Molecular and Cellular Biophysics

Cambridge University Press
052162441X - Molecular and Cellular Biophysics - by Meyer B. Jackson
Frontmatter/Prelims

Molecular and Cellular Biophysics

This book provides advanced undergraduate and beginning graduate students with a foundation in the basic concepts of molecular and cellular biophysics. Students who have taken physical chemistry and calculus courses will find this book an accessible and valuable aid in learning how these concepts can be used in biological research. The text provides a rigorous treatment of the fundamental theories in biophysics and illustrates their application with examples. Conformational transitions of proteins are studied first using thermodynamics, and subsequently with kinetics. Allosteric theory is developed as the synthesis of conformational transitions and association reactions. Basic ideas of thermodynamics and kinetics are applied to topics such as protein folding, enzyme catalysis and ion channel permeation. These concepts are then used as the building blocks in a treatment of membrane excitability. Through these examples, students will gain an understanding of the general importance and broad applicability of biophysical principles to biological problems.

Meyer B. Jackson is the Kenneth Cole Professor of Physiology at the University of Wisconsin Medical School. He has been teaching graduate level biophysics for nearly 25 years.

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Molecular and Cellular Biophysics

Meyer B. Jackson

University of Wisconsin Medical School

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CAMBRIDGE UNIVERSITY PRESS
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© Cambridge University Press 2006

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the written permission of Cambridge University Press.

First published 2006

Printed in the United Kingdom at the University Press, Cambridge

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ISBN-13 978-0-521-62441-1 hardback

