Abstract
There is an ambiguity in the theoretical models for computing association constants, the key observable in a laboratory, of non-covalent associations. We show that three different models give unique result asymptotically in the limit of strong associate. For weak associations, the disagreement reflects the nature of ill-defined ``associated complex'' which can be defined, among various ways, either geometrically or thermodynamically depending on measurement techniques. Furthermore, even when the free energy of association is unique, the corresponding entropy and enthalpy can still be different from different types of measurements – a surprising source of entropy-enthalpy compensation. This work provides a mathematical basis for modeling non-covalent association processes in biology.
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References
Amzel, L.M.: Loss of translational entropy in binding, folding, and catalysis. Prot: Struct. Funct. Genet. 28, 144–149 (1997)
Balsera, M., Stepaniants, S., Izrailev, S., Oono, Y., Schulten, K.: Reconstructing potential energy functions from simulated force-induced unbinding processes. Biophys. J. 73, 1281–1287 (1997)
Bender, C.M., Orszag, S.A.: Advanced mathematical methods for scientists and engineers. McGraw-Hill, New York, 1978
Ben-Naim, A.: Standard thermodynamics of transfer. Uses and misuses. J. Phys. Chem. 82, 792–803, (1978)
Bjerrum, N.: Niels bjerrum selected papers. Einar Munksgaard, Copenhagen, 1949
Chilkoti, A., Boland, T., Ratner, B.D., Stayton, P.S.: The relationship between ligand-binding thermodynamics and protein-ligand interaction forces measured by atomic force microscopy.Biophys. J. 69, 2125–2130 (1995)
Chilkoti, A., Tan, P.H., Stayton, P.S.: Site-directed mutagenesis studies of the high-affinity streptavidin-biotin complex: contributions of tryptophan residues 79, 108, and 120. Proc. Natl. Acad. Sci. USA 92, 1754–1758 (1995)
Derjaguin, B., Landau, L.: Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes. Acta Physicochim. U.R.S.S. 14, 633–662 (1941)
Doyle, R., Simons, K., Qian, H., Baker, D.: Local interactions and the optimization of protein folding. Prot: Struct. Funct. Genet. 29, 282–291 (1997)
Evans, E., Ritchie, K.: Dynamic strength of molecular adhesion bonds. Biophys. J. 72, 1541–1555 (1997)
Florin, E., Moy, V.T., Gaub, H.E.: Adhesion forces between individual ligand-receptor pairs. Science 264, 415–417 (1994)
Gilson, M.K., Given, J.A., Bush, B.L., McCammon, J.A.: The statistical-thermodynamic basis for computation of binding affinities: a critical review. Biophys. J. 72, 1047–1069 (1997)
Grubmüller, H., Heymann, B., Tavan, P.: Ligand binding: molecular mechanics calculation of the streptavidin-biotin rupture force. Science 271, 997–999 (1996)
Hill, T.L.: Theory of protein solutions. I.J. Chem. Phys. 23, 623–636 (1955)
Hill, T.L.: An introduction to statistical thermodynamics. Dover Pub., New York, 1960
Hill, T.L.: Effect of rotation on the diffusion-controlled rate of ligand-protein association.Proc. Natl. Acad. Sci. USA 72, 4918–4922 (1975)
Hill, T.L.: Diffusion frequency factors in some simple examples of transition-state rate theory. Proc. Natl. Acad. Sci. USA 73, 679–683 (1976)
Izrailev, S., Stepaniants, S., Balsera, M., Oono, Y., Schulten, K.: Molecular dynamics study of unbinding of the avidin-biotin complex. Biophys. J. 72, 1568–1581 (1997)
Jeppesen, C., Wong, J.Y., Kuhl, T.L., Israelachvili, J.N., Mullah, N., Zalipsky, S., Marques, C.M.: Impact of polymer tether length on multiple ligand-receptor bond formation. Science 293, 465–468 (2001)
Kirkwood, J., Buff, F.: The statistical mechanical theory of solution. I.J. Chem. Phys. 19, 774–777 (1951)
Kramers, H.A.: Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7, 284–304 (1940)
Merkel, R., Nassoy, P.,Leung, A., Ritchie, K., Evans, E.: Energy landscapes of receptor-ligand bonds explored with dynamic force spectroscopy. Nature 397, 50–53 (1999)
Moy, V.T., Florin, E., Gaub, H.E.: Intermolecular forces and energies between ligands and receptors. Science 266, 257–259 (1994)
Murray, J.D.:Asymptotic analysis. Springer-Verlag, New York, 1984
Qian, H.: Entropy-enthalpy compensation: conformational fluctuation and induced-fit. J. Chem. Phys. 109, 10015–10017 (1998)
Qian, H.: A mathematical analysis of the Brownian dynamics of DNA tether. J. Math. Biol. 41, 331–340 (2000)
Qian, H.: An analysis of the thermodynamics of Hydrophobic Solvation based on scaled particle theory. E-print, http://arxiv.org/abs/physics/0104085 (2001)
Qian, H.: From discrete protein kinetics to continuous Brownian dynamics: a new perspective. Prot. Sci. 11, 1–5 (2002)
Qian, H., Hopfield, J.J.: Entropy-enthalpy compensation: perturbation and relaxation in thermodynamic systems. J. Chem. Phys. 105, 9292–9296 (1996)
Qian, H., Shapiro, B.E.: A graphical method for force analysis: macromolecular mechanics with atomic force microscopy. Prot: Struct. Funct. Genet. 37, 576–581 (1999)
Qian, H., Schellman, J.A.: Transformed Poisson-Boltzmann relations and ionic distributions. J. Phys. Chem. B 104, 11528–11540 (2000)
Reiss, H.: Scaled particle methods in the statistical thermodynamics of fluids. Adv. Chem. Phys. 9, 1–84 (1965)
Schellman, J.A.: Solvent denaturation. Biopolymers 17, 1305–1322 (1978)
Schellman, J.A.: Fluctuation and linkage relations in macromolecular solution. Biopolymers 29, 215–224 (1990)
Schellman, J.A.: The relation between the free energy of ineraction and binding. Biophys. Chem. 45, 273–279 (1993)
Schlick, T.: Molecular modeling and simulation. Springer-Verlag, New York, 2002
Shapiro, B.E., Qian, H.: A quantitative analysis of single protein-ligand complex separation with the atomic force microscope. Biophys. Chem. 67, 211–219 (1997)
Shapiro, B.E., Qian, H.: Hysteresis in force probe measurements: a dynamic systems perspective. J. Theoret. Biol. 194, 551–559 (1998)
Szabo, A., Schulten, K., Schulten, Z.: First passage time approach to diffusion controlled reactions. J. Chem. Phys. 72, 4350–4357 (1980)
Wong, J.Y., Kuhl, T.L., Israelachvili, J.N., Mullah, N., Zalipsky, S.: Direct measurement of a tethered ligand-receptor interaction potential. Science 275, 820–822 (1997)
Zwanzig, R.: Simple model of protein folding kinetics. Proc. Natl. Acad. Sci. USA 92, 9801–9804 (1995)
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Qian, H. An Asymptotic Comparative Analysis of the Thermodynamics of Non-Covalent Association. J. Math. Biol. 52, 277–289 (2006). https://doi.org/10.1007/s00285-005-0353-3
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DOI: https://doi.org/10.1007/s00285-005-0353-3