just show part of the whol e stimulation train (First 1000 ms). Figure 3.5 Measured voltage si gnal that is applied on the cell membrane during the experiment (The first 1000 ms), which is similar to the designed potential. By cutting the long current signal an d putting all pieces together, Figure 3.7 shows the same result as Figure 3.6 but with a different view. It shows clearly the decrease of K+ channel currents with an increase of the number of pulses. Figure 3.8 demonstrates the relationship between num ber of pulses and the corresponding K+ currents. After 200 pulses, there is still 18% K+ current remaining in this experiment. 54

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Figure 3.6 Recorded K+ channel current (The first 1000 ms). Figure 3.7 Recorded K+ channel current (all 200 pulses) viewed from another perspective compared to Figure 3.6. 55

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Figure 3.8 Demonstration of the relationshi p between the number of pulses and K+ channel saturation currents under each pulse. If an electric field indeed can inactivat e K+ channel proteins, experiment results should be independent to the intracellular c oncentration of K+ ions. We performed other experiments to confirm this assumption. Th ree internal solutions with 20, 40, 70 mM concentration of K+ ions are used separately in three fibers with the same experiment procedures. The measured K+ channel curr ents are shown in Figure 3.9. The top curve represents K+ ions concentration of 70mM inside of the cell, the middle curve 40 mM and the bottom curve 20 mM. These three curv es have similar characteristics with different absolute values. Figure 3.10 shows th at the three curves match each other after normalization, which indicates the independent inactivation mechanism of K+ channel proteins by electric stimulation. 56

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Figure 3.9 Three different internal solutions with 20, 40, 70 mM concentrations of K+ ions are used in three fibers through the same experiment procedures. The top curve represents a K+ ions concentration of 70 mM, the middle 40 mM and the bottom 20 mM, respectively. Figure 3.10 Three curves (Figure 3.9) closel y match each other after normalization. 57

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In Figure 3.8, there is still 18% K+ curre nt left behind after K+ channel currents reach saturation state after 200 pulses. By us ing different magnitude and duration trains to re-accomplish this experiment, the lowest remaining K+ current is about 8%, which is still higher than Na+ channel curr ent by electric stimulation train. The last step of this experiment is to change the resting po tential duration. The result is just like what we expected that when resting time is longer, more channel proteins can return back to the initial position and more K+ channel proteins can conduct in second pulse. This result is similar to Na+ channel experiments. Figure 3.11 shows the same muscle fiber experiment result, with top curve having double resting time compared to the bottom curve. 0 100 200 300 400 0 50 100 150 200Number of PulsesK Channel Current (nA) ) Figure 3.11 K+ channel currents measurement (same muscle fiber) under two electric stimulation trains, with the top curv e having twice resting time than the bottom curve. 58

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59 The symmetric stimulation pulse trai n (like Figure 2.13, chapter two) with magnitudes of -10 mV/-170 mV and duration of 10 ms is applied to the muscle fiber after unidirectional stimulation pulse train (Fi gure 3.1). There is no difference between symmetric train and unidirectional train expe riment results which are totally different from Na+ channel inactivation experiments. For Na+ channel inactivation, the restoration potential is very important for the balls to re turn from the inactive position to the resting position. Because there are no balls existing on the K+ channel protein structure, so the two experiments (symmetric and unidirec tional trains) have similar results. Discussion and Modeling The central event of K+ channel opening is the movement of S4 trans-membrane segments which carry numerous positive charged residues [61]. This process is energetically favored to the depolarizing memb rane potential, but how this S4 segments movement is actually coupled with the opening of the pore is still unclear. However, we do know that when all of the four S4 segments physically move to the opening configuration, the K+ channel is co nductive with an initial delay. C-type inactivation is present in many voltage-gated K+ channels and probably related to slowing inactivation in Ca+2 channels also. Thus, C-type inactivation is a general gating mechanism with application to a broad number of channels. For a long time, researchers thought that there were no automatic inactivation processes in voltagegated delayed rectifier K+ cha nnels, but later found out that there is an inactivation but with a very long time-constant [68, 71, 73] Under membrane-poten tial depolarization,

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60 the external mouth of channels is slowly occluded which process involves conformational change between the four domains and has a relatively long time-constant. Many details of the basic ch annel electrical activities re sulted from a series of experiments in the early 1950's, which led to the award of the Nobel Prize to English physiologists A. L. Hodgkin and A. F. Huxl ey who applied Ohms law to ionic channel current [70]: I k= g k n4 (V-V k) I Na= g Na m3 h (V-V Na) where I Na and I k are Na+ and K+ ion channel currents, g Na and g k are constant. V is the membrane potential, V Na and V k are the Na+ and K+ equilibrium potential, and m, n, and h are voltage-dependent parameters. The n parameter for K+ channels is similar to the m parameter for Na+ channels (activation parameters); both increase with the increase of the potential. The h parame ter in Na+ channels decreases with the increase of the potential which represents th e inactivation part. For K+ channels, there is no h parameter to represen t the inactivation. So modifi cation of the H-H model is necessary to explain the auto matic inactivation of K+ channels with a very long timeconstant. Some new theories [67, 71] have devel oped to explain the Ctype inactivation by modifying the H-H model. In Gerald Hrenstei n and Daniel L. Gilb erts paper [71], the authors referred to a new parameter k to correspond with K+ channel inactivation parameter and proposed that the H-H equati on for K+ channels can be modified to

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I k= g k n4 k (V-V k) where k is a voltage-dependent parameter. If this modification is correct, the inactivation should follow a single exponentia l decay, but Figure 3.12 does not show the expected result. This result suggests someth ing other than a single voltage-dependent first-order transition between open and inactive states of the K+ channel. 0 100 200 300 400 500 0 50 100 150 200Number of PulsesK Channel Current (nA) ) Figure 3.12 Inactivation curve is fitte d to a single exponential decay. Recently, researchers found out that the in activation kinetics of K+ channels were approximated by the sum of two exponential co mponents [67, 71, 72] with fast and slow time constants. In our experiments, the outwa rd K+ currents for each pulse decrease in magnitude as a result of the accelerated inac tivation of K+ channels. Inactivation curves 61

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from experiments can be approximated by th e sum of two exponentia l decays with time constants differing by almost an order of magnitude (Figure 3.13). 0 100 200 300 400 500 0 50 100 150 200Number of PulsesK Channel Current (nA) ) Figure 3.13 Inactivation curve can be approxi mated by the sum of two exponential decay curves with time constants differing by almost an order. A simple explanation of this behavior is that two voltage-d ependent inactivation processes occurred during the train stimula tion. A specific case would be that the two inactivation processes are taken to be separate processes for inactivation of either closed or open channels. The rate of inactivation depends upon the state of the channels. The closed channels have a higher probability of inactivation dur ing a voltage step than the open channels. After the first pulse of th e train stimulation, the membrane potential returns to the normal holdi ng potential. Most channels go back to the closing configuration, but a small pe rcentage of channels woul d stay in the un-conductive 62

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63 configuration. The same situation occurs on the third, fourth, fifth currents, so on and so forth until almost all channels stay in un-conductive state. Finally, the pathway for K+ ions conduction is almost blocked, which m eans that the stimulation train forces individual proteins to stay in un-conductive configurati on temporarily. However, which two parts of the protein inactivate the channels (there is no ball on the protein structure) and why the channels can not be inactivated 100% are still unknown. Conclusion Voltage-gated delayed rec tifier K+ channel plays a fundamental role in the excitability of the cell membrane. The channel opens upon depol arization of the membrane potential and closes in a relatively long time. We studied the relationship between electric field and inactivation of K+ channels, which shows that K+ channel proteins can be inactivated by el ectric field. Another feature of this inactivation is that the inactivation curve can be ch aracterized by the sum of tw o exponential decay curves. These results could help us better un derstand the underlying mechanism of the inactivation of K+ channel proteins.

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64 Chapter 4 Synchronization of Na/K Pump Molecules by Oscillation Electric Train Introduction Discovered by J. C. Skou in microsome of crab nerve a half century ago, the Na/K pump protein represents the fi rst enzymatic transport system [74] in nature which is essential for living creatures and is expressed virtually in all cell membranes [9, 10, 89, 97]. The Na/K pump protein is more like a precise complex mach ine which never stops working [80]. It uses a lot of energy in the form of ATP and brings various products. For example, for a resting human being, Na /K pump proteins c onsume 20% of ATP to actively transport Na+ out and K+ into the cell [105]. In nerv e cells, approximately 70% of ATP is consumed to fuel Na/K pu mps [75]. Ionic transport conducted by the Na/K pumps create both elec trical and chemical gradie nts across the cell membrane which are critical to maintain the membrane resting potential, cell volume, and secondary active transport of other solutes, etc. [1, 76, 91]. The steady-state binding method has been us ed to determine the density of Na/K pump proteins on different cell membranes, assuming that one molecule of Ouabain binds to one Na/K pump site [1, 77, 78, 79]. It is estimated that pump densities, in unit of pump sites/um2, are 500-5000 in nerves and muscle ce lls, much higher in kidney tubular

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65 cells and heart cells [1], but less than 1 in erythrocyte membranes [1]. Na/K pump proteins may be distributed fairly evenly, or clustered in certain membrane domains. The Na/K pump protein is the largest pr otein complex in the family of P-type cation pumps [82]. The minimum functional units are alpha ( ) and beta ( ) subunits. Currently, four -subunits and three -subunits of Na/K pump protein have been identified in mammal cells [83]. The subunits combine to form Na/K pumps that are expressed in either a tissueor a cell-specific manner. The bigger subunit (~113 kDa glycoprotein) is the action pa rt it binds ATP and both Na+ and K+ ions. The smaller subunit (~35 kDa glycoprotein) is necessa ry to activate the complex [83]. The subunit is also the receptor for cardiac glycosides su ch as digitalis and Ouabain [18, 22]. Binding these widely-used drugs to Na/K pumps inhibits the pumps activity. The Na/K pump mechanism is highly as ymmetric [1, 9, 10]. It is activated by intracellular presence of Na+ ions, Mg+2 ions, and ATP and by ex tra-cellular presence of K+ ions [88]. Normally, a single pump cycle involves hydrolysis of one molecule of ATP to one molecule of ADP and one molecule of phosphate, extrusion of three molecules of Na+ ions and uptake of two molecules of K+ ions, a simple relationship of 1:2:3. (ATP : K+ : Na+) [8]. Na/K pump is also an electrogenic [86, 87, 90, 98] protein because during a single pump cycle, it transports 3 Na+ and 2 K+ ions in the opposite directions across the cell membrane, resulting in a net positive charge across the cell membrane. Traditionally, Na/K pump current measurem ent is a summation of individual pump currents by a step function. This pump current is a net outward current without inward component.