ISBN-10 0-521-62441-X hardback

ISBN-13 978-0-521-62470-1 paperback

ISBN-10 0-521-62470-3 paperback

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Contents

Preface			page xii
Acknowledgements			xiv
Chapter 1    Global transitions in proteins			1
1.1	Defining a global state		2
1.2	Equilibrium between two global states		4
1.3	Global transitions induced by temperature		5
1.4	Lysozyme unfolding		7
1.5	Steepness and enthalpy		9
1.6	Cooperativity and thermal transitions		11
1.7	Transitions induced by other variables		12
1.8	Transitions induced by voltage		14
1.9	The voltage sensor of voltage-gated channels		17
1.10	Gating current		18
1.11	Cooperativity and voltage-induced transitions		19
1.12	Compliance of a global state		21
Chapter 2    Molecular forces in biological structures			25
2.1	The Coulomb potential		25
2.2	Electrostatic self-energy		27
2.3	Image forces		29
2.4	Charge–dipole interactions		31
2.5	Induced dipoles		32
2.6	Cation–π interactions		33
2.7	Dispersion forces		35
2.8	Hydrophobic forces		36
2.9	Hydration forces		39
2.10	Hydrogen bonds		39
2.11	Steric repulsions		43
2.12	Bond flexing and harmonic potentials		44
2.13	Stabilizing forces in proteins		46
2.14	Protein force fields		50
2.15	Stabilizing forces in nucleic acids		52
2.16	Lipid bilayers and membrane proteins		53
Chapter 3    Conformations of macromolecules			56
3.1	n-Butane		56
3.2	Configurational partition functions and polymer chains		58
3.3	Statistics of random coils		60
3.4	Effective segment length		62
3.5	Nonideal polymer chains and theta solvents		63
3.6	Probability distributions		65
3.7	Loop formation		66
3.8	Stretching a random coil		67
3.9	When do molecules act like random coils?		68
3.10	Backbone rotations in proteins: secondary structure		68
3.11	The entropy of protein denaturation		71
3.12	The helix–coil transition		73
3.13	Mathematical analysis of the helix–coil transition		74
3.14	Results of helix–coil theory		78
3.15	Helical propensities		80
3.16	Protein folding		82
3.17	Cooperativity in protein folding		86
Chapter 4    Molecular associations			89
4.1	Association equilibrium in solution		89
4.2	Cooperativity		91
	4.2.1	Concerted binding	91
	4.2.2	Sequential binding	93
	4.2.3	Nearest neighbor interactions	94
4.3	Thermodynamics of associations		94
4.4	Contact formation		95
4.5	Statistical mechanics of association		96
4.6	Translational free energy		98
4.7	Rotational free energy		101
4.8	Vibrational free energy		102
4.9	Solvation effects		105
4.10	Configurational free energy		106
4.11	Protein association in membranes – reduction of dimensionality		107
4.12	Binding to membranes		108
Chapter 5    Allosteric interactions			111
5.1	The allosteric transition		112
5.2	The simplest case: one binding site and one allosteric transition		112
5.3	Binding and response		115
5.4	Energy balance in the one-site model		116
5.5	G-protein coupled receptors		117
5.6	Binding site interactions		121
5.7	The Monod–Wyman–Changeux (MWC) model		123
5.8	Hemoglobin		126
5.9	Energetics of the MWC model		127
5.10	Macroscopic and microscopic additivity		128
5.11	Phosphofructokinase		130
5.12	Ligand-gated channels		132
5.13	Subunit–subunit interactions: the Koshland–Nemethy–Filmer (KNF) model		134
5.14	The Szabo–Karplus (SK) model		137
Chapter 6    Diffusion and Brownian motion			142
6.1	Macroscopic diffusion: Fick’s laws		142
6.2	Solving the diffusion equation		143
	6.2.1	One-dimensional diffusion from a point	144
	6.2.2	Three-dimensional diffusion from a point	146
	6.2.3	Diffusion across an interface	146
	6.2.4	Diffusion with boundary conditions	148
6.3	Diffusion at steady state		150
	6.3.1	A long pipe	151
	6.3.2	A small hole	152
	6.3.3	A porous membrane	153
6.4	Microscopic diffusion – random walks		154
6.5	Random walks and the Gaussian distribution		156
6.6	The diffusion equation from microscopic theory		159
6.7	Friction		160
6.8	Stokes’ law		162
6.9	Diffusion constants of macromolecules		163
6.10	Lateral diffusion in membranes		164
Chapter 7    Fundamental rate processes			167
7.1	Exponential relaxations		167
7.2	Activation energies		169
7.3	The reaction coordinate and detailed balance		170
7.4	Linear free energy relations		172
7.5	Voltage-dependent rate constants		175
7.6	The Marcus free energy relation		177
7.7	Eyring theory		179
7.8	Diffusion over a barrier – Kramers’ theory		180
7.9	Single-channel kinetics		183
7.10	The reaction coordinate for a global transition		186
Chapter 8    Association kinetics			194
8.1	Bimolecular association		194
8.2	Small perturbations		195
8.3	Diffusion-limited association		197
8.4	Diffusion-limited dissociation		200
8.5	Site binding		201
8.6	Protein–ligand association rates		203
	8.6.1	Evolution of speed	205
	8.6.2	Acetylcholinesterase	205
	8.6.3	Horseradish peroxidase	206
8.7	Proton transfer		207
8.8	Binding to membrane receptors		208
8.9	Reduction in dimensionality		212
8.10	Binding to DNA		214
Chapter 9    Multi-state kinetics			216
9.1	The three-state model		216
