Hostname: page-component-7c8c6479df-24hb2 Total loading time: 0 Render date: 2024-03-28T11:56:14.024Z Has data issue: false hasContentIssue false

Rate theories for biologists

Published online by Cambridge University Press:  09 August 2010

Huan-Xiang Zhou*
Affiliation:
Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, FL 32306, USA
*
*Author for Correspondence: H.-X. Zhou, Department of Physics and Institute of Molecular Biophysics, Florida State University, Tallahassee, FL 32306, USA. Tel.: (850) 645-1336; Fax: (850) 644-7244; Email: hzhou4@fsu.edu

Abstract

Some of the rate theories that are most useful for modeling biological processes are reviewed. By delving into some of the details and subtleties in the development of the theories, the review will hopefully help the reader gain a more than superficial perspective. Examples are presented to illustrate how rate theories can be used to generate insight at the microscopic level into biomolecular behaviors. An attempt is made to clear up a number of misconceptions in the literature regarding popular rate theories, including the appearance of Planck's constant in the transition-state theory and the Smoluchowski result as an upper limit for protein–protein and protein–DNA association rate constants. Future work in combining the implementation of rate theories through computer simulations with experimental probes of rate processes, and in modeling effects of intracellular environments so that theories can be used for generating rate constants for systems biology studies is particularly exciting.

Type
Review Article
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

9. References

Adam, G. & Delbruck, M. (1968). Reduction of dimensionality in biological diffusion processes. In Structural Chemistry and Molecular Biology (ed. Davidson, N.), pp. 198215. San Francisco: W. H. Freeman.Google Scholar
Agmon, N. (1984). Diffusion with back reaction. Journal of Chemical Physics 81, 28112817.CrossRefGoogle Scholar
Agmon, N. & Hopfield, J. J. (1983). Transient kinetics of chemical reactions with bounded diffusion perpendicular to the reaction coordinate: intramolecular processes with slow conformational changes. Journal of Chemical Physics 78, 69476959.CrossRefGoogle Scholar
Ai, X., Zhou, Z., Bai, Y. & Choy, W. Y. (2006). 15N NMR spin relaxation dispersion study of the molecular crowding effects on protein folding under native conditions. Journal of the American Chemical Society 128, 39163917.CrossRefGoogle ScholarPubMed
Alm, E., Morozov, A. V., Kortemme, T. & Baker, D. (2002). Simple physical models connect theory and experiment in protein folding kinetics. Journal of Molecular Biology 322, 463476.CrossRefGoogle ScholarPubMed
Alsallaq, R. & Zhou, H.-X. (2007a). Energy landscape and transition state of protein–protein association. Biophysical Journal 92, 14861502.CrossRefGoogle ScholarPubMed
Alsallaq, R. & Zhou, H.-X. (2007b). Prediction of protein-protein association rates from a transition-state theory. Structure 15, 215224.Google Scholar
Alsallaq, R. & Zhou, H. X. (2008). Electrostatic rate enhancement and transient complex of protein-protein association. Proteins-Structure Function and Bioinformatics 71, 320335.CrossRefGoogle ScholarPubMed
Altobelli, G. & Subramaniam, S. (2000). Kinetics of association of anti-lysozyme monoclonal antibody D44.1 and hen-egg lysozyme. Biophysical Journal 79, 29542965.CrossRefGoogle ScholarPubMed
Antikainen, N. M., Smiley, R. D., Benkovic, S. J. & Hammes, G. G. (2005). Conformation coupled enzyme catalysis: single-molecule and transient kinetics investigation of dihydrofolate reductase. Biochemistry 44, 1683516843.Google Scholar
Arrhenius, S. (1889). Über die Reaktionsgeschwindigkeit bei der Inversion von Rohrzucker durch Säuren. Zeitschrift für Physikalische Chemie 4, 226248.CrossRefGoogle Scholar
Astumian, R. D. (1997). Thermodynamics and kinetics of a Brownian motor. Science 276, 917922.CrossRefGoogle ScholarPubMed
Baerga-Ortiz, A., Rezaie, A. R. & Komives, E. A. (2000). Electrostatic dependence of the thrombin–thrombomodulin interaction. Journal of Molecular Biology 296, 651658.CrossRefGoogle ScholarPubMed
Bell, G. I. (1978). Models of the specific adhesion of cells to cells. Science 200, 618627.Google Scholar
Berezhkovskii, A. & Szabo, A. (2005). One-dimensional reaction coordinates for diffusive activated rate processes in many dimensions. Journal of Chemical Physics 122, 14503.Google Scholar
Berezhkovskii, A. M. & Bezrukov, S. M. (2004). Optimizing transport of metabolites through large channels: molecular sieves with and without binding. Biophysical Journal 88, L17L19.Google Scholar
Berezhkovskii, A. M., Pollak, E. & Zitserman, V. Y. (1992). Activated rate processes: generalization of the Kramers–Grote–Hynes and Langer theories. Journal of Chemical Physics 97, 24222437.CrossRefGoogle Scholar
Berg, O. G. (1985). Orientation constraints in diffusion-limited macromolecular association. The role of surface diffusion as a rate-enhancing mechanism. Biophysical Journal 47, 114.CrossRefGoogle ScholarPubMed
Berg, O. G. & Ehrenberg, M. (1982). Association kinetics with coupled three- and one-dimensional diffusion. Chain-length dependence of the association rate to specific DNA sites. Biophysical Chemistry 15, 4151.CrossRefGoogle ScholarPubMed
Berg, O. G., Winter, R. B. & Von Hippel, P. H. (1981). Diffusion-driven mechanisms of protein translocation on nucleic acids. I. Models and theory. Biochemistry 20, 69296948.Google Scholar
Berkowitz, M., Morgan, J. D., Mccammon, J. A. & Northrup, S. H. (1983). Diffusion-controlled reactions: a variational formula for the optimum reaction coordinate. Journal of Chemical Physics 79, 55635565.CrossRefGoogle Scholar
Berneche, S. & Roux, B. (2003). A microscopic view of ion conduction through the K+ channel. Proceedings of the National Academy of Sciences of the United States of America 100, 86448648.CrossRefGoogle ScholarPubMed
Bicout, D. J. & Szabo, A. (1997). First passage times, correlation functions, and reaction rates. Journal of Chemical Physics 106, 1029210298.Google Scholar
Bier, M. (2003). Processive motor protein as an overdamped Brownian stepper. Physical Review Letters 91, 148101.Google Scholar