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66 Studies show that the average of Na /K pumps turnover ra te at physiological condition is around 30-100 Hz (at neutral pH and room temperature) [84, 85]. Turnover rates are determined by the membrane pot ential and changed when the membrane potential is altered. Because most pump molecules work on or around the mean turnover rate and some work very fast while some work very slowly, the turnover rates of pump molecules on a cell membrane should have a bell-shape distribution, which depends on temperature, voltage and ionic concentra tion [106]. The turning phase of each Na/K pump molecule is random and should be uniform under normal conditions. As we mentioned before, Na/K pump pr oteins movement can be explained by a relatively simple chemical cycle that includes several steps: binding of ions, conformational change, and releas e of ions on other side of the cell, etc. The key toward understanding how the enzyme is regulated at the molecular level is to find out the ratelimiting steps of its complex reaction cycle. In each cycle, there are two steps that are rate-limiting steps: Na+ ions are exposed to the outside, and K+ ions are released in the cytoplasm [1, 8, 9]. In order to influence overall activity of the enzyme, the changing time of these steps is the key. Due to the opposit e transports of Na+ ions and K+ ions in the cycle, Na/K pump goes through two i nverse voltage dependence processes. The electric field will favor one ionic movement and prevent the other [89, 122], so we can not accelerate two steps simultaneously by depolarization or hyper-polarization of the cell membrane. In this chapter, we use an oscillating electric field to change pumpprotein activities. Under we ll designed electric field, both rate-limiting steps are accelerated, and the pump function is increased significantly.

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67 Methods and Materials (1) Skeletal muscle fiber preparation (see chapter two) (2) Solutions (Unit mM): Normal Ringer: (see chapter two) Relaxing Solution: (see chapter two) External Solution: 15 NaCl 5.4 KCl 87.6 TEA.Cl 2.15 Na2HPO4 0.85 NaH2SO4 1.8 CaCl2 1.5 RbCl2 1.5 BaCl 3, 4 DAP Internal Solution: 20 Na-glutamate 33.5 K-glutamate 5 Cs2-PIPES 20 Cs2-EGTA 6.8 MgSO4 5.5 Tris-ATP 20 Tris-Creatine Phosphate (3) Voltage clamp (see chapter two) (4) Electric stimulation pulses

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Figure 4.1 A step function is used to m easure Na/K pump current. The membrane potential jumps to -30 mV with a duration of 30 ms. Figure 4.2 A sequence of 15 stimulating pulses with 10 ms duration holding the membrane potentials from -120 mV to +20 mV. The time difference between two continuant pulses is 1 min. 68

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69 Figure 4.1 shows a step function. The memb rane potential jumps from -90 mV to -30 mV with 30 ms pulse duration. A step func tion is a typical function for the traditional measurement of Na/K pump current. Figure 4.2 shows pulses which are used to measure the Na/K pump I-V curve. The duration of each pulse is 10 ms; the step between two pulses is +10 mV; the potential changes from -120 mV to +20 mV; and the time difference between two con tinuant pulses is 30s. (5) Pump current measurement Through voltage clamp, the measured cu rrents include line ar and non-linear currents. The linear currents are first subtracted by P/4 method from all currents. Then, the nonlinear currents (includi ng Na/K pump current) in th e presence of Ouabain are subtracted from currents in absence of Ou abain. This way, other non-linear currents including charge movement currents are e liminated. The remaining current is Ouabainsensitive current, or Na/K pump current. (6) Electric stimulation train Figure 4.3 shows the stimulation pulse tr ain including a 100 pre-pulse followed by three data acquisition pulses (the current responding to the last three pu lses is recorded; we call those three pulses th e data acquisition pulses). A ll the pulses have the same magnitude (-30 mV/-150 mV) and duration (12 ms). These two potentials are symmetric relative to the membrane holdi ng potential (-90 mV). The pulses train is generated either by LabView or PClamp software program.

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Figure 4.3 A stimulation electric train which includes a 100 pre-pulses followed by three data acquisition pulses, with all pulse s having equal magnitudes and durations. The positive pulse potential is -30 mV, and the negative pulse potential is -150 mV, which are symmetric to the memb rane holding potential of -90 mV. The duration of each pulse is 12 ms. (7) Protocol The protocol of this experiment is as follows: data acquisition pulses (3 pulses) are first applied on the cell membrane as a control experiment (T0_C). Then, a stimulation pulse train (Fi gure 4.3) is applied on the cell membrane to examine oscillating-potential effects (T100_C) on Na/K pump functions. After that, the external solution is changed to the same external solution with 1 mM Ouabain to inhibit Na/K pump current. This is a vital step in the w hole experiment, which requires that the fiber must be maintained in the same conditions be fore and after the change of the external solution. The holding current is a good criteri on to inspect the success of this process, 70

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71 which must stay at the same value after the change of the external solution. Ten to twenty minutes later, which is the time for Ouabain to block Na/K pump proteins, the same two stimulations data-acquisition pulses and stimul ation pulses train are applied to the cell membrane again. The obtained currents ar e named T0_O and T100_O, respectively. The traditional measurement of Na/K pump curre nts equals T0_C minus T0_O and the electric-field-influen ce pump current equals T100_C minus T100_O. Experimental Results Figure 4.4 shows the Ouabain-sensitive cu rrent (Na/K pump current) elicited by a single 30 ms step pulse depolarizing the memb rane potential to -30 mV (Figure 4.1). The Na/K pump current shows only an outward current. The transient current peaks in response to the rising and falling phases of the pulse which are also shown in later figures are due to imperfect matc hing in P/4 subtraction.

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-30 -20 -10 0 10 20 30 02 04 06 08 01Time (ms)Current (nA)0 0 Figure 4.4 A Na/K pump current elicited by a single 30 ms step pulse depolarizing the membrane potential to -30 mV (Figure 4.1). Na/K pump current shows only an outward current component. A sequence of 15 stimulating pulses w ith 10 ms duration and holding membrane potential at a range from -120 mV to + 20 mV (Figure 4.2) is applied on the cell membrane to measure Na/K pump I-V curve. The trans-membrane current responding to each stimulation pulse is recorded. Then the external solution is changed to the same external solution with 1 mM Ouabain to inhibit Na/K pump current and the same sequences are used again. After subtracting linear currents (P/4 method) and non-linear currents (w/o Ouabain), Na/K pump currents responding to different potentials are plotted in Figure 4.5, which is typical sigmoid curve [97, 107, 109]. We have to stress two points on this I-V curve: (1) A positive slope is f ound between -80 mV and 0 mV; there is a less steep slope at potential smaller than -100 mV and a negative slope when the membrane 72

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potential is bigger than 0 mV. (2) Because the holding potential equals -90 mV, in this potential, pump proteins can still work (the pum p currents absolute value is not equal to zero at this potential). According to calcu lation, the Na/K pump should work when the potential is bigger than -300 mV [89, 121], which is much lo wer than the resting potential in physiological condition (-90 mV). Because of this, the negative currents are relative values to the pump current when the membrane potential is held at -90 mV (the negative currents are not inward currents). Figure 4.5 Na/K pump currents responding to different membrane potential pulses. After the measurement of the Na/K pump I-V curve, we use a stimulation train (Figure 4.3) to influence Na/K pump proteins and measure new pump currents. The two pump currents in Figure 4.6 (without the trai n stimulation) and Figur e 4.7 (with the train stimulation), both result from the difference between the current without Ouabain inside and the current after changing the external so lution with Ouabain inside. In other words, 73

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Figure 4.6 is the result of the pump current generated by T0_C minus T0_ O; and Figure 4.7 is the result of the pump curre nt generated by T100_C minus T100_O. Figure 4.6 A pump current generated by current T0_C (without Ouabain) minus current of T0_ O (with Ouabain), which is th e traditional method to measure Na/K pump currents. 74

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Figure 4.7 A pump current resulted from the difference between two data acquisition pulses with pre-train pulses (T100_C minus T100_O), which indicates the influence of the external elec tric field on pump proteins. After a train of stimulation, Na/K pump currents (Figure 4.7) become significantly different from t hose without the train of s timulation (Figure 4.6). This indicates the functional change of Na/K pump proteins by electric stimulation. First, Figure 4.6 shows that the pump currents are unidirectional outward current which responds largely to the positive parts of the pulses, and whose response to the negative parts is minimal and can be neglected. Fi gure 4.7 shows that the pump currents respond to data acquisition pulses w ith relatively big positive and negative components. Second, the outward currents in Figure 4.7 are rela tively 2-3 times higher than the outward currents shown in Figure 4.6. Third, the ratio of the outward currents over the inward currents in Figure 4.7 is close to 3: 2, whic h is the stoichiometric number of the Na/K 75

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pump protein. The electric stim ulation train can separate the outward and inward current components, which makes it very easy to m easure the stoichiometric number of Na/K pump. Traditionally, researchers have to measure radioactive-ion c oncentrations to get this number [8] which is a very different process. Through our ne w method, it is easy to verify this number. The separation is a st rong sign of synchronization of Na/K pump proteins: in positive half pulses, all pumps extrude Na+ ions out of the cell, and in negative half pulses, all pumps upt ake K+ ions into the cell. Figure 4.8 Pump currents elicited by the firs t 20 synchronization pul ses. Initially, the inward pump currents responding to the ne gative half-pulse are very small. After a few oscillating pulses, the inward currents start to be distinguishable and increase with the number of pulses. Both inward and outward pump currents become larger and larger. 76

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Figure 4.9 Pump currents elicited by the last 20 synchronization pulses become saturated and the magnitude ratio between the outwa rd and the inward pump currents is close 3:2. Figure 4.8 and Figure 4.9 show another view of the changes of pump currents in response to the synchronization pulse train. The pump currents shown in Figure 4.8 are elicited by the first 20 synchronization pulse s, while those shown in Figure 4.9 are elicited by the last 20 pulses. Clearly, as th e number of oscillating pulses increase, the magnitudes of pump currents increase signifi cantly. Initially (Figure 4.8), the inward pump currents responding to the negative ha lf-pulse are very small. After a few oscillating pulses, the inward currents start to be distinguishable a nd increase with the number of pulses, and both inward and outwa rd pump currents become larger and larger. 77

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Figure 4.9 shows that pump currents become saturated after 100 oscillating pulses, showing 3:2 ratio of outward pump cu rrents over inward pump currents. A certain number of oscillating electric pulses is necessary to synchronize Na/K pump molecules and reach the saturated st ate. Figure 4.10 shows outward currents as a function of a number of trai n pulses. During the period of 100 pulses, the outward current reaches a saturation state, which indicates that 100 pulses are needed to synchronize Na/K pump molecules with oscillating membrane potentials from 30 mV to -150 mV and 10 ms duration. Similar resu lts are received for several di fferent pulse potentials and durations as well. Figure 4.10 Outward pump currents as a func tion of a number of train pulses, which indicates that 100 pulses ar e needed to synchronize pump molecules with an oscillating memb rane potential from 30 mV to 150 mV and 10 ms duration. 78

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79 It is necessary to point out that a10 ms duration for both positive and negative pulses is very close to the average physiological turnover rate [84, 85]. To understand the dependence of the pump currents on the fre quency of pulses, different train pulse durations have been studied. We apply a different duration of pulses from 2 ms to 25 ms with the same magnitude to the same fiber using the same process mentioned before. The outward parts of the pump currents are plotted as a function of pulse dur ations or electric field frequencies (Figure 4.11). When the pulse duration is 10 ms (frequency is 50 Hz), close to the physiological turnov er rate, the oscillation train has the highest effect. When oscillating frequencies are much different from the physiological frequency, less effect is observed on the Na/K pump currents. This experiment shows the dependence of the synchronization effect on electr ic field frequency. Pump mo lecules whose turnover rates are the same as or close to the electric-fiel d frequency can be eventually synchronized. Pump molecules with a turnover rate beyond this range are not easily synchronized. If the oscillating electric field fre quency is too high or too low, a small number of pump proteins is synchronized in comparison to the frequency close to the physiological turnover rate.

