Theoretical Molecular Biophysics

by Scherer, P. O. J.; Fischer, Sighart F.

• ISBN13: 9783540856092
• ISBN10: 3540856099
• Format: Hardcover
• Copyright: 2010-09-04
• Publisher: Springer Verlag

Summary

"Theoretical Molecular Biophysics" is an advanced study book for students, shortly before or after completing undergraduate studies, in physics, chemistry or biology. It provides the tools for an understanding of elementary processes in biology, such as photosynthesis on a molecular level. A basic knowledge in Mechanics, Electrostatics, Quantum Theory and Statistical Physics is desirable. The reader will be exposed to basic concepts in modern biophysics such as entropic forces, phase separation, potentials of mean force, proton and electron transfer, heterogeneous reactions coherent and incoherent energy transfer as well as molecular motors.

Table of Contents

Statistical Mechanics of Biopolymers
Random Walk Models for the Conformation	p. 3
The Freely Jointed Chain	p. 3
Entropic Elasticity	p. 4
Force-Extension Relation	p. 6
Two-Component Model	p. 9
Force-Extension Relation	p. 9
Two-Component Model with Interactions	p. 11
Problems	p. 16
Flory-Huggins Theory for Biopolymer Solutions	p. 19
Monomeric Solution	p. 19
Polymeric Solution	p. 22
Phase Transitions	p. 26
Stability Criterion	p. 26
Critical Coupling	p. 28
Phase Diagram	p. 30
Problems	p. 33
Protein Electrostatics and Solvation
Implicit Continuum Solvent Models	p. 37
Potential of Mean Force	p. 37
Dielectric Continuum Model	p. 38
Born Model	p. 39
Charges in a Protein	p. 40
Generalized Born Models	p. 43
Debye-Hückel Theory	p. 45
Electrostatic Shielding by Mobile Charges	p. 45
1-1 Electrolytes	p. 46
Charged Sphere	p. 47
Charged Cylinder	p. 49
Charged Membrane (Goüy-Chapman Double Layer)	p. 52
Stern Modification of the Double Layer	p. 57
Problems	p. 58
Protonation Equilibria	p. 61
Protonation Equilibria in Solution	p. 61
Protonation Equilibria in Proteins	p. 64
Apparent pKaValues	p. 65
Protonation Enthalpy	p. 66
Protonation Enthalpy Relative to the Uncharged State	p. 68
Statistical Mechanics of Protonation	p. 69
Abnormal Titration Curves of Coupled Residues	p. 70
Problems	p. 71
Reaction Kinetics
Formal Kinetics	p. 75
Elementary Chemical Reactions	p. 75
Reaction Variable and Reaction Rate	p. 75
Reaction Order	p. 76
Zero-Order Reactions	p. 77
First-Order Reactions	p. 77
Second-Order Reactions	p. 77
Dynamical Equilibrium	p. 78
Competing Reactions	p. 79
Consecutive Reactions	p. 79
Enzymatic Catalysis	p. 80
Reactions in Solutions	p. 82
Diffusion-Controlled Limit	p. 83
Reaction-Controlled Limit	p. 84
Problems	p. 84
Kinetic Theory: Fokker-Planck Equation	p. 87
Stochastic Differential Equation for Brownian Motion	p. 87
Probability Distribution	p. 89
Diffusion	p. 90
Sharp Initial Distribution	p. 91
Absorbing Boundary	p. 92
Fokker-Planck Equation for Brownian Motion	p. 93
Stationary Solution to the Focker-Planck Equation	p. 94
Diffusion in an External Potential	p. 96
Large Friction Limit: Smoluchowski Equation	p. 98
Master Equation	p. 98
Problems	p. 98
Kramers' Theory	p. 101
Kramers' Model	p. 101
Kramers' Calculation of the Reaction Rate	p. 102
Dispersive Kinetics	p. 107
Dichotomous Model	p. 107
Fast Solvent Fluctuations	p. 110
Slow Solvent Fluctuations	p. 111
Numerical Example (Fig. 9.3)	p. 112
Continuous Time Random Walk Processes	p. 112
Formulation of the Model	p. 112
Exponential Waiting Time Distribution	p. 114
Coupled Equations	p. 115
Power Time Law Kinetics	p. 119
Problems	p. 121
Transport Processes
Nonequilibrium Thermodynamics	p. 125
Continuity Equation for the Mass Density	p. 125
Energy Conservation	p. 127
Entropy Production	p. 128
Phenomenological Relations	p. 130
Stationary States	p. 130
Problems	p. 132
Simple Transport Processes	p. 133
Heat Transport	p. 133
Diffusion in an External Electric Field	p. 134
Problems	p. 136
Ion Transport Through a Membrane	p. 139
Diffusive Transport	p. 139
Goldman-Hodgkin-Katz Model	p. 141
Hodgkin-Huxley Model	p. 144
Reaction-Diffusion Systems	p. 147
Derivation	p. 147
Linearization	p. 148
Fitzhugh-Nagumo Model	p. 149
Reaction Rate Theory
Equilibrium Reactions	p. 155