Blainey, P. C., Van Oijen, A. M., Banerjee, A., Verdine, G. L. & Xie, X. S. (2006). A base-excision DNA-repair protein finds intrahelical lesion bases by fast sliding in contact with DNA. Proceedings of the National Academy of Sciences of the United States of America 103, 57525757.CrossRefGoogle ScholarPubMed
Bryngelson, J. D. & Wolynes, P. G. (1989). Intermediates and barrier crossing in a random energy model (with applications to protein folding). Journal of Physical Chemistry 93, 69026915.CrossRefGoogle Scholar
Buchete, N.-V. & Hummer, G. (2008). Coarse master equations for peptide folding dynamics. Journal of Physical Chemistry B 112, 60576069.CrossRefGoogle ScholarPubMed
Bustamante, C., Keller, D. & Oster, G. (2001). The physics of molecular motors. Accounts of Chemical Research 34, 412420.CrossRefGoogle ScholarPubMed
Candia, S., Garcia, M. L. & Latorre, R. (1992). Mode of action of iberiotoxin, a potent blocker of the large conductance Ca2+-activated K+ channel. Biophysical Journal 63, 583590.Google Scholar
Cao, Y., Kuske, R. & Li, H. (2008). Direct observation of Markovian behavior of the mechanical unfolding of individual proteins. Biophysical Journal 95, 782788.CrossRefGoogle ScholarPubMed
Carrion-Vazquez, M., Oberhauser, A. F., Fowler, S. B., Marszalek, P. E., Broedel, S. E., Clarke, J. & Fernandez, J. M. (1999). Mechanical and chemical unfolding of a single protein: a comparison. Proceedings of the National Academy of Sciences of the United States of America 96, 36943699.CrossRefGoogle ScholarPubMed
Chahine, J., Oliveira, R. J., Leite, V. B. & Wang, J. (2007). Configuration-dependent diffusion can shift the kinetic transition state and barrier height of protein folding. Proceedings of the National Academy of Sciences of the United States of America 104, 1464614651.Google Scholar
Chandler, D. (1978). Statistical mechanics of isomerization dynamics in liquids and transition-state approximation. Journal of Chemical Physics 68, 29592970.CrossRefGoogle Scholar
Chen, G., Wen, J. D. & Tinoco, I. JR (2007). Single-molecule mechanical unfolding and folding of a pseudoknot in human telomerase RNA. RNA 13, 21752188.CrossRefGoogle ScholarPubMed
Cheung, M. S., Klimov, D. & Thirumalai, D. (2005). Molecular crowding enhances native state stability and refolding rates of globular proteins. Proceedings of the National Academy of Sciences of the United States of America 102, 47534758.Google Scholar
Chodera, J. D., Singhal, N., Pande, V. S., Dill, K. A. & Swope, W. C. (2007). Automatic discovery of metastable states for the construction of Markov models of macromolecular conformational dynamics. Journal of Chemical Physics, 126, 155101.Google Scholar
Chodera, J. D., Swope, W. C., Pitera, J. W. & Dill, K. A. (2006). Long-time protein folding dynamics from short-time molecular dynamics simulations. Multiscale Modeling and Simulation 5, 12141226.CrossRefGoogle Scholar
Cieplak, M., Henkel, M., Karbowski, J. & Banavar, J. R. (1998). Master equation approach to protein folding and kinetic traps. Physical Review Letters 80, 36503653.CrossRefGoogle Scholar
Collins, F. C. & Kimball, G. E. (1949). Diffusion-controlled reaction rates. Journal of Colloid Science 4, 425437.CrossRefGoogle Scholar
D'Abramo, M., Di Nola, A. & Amadei, A. (2009). Kinetics of carbon monoxide migration and binding in solvated myoglobin as revealed by molecular dynamics simulations and quantum mechanical calculations. The Journal of Physical Chemistry B 113, 1634616353.CrossRefGoogle ScholarPubMed
Darling, R. J., Kuchibhotla, U., Glaesner, W., Micanovic, R., Witcher, D. R. & Beals, J. M. (2002). Glycosylation of erythropoietin affects receptor binding kinetics: role of electrostatic interactions. Biochemistry 41, 1452414531.CrossRefGoogle ScholarPubMed
Debye, P. (1942). Reaction rate in ionic solutions. Transactions of the Electrochemical Society 82, 265272.CrossRefGoogle Scholar
Doi, M. (1975a). Theory of diffusion-controlled reaction between non-simple molecules. I. Chemical Physics 11, 107113.CrossRefGoogle Scholar
Doi, M. (1975b). Theory of diffusion-controlled reaction between non-simple molecules. II. Chemical Physics 11, 115121.CrossRefGoogle Scholar
Dong, W., Baros, F. & Andre, J. C. (1989). Diffusion-controlled reactions. I. Molecular dynamics simulation of a noncontinuum model. Journal of Chemical Physics 91, 46434650.Google Scholar
Du, R., Pande, V. S., Grosberg, A. Y., Tanaka, T. & Shakhnovich, E. S. (1998). On the transition coordinate for protein folding. Journal of Chemical Physics 108, 334350.Google Scholar
Dudko, O. K., Hummer, G. & Szabo, A. (2006). Intrinsic rates and activation free energies from single-molecule pulling experiments. Physical Review Letters 96, 108101.CrossRefGoogle ScholarPubMed
Dudko, O. K., Hummer, G. & Szabo, A. (2008). Theory, analysis, and interpretation of single-molecule force spectroscopy experiments. Proceedings of the National Academy of Sciences of the United States of America 105, 1575515760.CrossRefGoogle ScholarPubMed
Elcock, A. H., Gabdoulline, R. R., Wade, R. C. & Mccammon, J. A. (1999). Computer simulation of protein–protein association kinetics: acetylcholinesterase-fasciculin. Journal of Molecular Biology 291, 149162.CrossRefGoogle ScholarPubMed
English, B. P., Min, W., Van Oijen, A. M., Lee, K. T., Luo, G., Sun, H., Cherayil, B. J., Kou, S. C. & Xie, X. S. (2006). Ever-fluctuating single enzyme molecules: Michaelis–Menten equation revisited. Nature Chemical Biology 2, 8794.CrossRefGoogle ScholarPubMed
Escobar, L., Root, M. J. & Mackinnon, R. (1993). Influence of protein surface charge on the bimolecular kinetics of a potassium channel peptide inhibitor. Biochemistry 32, 69826987.CrossRefGoogle ScholarPubMed
Evans, E. & Ritchie, K. (1997). Dynamic strength of molecular adhesion bonds. Biophysical Journal 72, 15411555.CrossRefGoogle ScholarPubMed
Evans, M. G. & Polanyi, M. (1935). Some applications of the transition state method to the calculation of reaction velocities, especially in solution. Transactions of the Faraday Society 31, 875894.Google Scholar