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Figure 4.11 Outward parts of Na/K pump cu rrents are plotted as a function of the stimulation train pulse durations. There is an underlying dist ribution of the turnover rate s of Na/K pump molecules within the membrane in physiological condi tion; however, the char acteristic of the distribution is unknown. Our results imply that th e turnover rate of th e pump molecules is distributed as a bell-shaped curve with a la rge amount of pump mo lecules close to the center the physiological turnov er rate; and only a small am ount of pump molecules are pumping vary fast or very slowly. Chen s paper [106] give s us a reasonable understanding of the distribu tion of pump molecules pum ping rates, which depend on temperature, voltage an d ionic concentration. To further prove that we have sync hronized Na/K pump molecules, we did several other experiments. In the first experiment, after 100 pulses with duration 6 ms are applied on the cell membrane, the membrane potential still held on mV for 50 ms 80

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before return to the holding potential (Figure 4.12). Without the oscillating field, pump molecules should change from their synchroni zed state to a random state after the last pulse of the train. The pump current should go back to zero even when membrane potential is still held at 150 mV. Figure 4.13 shows that af ter 3 data acquisition pulses, without stimulation pulses, Na/K pump current drops to zero as expected. This decay in the inward pump current signifi es that pump molecules return to a random pumping pace. Figure 4.12 New stimulation protoc ol: a 100-pulse train with a duration of 6 ms followed by a membrane potential of mV for a nother 50 ms before return to -90 mV. 81

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Figure 4.13 After 3 data acquisition pulses, without stimulation pulses, Na/K pump current drops to zero during 6 ms. Figure 4.14 Stimulation train is the same as that in Figure 4.12 except that the duration is 12 ms instead of 6 ms. 82

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83 Figure 4.13 clearly demonstrates that there is a time pe riod in maintenance of the inward pump current after cessation of the os cillation on the membrane, which is almost equal to pulse duration (6 ms, point out with an arrow in Figure 4.13). If the electric field has synchronized pump molecules, the time to keep inward current before decay should be exactly the same as the pulse duration of the synchronization train (half-cycle of synchronized pumping loop). Thereafter, we repeated this experiment using another modified synchronization train. All parameters of the new pulse train are the same as those shown in Figure 4.12 excep t that the pulse duration is changed to 12 ms. Again, the oscillating membrane potential is terminated at the value of negative -150 mV. The pump current is shown in Figure 4.14. Afte r the end of the os cillation, inward pump current is kept for another 12 ms (duration of oscillating pulse) befo re the pump current decays to zero. Both Figure 4.13 and Figure 4.14 consistently show that after the membrane potential is ended at negative half -pulse, the inward pump current remains for another pulse duration before decreasing to zero. These results provide strong evidence that pump molecules have been synchronized by the oscillating pulse train. To verify this synchronization theory we conducted another experiment. The magnitudes of electric potential are changed from mV to mV instead of from mV to mV for the last two data acquisition pulses af ter three data acquisition pulses (Figure 4.15). After pump molecules ar e synchronized, the pumps turnover rates are restricted by the field frequency, and the stoichiometric number of Na/K pumps remains constant in a wide range of membra ne potentials, so the pump currents should be independent of the membrane potential which just maintains the functions of the pumps.

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84 If this hypothesis is correct, there should be no change in pump currents by the increase of pulse magnitude but maintaining the same oscillating frequency. After the train stimulation (Figure 4.16), the negative part of the pump currents magnitude does not change and represents th e total number of synchronized molecules. In contrast, the positive part of the pump currents magnitude show s noticeable increases because both synchronized and unsynchronized pump molecules have contributed to the outward pump currents. Even though the cu rrents generated by the synchronized pump molecules remain the same, those generated by the unsynchronized pump molecules increase because of their voltage-dependen ce (Figure 4.5). Therefore, the total outward pump currents are increased. The results (F igure 4.16) indicate that the increase in magnitude of the last two data-acquisiti on pulses only increas es the outward pump currents, but has no effects on the inward pum p currents. This proves that some pump molecules have been synchronized by the oscillating electric train.

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Figure 4.15 New stimulation protocol: the membrane potential is changed from 10 mV to mV instead of from mV to mV for the last two data acquisition pulses after three data acquisition pulses. Figure 4.16 Na/K pump currents measurement by using Figure 4.15 stimulation protocol. 85

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86 Discussion and Modeling Na/K pump transport process is a loop including two direc tional operations. In each loop, 3 Na+ ions are pumped out of the ce ll and 2 K+ ions are carried into the cell. Because of structural independence, pump molecules may run at individual pumping rates and random pumping phases. The meas ured pump currents are the sum of all individual Na/K pump currents: the outward component represents 3 Na+ ions extrusion and the inward component represents 2 K+ ions being pumped in. The pumping out Na+ ions and the pumping in K+ i ons can not be distinguished (l eft side of Figure 4.17 [110]), resulting in one net ion out of the cell in each cycle. In this research project, the external electric field has signifi cant effects on the steps of the ions which are moved across the cell membrane. As the membrane potential is continuously oscillated with a frequency comparable to th e pump natural turnover rate, the magnitude of pump currents is changed gradually. Eventually, the net outward pump currents are separated into two components: outward and inward currents alternatively corresponding to the two half-c ycles of oscillating pulses. The magnitude of outward pump currents is increased by about three times and the magnitude of inward pump currents is increased by about two times. The ratio of outward over inward components is about 3:2, which reflects the stoichiometric number of Na/K pump protein. So under the influence of the electric field, the pump ing rate and pumping phase are changed accordingly by the designed electric field synchronization (right side of Figure 4.17 [110]).

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Figure 4.17 Left: Na/K pump currents from random pump molecules in response to a single pulse; Right: the synchronized pump currents in response to an oscillating pulse train [110]. Many phenomena of the Na/K pump pr otein can be expressed by a carriermediated model [108, 110], which postulates the existence of a chemical intermediate, a carrier which binds the solutes. The most su ccessful model is the Po st-Albers [92, 95, 96] model, which explains the biochemical behavior of the isolated enzyme, and is still the backbone of current biophysical models fo r electrogenic Na/K pump. The Post-Albers model is designed to accommodate the obser ved kinetics of enzyme phosphorylation and dephosphorylation catalyzed by Na+ and K+ ions respectively. According to the model, 87

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88 enzyme is phosphorylated by ATP (in the presence of Na+ ions and Mg2+ ions) in one conformation state (a highenergy intermediate E1 state), and then undergoes a conformational change to a low-energy E2 state, which process is rapidly dephosphorylated in the presence of K+ i ons. Figure 4.18 is a modified Post-Albers model adopted from Fonsecas paper [101]. The Post-Albers cycle in this figure indicates the main stages of conformational changes (E 1-E2), ions binding, ions release, ions occlusion, and ATP hydrolysis. K+ ions ar e released and Na+ ions are bound on the intracellular side, while Na+ i ons are released and K+ ions are bound on the extra-cellular side. The arrows of circle i ndicate forward pump cycle.

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Figure 4.18 Albers-Post model: This figure show s the stages of conformational changes (E1 E2): ion binding, release and occl usion, and ATP hydrolysis. The circle of arrows indicates the forward pump cycle [101]. From the Post-Albers model of Na/K pu mp, we can observe the following facts. First, the transport steps of both Na+ and K+ ions are voltage dependent due to the ions movements. Because charges move across the me mbrane, the external electric field will influence those steps. Second, Na+ ions and K+ ions transports are in opposite directions; therefore, any membrane potential cha nge will have opposing effects on those two transports. Third, those two ionic transports the extrusion of Na+ ions and pumping in of K+ ions are the two slow est steps in the whole loop and have rate coefficients many 89

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folds slower than any other steps in the l oop (rate-limiting steps). The change in either step will affect the whole pumping rate. Finally, these two transports do not happen simultaneously, but instead ar e in a sequential pattern. Figure 4.19 Asymmetric six-state mo del of Na/K pump cycle [110]. In Chens paper [110], he simplified the Post-Albers model to an asymmetric 6state (Figure 4.19) model. Asymmetry mean s that the transporte rs have different binding affinities to different ions when facing different sides of the cell membrane. All voltage-dependent steps, primarily Na+ and K+ ions transport steps, are incorporated into two voltage-dependent steps. Four voltage-independent steps repres ent other processes, including binding and unbinding steps. These assumptions make it possible to calculate numerical results because the kinetic differential equations describing the loop functions 90

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now can be simplified to algebraic equati ons. After all parameters are taken into calculation, pump flux from the six-state model is: VBVA VB VA VBB VAAeCeCeCeC eCeC ETc2 4 2 3 1 2 1 1 ) 21 ( 6 ) 21 ( 51 (4.1)[110] Figure 4.20 Calculated Na/K pu mping flux as a function of the membrane potential from six-state mode [110]. By using equation 4.1, the analytically calculated pumping flux is a nonlinear sigmoid curve as a function of the increas e of the membrane potential, exhibiting a shallow slope first, followed by a very sharp sl ope, a saturation state and a negative slope (Figure 4.20 [110]). These results are consistent with our pr evious experimental results (Figure 4.5) and experimental results of others [107, 108]. Th is calculated curve indicates 91

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that membrane potential depolarization can not significantly increase pump current, and there exists an upper limit of pump current When the membrane potential is further depolarized, the Na/K pump current will eventually go down. In equation 4.1, the numerator is a subtraction between two exponential terms where the first term index is (A1-A2) and the second term index is (B1-B2). When two forward reaction rates and two backward reaction rates are comparable in normal situation, the results of the tw o subtractions are small. E quation 4.1 shows that the value of the first term cannot be too high, and the value of the second term cannot be too low. As a result, the pumping flux can not be si gnificantly increased even when a large membrane potential is applied to the cell membrane. In order to increase the pumping flux, we need a large value of numerator in equation 4.1, which can be realized by increasing the first term and decreasing the s econd term. It is impossible to accelerate two opposite voltage-dependent ion-transport st eps at the same time by polarized or depolarized membrane potential In our experimental protoc ol, we apply an oscillating electric field with both positive and negative potentials relative to -90 mV. During the positive half-cycle, Na+ ions transport is acce lerated, and during the negative half-cycle, K+ ions transport is accelerated. Thus, the oscillating electric field can alternatively facilitate both ion-transports, which proce ss we call synchronization. Now, equation 4.1 becomes VB VAVB VA VBB VAAeCeCeCeC eC eC ETc2 4 2 3 1 2 1 1 ) 21 ( 6 ) 21 ( 51 (4.2)[110] 92

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Figure 4.21 Calculated Na/K pu mping flux under the influence of an oscillating electric field is increases dramatically [110]. The calculated flux from equation 4.2 is increased dramatically with the increase of the membrane potential (Figure 4.21). As we mentioned before, the two steps of Na+ pumping out and K+ pumping in do not happen simultaneously in the loop. Instead, they work in a sequential pattern. When an oscillating electric field with a frequency comparable to the pumps turnover rate is applied on the cell memb rane, the fields two half-cycles match the time courses of two i on-transports. The osci llating electric field will treat individual pumps differently, base d on their turnover rates and phases. For pumps whose turnover rate is a little lower than the field frequency, the electric field may facilitate both Na+ and K+ transport step s, alternatively and loop by loop, until the pumps turnover rate matches the field frequenc y. For those whose tur nover rate is a little higher than the field frequency, the electric field may slow them down until they reach 93