Arrhenius Law	p. 155
Statistical Interpretation of the Equilibrium Constant	p. 157
Calculation of Reaction Rates	p. 159
Collision Theory	p. 159
Transition State Theory	p. 162
Comparison Between Collision Theory and Transition State Theory	p. 164
Thermodynamical Formulation of TSt	p. 165
Kinetic Isotope Effects	p. 166
General Rate Expressions	p. 168
The Flux Operator	p. 168
Problems	p. 170
Marcus Theory of Electron Transfer	p. 173
Phenomenological Description of ET	p. 173
Simple Explanation of Marcus Theory	p. 175
Free Energy Contribution of the Nonequilibrium Polarization	p. 177
Activation Energy	p. 180
Simple Model Systems	p. 184
Charge Separation	p. 186
Charge Shift	p. 186
The Energy Gap as the Reaction Coordinate	p. 187
Inner-Shell Reorganization	p. 189
The Transmission Coefficient for Nonadiabatic Electron Transfer	p. 189
Problems	p. 190
Elementary Photophysics
Molecular States	p. 195
Born-Oppenheimer Separation	p. 195
Nonadiabatic Interaction	p. 197
Optical Transitions	p. 201
Dipole Transitions in the Condon Approximation	p. 201
Time Correlation Function Formalism	p. 202
Problems	p. 203
The Displaced Harmonic Oscillator Model	p. 205
The Time Correlation Function in the Displaced Harmonic Oscillator Approximation	p. 205
High-Frequency Modes	p. 206
The Short-Time Approximation	p. 207
Spectral Diffusion	p. 209
Dephasing	p. 209
Gaussian Fluctuations	p. 211
Long Correlation Time	p. 212
Short Correlation Time	p. 213
Markovian Modulation	p. 214
Problems	p. 217
Crossing of Two Electronic States	p. 219
Adiabatic and Diabatic States	p. 219
Semiclassical Treatment	p. 223
Application to Diabatic Et	p. 224
Crossing in More Dimensions	p. 225
Problems	p. 227
Dynamics of an Excited State	p. 229
Green's Formalism	p. 230
Ladder Model	p. 233
A More General Ladder Model	p. 237
Application to the Displaced Oscillator Model	p. 240
Problems	p. 242
Elementary Photoinduced Processes
Photophysics of Chlorophylls and Carotenoids	p. 247
MO Model for the Electronic States	p. 248
The Free Electron Model for Polyenes	p. 249
The LCAO Approximation	p. 250
Hückel Approximation	p. 251
Simplified CI Model for Polyenes	p. 253
Cyclic Polyene as a Model for Porphyrins	p. 253
The Four Orbital Model for Porphyrins	p. 254
Energy Transfer Processes	p. 256
Problems	p. 257
Incoherent Energy Transfer	p. 259
Excited States	p. 259
Interaction Matrix Element	p. 260
Multipole Expansion of the Excitonic Interaction	p. 262
Energy Transfer Rate	p. 263
Spectral Overlap	p. 264
Energy Transfer in the Triplet State	p. 268
Coherent Excitations in Photosynthetic Systems	p. 269
Coherent Excitations	p. 270
Strongly Coupled Dimers	p. 270
Excitonic Structure of the Reaction Center	p. 273
Circular Molecular Aggregates	p. 274
Dimerized Systems of LH2	p. 280
Influence of Disorder	p. 285
Symmetry-Breaking Local Perturbation	p. 285
Periodic Modulation	p. 287
Diagonal Disorder	p. 290
Off-Diagonal Disorder	p. 292
Problems	p. 293
Ultrafast Electron Transfer Processes in the Photosynthetic Reaction Center	p. 297
Proton Transfer in Biomolecules	p. 301
The Proton Pump Bacteriorhodopsin	p. 301
Born-Oppenheimer Separation	p. 303
Nonadiabatic Proton Transfer (Small Coupling)	p. 305
Strongly Bound Protons	p. 306
Adiabatic Proton Transfer	p. 308
Molecular Motor Models
Continuous Ratchet Models	p. 311
Transport Equations	p. 311
Chemical Transitions	p. 313
The Two-State Model	p. 314
The Chemical Cycle	p. 314
The Fast Reaction Limit	p. 317
The Fast Diffusion Limit	p. 317
Operation Close to Thermal Equilibrium	p. 319
Problems	p. 320
Discrete Ratchet Models	p. 323
Linear Model with Two Internal States	p. 324
Appendix
The Grand Canonical Ensemble	p. 329
Grand Canonical Distribution	p. 329
Connection to Thermodynamics	p. 331
Time Correlation Function of the Displaced Harmonic Oscillator Model	p. 333
Evaluation of the Time Correlation Function	p. 333
Boson Algebra	p. 334
Derivation of Theorem 1	p. 334
Derivation of Theorem 2	p. 335
Derivation of Theorem 3	p. 335
Derivation of Theorem 4	p. 336
The Saddle Point Method	p. 339
Solutions	p. 341
References	p. 365
Index	p. 369
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