Eyring, H. (1935). The activated complex in chemical reactions. Journal of Chemical Physics 3, 107115.Google Scholar
Farkas, L. (1927). Keimbildungsgeschwindigkeit in ubersattigten Dampfen. Zeitschrift für Physikalische Chemie 125, 236242.CrossRefGoogle Scholar
Flomenbom, O., Velonia, K., Loos, D., Masuo, S., Cotlet, M., Engelborghs, Y., Hofkens, J., Rowan, A. E., Nolte, R. J., Van Der Auweraer, M., De Schryver, F. C. & Klafter, J. (2005). Stretched exponential decay and correlations in the catalytic activity of fluctuating single lipase molecules. Proceedings of the National Academy of Sciences of the United States of America 102, 23682372.Google Scholar
Foote, J. & Eisen, H. N. (1995). Kinetic and affinity limits on antibodies produced during immune responses. Proceedings of the National Academy of Sciences of the United States of America 92, 12541256.Google Scholar
Gabdoulline, R. R., Kummer, U., Olsen, L. F. & Wade, R. C. (2003). Concerted simulations reveal how peroxidase compound III formation results in cellular oscillations. Biophysical Journal 85, 14211428.Google Scholar
Gabdoulline, R. R. & Wade, R. C. (1997). Simulation of the diffusional association of barnase and barstar. Biophysical Journal 72, 19171929.Google Scholar
Gabdoulline, R. R. & Wade, R. C. (2001). Protein–protein association: investigation of factors influencing association rates by Brownian dynamics simulations. Journal of Molecular Biology 306, 11391155.CrossRefGoogle ScholarPubMed
Gao, Y. Q., Yang, W. & Karplus, M. (2005). A structure-based model for the synthesis and hydrolysis of ATP by F1-ATPase. Cell 123, 195205.Google Scholar
Gardiner, C. W. (1985). Handbook of Stochastic Methods, 2nd edn.Berlin: Springer-Verlag.Google Scholar
Gianni, S., Engstrom, A., Larsson, M., Calosci, N., Malatesta, F., Eklund, L., Ngang, C. C., Travaglini-Allocatelli, C. & Jemth, P. (2005). The kinetics of PDZ domain-ligand interactions and implications for the binding mechanism. Journal of Biological Chemistry 280, 3480534812.CrossRefGoogle ScholarPubMed
Gillespie, D. T. (1977). Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry 81, 23402361.Google Scholar
Goldstein, S. A. N. & Miller, C. (1993). Mechanism of charybdotoxin block of a voltage-gated K+ channel. Biophysical Journal 65, 16131619.CrossRefGoogle ScholarPubMed
Gopich, I. V. & Doktorov, A. B. (1996). Kinetics of diffusion-influenced reversible reaction A+B <-> C in solutions. Journal of Chemical Physics 105, 23202332.CrossRefGoogle Scholar
Gopich, I. V. & Szabo, A. (2002). Kinetics of reversible diffusion influenced reactions: the self-consistent relaxation time approximation. Journal of Chemical Physics 117, 507517.CrossRefGoogle Scholar
Goychuk, I. & Hanggi, P. (2002). Ion channel gating: a first-passage time analysis of the Kramers type. Proceedings of the National Academy of Sciences of the United States of America 99, 35523556.Google Scholar
Greenleaf, W. J., Frieda, K. L., Foster, D. A., Woodside, M. T. & Block, S. M. (2008). Direct observation of hierarchical folding in single riboswitch aptamers. Science 319, 630633.CrossRefGoogle ScholarPubMed
Grote, R. F. & Hynes, J. T. (1980). The stable states picture of chemical reactions. II. Rate constants for condensed and gas phase reaction models. Journal of Chemical Physics 73, 27152732.CrossRefGoogle Scholar
Halford, S. E. & Marko, J. F. (2004). How do site-specific DNA-binding proteins find their targets? Nucleic Acids Research 32, 30403052.CrossRefGoogle ScholarPubMed
Hanggi, P., Talkner, P. & Borkovec, M. (1990). Reaction rate theory: 50 years after Kramers. Reviews of Modern Physics 62, 251341.CrossRefGoogle Scholar
Hemsath, L., Dvorsky, R., Fiegen, D., Carlier, M. F. & Ahmadian, M. R. (2005). An electrostatic steering mechanism of Cdc42 recognition by Wiskott–Aldrich syndrome proteins. Molecular Cell 20, 313324.Google Scholar
Herzfeld, K. F. (1919). Zur Theorie der Reaktionsgeschwindigkeiten in Gasen. Annalen der Physik 59, 635667.CrossRefGoogle Scholar
Hill, T. L. (1975). Effect of rotation on diffusion-controlled rate of ligand-protein association. Proceedings of the National Academy of Sciences of the United States of America 72, 49184922.CrossRefGoogle ScholarPubMed
Hoffman, T. L., Labranche, C. C., Zhang, W., Canziani, G., Robinson, J., Chaiken, I., Hoxie, J. A. & Doms, R. W. (1999). Stable exposure of the coreceptor-binding site in a CD4-independent HIV-1 envelope protein. Proceedings of the National Academy of Sciences of the United States of America 96, 63596364.CrossRefGoogle Scholar
Hummer, G. & Kevrekidis, I. G. (2003). Coarse molecular dynamics of a peptide fragment: free energy, kinetics, and long-time dynamics computations. Journal of Chemical Physics 118, 1076210773.CrossRefGoogle Scholar
Johnson, R. J., Mccoy, J. G., Bingman, C. A., Phillips, G. N. JR & Raines, R. T. (2007). Inhibition of human pancreatic ribonuclease by the human ribonuclease inhibitor protein. Journal of Molecular Biology 368, 434449.Google Scholar
Junge, W. (1999). ATP synthase and other motor proteins. Proceedings of the National Academy of Sciences of the United States of America 96, 47354737.CrossRefGoogle ScholarPubMed
Keck, J. C. (1960). Variational theory of chemical reaction rates applied to three-body recombination. Journal of Chemical Physics 32, 10351050.Google Scholar
Kellermayer, M. S., Smith, S. B., Granzier, H. L. & Bustamante, C. (1997). Folding-unfolding transitions in single titin molecules characterized with laser tweezers. Science 276, 11121116.Google Scholar
Kiel, C. & Serrano, L. (2009). Cell type-specific importance of ras-c-raf complex association rate constants for MAPK signaling. Science Signaling 2, ra38.Google Scholar
Kim, J. S. & Yethiraj, A. (2009). Effect of macromolecular crowding on reaction rates: a computational and theoretical study. Biophysical Journal 96, 13331340.CrossRefGoogle Scholar
Kinosita, K. JR, Adachi, K. & Itoh, H. (2004). Rotation of F1-ATPase: how an ATP-driven molecular machine may work. Annual Review of Biophysics and Biomolecular Structure 33, 245268.CrossRefGoogle ScholarPubMed
Kolomeisky, A. B. & Fisher, M. E. (2007). Molecular motors: a theorist's perspective. Annual Review of Physical Chemistry 58, 675695.Google Scholar