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the field frequency. As a result, the pace of the Na+ and K+ ions transports will be dominated by the two half-cycles of the osci llating electric field, respectively. In other words, Na/K pump molecules are synchronize d by the oscillating electric field. Na/K pump currents are separated into distinguishable outward and inward components. During the positive half-cycle, the pump molecules pump out 3 Na+ ions, which is three times of that from randomly paced pump curre nts. Then, the pumps bring 2 K+ ions into the cells during the negative half-cycle, re sulting in an inward pump current. The magnitude ratio of the outward pump currents over the inward pump currents, 3:2, represents the stoichiometric number of the Na/K pump. Figure 4.22 The figure on the left side represen ts the normal configuration of Na/K pump proteins; the figure on the right si de represents the synchronized configuration of Na/K pump proteins. 94

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95 The simplest demonstration of synchroni zation is shown in Figure 4.22. The left side represents the pumps normal configura tion; the right side represents the pumps synchronized configuration after a long stimulation pulse train. Conclusion We use a pulsed, symmetric, oscillating elec tric field with frequency close to the mean physiological turnover ra te across the cell membrane to synchronize Na/K pump molecules. The pump molecules work as a gr oup, pumping at a sync hronized pace after a long stimulation train, through which the pump functions can be si gnificantly increased. The results clearly show separated outward a nd inward currents in an alternative pattern. The ratio is close to 3:2, which reflects the predicted stoichiometric number for the Na/K pump loop. Synchronization of pump molecule s can become a new method to study the functions of Na/K pump molecules. This method has huge potential applications in medical treatment. Pathophysiology for different diseases differ sign ificantly, such as Heart Failure, Alzheimers Disease, Cys tic Fibrosis, Diabetes, Hyperthyroidism, Myotonic Dystrophy, Hypertension [80, 81], but all are related to dysfunction of Na/K pump molecules either due to a lack of AT P to fuse Na/K pumps or a low density of Na/K pump molecules on the cell membrane. A lot of researchers are studying how to make Na/K pumps work faster to restore the membrane pot ential and ions concentration so as to cure those diseases by either electrical force or chemical agents [93, 94, 99, 100, 102, 104]. Our research synchr onization Na/K pump proteins presents a potential new method to conquer those diseases.

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96 Chapter 5 Synchronization of Na/K Pumps under Na/Na and K/K Exchange Modes by Electric Field Introduction Normally, Na/K pump proteins need Na+ ions, K+ ions and ATP [9, 10, 88] present to achieve basic functions, includi ng pumping 3 Na+ ions outside and pumping 2 K+ ions into the cells to maintain ionic c oncentrations and the potential across the cell membrane [8]. The motion of Na/K pumps can be separated into two mechanisms. One mechanism depends on the inside concentrati on of Na+ ions; the other depends on extracellular concentration of K+ ions. Both w ould depend on the presence of ATP as energy source [1,111]. Changing one of the three parame ters (the concentration of Na+ ions, the concentration of K+ ions, and presence of ATP) will change the functions of Na/K pump proteins. For example, if metabolic poisons such as cyanide, block the production of ATP molecules, the efflux of Na+ ions are reduced [111, 112]. According to other researchers results, Na/K pump proteins can have several modes of exchange beside normal Na/K exchange mode[8, 9], like the Na/Na [111, 113, 118, 119] and the K/K [114, 115, 120 ] exchange modes, which all depend on the concentration of Na+ and K+ ions. Some papers [114, 115] suggest that ADP is a necessary factor for the K/K exchange m ode. Some papers [117] suggest the K/K

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97 exchange mode is a result of mis-measuremen ts and there are just two modes existing: one is Na/K normal exchange mode, a nd one is the Na/Na exchange mode. Na+ efflux depends on the extra-cellular con centration of K+ ions. An increase in the external K+ ion concentra tion will increase Na+ ion efflux [1]. If extra-cellular K+ ions are removed, the coupled efflux of Na+ i ons and influx of K+ ions are reduced to near zero [1]. What will happen when there are some other cations with characteristics similar to those of K+ ions existing in the extra-cellular fluid? In general, it has been found that K+ ions have a number of extracellular agonistic ions which compete for activation of Na/K pumps. Evidence suggests that the effectivene ss of different extracellular cations to activate Na/K pump proteins satisfies the se quence of Tl > K > Rb > Li > Na [1]. Papers written by Tosteson and Hoffman [118], and Garrahan and Glynn [116], show that Na/K pumps on the red blood cell membrane, in absence of extra-cellular K+ ions but with Na+ ions presen t, exchange Na+ ions between the inside of the cell and the outside of the cell with the ratio of 1:1. Similarly, the Na/K pump is activated by intracellular Na+ ions also. In absence of intracellular Na+ i ons, the coupled efflux of Na+ ions and influx of K+ ions also reduce to zero [1]. But if other ions replace Na+ ions in the intra-cellular solution, different researchers come up w ith totally different results on the K/K exchange mode. In Simonss paper [120], he points out that there is a K/K exch ange mode carried out by the Na/K pumps in human red cells with intracellula r K+ ions instead of Na+ ions. In Kaplan and Kenneys paper [114], K/K exchange th rough Na/K pump has been measured as Ouabain sensitive Pb+ uptake in Na-free ghosts with 1:1 ratio. But some researchers did not observe the same result [1, 117]. Their conclusion is that Na/K pumps are activated

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98 by intracellular Na+ ions; at is Na+ ions can not be replaced by other monovalent cations in the cycle of the Na/K pum p. In Feraille and Doucets paper, they claim that the requirement for intracellular Na+ ions to activ e the Na/K pumps is almost absolute except for Li+ ions [174]. In the previous chapter, we use elec tric field to synchronize Na/K pump molecules and make the measurement of pump currents much easier than the traditional measurement. In this chapter, we will use the same stimulation train to examine the Na/Na exchange mode and the K/K exchange mode. If two modes exist in our experimental condition, we should see separa te inward and outward currents for both modes. Methods and Materials (1) Skeletal muscle fiber preparation (see chapter two) (2) Solutions (unit mM): Normal Ringer: (see chapter two) Relaxing Solution: (see chapter two) For the Na/Na exchange mode External Solution: 15 NaCl 83 CsCl 87.6 TEA.Cl 1.8 CaCl2 1.5 RbCl2 1.5 BaCl2

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99 3 3, 4 DAP 0.1 EGTA Internal Solution: 20 Na-glutamate 33.5 K-glutamate 5 Cs2-PIPES 20 Cs2-EGTA 6.8 MgSO4 10 Na2-C.P. 5.5 Tris-ATP 20 Tris-Creatine Phosphate For the K/K exchange mode External Solution: 15 NaCl 5.4 KCl 87.6 TEA.Cl 2.15 Na2HPO4 0.85 NaH2SO4 1.8 CaCl2 1.5 RbCl2 1.5 BaCl Internal Solution: 40 Cs-glutamate 33.5 K-glutamate 5 Cs2-PIPES 20 Cs2-EGTA

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6.8 MgSO4 10 Tris-C.P. 5.5 Tris-ATP (3) Voltage clamp (see chapter two) (4) Electric stimulation pulses (see chapter four) Experimental Results (1) The Na/Na exchange mode (external solution without K+ ions) Figure 5.1 A single step pulse is used on the mu scle fiber to measure Na/K pump currents under the Na/Na exchange mode. First, a single step puls e (Figure 5.1) is a pplied on the fiber to measure Na/K pump current under the Na/Na exchange mode condition. Because of the absence of K+ ions outside the cell, Na/K pump proteins should work on the Na/Na exchange mode. For each loop of Na/K pumps, same amount of Na + ions are transported in and out through the cell membrane, which is no longer electrogenic process. Due to the random phase of 100

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pump proteins movement, pump current must be equal to zero under a single pulse. The experimental result proves our expectation (Figure 5.2). The transi ent current peaks in response to the rising and falling phases of pul ses are due to imperfect matching in P/4 method. -20 -10 0 10 20 02 04 06 08 01Time (ms)Current (nA)0 0 Figure 5.2 When Na/K pump proteins are wo rking under the Na/Na exchange mode, for each loop of Na/K pumps, the same amount of Na+ ions is transported in and out through the cell membrane. This pro cess is no longer electrogenic. Under a single pulse (Figure 5.1), Na/K pump current equals zero. Using a stimulation train which is sim ilar to Figure 4.3 in chapter four on the muscle fiber, we can measure pump current s during the whole train stimulation. Five minutes later after the train stimulation, the external solution is replaced by the same external solution except with 1 mM Ouabain, and the same elec tric train is applied on the same fiber again. After subtraction, we can ge t an Ouabain-sensitive currents, the Na/K 101

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pump currents. Figure 5.3 and Figure 5.4 show the currents during fi rst 300 ms and last 300 ms stimulation. Several char acteristics are worth of ment ioning in those two figures. (1) Both inward and outward currents greatly increase with an increasing number of pulses. After 100 pulses, the currents reach a steady state, just like the result from synchronization we obtained in chapter four. (2) Results clearly show the separation of two currents: one is positive a nd the other is negativ e with almost 1:1 ratio. This directly proves that Na/K pumps work in the Na/Na exchange mode. -20 -15 -10 -5 0 5 10 15 20 050100150200250300Time (ms)Current (nA) Figure 5.3 Pump currents under the Na/Na excha nge mode during the first 300 ms of the oscillation pulse train. 102

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-20 -15 -10 -5 0 5 10 15 201700175018001850190019502000Time (ms)Current (nA) Figure 5.4 Pump currents under the Na/Na exch ange mode during the last 300ms of the oscillation pulse train. -20 -15 -10 -5 0 5 10 15 20 0102030405060708090100Number of PulsesCurrent (nA) 103 Figure 5.5 The X-axis represents the number of pulses, the Y+ axis represents the positive pulse pump currents and the Yaxis represents the negative pulse pump currents. The ratio between the positive currents and the negative currents is close to 1:1

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In figure 5.5, the X-axis represents the number of pulses, the Y+ axis represents the positive pulse pump current value, and the Yaxis represents the negative pulse pump current value. From this figure, we can observe two very impo rtant results as we mentioned before: (1) Na/K pump currents are saturated within 100 pulses; (2) the ratio of the positive current with the negative current is very close to 1:1 in the whole period of the train oscillation. (2) The K/K exchange mode (internal solution without Na+) With the same process, internal solution without Na+ ions is used on a single fiber to verify the K/K exchange mode. Under the same electric stimulation pulses, the measurement of pump currents has not s hown significant chan ge during the whole stimulation train. Figure 5.6 and Figure 5.7 show first 300 ms and last 300 ms pump currents. There is maybe a little but no not able effect on pump currents by an electric stimulation train in this experiment. -20 -15 -10 -5 0 5 10 15 20 050100150200250300Time (ms)Current (nA) Figure 5.6 Pump currents during the first 300 ms of the oscillation pulse train under the K/K exchange mode. 104

