Abstract
Reactions and conformational fluctuations govern all aspects of biological processes, from enzyme catalysis to transfer of charge, matter, and information. Any deep understanding of biological reactions must be based on a sound theory of reaction dynamics. Most of the knowledge of reaction dynamics, however, has been deduced from two-body interactions of small molecules in the gas phase [1]. In contrast, biomolecules provide a complex but highly organized environment that can affect the course of the reaction. Fortunately, the complexity implies a richness of phenomena that allows the examination of fundamental aspects of reaction dynamics. Biomolecules, in particular heme proteins , form an excellent laboratory.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
S. Glasstone, K. J. Laidler, and H. Eyring. The Theory of Rate Processes. McGraw-Hill, 1941 (the standard work).
P. Hänggi, P. Talkner, and M. Borkovec. Reaction-rate theory: Fifty years after Kramers. Rev. Mod. Phys., 62:251–341, 1990.
S. Arrhenius. Über die Reaktionsgeschwindigkeit der Inversion von Rohrzucker durch Sôuren. Z. Physik. Chem., 4:226–48, 1889.
B. G. Wicke and D. O. Harris. Comparison of three numerical techniques for calculating eigenvalues of an unsymmetrical double minimum oscillator. J. Chem. Phys., 64:5236–42, 1976.
See, for instance, R. S. Berry, S. A. Rice, and J. Ross, Physical Chemistry, 2nd edition, Oxford Univ. Press, New York, 2000.
M. Dresden. H. A. Kramers: Between Tradition and Revolution. Springer, New York, 1987.
H.A. Kramers. Brownian motion in a field force and the diffusion of chemical reactions. Physica, 7:284–304, 1940.
H. C. Brinkman. Brownian motion in a field of force and the diffusion theory of chemical reactions. 2. Physica, 22:149–55, 1956.
R. Landauer and J. A. Swanson. Frequency factors in the thermally activated process. Phys. Rev., 121:1668–74, 1961.
P. Hänggi. Escape from a metastable state. J. Stat. Phys., 42:105–48, 1986.
H. Frauenfelder and P. G. Wolynes. Rate theories and puzzles of hemeprotein kinetics. Science, 229(4711):337–45, 1985.
B. Somogyi and S. Damjanovich. Relationship between the lifetime of an enzyme-substrate complex and the properties of the molecular environment. J. Theor. Bio., 48:393–401, 1975.
B. Gavish. The role of geometry and elastic strains in dynamic states of proteins. Biophys. Struct. Mech., 4:37–52, 1978.
B. Gavish and M. M. Werber. Viscosity-dependent structural fluctuations in enzyme catalysis. Biochemistry, 18:1269–75, 1979.
D. Beece, L. Eisenstein, H. Frauenfelder, D. Good, M. C. Marden, L. Reinisch, A. H. Reynolds, L. B. Sorensen, and K. T. Yue. Solvent viscosity and protein dynamics. Biochemistry, 19:5147–57, 1980.
D. Beece, S. F. Bowne, J. Czégé, L. Eisenstein, H. Frauenfelder, D. Good, M. C. Marden, J. Marque, P. Ormos, L. Reinisch, and K. T. Yue. The effect of viscosity on the photocycle of bacteriorhodopsin. Photochem. Photobiol., 33:517–22, 1981.
D. G. Truhlar, W. L. Hase, and J. T. Hynes. The current status of transition state theory. J. Phys. Chem., 87:2664–82, 1983.
G. R. Fleming, S. H. Courtney, and M. W. Balk. Activated barrier crossing: Comparison of experiment and theory. J. Stat. Phys., 42:83–104, 1986.
R. F. Grote and J. T. Hynes. The stable states picture of chemical reactions. II. Rate constants for condensed and gas phase reaction models. J. Chem. Phys., 73:2715–32, 1980.
R. F. Grote and J. T. Hynes. Saddle point model for atom transfer reactions in solution. J. Chem. Phys., 75:2791–98, 1981.
R. F. Grote and J. T. Hynes. Energy diffusion-controlled reactions in solution. J. Chem. Phys., 77:3736–43, 1982.
P. Hänggi and F. Mojtabai. Thermally activated escape rate in presence of long-time memory. Phys. Rev., A26:1168–70, 1982.
P. Hänggi. Physics of ligand migration in biomolecules. J. Stat. Phys., 73:401–12, 1983.
B. Chance et al., editors. Tunneling in Biological Systems. Johnson Research Foundation Colloquia. Academic Press, New York, 1979.
R. P. Bell. The Tunnel Effect in Chemistry. Chapman and Hall, London, 1980.
D. DeVault. Quantum-Mechanical Tunnelling in Biological Systems, 2nd edition. Cambridge Univ. Press, Cambridge, 1984.
V. I. Goldanskii, L. I. Trakhtenberg, , and V. N. Fleurov. Tunneling Phenomena in Chemical Physics. Gordon and Breach, New York, 1989.
V. I. Goldanskii. The role of the tunnel effect in the kinetics of chemical reactions at low temperatures. Dokl. Akad. Nauk SSSR, 124:1261–4, 1959. See also P. Hänggi, et al., Phys. Rev. Lett., 55:761-4, 1985.