Korennykh, A. V., Correll, C. C. & Piccirilli, J. A. (2007). Evidence for the importance of electrostatics in the function of two distinct families of ribosome inactivating toxins. Nucleic Acids Research 13, 13911396.Google ScholarPubMed
Korennykh, A. V., Piccirilli, J. A. & Correll, C. C. (2006). The electrostatic character of the ribosomal surface enables extraordinarily rapid target location by ribotoxins. Nature Structural and Molecular Biology 13, 436443.Google Scholar
Kou, S. C., Cherayil, B. J., Min, W., English, B. P. & Xie, X. S. (2005). Single-molecule Michaelis-Menten equations. Journal of Physical Chemistry B 109, 1906819081.Google Scholar
Kramers, H. A. (1940). Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7, 284304.CrossRefGoogle Scholar
Krivov, S. V. & Karplus, M. (2002). Free energy disconnectivity graphs: application to peptide models. Journal of Chemical Physics 117, 1089410903.Google Scholar
Kuttner, Y. Y., Kozer, N., Segal, E., Schreiber, G. & Haran, G. (2005). Separating the contribution of translational and rotational diffusion to protein association. Journal of the American Chemical Society 127, 1513815144.CrossRefGoogle ScholarPubMed
Langer, J. S. (1969). Statistical theory of decay of metastable states. Annals of Physics 54, 258275.Google Scholar
Lauger, P., Stephan, W. & Frehland, E. (1980). Fluctuations of barrier structure in ionic channels. Biochimica et Biophysica Acta 602, 167180.CrossRefGoogle ScholarPubMed
Laurence, T. A., Kwon, Y., Johnson, A., Hollars, C. W., O'Donnell, M., Camarero, J. A. & Barsky, D. (2008). Motion of a DNA sliding clamp observed by single molecule fluorescence spectroscopy. Journal of Biological Chemistry 283, 2289522906.CrossRefGoogle ScholarPubMed
Law, M. J., Linde, M. E., Chambers, E. J., Oubridge, C., Katsamba, P. S., Nilsson, L., Haworth, I. S. & Laird-Offringa, I. A. (2006). The role of positively charged amino acids and electrostatic interactions in the complex of U1A protein and U1 hairpin II RNA. Nucleic Acids Research 34, 275285.Google Scholar
Lear, J. D. (2003). Proton conduction through the M2 protein of the influenza A virus; a quantitative, mechanistic analysis of experimental data. FEBS Letters 552, 1722.CrossRefGoogle ScholarPubMed
Lebowitz, J. L., Helfand, E. & Praestgaard, E. (1965). Scaled particle theory of fluid mixtures. Journal of Chemical Physics 43, 774779.CrossRefGoogle Scholar
Lee, S. & Karplus, M. (1987). Kinetics of diffusion-influenced bimolecular reactions in solution. I. General formalism and relaxation kinetics of fast reversible reactions. Journal of Chemical Physics 86, 18831903.Google Scholar
Levitt, D. G. (1986). Interpretation of biological ion channel flux data-reaction-rate versus continuum theory. Annual Review of Biophysics and Biophysical Chemistry 15, 2957.Google Scholar
Li, C. G., Wang, Y. Q. & Pielak, G. J. (2009). Translational and rotational diffusion of a small globular protein under crowded conditions. Journal of Physical Chemistry B 113, 1339013392.CrossRefGoogle ScholarPubMed
Liphardt, J., Onoa, B., Smith, S. B., Tinoco, I. J. & Bustamante, C. (2001). Reversible unfolding of single RNA molecules by mechanical force. Science 292, 733737.Google Scholar
Lu, H. P., Xun, L. & Xie, X. S. (1998). Single-molecule enzymatic dynamics. Science 282, 18771882.CrossRefGoogle ScholarPubMed
Lukzen, N. N., Doktorov, A. B. & Burshtein, A. I. (1986). Non-markovian theory of diffusion-controlled excitation transfer. Chemical Physics 102, 289304.CrossRefGoogle Scholar
Marshall, B. T., Sarangapani, K. K., Lou, J., Mcever, R. P. & Zhu, C. (2005). Force history dependence of receptor–ligand dissociation. Biophysical Journal 88, 14581466.CrossRefGoogle ScholarPubMed
Martin, J., Mayhew, M., Langer, T. & Hartl, U. (1993). The reaction cycle of GroEL and GroES in chaperonin-assisted protein folding. Nature 366, 228233.Google Scholar
Mathé, J., Visram, H., Viasnoff, V., Rabin, Y. & Meller, A. (2004). Nanopore unzipping of individual DNA hairpin molecules. Biophysical Journal 87, 32053212.Google Scholar
Mccammon, J. A. & Harvey, S. C. (1987). Dynamics of Proteins and Nucleic Acids. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Mcguffee, S. R. & Elcock, A. H. (2006). Atomically detailed simulations of concentrated protein solutions: the effects of salt, pH, point mutations, and protein concentration in simulations of 1000-molecule systems. Journal of the American Chemical Society 128, 1209812110.CrossRefGoogle ScholarPubMed
Melnikov, V. I. & Meshkov, S. V. (1986). Theory of activated rate processes: exact solution of the Kramers problem. Journal of Chemical Physics 85, 10181027.Google Scholar
Merkel, R., Nassoy, P., Leung, A., Ritchie, K. & Evans, E. (1999). Energy landscapes of receptor–ligand bonds explored with dynamic force spectroscopy. Nature 397, 5053.Google Scholar
Merlo, C., Dill, K. A. & Weikl, T. R. (2005). Φ values in protein-folding kinetics have energetic and structural components. Proceedings of the National Academy of Sciences of the United States of America 102, 1017110175.CrossRefGoogle ScholarPubMed
Miller, C. (1990). Diffusion-controlled binding of a peptide neurotoxin to its K+ channel receptor. Biochemistry 29, 53205325.CrossRefGoogle ScholarPubMed
Min, W., Gopich, I. V., English, B. P., Kou, S. C., Xie, X. S. & Szabo, A. (2006). When does the Michaelis–Menten equation hold for fluctuating enzymes? Journal of Physical Chemistry B 110, 2009320097.Google Scholar
Min, W., Luo, G., Cherayil, B. J., Kou, S. C. & Xie, X. S. (2005). Observation of a power-law memory kernel for fluctuations within a single protein molecule. Physical Review Letters 94, 198302.Google Scholar
Min, W. & Xie, X. S. (2006). Kramers model with a power-law friction kernel: dispersed kinetics and dynamic disorder of biochemical reactions. Physical Review E 73, 010902.CrossRefGoogle ScholarPubMed
Minh, D. D., Chang, C. E., Trylska, J., Tozzini, V. & Mccammon, J. A. (2006). The influence of macromolecular crowding on HIV-1 protease internal dynamics. Journal of the American Chemical Society 128, 60066007.Google Scholar