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-20 -15 -10 -5 0 5 10 15 20 1700175018001850190019502000Time (ms)Current (nA) Figure 5.7 Pump currents during the last 300 ms of the oscillation pulse train under the K/K exchange mode. Compared to Figure 5.6, there is no significant difference between those two figures. Discussion Experiments show that in the absence of K+ ions and in the presence of relatively high level of extra-cellular Na+ ions, Na/K pu mp can operate in a mode where Na+ ions influx and efflux are associated. The experime ntal results show that the efflux of Na+ ions is approximately equal to the influx of Na+ ions, which indicates a 1:1 ratio of the Na/Na exchange mode. Previously, the stoichiometric numbe rs under the Na/Na exchange mode have been reported as 1:1 [123], 2:1[124], or varying with the Na+ ions concentration [125]. In our experiment to s ynchronize pump proteins, we can separate the influx and the efflux currents and clearly obs erve that the stoichiometric number. The Na/Na exchange mode is no l onger an electroge nic process. 105

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106 Two types of Na/Na exchange reactions of Na/K pumps have been previously reported [126]. The electroneutral exchange is a one-to-one Na+ ions counter-transport mechanism [127]. This mode need s relatively high concentrations of Na+ outside the cell which is similar to our experimental result s. The second type of the Na/Na exchange reaction is that the wild-type enzyme uses Na+ ions as a low-affinity K+ substitute to move charges across the cell membrane [128, 129, 135]. This electrogenic exchange occurs in the present of ADP and is generally much smaller than the electroneutral Na/Na exchange mode with a stoichiometric number close to 3:2 [132, 133, 134]. It is clear that the electroneutral Na/Na exchange mode does not require ADP and our research belongs to this type. On the other hand, in the absence of Na+ ions and in the presence of relatively high level of intra-ce llular K+ ions, Na/K pumps should work on the K/K exchange mode according to other researchers [114, 115, 120]. If so, we should get separate K+ currents just like the Na/Na exchange mode by elec tric stimulation. Even though we have changed different concentrations of K+ ions inside th e cell, results can not prove the existence of this K/K exchange mode. No separate cu rrents can be measured. The reason is either that there is no K/K exchange mode on this experiment setup, or electric stimulation can not turn on synchronization process of Na/K pu mp molecules due to a lack of Na+ ions inside the cell. Conclusion We use an oscillating electric train to synchronize Na/K pump molecules under the Na/Na and the K/K exchange-mode conditi ons. After a long train stimulation, we are

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107 able to measure the separate outward and inwa rd currents in an alternative pattern under the Na/Na exchange mode. The ratio is close to 1:1, which reflects the fact that Na/K pumps can transport the same amount Na+ i ons through the cell membrane in each loop, and the Na/Na exchange mode is not longe r electrogenic. For K/K exchange mode measurement, there is no significant change in the measurement of pump currents during a long period of stimulation. No separate curr ents can be measured. The reason is that either there is no K/K exchange mode on this experiment setup, or electric stimulation can not turn on synchronizati on process of Na/K pump molecules due to a lack of Na+ ions inside the cell. In other words, inte rnal Na+ ions are the trigger of Na/K pump proteins [1].

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108 Chapter 6 Modulation of Na/K Pump Proteins by Electric Field Introduction Previous results indicate that a symmetri c, oscillating electri c pulse train with a frequency close to the physio logical turnover rate can sync hronize Na/K pump molecules by using a traditional voltage clamp and can separate the inward and outward pump currents [136]. The field-induced activation of the pumps can effectively reinstate (hyperpolarize) the cel l membrane resting potential a nd ion concentrations [130, 131], which are critical to many cell functions, including controlling ce ll volume, generating electrical signals, and providing energy for other active transporte rs. Synchronization of pump molecules provides a new method to ge t more detailed information about Na/K pump proteins. In this chapter, we further pr esent results of our st udies in modulation of pump proteins after synchroniza tion: the external electric fi eld with increased frequency can accelerate turnover rate of Na/K pump molecules. After Na/K pump molecules are synchroni zed, the applied electric field frequency is gradually increased in order to synchr onize Na/K pump molecules to a new high frequency. There are two basic questions: (1) what is the new frequency after synchronization? (2) How many pulses should be applied for the new frequency? For the first question, it is clear that pump molecules can only follow a gradual change (higher) in electric field frequency. If electric-fiel d frequency jumps too much, the synchronized

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109 pump molecules may not follow the new frequency. For the second question, our experiments have shown that 100 pulses ar e good enough to synchronize most molecules with pulse potential changi ng from mV to mV. Af ter synchronization, a new frequency which is slightly higher than the previous frequency will force the synchronized group molecules to move to the ne w frequency. It is estimated that at most 50 pulses will be needed for the new frequency. Our goal is to modulate Na/K pump mol ecules to a higher frequency that should lead to a large increase of pump currents and, therefore, Na/K pump functions by the synchronization and modulati on stimulation pulse train. Methods and Materials (1) Skeletal muscle fiber pr eparation (see chapter two) (2) Solutions (see chapter four): (3) Voltage clamp (see chapter two) (4) Electric synchronization-modul ation stimulation pulse train The synchronization-modulation pulse train consists of five parts with gradually reduced durations of electric pulses. The durat ion of pulses initially is 15 ms, followed by 10 ms, 6ms, 4 ms and 3ms. There is no time-ga p between any two parts. The first part has 100 pulses; the second to the final parts have 50 pulses each. The magnitudes of pulses are +/60 mV on the basis of -90 mV holding potential. The synchronization-modulation pulse train is sketched and shown in Figure 6.1. The last th ree pulses of each different group are the data acquisition pulses, which are used to generate final results of Na/K pump currents.

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100 oscillation pulses 3 data acquisition pulses mV 30 90 150 Pulse D uration T= 15 ms T = 10 ms T= 6 ms T = 4 ms T = 3 ms Figure 6.1 Synchronization-modulation pulse train, the duration of the first part of which is 15 ms, followed by 10 ms, 6ms. (5) Protocol Experimental protocol is as follows: the s timulation pulse train (Figure 6.1) is first applied to the cell membrane five times. After that, the external solution is changed to the solution with 1 mM Ouabain, and the same process is repeated five times. The measured currents from five repeated stimulations are averaged to increase signal/noise ratio. Then, P/4 method is used to elicit linear trans-memb rane currents. After th at, the current with Ouabain is subtracted from that without Ou abain present to get Na/K pump currents for different pulses. Experimental Results We have shown that individual pump mol ecule working at random paces can be synchronized by an oscillating electric field in chapter f our. After synchronization, when 110

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we increase the field frequency by a small step, the electric fi eld is able to re-synchronize the pump proteins to the new frequency. If the frequency step is small enough and the electric field is applied for long enough, which means by gradually increasing field frequency and keeping the Na/K pump molecu les synchronized, pumping rates can be accelerated and the Na/K pump molecules can be synchronized to the higher frequencies. In this experiment, the synchronization-modulati on stimulation train consists of five parts with the duration gradually reduced from 15 to 3 ms. The equivalent oscillating frequency of the first part is 33 Hz and 167 Hz for the last part of the train. -20 -10 0 10 20 05101520253035 Time (ms)Current (nA) Figure 6.2 Pump currents when the pulse duration is 15 ms (synchronization). 111

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-20 -10 0 10 20 05101520253035 Time (ms)Current (nA) Figure 6.3 Pump currents when the pulse duration is 10 ms (first modulation). -20 -10 0 10 20 05101520253035 Time (ms)Current (nA) Figure 6.4 Pump currents when the pulse duration is 6 ms (second modulation). 112

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-20 -10 0 10 20 05101520253035 Time (ms)Current (nA) Figure 6.5 Pump currents when the pulse duration is 4 ms (third modulation). -20 -10 0 10 20 05101520253035 Time (ms)Current (nA) Figure 6.6 Pump currents when the pulse duration is 3 ms (fourth modulation). 113

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114 Oscillation group 1 Oscillation group 2 Oscillation group 3 Oscillation group 4 Oscillation group 5 Integral outward current (nA ms) 43.6 46.5 45.3 41.0 39.4 Integral inward current (nA ms) -30.3 -30.4 -30.4 -29.0 -27.4 Average outward current (nA) 2.90 4.65 7.55 10.2 13.1 Average inward Current (nA) -2.02 -3.04 -5.07 -7.26 -9.12 Table 6.1 Areas and magnitudes of pump currents responding to both positive and negative half-pulse under synchronization-modulati on electric stimulation train. The final results of Na/K pump currents for the five parts are shown in Figure 6.2 to Figure 6.6, respectively (15 ms is considered the middle point for comparison). For each of five different figures, the ratios of outward pump currents to inward currents are similar, close to 3:2. However, the magnit udes of pump currents are progressively increased when the duration is reduced. The magnitudes of pump currents responding to both positive and negative pulses are listed in the third and fourth rows in Table 6.1, respectively. In the first part of the train where the durati on is 15 ms, the magnitude of

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115 outward pump currents is only 2.9 nA. In the last part of the train, the magnitude of outward pump currents increases to 13.1 nA, a little less than a five fold increase increment from the first part. Similar result s can be observed by comparing inward pump currents. The value of inward pump currents in duced in the first part is initially about 2.02 nA and finally reaches a value of 9.12 nA, still a little less than a five-times increase. The first and second rows in Table 6.1 are the areas of outward and inward ionic fluxes carried by the Na/K pumps and obtained by the integration of time and current trace. The first row represents the total num ber of charges extruded from the cell during the positive half-pulse. Similarly, the total num ber of charges pumped into the cell during the negative half-pulses is listed in the second row. Th e numbers of charges moved during both half-pulses are approximately the same for all groups. This similarity is because of a fixed number of pump molecu les being synchronized on the cell membrane and a fixed stoichiometric number of Na/K pu mps. In fact, this si milarity is a good sign indicating that most of sync hronized pump molecules have been re-synchronized at each new frequency. To further compare frequency-modulation effects on Na/K pump proteins, we superimposed all the pump-current traces in Fi gure 6.7. The traces are aligned so that the reversals of polarity in the cu rrent all occur at 15 ms. On the left side are outward currents responding to the positive half-pulse, and on the right side are inward currents responding to the negative half pulse. The fi gure clearly shows that the areas underneath either outward or inward pump currents remain almost the same regardless of pulse durations. Both outward and in ward pump currents are cont inuously increased when the synchronization frequency is gradually increased.