9.2	Initial conditions		219
9.3	Separation of timescales		220
9.4	General solution to multi-state systems		221
9.5	The three-state model in matrix notation		225
9.6	Stationarity, conservation, and detailed balance		226
9.7	Single-channel kinetics: the three-state model		229
9.8	Separation of timescales in single channels: burst analysis		232
9.9	General treatment of single-channel kinetics: state counting		235
9.10	Relation between single-channel and macroscopic kinetics		236
9.11	Loss of stationarity, conservation, and detailed balance		237
9.12	Single-channel correlations: pathway counting		240
9.13	Multisubunit kinetics		242
9.14	Random walks and “stretched kinetics”		244
Chapter 10    Enzyme catalysis			248
10.1	Basic mechanisms – serine proteases		248
10.2	Michaelis–Menten kinetics		251
10.3	Steady-state approximations		254
10.4	Pre-steady-state kinetics		256
10.5	Allosteric enzymes		257
10.6	Utilization of binding energy		258
10.7	Kramers’ rate theory and catalysis		259
10.8	Proximity and translational entropy		260
10.9	Rotational entropy		263
10.10	Reducing E†: transition state complementarity		264
10.11	Friction in an enzyme–substrate complex		267
10.12	General-acid–base catalysis and Brønsted slopes		268
10.13	Acid–base catalysis in β-galactosidase		270
10.14	Catalysis in serine proteases and strong H-bonds		272
10.15	Marcus’ theory and proton transfer in carbonic anhydrase		273
Chapter 11    Ions and counterions			276
11.1	The Poisson–Boltzmann equation and the Debye length		277
11.2	Activity coefficient of an ion		279
11.3	Ionization of proteins		283
11.4	Gouy–Chapman theory and membrane surface charge		285
11.5	Stern’s improvements of Gouy–Chapman theory		288
11.6	Surface charge and channel conductance		291
11.7	Surface charge and voltage gating		293
11.8	Electrophoretic mobility		294
11.9	Polyelectrolyte solutions I. Debye–Hückel screening		297
11.10	Polyelectrolyte solutions II. Counterion-condensation		300
11.11	DNA melting		302
Chapter 12    Fluctuations			307
12.1	Deviations from the mean		307
12.2	Number fluctuations and the Poisson distribution		309
12.3	The statistics of light detection by the eye		311
12.4	Equipartition of energy		313
12.5	Energy fluctuations in a macromolecule		315
12.6	Fluctuations in protein ionization		317
12.7	Fluctuations in a two-state system		319
12.8	Single-channel current		320
12.9	The correlation function of a two-state system		322
12.10	The Wiener–Khintchine theorem		324
12.11	Channel noise		327
12.12	Circuit noise		329
12.13	Fluorescence correlation spectroscopy		332
12.14	Friction and the fluctuation–dissipation theorem		336
Chapter 13    Ion permeation and membrane potential			339
13.1	Nernst potentials		339
13.2	Donnan potentials		341
13.3	Membrane potentials of cells		343
	13.3.1	Neurons	345
	13.3.2	Vertebrate skeletal muscle	345
13.4	A membrane permeable to Na+ and K+		347
13.5	Membrane potentials of neurons again		350
13.6	The Ussing flux ratio and active transport		351
13.7	The Goldman–Hodgkin–Katz voltage equation		352
13.8	Membrane pumps and potentials		354
13.9	Transporters and potentials		355
13.10	The Goldman–Hodgkin–Katz current equation		357
13.11	Divalent ions		360
13.12	Surface charge and membrane potentials		361
13.13	Rate theory and membrane potentials		362
Chapter 14    Ion permeation and channel structure			367
14.1	Permeation without channels		367
14.2	The Ohmic channel		370
14.3	Energy barriers and channel properties		371
14.4	Eisenman selectivity sequences		374
14.5	Forces inside an ion channel		376
14.6	Gramicidin A		378
14.7	Rate theory for multibarrier channels		380
14.8	Single-ion channels		384
14.9	Single-file channels		390
14.10	The KcsA channel		394
Chapter 15    Cable theory			400
15.1	Current through membranes and cytoplasm		401
15.2	The cable equation		403
15.3	Steady state in a finite cable		406
15.4	Voltage steps in a finite cable		408
15.5	Current steps in a finite cable		411
15.6	Branches and equivalent cylinder representations		412
	15.6.1	Steady state	413
	15.6.2	Time constants	415
15.7	Cable analysis of a neuron		418
15.8	Synaptic integration in dendrites: analytical models		422
	15.8.1	Impulse responses	423
	15.8.2	Realistic synaptic inputs	425
15.9	Compartmental models and cable theory		428
15.10	Synaptic integration in dendrites: compartmental models		430
Chapter 16    Action potentials			434
16.1	The action potential		434
16.2	The voltage clamp and the properties of Na+ and K+ channels		439
16.3	The Hodgkin–Huxley equations		442
16.4	Current–voltage curves and thresholds		447
16.5	Propagation		450
16.6	Myelin		453
16.7	Axon geometry and conduction		455
16.8	Channel diversity		457
16.9	Repetitive activity and the A-current		458
16.10	Oscillations		461
16.11	Dendritic integration		466
Appendix 1    Expansions and series			470
A1.1	Taylor series		470
A1.2	The binomial expansion		471
A1.3	Geometric series		471

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