Minton, A. P. (1989). Holobiochemistry: an integrated approach to the understanding of biochemical mechanism that emerges from the study of proteins and protein associations in volume-occupied solutions. In Structural and Organizational Aspects of Metabolic Regulation (eds. Srere, P., Jones, M. E. & Mathews, C.), pp. 291306. New York: Liss.Google Scholar
Mittal, J. & Best, R. B. (2010). Dependence of protein folding stability and dynamics on the density and composition of macromolecular crowders. Biophysical Journal 98, 315320.Google Scholar
Miyashita, O., Onuchic, J. N. & Okamura, M. Y. (2004). Transition state and encounter complex for fast association of cytochrome c2 with bacterial reaction center. Proceedings of the National Academy of Sciences of the United States of America 101, 1617416179.Google Scholar
Muñoz, V., Henry, E. R., Hofrichter, J. & Eaton, W. A. (1998). A statistical mechanical model for β-hairpin kinetics. Proceedings of the National Academy of Sciences of the United States of America 95, 58725879.Google Scholar
Murrell-Lagnado, R. D. & Aldrich, R. W. (1993). Energetics of Shaker K channel's block by inactivation peptides. Journal of General Physiology 102, 9771003.Google Scholar
Naumann, W. (1994). Competitive reversible binding: a theoretical study of density effects on the long-time relaxation. Journal of Chemical Physics 101, 1095310960.CrossRefGoogle Scholar
Nitzan, A. (1987). Non-Markovian theory of activated rate processes. VI. Unimolecular reactions in condensed phases. Journal of Chemical Physics 86, 27342749.Google Scholar
Noe, F. & Fischer, S. (2008). Transition networks for modeling the kinetics of conformational change in macromolecules. Current Opinion in Structural Biology 18, 154162.Google Scholar
Nolte, H. J., Rosenberry, T. L. & Neumann, E. (1980). Effective charge on acetylcholinesterase active sites determined from the ionic strength dependence of association rate constants with cationic ligands. Biochemistry 19, 37053711.Google Scholar
Northrup, S. H. & Erickson, H. P. (1992). Kinetics of protein–protein association explained by Brownian dynamics computer simulation. Proceedings of the National Academy of Sciences of the United States of America 89, 33383342.Google Scholar
Northrup, S. H. & Hynes, J. T. (1980). The stable states picture of chemical reactions. I. Formulation for rate constants and initial condition effects. Journal of Chemical Physics 73, 27002714.Google Scholar
Northrup, S. H., Reynolds, J. C. L., Miller, C. M., Forrest, K. J. & Boles, J. O. (1986). Diffusion-controlled association rate of cytochrome c and cytochrome c peroxidase in a simple electrostatic model. Journal of the American Chemical Society 108, 81628170.Google Scholar
Okada, Y. & Hirokawa, N. (2000). Mechanism of the single-headed processivity: diffusional anchoring between the K-loop of kinesin and the C terminus of tubulin. Proceedings of the National Academy of Sciences of the United States of America 97, 640645.Google Scholar
Onsager, L. (1931). Reciprocal relations in irreversible processes. II. Physical Review 38, 22652279.Google Scholar
Ordentlich, A., Barak, D., Kronman, C., Flashner, Y., Leitner, M., Segall, Y., Ariel, N., Cohen, S., Velan, B. & Shafferman, A. (1993). Dissection of the human acetylcholinesterase active-center determinants of substrate-specificity – Identification of residues constituting the anionic site, the hydrophobic site, and the acyl pocket. Journal of Biological Chemistry 268, 1708317095.Google Scholar
Pape, T., Wintermeyer, W. & Rodnina, M. (1998). Complete kinetic mechanism of elongation factor Tu-dependent binding of aminoacyl-tRNA to the A site of the E. coli ribosome. The EMBO Journal 17, 74907497.Google Scholar
Park, C. & Raines, R. T. (2001). Quantitative analysis of the effect of salt concentration on enzymatic catalysis. Journal of the American Chemical Society 123, 1147211479.Google Scholar
Pollak, E. (1986). Theory of activated rate processes: a new derivation of Kramers' expression. Journal of Chemical Physics 85, 865867.Google Scholar
Pollak, E., Grabert, H. & Hanggi, P. (1989). Theory of activated rate processes for arbitrary frequency dependent friction: solution of the turnover problem. Journal of Chemical Physics 91, 40734087.CrossRefGoogle Scholar
Pontryagin, L., Andronov, A. & Vitt, A. (1933). On the statistical treatment of dynamical systems. Journal of Experimental and Theoretical Physics 3, 165180.Google Scholar
Pryor, A. N., Selwood, T., Leu, L. S., Andracki, M. A., Lee, B. H., Rao, M., Rosenberry, T., Doctor, B. P., Silman, I. & Quinn, D. M. (1992). Simple general acid-base catalysis of physiological acetylcholinesterase reactions. Journal of the American Chemical Society 114, 38963900.Google Scholar
Qian, H. (1997). A simple theory of motor protein kinetics and energetics. Biophysical Chemistry 67, 263267.Google Scholar
Qian, H. (2000). A simple theory of motor protein kinetics and energetics. II. Biophysical Chemistry 83, 3543.CrossRefGoogle ScholarPubMed
Qian, H. (2008). Cooperativity and specificity in enzyme kinetics: a single-molecule time-based perspective. Biophysical Journal 95, 1017.Google Scholar
Qin, S., Minh, D. D., Mccammon, J. A. & Zhou, H.-X. (2010). Method to predict crowding effects by postprocessing molecular dynamics trajectories: application to the flap dynamics of HIV-1 protease. Journal of Physical Chemistry Letters 1, 107110.Google Scholar
Qin, S. & Zhou, H. X. (2008). Prediction of salt and mutational effects on the association rate of U1A protein and U1 small nuclear RNA stem/loop II. Journal of Physical Chemistry B 112, 59555960.Google Scholar
Qin, S. & Zhou, H.-X. (2009). Dissection of the high rate constant for the binding of a ribotoxin to the ribosome. Proceedings of the National Academy of Sciences of the United States of America 106, 69746979.CrossRefGoogle ScholarPubMed
Qin, S. & Zhou, H.-X. (2010). Generalized fundamental measure theory for atomistic modeling of macromolecular crowding. Physical Review E 81, 031919.Google Scholar
Radic, Z., Kirchhoff, P. D., Quinn, D. M., Mccammon, J. A. & Taylor, P. (1997). Electrostatic influence on the kinetics of ligand binding to acetylcholinesterase. Journal of Biological Chemistry 272, 2326523277.Google Scholar