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-20 -10 0 10 20 05101520253035 Time (ms)Current (nA) Figure 6.7 All Na/K pump current traces s uperimposed together shows that both outwards and inwards pump currents ar e continuously increasing when the field frequency is gradually increa sed. The areas underneath either the outwards or the inwards pump currents remain the same regardless of the pulse durations. Discussion When the frequency of the oscillating electric field is increased, Na/K pump proteins are forced to be s ynchronized to the new frequency if the step is small enough and the electric field is applied long enough. Once the new synchronization is reached, the field frequency can be increased again to re-synchronize Na/K pumps to the next higher frequency. By using this method, Na/K pump molecules can be gradually modulated to higher and higher pumping rates. It has been well documented that the stoichiometric number of the Na/K pumps remains constant over a wide range of 116

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117 membrane potentials [137]. Therefore, the modulation of pumping rate to a higher value results in an increase in pump currents. Th is can be seen by comparison of five current traces shown in Figure 6.2 to Figure 6.6 and th e measurements listed in Table 6.1. It is clear that by slowly increasing the oscillat ing electric-field frequency and keeping the pumps synchronized, the times needed for th e two rate-limiting ionic transports are reduced step by step, and the pumps turnover ra tes are gradually accelerated. As a result, Na/K pump currents are increased. It is n ecessary to point out that in all of our experiments the pulse magnitudes remain sa me. The increase in pump currents results solely from the pumping-rate modulation. In this experiment, we only increase the oscillating frequency up to five times which re sults in close to a five-fold increase in pump currents. Further increase in field fre quency may lead to a progressively greater increase in Na/K pump currents. Conclusion The previous results indicate that a symm etric, oscillating pulse train with the frequency close to the physio logical turnover rate can sync hronize Na/K pump molecules. In this chapter, we can accelerate the tur nover rate of pump molecules by increasing the electric-field frequency gradually in order to re-synchronize molecu les to the new higher frequency. After a synchroni zation-modulation stimulati on pulse train, Na/K pump proteins are modulated to th e higher frequency with a larg e increase of pum p currents.

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118 Chapter 7 Increase Lumen Potential in Rat Proximal Tubule by Synchronization and Modulation of Na/K Pumps Introduction Mammalian kidneys are vital organ whic h clean the blood and maintain chemical balance inside of the body [139, 140, 141]. Kidneys are sophisticated reprocessing machines dealing with metabolic waste products such as uric acid, urea, and creatinine, etc. The extra water and waste products flow to the bladder through ureters and become urine eventually. Every day, an adult humans kidneys process about 200 quarts of blood and squeeze out about 2 quarts of waste produc ts and extra water [139]. However, the role of the kidneys is not only excretion; th ey are also regulatory organs, controlling and maintaining the volume, composition, osmolality and ionic concentrations of blood within very narrow margins. For example, Na+ ions concentrati on, which is the main factor in biological system to determine th e blood pressure [141, 144, 145], is controlled by kidneys. Figure 7.1 shows the basic stru cture of kidney [169]. The outer layer of the kidney is the renal cortex which sits directly beneath the kidney's connective tissue and fibrous capsule The thin membrane-like coverage is very important to keep water on the kidney surface. The deeper layer of the cortex is called the renal medulla The renal medullar is divided into many renal pyramids which together with the associated overlying cortex

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form a renal lobe. The tip of each pyramid empties into a calyx and the calices empty into the renal pelvis which transmits urine by ureter s to the bladder Figure 7.1 The basic struct ure of kidney [169] 1. Renal Vein 2. Renal Artery 3. Renal Calyx 4. Medullary Pyramid 5. Renal Cortex 6. Segmental Artery 7. Interlobar Artery 8. Arcuate Artery 9. Arcuate Vein 10. Interlobar Vein 11. Segmental Vein 12. Renal Column 13. Renal Papillae 14. Renal Pelvis 15. Ureter 119

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120 The actual filtering and reabsorption processes occur in many tiny functional units inside the kidneys called nephrons. Each kidney contains approximately one million of these units [140]. Each nephron begins in a re nal corpuscle, which contains a cluster of blood vessels (glomerulus), surrounded by th e hollow Bowman's capsule. Ions, water, and small molecules, except for blood cells, big proteins, and large molecules, can be filtered out of glomerulus by different pr essures between inand outbloodstreams. After glomerulus of ultrafiltration resemblant plasma enters Bowman's space. Bowman's capsule leads into a membrane-enclosed, U-sh aped tubule, which is divided into four parts, namely the proximal tubule the loop of Henle the distal convoluted tubule and the collecting duct (Figure 7.2). The liquid fr om the collecting ducts through various nephrons merges together and ultimately flows into the bladder and becomes urine. Figure 7.2 shows the basic st ructure of the nephron [ 138]. Each nephrons tube has four basic parts according to each segmen ts structures and functions as mentioned before. Each part has different functions, es pecially in reabsorption of different matter [142, 143]. For example, 100% glucose and amino acids and probably 65% Na+ ions are reabsorbed in the proximal tubule (Table 7.1). The loop of Henle can reabsorb probably 25 % Na+ ions.

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Figure 7.2 The basic structure of naphron [138] 121

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122 Substance Proximal tubule The Loop of Henle Distal tubule Collecting duct glucose reabsorption (almost 100%) amino acids reabsorption (Almost 100%) urea reabsorption (50%) secretion reabsorption in medullary ducts Na+ reabsorption (65%) reabsorption (25%) reabsorption (5%) reabsorption (5%, principal cells) chloride reabsorption reabsorption reabsorption water reabsorption (descending) reabsorption bicarbonate reabsorption (80-90%) reabsorption (thick ascending) reabsorption protons secretion (intercalated cells) K+ reabsorption reabsorption (20%) secretion calcium reabsorption reabsorption (thick ascending) magnesium reabsorption reabsorption (thick ascending) reabsorption phosphate reabsorption (85%). Table 7.1Re-absorptions of different matters on different kidney segments including the proximal tubule the loop of Henle, the distal convoluted tubule and the collecting duct [140]. Kidneys are the richest organ containing Na/K pump proteins [161]. Na/K pump proteins are present in per itubular cell membranes (Figur e 7.3), where they play a prominent role in Na+ ion reabsorption [ 142, 143]. Na/K pumps can generate membrane

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potential and concentration differences whic h are the main driving forces for Na+ ion reabsorption from lumen fluid to blood [ 149, 151, 160]. Net Na+ ion reabsorption is the major function of renal Na/K pump proteins and a close relations hip exists between Na/K pump molecules density and the Na+ ions reabsorptio n capacity of the different segments of a nephron. Renal Na/K pumps are the driving force not only for Na+ reabsorption, but also for secondary active transport of large amounts of a wide variety of other ions and uncharged solutes. Peritubular fluid 0 mV Proximal cell -50 ~ -60 mV Lumen -5 ~ -25 mV Na/K pump Na+ ions Figure 7.3 The electric potential difference acr oss the renal tubular cell and the direction of net Na+ ions re-absorption in the tubule. The potential of the interior of the tu bular cell (proximal segment) is negative [156,159] that compared to of the peritubular fluid (assume 0 mV) and the lumen fluid. Figure 7.3 shows typical potential s. The potential of the insi de of the tubular cell is proportional to the rate of Na+ ions being pumped out, which depends directly on Na/K pump activity [146, 147, 148, 149, 150]. It is gene rally agreed that the magnitudes of trans-tubular potential are different in different segments [152, 153, 154, 155]. Smaller 123

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124 potential differences between th e lumen fluid and the peritubular fluid are obtained on the loop of Henle distal convoluted tubule and collecting ducts [152]. This project is the first application of the synchronization-modulation method at the organ level after our singl e-cell study (chapter 4, 5 and 6). The main goal is to use synchronization-modulation electr ic field to activate Na/K pu mp proteins and, therefore, increase Na+ and other ions reabsorption sp eed, which will result in an increase in potential of the inside of proximal tubular lumen. Rat kidney is well suitable for the study of proximal distal tubular functions because the surface of rat kidney is composed almost exclusively of proximal tubule s (95%) and distal c onvoluted tubules (5%). Experiment Setup and Methods (1) Animal preparation All animal experiments are carried and processed in accordance with provisions of National Institutes of Health Guide for the Care and Use of Laboratory Animals and approved protocols by the Institu tional Animal Care and Use Committee at the University of South Florida. Male rats (250 g to 380 g) fed with st andard rat chow and provided with free access to water are used for all experiments. After being anesthetized by intraperitoneal injection of thiobutabarbital sodium (Inactin, 100mg/Kg), the rat is placed on a constanttemperature (37 oC ) pad which connects to a TP 500 h eating pump (heat pump supplies a temperature controlled flow of heated water through a set of hoses to a pad which is then applied to the rat). After adequate waiting tim e (10 min to 15 min) to make sure the rat has fallen deeply asleep, the left kidney is exposed by a flank incision. Connected tissue

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125 and fat around the kidney are carefully rem oved, but without touch and harm to the membrane of the kidney. Then, the kidney is placed to a plastic cup which connects to a magnetic stand to minimize the vibrations from the rat heart while blood vessels and ureter are still in the normal functional condi tion and connected to the kidney. The empty space around the kidney is covered with abso rbent cotton. The surface of the kidney is covered by the paraffin oil to keep surface water from evaporating. (2) Solutions (mM) Solution One: 110 NaCl 2.5 KCl 2.15 Na2HPO4 0.85 NaH2PO4. H2O 1.8 CaCl2.H2O 10 NaHCO3 Solution Two: 120 NaCl 2.5 KCl 2.15 Na2HPO4 0.85 NaH2PO4. H2O 1.8 CaCl2.H2O (3) Microelectrodes for the lu men potential measurements Micropipettes (40-60 mm) are pulled by a heat puller (Model PB-7, Narishige) from 1.0 mm I.D. to 2-5 um on the tip. There are three setups involving the solutions to prepare microelectrode in experiments (1) Mi cropipette is filled with Solution One, which is used to measure the lumen potenti al without blockage of the tubule. (2)

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Micropipette is first filled with tiny Sudan black mixed castor oil in the tip and later Solution One (Figure 7.4). The mixed oil is used to block the tubule segment. (3) The same process is used as (2) except Ouabain is solved in the Solution One to block Na/K pump proteins. After the required solution is prepared, the micropipette is inserted into a connector while a silver wire is put into th e solution inside of a glass pipette. The next step is to connect it with channel st age one in a voltage-monitor-mode of TEV-200 voltage clamp (Figure 7.5 shows a sketch; Figure 7.6 shows a real picture). The connector has a side-open-hose to join a pipe which can control the pressure inside the connector. Figure 7.4 Photograph of a micr opipette tip (microelectrode) which is filled with tiny Sudan black mixed castor o il and measurement solution. 126

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1 3 2 6 4 5 1 Stage of channel one 2 Silver wire 3 Pressure hose 4 Solution 5 Micropipette 6 Mixed oil Figure 7.5 Schematic diagram of a microelectrode and a connector setup. Figure 7.6 Photograph of a microele ctrode and a connector setup. 127

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128 (4) Micropuncture and microinjection Micropunctures are finished by using a high-magnifying lens on a microscope stand. Proximal tubular cells ar e punctured by a micropipette with the tip about 2-5 um diameter which is filled with mixed oil and measurement solution. After the tip is pushed into the proximal tubule lumen on the kidney su rface, the mixed oil is first injected into the lumen controlled by a high pressure which is generated by a pumping machine. After the oil injection, a tiny solution is also inject ed into the tubule by carefully controlling the pressure and making sure that the oil is pus hed away and stays at the two sides of the solution while the silver wire remains inside of the solution. Through this way, we create an independent tubular segment and cut off a ll feedback system insi de the tubule (Figure 7.7). The measured potentials inside of th e tubule reflect direct ly the tubular cell reabsorption process. The success rate of this process is very low. Quite often, the following situations will occur: (1) The tiny glass tip is blocked by big particles in the mixed oil or during micropuncture through the kidney membrane a nd the tubular cell membrane; as result, the mixed oil can not be pushed into the lumen space by the high pressure. (2) The tip is broken due to the micropuncture through the membrane or due to the kidneys vibration after successful micropuncture. (3) The mixed oil is swept away by the tubular fluid or during the solution injection by the high pressure There is no independent tubular segment for the measurement.

