1. Introduction 563

2. Obtaining rate constants from molecular-dynamics simulations 564

2.1 General relationships between quantum electronic structures and reaction rates 564

2.2 The transition-state theory (TST) 569

2.3 The transmission coefficient 572

3. Simulating biological electron-transfer reactions 575

3.1 Semi-classical surface-hopping and the Marcus equation 575

3.2 Treating quantum mechanical nuclear tunneling by the dispersed-polaron/spin-boson method 580

3.3 Density-matrix treatments 583

3.4 Charge separation in photosynthetic bacterial reaction centers 584

4. Light-induced photoisomerizations in rhodopsin and bacteriorhodopsin 596

5. Energetics and dynamics of enzyme reactions 614

5.1 The empirical-valence-bond treatment and free-energy perturbation methods 614

5.2 Activation energies are decreased in enzymes relative to solution, often by electrostatic effects that stabilize the transition state 620

5.3 Entropic effects in enzyme catalysis 627

5.4 What is meant by dynamical contributions to catalysis? 634

5.5 Transmission coefficients are similar for corresponding reactions in enzymes and water 636

5.6 Non-equilibrium solvation effects contribute to catalysis mainly through Δg[Dagger], not the transmission coefficient 641

5.7 Vibrationally assisted nuclear tunneling in enzyme catalysis 648

5.8 Diffusive processes in enzyme reactions and transmembrane channels 651

6. Concluding remarks 658

7. Acknowledgements 658

8. References 658

Obtaining a detailed understanding of the dynamics of a biochemical reaction is a formidable challenge. Indeed, it might appear at first sight that reactions in proteins are too complex to analyze microscopically. At room temperature, even a relatively small protein can have as many as 1034 accessible conformational states (Dill, 1985). In many cases, however, we have detailed structural information about the active site of an enzyme, whereas such information is missing for corresponding chemical systems in solution. The atomic coordinates of the chromophore in bacteriorhodopsin, for example, are known to a resolution of 1–2 Å. In addition, experimental studies of biological processes such as photoisomerization and electron transfer have provided a wealth of detailed information that eventually may make some of these processes classical problems in chemical physics as well as biology.