Richter, P. H. & Eigen, M. (1974). Diffusion controlled reaction rates in spheroidal geometry. Application to repressor–operator association and membrane bound enzymes. Biophysical Chemistry 2, 255263.Google Scholar
Rief, M., Clausen-Schaumann, H. & Gaub, H. E. (1999). Sequence-dependent mechanics of single DNA molecules. Nature Structural Biology 6, 346349.Google Scholar
Rief, M., Gautel, M., Oesterhelt, F., Fernandez, J. M. & Gaub, H. E. (1997). Reversible unfolding of individual titin immunoglobulin domains by AFM. Science 276, 11091112.Google Scholar
Riggs, A. D., Bourgeois, S. & Cohn, M. (1970). The lac repressor–operator interaction. III. Kinetic studies. Journal of Molecular Biology 53, 401417.Google Scholar
Risken, H. (1989). The Fokker–Planck Equation, 2nd edn.Berlin: Springer-Verlag.Google Scholar
Rodnina, M. V., Gromadski, K. B., Kothe, U. & Wieden, H. J. (2005). Recognition and selection of tRNA in translation. FEBS Letters 579, 938942.CrossRefGoogle ScholarPubMed
Roux, B., Allen, T., Berneche, S. & Im, W. (2004). Theoretical and computational models of biological ion channels. Quarterly Reviews of Biophysics 37, 15103.CrossRefGoogle ScholarPubMed
Schaad, O., Zhou, H. X., Szabo, A., Eaton, W. A. & Henry, E. R. (1993). Simulation of the kinetics of ligand binding to a protein by molecular dynamics: geminate rebinding of nitric oxide to myoglobin. Proceedings of the National Academy of Sciences of the United States of America 90, 95479551.Google Scholar
Schlierf, M. & Rief, M. (2006). Single-molecule unfolding force distributions reveal a funnel-shaped energy landscape. Biophysical Journal 90, L33L35.Google Scholar
Schlosshauer, M. & Baker, D. (2002). A general expression for bimolecular association rates with orientational constraints. Journal of Physical Chemistry B 106, 1207912083.Google Scholar
Schlosshauer, M. & Baker, D. (2004). Realistic protein–protein association rates from a simple diffusional model neglecting long-range interactions, free energy barriers, and landscape ruggedness. Protein Science 13, 16601669.Google Scholar
Schonbrun, J. & Dill, K. A. (2003). Fast protein folding kinetics. Proceedings of the National Academy of Sciences of the United States of America 100, 1267812682.Google Scholar
Schranner, R. & Richter, P. H. (1978). Rate enhancement by guided diffusion. Chain length dependence of repressor-operator association rates. Biophysical Chemistry 8, 135150.Google Scholar
Schreiber, G. & Fersht, A. R. (1993). Interaction of barnase with its polypeptide inhibitor barstar studied by protein engineering. Biochemistry 32, 51455150.CrossRefGoogle ScholarPubMed
Schreiber, G. & Fersht, A. R. (1996). Rapid, electrostatically assisted association of proteins. Nature Structural Biology 3, 427431.Google Scholar
Schreiber, G., Haran, G. & Zhou, H.-X. (2009). Fundamental aspects of protein-protein association kinetics. Chemical Reviews 109, 839860.Google Scholar
Schurr, J. M. (1979). One-dimensional diffusion coefficient of proteins absorbed on DNA. Hydrodynamic considerations. Biophysical Chemistry 9, 413414.Google Scholar
Shapiro, B. E. & Qian, H. (1997). A quantitative analysis of single protein–ligand complex separation with the atomic force microscope. Biophysical Chemistry 67, 211219.Google Scholar
Shapiro, R., Ruiz-Gutierrez, M. & Chen, C.-Z. (2000). Analysis of the interactions of human ribonuclease inhibitor with angiogenin and ribonuclease A by mutagenesis: importance of inhibitor residues inside versus outside the C-terminal ‘hot spot’. Journal of Molecular Biology 302, 497519.Google Scholar
Shen, B. J., Hage, T. & Sebald, W. (1996). Global and local determinants for the kinetics of interleukin-4/interleukin-4 receptor alpha chain interaction. A biosensor study employing recombinant interleukin-4-binding protein. European Journal of Biochemistry 240, 252261.CrossRefGoogle ScholarPubMed
Shi, J., Dertouzos, J., Gafni, A., Steel, D. & Palfey, B. A. (2006). Single-molecule kinetics reveals signatures of half-sites reactivity in dihydroorotate dehydrogenase A catalysis. Proceedings of the National Academy of Sciences of the United States of America 103, 57755780.Google Scholar
Shoup, D., Lipari, G. & Szabo, A. (1981). Diffusion-controlled bimolecular reaction rates. The effect of rotational diffusion and orientation constraints. Biophysical Journal 36, 697714.Google Scholar
Shoup, D. & Szabo, A. (1982). Role of diffusion in ligand binding to macromolecules and cell-bound receptors. Biophysical Journal 40, 3339.Google Scholar
Skinner, J. L. & Wolynes, P. G. (1978). Relaxation processes and chemical kinetics. Journal of Chemical Physics 69, 21432150.Google Scholar
Smoluchowski, M. V. (1917). Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen. Zeitschrift für Physikalische Chemie 92, 129168.Google Scholar
Solc, K. & Stockmayer, W. H. (1971). Kinetics of diffusion-controlled reaction between chemically asymmetric molecules. I. General theory. Journal of Chemical Physics 54, 29812988.Google Scholar
Solc, K. & Stockmayer, W. H. (1973). Kinetics of diffusion-controlled reaction between chemically asymmetric molecules. II. Approximate steady-state solution. International Journal of Chemical Kinetics 5, 733752.Google Scholar
Spaar, A., Dammer, C., Gabdoulline, R. R., Wade, R. C. & Helms, V. (2006). Diffusional encounter of barnase and barstar. Biophysical Journal 90, 19131924.Google Scholar
Stewart, R. C. & Van Bruggen, R. (2004). Association and dissociation kinetics for CheY interacting with the P2 domain of CheA. Journal of Molecular Biology 336, 287301.Google Scholar
Stoer, M. & Wagner, F. (1997). A simple min-cut algorithm. Journal of the ACM 44, 585591.Google Scholar
Straub, J. E., Borkovec, M. & Berne, B. J. (1986). Non-Markovian activated rate processes: comparison of current theories with numerical simulation data. Journal of Chemical Physics 84, 17881794.Google Scholar
Swaminathan, R., Hoang, C. P. & Verkman, A. S. (1997). Photobleaching recovery and anisotropy decay of green fluorescent protein GFP-S65T in solution and cells: cytoplasmic viscosity probed by green fluorescent protein translational and rotational diffusion. Biophysical Journal 72, 19001907.Google Scholar