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Measurement Solution Mixed oil Tubular cell 20-30 um Micropipette Figure 7.7 After micropuncture and oil injection, a tiny solution is also in jected into the tubule. Through this way, an independent tubular segment is created and the tubule feedback system is cut off. (5) Synchronization-modulation electric field and electrodes Synchronization-modulation electric stimul ation trains generated by the MatLab computer program are applied. The stimulati on train frequency is gradually increased from 10 Hz (pulse duration is 50 ms) to 500 Hz (pulse duration is 1 ms). Each following pulse frequency is increased within 2% compared to the previous one. Each frequency has 50 pulses except that the first one (10 Hz) has 100 pulse s and the last one (500 Hz) has 1000 pulses. The trains have the same magnitudes of +1 to -1 V peak to peak. The stimulation trains are delivered by two pin-shaped electrodes which are carefully inserted into the tw o sides of the kidney. The conne cting wires are tied to the stand; otherwise, if electrodes slide from th e original positions, the blood from the kidney is hard to stop. 129

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Experimental Results (1) Control experiments In the first control experiment, we use a micropipette without oil in the tip (filled with Solution One only) to test the system After micropuncture process, in order to ensure that the tip of electrode is in th e lumen space, a small amount of solution is injected to see whether the solution flows along proximal tubule in a very short time. Because the kidney still stays in normal functional condition after micropuncture, the potential inside the tubule should not cha nge with time. Figure 7.8 shows one of the results. -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 050100150200250300350400450500Time (s)Voltage (mV) Figure 7.8 The potential inside the tubule in normal functiona l condition does not change with time. 130

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After testing the system, we use a micropi pette filled with mixed oil and Solution One for a series of experiments. After successful microinjection of the oil and the solution, the lumen potential is recorded im mediately. With the tubule blocked and Na+ ions, water and other ions r eabsorbed, the lumen potential increases until it reaches saturation (Figure 7.9) with a time constant of 297+/-41 s. For diffe rent individual rats, the voltages increase differently, and the ra nge of the lumen potential increase when reaching a saturation state is 3-8 mV. -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 050100150200250300350Time (s)Voltage (mV) Figure 7.9 With reabsorption of ions and wate r, the lumen potential is increased until it reaches the saturation state after the t ubule is blocked. The time to reach the saturation state is about 297+/-41 s. 131

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132 (2) Experiments with blockage of proximal tubule and under electric field stimulation After control experiments, the next step of the experiment is to find out how an electric field influences Na/K pump activit ies and the lumen potential. In our previous chapters, we have experimentally proved that (1) when a symmetric, oscillating membrane potential train with a frequency close to the mean physiological turnover rate is applied across the cell membrane; the Na /K pump molecules can be synchronized. The Na/K pump molecules work as a group, pumpi ng at a synchronized pace after a long train stimulation. (2) After synchronizing the Na/K pump molecules, we can accelerate the turnover rate of pump molecules by increasing the electric field frequency gradually in order to re-synchronize molecules to a higher frequency. After a synchronizationmodulation stimulation pulse train, the Na/K pump proteins are modulated to the higher frequency with a large increas e of pump currents, and the membrane resting potential can be hyperpolarized [130, 131] as a result. In Jorgensens paper [148] Jorgensen pointed out that the turnover rate of the Na/K pu mps on proximal cells is about 20-90 Hz in normal physiological condition, which is similar to the turnover rate of the Na/K pump proteins on the muscle cell membrane which is used in our previous paper [136]. Our synchronization-modulation method should work on the kidneys Na/K pumps as well. Micropipettes filled with oil and Solution One are used as described before. After the lumen potential reaches a constant value, synchronization-modulation stimulation electric train is applied to the kidney. In this experiment, two different trains with a slight difference are used: in the first train, the poten tial of the last pulse of the train changes from -1 V to 0 V, and in the second train, the potential of the last pulse changes from 1 V to 0 V. Two examples of th e results are shown in Figur e 7.10 and Figure 7.11. The lumen

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potential reaches the highest value after the st imulation train stops in both experiments. Then the potential gradually (the time constant is about a range of 50 s to 150 s) returns to a new saturation state; however, the value of the potential is higher than the potential obtained without a train stimul ation. The potential increases about 3-7 mV which is about 25%~35% increase over the original lumen potential. 133 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 0 50100150200250Time (s)Voltage (mV) Figure 7.10 After the lumen potentia l reaches a constant value, the stimulation electric field train (synchronization-modulation) is applied to the kidney. The new build-up potential is in creased about 3-7 mV.

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134 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 050100150200250300350Time (s)Voltage (mV) Figure 7.11 Same as Figure 7.10 except that th e potential of the last pulse of the stimulation train changes from -1 V to 0 V instead of from 1 V to 0 V. In Figure 7.12 and Figure 7.13, the detailed information of the last pulse for both experiments is shown. We obtain the same result no matter if the potential changes from 1 V to 0 V or from -1 V to 0 V. The lume n potentials have similar shape and magnitude after the trains are finished. The highes t lumen potential reaches around zero voltage, which is probably due to the f act that most of Na+ ions are absorbed by the tubular cells.

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135 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 99 149 199 Time (s)Voltage (mV) 0 V -1 V Figure 7.12 Detailed information of the last pulse in Figure 7.10

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-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 158 208 Time (s)Voltage (mV) 136 Figure 7.13 Detailed information of the last pulse in Figure 7.11 (3) Confirm experiments To confirm that the potential increase inside the lumen is caused by the high activities of Na/K pumps and Na+ ions reabsorption process due to the electric stimulation train, we conducted several experiments. In the first experiment, high concentration Ouabain (20 mM) is used in Solution One in order to block most Na/K pump prot eins, pursuant to Jo rgensens paper [148]. With high concentration Ouabain inside of th e solution, the potentia l of the lumen after 1 V 0 V

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synchronization-modulation electric stimulation train does not show a significant increase (Figure 7.14). This experiment proves that th e increase of the lumen potential is resulted from the Na/K pump activities. Figure 7.14 When high concentration Ouabain is resolved in the injected solution, the lumen potential does not show significan t change after stimulation train. In the second experiment, only two electri c stimulation pulses are applied to the kidney (Figure 7.15 and Figure 7.16) to see whet her the lumen potential increases with a short electric field stimulation. Figure 7.15 shows that the train changes from -1V to 0V during the last pulse; and Figur e 7.16 shows that the potential changes from 1V to 0V during the last pulse. The results reveal that the lumen potential does not change significantly under those two stimulations. This experiment proves that the potential increases only under long synchronizationmodulation electric stimulation train. 137

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1 V 138 -200 -150 -100 -50 0 50 100 150 200 02 04 06 08Time (ms)Voltage (mV)0 Figure 7.15 The top of the Figure shows two elec tric stimulation pulses which are applied to the kidney. The bottom of the Figur e shows the lumen potential responding to the pulses. 0 V -1 V

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1 V 0 V -1 V -200 -150 -100 -50 0 50 100 150 20002 04 06 08Time (ms)Voltage (mV)0 Figure 7.16 Same as 7.15 except that the potential of the last pul se changes from 1 V to 0 V instead of from -1 V to 0 V. In the third experiment, 95% of the Na+ ions are replaced by K+ ions in Solution One, which is injected into the tubule af ter the mixed oil inje ction. Under electric stimulation, the potential of th e inside of the lumen changes slightly (the result is, therefore, omitted here. See Figure 7.14 for sim ilar result) compared to the result in the previous experiment. The driving force of Na+ ions reabsorption is based on the concentration difference across the membrane generated by Na/K pump proteins; and the driving force of other ionic transport system s is based on the reabsorption of Na+ ions. Actually, in kidney, more than 99% of the tr ansported electrolytes are coupled with the 139

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primary active Na/K pumps [157]. In this experiment, only a very small amount of Na+ ions are available to be trans ported inside of the lumen, so it is a reasonable result that the potential does not change too much inside of the lumen. The experiment proves that Na+ ions play an indispensable role in the increase of the lumen potential. In proximal tubule, Na+, HCO3H+ and Clions are the most important ions to contribute to the lumen potenti al change. In the fourth experiment, Solution Two (without HCO3ions) is used instead of Solution One. After electric stimulation train, the result shows that the lumen potential can still be in creased, but with less value (1 mV to 4 mV, Figure 7.17). This experiment proves that HCO3-, like Clions, contributes partially to the increase of the lumen potential. 140 -24 -22 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 050100150200250300350 Time (s)Voltage (mV) Figure 7.17 Solution Two (without HCO3ions) is used instead of Solution One. After electric stimulation train, the lumen potential can s till be increased, but with less value compared to Figure 7.10.

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141 The above four confirm experiments prove that the lumen potential increase results from high Na/K pump activity genera ted by synchronizationmodulation electric train. The high Na/K pump turnover rate will re quire more Na+ ions to be absorbed. Na+ ions and others ions, such as HCO3-, H+ and Clions, work together to increase the lumen potential. (4) Experiments without blockage of proxima l tubular segment and under electric field stimulation This group of experiments is to test th e lumen potential without oil blockage of the segment. If electric field can generate po tential difference in the insulating segments as mentioned before, it should affect Na/K pu mp proteins even without oil blockage. The only difference is that after stimulation, th e lumen potential cannot stay at the new potential level, because the kidney will return to the normal condition after the stimulation train. Figure 7.18 confirms that the potential changes in a way as we expected under the synchronization-modulation electric stimulation train. Within 100-150 s after the stimulation train stops, the lumen potential gradually decreases to the original value.

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142 -30 -25 -20 -15 -10 -5 0 5 10 15 20 050100150200250300350 Time (s)Voltage (mV) Figure 7.18 After the stimulation tr ain is finished, the lumen potential gradually decreases to the original value when the tubule is not blocked by oil. Discussion The Na/K pumps in a renal tubular cell ar e exclusively located in the peritubular membrane and are considered to play a majo r role in ions transport across the cell membrane through hydrolysis of ATP to genera te electro-chemical gradients. The most important substrates in proximal tubule ce ll transport system which can affect the potential are Na+, H+, Cland HCO3-, each of which may involve passive or active transports. But almost all ions reabsorption process is based on th e Na+ ion reabsorption which is determined by Na/K pump activity.