See, for instance, L. D. Landau and E. M. Lifshitz, Quantum Mechanics, Pergamon Press, London, 1958.
N. Alberding, R. H. Austin, K. W. Beeson, S. S. Chan, L. Eisenstein, H. Frauenfelder, and T. M. Nordlund. Tunneling in ligand binding to heme proteins. Science, 192(4243):1002–4, 1976.
N. Alberding, S. S. Chan, L. Eisenstein, H. Frauenfelder, D. Good, I. C. Gunsalus, T. M. Nordlund, M. F. Perutz, A. H. Reynolds, and L. B. Sorensen. Binding of carbon monoxide to isolated hemoglobin chains. Biochemistry, 17:43–51, 1978.
H. Frauenfelder. In B. Chance et al., editors, Tunneling in Biological Systems. Academic Press, New York, 1979. pp. 627-49.
J. O. Alben, D. Beece, S. F. Bowne, L. Eisenstein, H. Frauenfelder, D. Good, M. C. Marden, P. P. Moh, L. Reinisch, A. H. Reynolds, and K. T. Yue. Isotope effect in molecular tunneling. Phys. Rev. Lett., 44:1157–60, 1980.
J. O. Alben, D. Beece, S. F. Bowne, W. Doster, L. Eisenstein, H. Frauenfelder, D. Good, J. D. McDonald, M. C. Marden, P. P. Moh, L. Reinisch, A. H. Reynolds, and K. T. Yue. Infrared spectroscopy of photodissociated carboxymyoglobin at low temperatures. Proc. Natl. Acad. Sci. USA, 79:3744–8, 1982.
J. A. Sussman. A comprehensive quantum theory of diffusion. Ann. Phys. Paris, 6:135–56, 1971.
A. O. Caldeira and A. J. Leggett. Influence of dissipation on quantum tunneling in macroscopic systems. Phys. Rev. Lett., 46:211–14, 1981.
A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zerger. Dynamics of the dissipative two-state system. Rev. Mod. Phys., 59:1–85, 1987.
P. G. Wolynes. Quantum theory of activated events in condensed phases. Phys. Rev. Lett., 47:968–71, 1981.
J. Jortner and J. Ulstrup. Dynamics of nonadiabatic atom transfer in biological systems. Carbon monoxide binding to hemoglobin. J. Amer. Chem. Soc., 101–4:3744, 1979.
J. Ulstrup. Charge Transfer Processes in Condensed Media (Lecture Notes in Chemistry, 10). Springer, Berlin, 1979.
G. Pfister and W. Känzig. Isotopeneffekt in der paraelastischen Relaxation. Zeitschrift fr Physik B Condensed Matter, 10:231–64, 1969.
D. A. Case and M. Karplus. Dynamics of ligand binding to heme proteins. J. Mol. Bio., 132:343–68, 1979.
J. A. McCammon and S. H. Northrup. Gated binding of ligands to proteins. Nature, 293:316–17, 1981.
A. Szabo, D. Shoup, S. H. Northrup, and J. A. McCammon. Stochastically gated diffusion-influenced reactions. J. Chem. Phys., 77:4484–93, 1982.
Y. A. Berlin, A. L. Burin, L. D. A. Siebbeles, and M. A. Ratner. Conformationally gated rate processes in biological macromolecules. J. Phys. Chem. A, 105:5666–78, 2001.
G. Baym, editor. Lectures on Quantum Mechanics. W. A. Benjamin, New York, 1969.
L. D. Landau and E. M. Lifshitz. Quantum Mechanics. Pergamon Press, London, 1958.
W. Kauzmann. Quantum Chemistry. Academic Press, New York, 1957.
E. J. Heller and R. C. Brown. Vibrational relaxation of highly excited diatomics. V. the V-V channel in HF(v)+HF(0) collision. J. Chem. Phys., 79:3336–66, 1983.
L. Landau. Phys. Z. Sow., 1:89, 1932. Z. Phys. Sov. 2:46 (1932).
C. Zener. Non-adiabatic crossing of energy levels. Proc. Roy. Soc. London, A137:696–702, 1932.
E. C. G. Stueckelberg. Helv. Phys. Acta, 5:369–422, 1932.
J. Ulstrup. Charge Transfer Processes in Condensed Media. Springer, Berlin, 1979.
L. D. Zusman. Outer-sphere electron transfer in polar solvents. Chem. Phys., 49:295–304, 1980.
R. E. Cline, Jr. and P. G. Wolynes. Stochastic dynamic models of curve crossing phenomena in condensed phases. J. Chem. Phys., 86:3836–44, 1987.
I. V. Aleksandrov and V. I. Goldanskii. Sov. Sci. Rev. B. Chem., 11:1–67, 1988.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Frauenfelder, H. (2010). Reaction Theory. In: Chan, S., Chan, W. (eds) The Physics of Proteins. Biological and Medical Physics, Biomedical Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1044-8_13
Download citation
DOI: https://doi.org/10.1007/978-1-4419-1044-8_13
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-1043-1
Online ISBN: 978-1-4419-1044-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)