Szabo, A. (1989). Theory of diffusion-influenced fluorescence quenching. Journal of Physical Chemistry 93, 69296939.Google Scholar
Szabo, A. (1991). Theoretical approaches to reversible diffusion-influenced reactions: monomer–excimer kinetics. Journal of Chemical Physics 95, 24812490.Google Scholar
Szabo, A., Schulten, K. & Schulten, Z. (1980). First passage time approach to diffusion controlled reactions. Journal of Chemical Physics 72, 43504357.CrossRefGoogle Scholar
Szabo, A., Shoup, D., Northrup, S. H. & Mccammon, J. A. (1982). Stochastically gated diffusion-influenced reactions. Journal of Chemical Physics 77, 44844493.Google Scholar
Temkin, S. I. & Yakobson, B. I. (1984). Diffusion-controlled reactions of chemically anisotropic molecules. Journal of Physical Chemistry 88, 26792682.Google Scholar
Terlau, H., Shon, K.-J., Grilley, M., Stocker, M., Stuhmer, W. & Baldomero, O. M. (1996). Strategy for rapid immobilization of prey by a fish-hunting marine snail. Nature 381, 148151.Google Scholar
Tjong, H. & Zhou, H.-X. (2010). The folding transition-state ensemble of a four-helix bundle protein: helix propensity as a determinant and macromolecular crowding as a probe. Biophysical Journal 98, 22732280.Google Scholar
Tokuyama, M. (2009a). Self-diffusion in multi-component glass-forming systems. Physica A 388, 30833092.Google Scholar
Tokuyama, M. (2009b). Universality in multicomponent glass-forming liquids near the glass transition. Physical Review E 80, 031503.Google Scholar
Tokuyama, M. & Oppenheim, I. (1994). Dynamics of hard-sphere suspensions. Physical Review E 50, R16R19.Google Scholar
Tokuyama, M. & Oppenheim, I. (1995). On the theory of concentrated hard-sphere suspensions. Physica A 216, 85119.Google Scholar
Uter, N. T., Gruic-Sovulj, I. & Perona, J. J. (2005). Amino acid-dependent transfer RNA affinity in a class I aminoacyl-tRNA synthetase. Journal of Biological Chemistry 280, 2396623977.Google Scholar
Van Oijen, A. M., Blainey, P. C., Crampton, D. J., Richardson, C. C., Ellenberger, T. & Xie, X. S. (2003). Single-molecule kinetics of lambda exonuclease reveal base dependence and dynamic disorder. Science 301, 12351238.Google Scholar
Van't Hoff, J. H. (1884). Etudes de Dynamique Chimique. Amsterdam: F. Muller and Co.Google Scholar
Vellom, D. C., Radic, Z., Li, Y., Pickering, N. A., Camp, S. & Taylor, P. (1993). Amino acid residues controlling acetylcholinesterase and butylcholinesterase specificity. Biochemistry 32, 1217.Google Scholar
Vijayakumar, M., Wong, K. Y., Schreiber, G., Fersht, A. R., Szabo, A. & Zhou, H.-X. (1998). Electrostatic enhancement of diffusion-controlled protein–protein association: comparison of theory and experiment on barnase and barstar. Journal of Molecular Biology 278, 10151024.CrossRefGoogle ScholarPubMed
Walker, D., Moore, G. R., James, R. & Kleanthous, C. (2003). Thermodynamic consequences of bipartite immunity protein binding to the ribosomal ribonuclease colicin E3. Biochemistry 42, 41614171.Google Scholar
Wallis, R., Moore, G. K., James, R. & Kleanthous, C. (1995). Protein–protein interactions in colicin E9 DNase-immunity protein complexes. 1. Diffusion-controlled association and femtomolar binding for the cognate complex. Biochemistry 34, 1374313750.Google Scholar
Wang, Y. M., Austin, R. H. & Cox, E. C. (2006). Single molecule measurements of repressor protein 1D diffusion on DNA. Physical Review Letters 97, 048302.Google Scholar
Wassaf, D., Kuang, G., Kopacz, K., Wu, Q. L., Nguyen, Q., Toews, M., Cosic, J., Jacques, J., Wiltshire, S., Lambert, J., Pazmany, C. C., Hogan, S., Ladner, R. C., Nixon, A. E. & Sexton, D. J. (2006). High-throughput affinity ranking of antibodies using surface plasmon resonance microarrays. Analytical Biochemistry 351, 241253.Google Scholar
Weikl, T. R., Palassini, M. & Dill, K. A. (2004). Cooperativity in two-state protein folding kinetics. Protein Science 13, 822829.Google Scholar
Wendt, H., Leder, L., Harma, H., Jelesarov, I., Baici, A. & Bosshard, H. R. (1997). Very rapid, ionic strenghth-dependent association and folding of a heterodimeric leucine zipper. Biochemistry 36, 204213.Google Scholar
Wieczorek, G. & Zielenkiewicz, P. (2008). Influence of macromolecular crowding on protein–protein association rates – a Brownian dynamics study. Biophysical Journal 95, 50305036.Google Scholar
Wigner, E. (1937). Calculation of the rate of elementary association reactions. Journal of Chemical Physics 5, 720725.Google Scholar
Wilemski, G. & Fixman, M. (1973). General theory of diffusion-controlled reactions. Journal of Chemical Physics 58, 40094019.Google Scholar
Wu, Y., Gao, Y. Q. & Karplus, M. (2007). A kinetic model of coordinated myosin V. Biochemistry 46, 63186330.Google Scholar
Xing, J., Wang, H., Dimroth, P., Von Balmoos, C. & Oster, G. (2004). Torque generation by the sodium Fo-ATPase. Biophysical Journal 87, 21482163.Google Scholar
Yamamoto, T. (1960). Quantum statistical mechanical theory of the rate of exchange chemical reactions in the gas phase. Journal of Chemical Physics 33, 281289.Google Scholar
Yang, G., Cecconi, C., Baase, W. A., Vetter, I. R., Breyer, W. A., Haack, J. A., Matthews, B. W., Dahlquist, F. W. & Bustamante, C. (2000). Solid-state synthesis and mechanical unfolding of polymers of T4 lysozyme. Proceedings of the National Academy of Sciences of the United States of America 97, 139144.Google Scholar
Yang, M., Lee, S. & Shin, K. J. (1998). Kinetic theory of bimolecular reactions in liquid. III. Reversible association–dissociation: A+B <->C. Journal of Chemical Physics 108, 90699085.Google Scholar
Yi, M., Cross, T. A. & Zhou, H. X. (2009). Conformational heterogeneity of the M2 proton channel and a structural model for channel activation. Proceedings of the National Academy of Sciences of the United States of America 106, 1331113316.Google Scholar
Yildiz, A., Tomishige, M., Vale, R. & Selvin, P. R. (2004). Kinesin walks hand-over-hand. Science 303, 676678.Google Scholar
Yuan, J.-M., Chyan, C.-L., Zhou, H.-X., Chung, T.-Y., Peng, H., Ping, G. & Yang, G. (2008). The effects of macromolecular crowding on the mechanical stability of protein molecules. Protein Science 17, 21562166.Google Scholar