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143 In the previous chapters, we have experimentally demonstrated that synchronization-modulation electr ic train can accelerate Na/K pump turnover rate, which forces Na/K pumps to follow the train frequenc ies, resulting in a large increase in pump currents. In Chen and Dandos paper [130,131], the same method is applied to intact fibers. The membrane resting po tential can be hyperpolarized. In this research, the tubule cells, under the high activities of the Na/K pumps resulting from the influence of an electric field, can absorb more Na+ ions from the lumen fluid to the peritubular fluid. The process of Na+ and other ion reabsorption and se cretion will result in an increase of the lumen potential. In Jorgensens paper [148], th e author reached the same conclusion: the lumen potential changes positively due to anion transport from lumen to peritubular fluid or due to secretion of cation from cytoplas m to lumen. We already confirmed that the potential increase inside the lumen is caused by the high activity of Na/K pumps and Na+ ions reabsorption process due to the electric stim ulation train. However, what is the mechanism of the potential increase? In order to explain the potential change resulting from high Na/K pump activity due to the influence of an electric field, Na+, H+, HCO3and Clions transports have to be taken into consideration, which make the transport process a very co mplex secretion and reabsorption system in proximal tubule. The reabsorption of Na+ ions is a major event in proximal tubule transport system which is combined with other ions transpor t system. We will consider two reabsorption and secretion groups: (1) Na+ / H+ / HCO3and (2) Na+ / Cl/ HCO3-, to find out how the lumen potential can be increased unde r high activities of the Na/K pump by the

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144 influence of the electric field stimulati on, although those two groups are not totally independent processes. (1) Proximal tubule cells have a relativel y high density of Na/H exchangers at both sides of the cell membrane. The Na/H ex changer results in ne t Na+ ions absorption. The Na/H exchanger serves as a pathway for cellular influx of Na+ and is a major mechanism of extrusion of intracellular H+ ions to the lumen, which is a main factor to absorb the HCO3ions. The secretion of H+ ions is opposed to reabsorption of HCO3ions. Results from other researchers [163, 164] demonstrate that the in crease of the Na/K pumping rate requires an increase of intr acellular Na+ ions which can be achieved by increasing Na+ influx through increased Na/H exchangers. There is an indirect way to couple HCO3ions reabsorption and Na+ ions reabsorption on the renal reabsorption system (Figure 7.19). First, Na/H exchangers transfer H+ ions to the lu men fluid. There, the H+ ions are used to combine HCO3ions and convert to CO2 and H2O. These two products (CO2 + H2O) enter the proximal tubular cells through water single-ports which assist in diffusion of H2O and may also play a role in CO2 uptake. Inside the cell, CO2 and H2O are converted to H+ (which is extruded into the lumen by Na/H exchangers) and HCO3again. Sym-ports on the membrane between th e tubular cells and peritubular fluid operate with a stoichiometry of 1:3 of Na /HCO3[163, 171] (export three HCO3ions to peritubular fluid with each Na + ion). As a result, two net negative charges (HCO3ions) cross the plasma membrane. This process will affect the potential difference between the lumen and the peritubular fluid and make the lumen potential more positive. Under synchronization-modulation electr ic train, more Na+ ions are transported from the lumen

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and more HCO3ions are transported across the tubular cells which result in the increase of the lumen potential. In his paper [148], Jorgensen came to the same conclusion. 145 Figure 7.19 A sketch of Na+ / H+ / HCO3ions transport system in the proximal tubule segment. (2) In the reabsorption process of Na+ and HCO3ions as we described before, water molecules are also reabsorbed when HCO3ions are transported into the cell, which will increase the concentration of Clions inside of the lumen from 1 to 1.2-1.4 [167, 168]. According to Karols paper [167] the reabsorption process of HCO3ions is preferred over Clions in the proximal-tubule reabsorption system. In John and Edwards Tubular Cell Lumen Peritubular Flui d 3Na+ Na+ 2K+ 3 HCO3H+ + HCO3CO2 + H2O H2CO3 Na+ Na/3HCO3 sym-port Na/K pump H+ Na/H exchanger

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146 paper [168], experimental results indicate that the ab sorption process of HCO3ions can partially inhibit net Clions absorption in the early proximal tubule system and when luminal Clconcentration is raised, the lumen potential becomes more positive [168,170]. Although HCO3ions dominate when HCO3and Clions are present at the same time, the Clions still can be transporte d into the peritubular fluid. Because the mechanism of H+ ions secreti on favors the reabsorption of HCO3over that of Clions, tubular flows pH and HCO3concentrations both decrease [148,151], whereas net Clabsorption increases [167]. The luminal fluid acidification will reduce the efficiency of the Na/H exchangers. Clions transport across membrane is also coupled to Na+ ion uptake (Figure 7.20). Experimental evidence indicates that a pproximately 50% of Clions reabsorption is dependent on the presence of Na+ ions, and this sym-ports absorption is electroneutral since Na+/Cl= 1. The other 50% of Clions is diffused into the peritubular fluid (Figure 7.20). Clions transport systems in proxima l tubule are both active and passive and the process depends on Na+, H+ and HCO3ions as well as acid-base metabolism [174]. The whole process of Clions reabsorption is electrogenic since the net negative charges cross the membrane, which results in the increase of the lumen potential. Na+ ions working together with other ions (Cl-, H+ and HCO3-) can generate the positive potential increase in the proximal t ubule lumen by high activities of Na/K pumps due to the electric synchronizatio n-modulation stimulation trains

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147 Figure 7.20 A sketch of Na+ / Cl/ HCO3ions transport system in the proximal tubule segment. Conclusion In the previous chapters, we have pr oved the synchronization-modulation method at the single cell level, whic h can effectively build up a new potential difference across the cell membrane by high activities of Na /K pumps. For this research, the same synchronization and modulation pr otocol is applied to the ra t kidney, which is the first step to apply this theory at the organ level. Under the influence of electric field, more Na+ ions are reabsorbed, and the potential of th e inside of the tubule is more depolarized. The increase of the potential is a result of the complex combination of Na+, H+, HCO3and Clions secretion and reabsorption processes inside of the proximal tubule. Na+ Cl2K+ Lumen HCO3ClTubular Cell Peritubular Flui d 3Na+ Na/K pump

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148 Chapter 8 Conclusion and Future Study A large number of pharmacological agents (n eurotoxins) have b een identified that can affect electrically exc itable cell channel currents. The most important channel blockers are Tetrodotoxin (TTX) and Ter aethylammonium (TEA), which selectively block Na+ and K+ channels. These agents en able investigators to block either Na+ current or K+ current in a reversible ma nner and make the study of individual ionic current more convenient. In first part of my research, we su ccessfully used well-designed electric stimulation pulse train to block Na+ and K+ channels and found out that almost all of individual Na+ and K+ channel proteins are forced to stay in un-conductive state under electric field. Those results indicate that Na+ and K+ channel prot eins can be blocked by an electric method, instead of using chemical s such as TTX and TEA. This research not only introduces a new method in basic scien ce research but also has great clinical potential. Numerous diseases and disorders are dire ctly related to the functions of Na/K pump proteins, like heart failure, hypothyroidis im, McArdle disease, diabetes and cystic fibrosis. Failures of Na/K pump molecules can be grouped into two categories. In some diseases, patients have very low density of Na/K pump molecules on the cell membrane. In other cases, patients have normal density of pump molecules, but they face a shortage

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149 of nourishment or oxygen which re sults in a lack of ATP mo lecules to fuel Na/K pump molecules. A common phenomenon of these di seased cells is a reduction in ionic concentration gradient or depolarization of the membrane potential. In order to restore these features, a possible fast and economic option is to activate Na/K pump proteins. Significant efforts have been made to study Na/K pump proteins. We recently developed a new approach: dynamic entrainment of Na/K molecules. In this approach we consider molecules energy absorption as a procedure of electric al synchronization and modulation of pump molecules, instead of transient event. In the first step, we organized pump molecules together at the same p ace by electric train. The pumping rate of synchronized pump molecule is then further gradually modulated to a higher value by a well designed oscillating electric field. Our e xperiments in skeletal muscle fibers have demonstrated synchronization and modulati on phenomena of Na/K pump molecules and up to several fold increase in pump currents. After single cell level stu dy, we move to the organ level rats kidney because kidney has plenty of Na/K pump molecules on the cell membrane to reabsorb ions in all tubular segments. Active Na/K pumps directly increase the rate of ions reabsorption and the potential inside the lumen. This research proves that the synchronization-modulation method can work at the organ level as well. Our research has huge potential in clinical applications, but we have to figure out how to non-invasively put electric stimula tion train on the project not only kidney but also other organs like hear t, brain and skin, etc.

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170 List of Publications 1. Z-S. Zhang, D.A. Rabson, Diagnosis and Lo cation of a Pinhole in a Tunnel Junction Using Only Electrical Measurements, J. Appl. Phys. 95 199-203 (2004) 2. Z.-S. Zhang, D.A. Rabson, Electrical a nd Thermal Modeling of the Non-Ohmic Differential Conductance in a Tunnel Junction Containing a Pinhole, J. Appl. Phys. 95, 557-560 (2004) 3. Wei Chen, Zhongsheng Zhang, Raphael C. Lee, Supramembrane potential-induced electroconformational changes in sodium channel proteins: A potential mechanism involved in electric inju ry, Burns 32, 52-59 (2005) 4. Wei Chen, Zhongsheng Zhang, Synchronization of Na/K pump molecules by a train of squared pulses, J Bioenerg Biomembr 38:319(2006) 5. Wei Chen, Zhongsheng Zhang, Feiran Huang, Entrainment of Na/K pumps by a synchronization modulation electric field J Bioenerg Biomembr 39:331 (2007)

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About the Author Zhongsheng Zhang graduated from Beijing In stitute of Machinery in P. R. China (1994) with a Bachelor degree in Mechanical Engineering. He trav eled to U.S.A. to complete his Ph. D. degree at University of South Florida. Before he joined Dr. Chens Biophysics group, he has received two Masters degrees (2003) from the Department of Physics and the Department of Electrical Engineering. He ha s published four papers (one paper is in press) in the field of Biophysic s and two papers in Co mputational Physics.


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ABSTRACT: The most important and most common channels on cell membrane are voltage-gated Na+ and K+ channels. In so-called "excitable cells" like neurons and muscle cells, these channels open or close in response to changes in potential across the membrane in order to accomplish muscle contraction and transmit signals. By controlling the membrane potential, we observe extraordinary inactivation behaviors of the voltage-gated Na+ channels and the voltage-gated delayed rectifier K+ channels, which shows that electric stimulation pulses can temporarily close the Na+ and K+ channels, just as drugs, like tetrodotoxin (TTX) and tetraethylammonium (ETA), do. The Na/K pump is essential for living system and is expressed in virtually all cell membranes.The ionic transport conducted by Na/K pumps creates both an electrical and a chemical gradient across the plasma membrane, which are required for maintaining membrane potentials, cell volume, and secondary active transport of other solutes, etc. We use a pulsed, symmetric, oscillating membrane potential with a frequency close to the mean physiological turnover rate across the cell membrane to synchronize Na/K pump molecules. The pump molecules can work as a group, pumping at a synchronized pace after a long train of pulses. As a result, the pump functions can be significantly increased. After the pump molecules are synchronized, the applied electric-field frequency can gradually increase in order to resynchronize the molecules to a new, higher frequency. Modulating the pump molecules to a higher frequency leads to a significant increase of pump current. Synchronization and modulation of pump molecules can become a new method to study the function of Na/K pump molecules.This method has huge potential applications in clinic medical treatment. After single-fiber-level study, the final project is on organ level, the rat kidney, by using synchronization and modulation of Na/K pump molecules on the proximal tubule membrane. Because Na+ re-absorption is directly related to the function of the Na/K pump, the more active Na/K pumps are, the more Na+ ions can be absorbed, which results in an increased potential inside the renal proximal tubule. This project is the first step of synchronization and modulation applied on the level of an organ.
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