Zhang, Z., Rajagopalan, P. T., Selzer, T., Benkovic, S. J. & Hammes, G. G. (2004). Single-molecule and transient kinetics investigation of the interaction of dihydrofolate reductase with NADPH and dihydrofolate. Proceedings of the National Academy of Sciences of the United States of America 101, 27642769.Google Scholar
Zhou, H.-X. (1989). The exponential nature of barrier crossings studied by Langevin dynamics. Chemical Physics Letters 164, 285290.Google Scholar
Zhou, H.-X. (1993). Brownian dynamics study of the influences of electrostatic interaction and diffusion on protein–protein association kinetics. Biophysical Journal 64, 17111726.Google Scholar
Zhou, H.-X. (1996). Effect of interaction potentials in diffusion-influenced reactions with small reactive regions. Journal of Chemical Physics 105, 72357237.CrossRefGoogle Scholar
Zhou, H.-X. (1997). Enhancement of protein-protein association rate by interaction potential: accuracy of prediction based on local Boltzmann factor. Biophysical Journal 73, 24412445.Google Scholar
Zhou, H.-X. (1998). Theory of the diffusion-influenced substrate binding rate to a buried and gated active site. Journal of Chemical Physics 108, 81468154.Google Scholar
Zhou, H.-X. (2001a). Disparate ionic-strength dependencies of on and off rates in protein–protein association. Biopolymers 59, 427433.Google Scholar
Zhou, H.-X. (2001b). The affinity-enhancing roles of flexible linkers in two-domain DNA-binding proteins. Biochemistry 40, 1506915073.CrossRefGoogle ScholarPubMed
Zhou, H.-X. (2001c). Single-chain versus dimeric protein folding: thermodynamic and kinetic consequences of covalent linkage. Journal of the American Chemical Society 123, 67306731.Google Scholar
Zhou, H.-X. (2002). A model for the binding of the inactivation N-terminal to the ion pore of Shaker potassium channel: both electrostatic attraction and covalent linkage are required for rapid inactivation. Journal of Physical Chemistry B 106, 23932397.Google Scholar
Zhou, H.-X. (2003a). Association and dissociation kinetics of colicin E3 and immunity protein 3: convergence of theory and experiment. Protein Science 12, 23792382.Google Scholar
Zhou, H.-X. (2003b). Quantitative account of the enhanced affinity of two linked scFvs specific for different epitopes on the same antigen. Journal of Molecular Biology 329, 18.Google Scholar
Zhou, H.-X. (2004). Protein folding and binding in confined spaces and in crowded solutions. Journal of Molecular Recognition 17, 368375.Google Scholar
Zhou, H.-X. (2005a). How do biomolecular systems speed up and regulate rates? Physical Biology 2, R1R25.Google Scholar
Zhou, H.-X. (2005b). A model for the mediation of processivity of DNA-targeting proteins by nonspecific binding: dependence on DNA length and presence of obstacles. Biophysical Journal 88, 16081615.Google Scholar
Zhou, H.-X. (2008). A minimum-reaction-flux solution to master-equation models of protein folding. Journal of Chemical Physics 128, 195104.Google Scholar
Zhou, H.-X., Briggs, J. M. & Mccammon, J. A. (1996). A 240-fold electrostatic rate-enhancement for acetylcholinesterase–substrate binding can be predicted by the potential within the active site. Journal of the American Chemical Society 118, 1306913070.Google Scholar
Zhou, H.-X., Briggs, J. M., Tara, S. & Mccammon, J. A. (1998a). Correlation between rate of enzyme–substrate diffusional encounter and average Boltzmann factor around active site. Biopolymers 45, 355360.Google Scholar
Zhou, H.-X. & Chen, Y.-D. (1996). Chemically driven motility of Brownian particles. Physical Review Letters 77, 194197.Google Scholar
Zhou, H.-X. & Gilson, M. K. (2009). Theory of free energy and entropy in noncovalent binding. Chemical Reviews 109, 40924107.CrossRefGoogle ScholarPubMed
Zhou, H.-X. & Mccammon, J. A. (2010). The gates of ion channels and enzymes. Trends in Biochemical Sciences 35, 179185.Google Scholar
Zhou, H.-X., Rivas, G. & Minton, A. P. (2008). Macromolecular crowding and confinement: biochemical, biophysical, and potential physiological consequences. Annual Review of Biophysics 37, 375397.Google Scholar
Zhou, H.-X. & Szabo, A. (1991). Comparison between molecular dynamics simulations and the Smoluchowski theory of reactions in a hard sphere liquid. Journal of Chemical Physics 95, 59485952.Google Scholar
Zhou, H.-X. & Szabo, A. (1996a). Theory and simulation of the time-dependent rate coefficients of diffusion-influenced reactions. Biophysical Journal 71, 24402457.Google Scholar
Zhou, H.-X. & Szabo, A. (1996b). Theory and simulation of stochastically-gated diffusion-influenced reactions. Journal of Physical Chemistry 100, 25972604.Google Scholar
Zhou, H.-X. & Szabo, A. (2004). Enhancement of association rates by nonspecific binding to DNA and cell membranes. Physical Review Letters 93.Google Scholar
Zhou, H.-X., Wlodek, S. T. & Mccammon, J. A. (1998b). Conformation gating as a mechanism for enzyme specificity. Proceedings of the National Academy of Sciences of the United States of America 95, 92809283.Google Scholar
Zhou, H.-X., Wong, K. Y. & Vijayakumar, M. (1997). Design of fast enzymes by optimizing interaction potential in active site. Proceedings of the National Academy of Sciences of the United States of America 94, 1237212377.Google Scholar
Zhou, H.-X. & Zwanzig, R. (2002). Barrier crossing coupled to a small set of oscillators. Journal of Physical Chemistry A 106, 75627564.Google Scholar
Zimmerman, S. B. & Trach, S. O. (1991). Estimation of macromolecule concentrations and excluded volume effects for the cytoplasm of Escherichia coli. Journal of Molecular Biology 222, 599620.Google Scholar
Zwanzig, R. (1988). Diffusion in a rough potential. Proceedings of the National Academy of Sciences of the United States of America 85, 20292030.Google Scholar
Zwanzig, R. (1995). Simple model of protein folding kinetics. Proceedings of the National Academy of Sciences of the United States of America 92, 98019804.CrossRefGoogle ScholarPubMed
Zwanzig, R. (2001). Nonequilibrium Statistical Mechanics. New York: Oxford University Press.Google Scholar