Research Article: The Universal Statistical Distributions of the Affinity, Equilibrium Constants, Kinetics and Specificity in Biomolecular Recognition

Date Published: April 17, 2015

Publisher: Public Library of Science

Author(s): Xiliang Zheng, Jin Wang, Guanghong Wei

Abstract: We uncovered the universal statistical laws for the biomolecular recognition/binding process. We quantified the statistical energy landscapes for binding, from which we can characterize the distributions of the binding free energy (affinity), the equilibrium constants, the kinetics and the specificity by exploring the different ligands binding with a particular receptor. The results of the analytical studies are confirmed by the microscopic flexible docking simulations. The distribution of binding affinity is Gaussian around the mean and becomes exponential near the tail. The equilibrium constants of the binding follow a log-normal distribution around the mean and a power law distribution in the tail. The intrinsic specificity for biomolecular recognition measures the degree of discrimination of native versus non-native binding and the optimization of which becomes the maximization of the ratio of the free energy gap between the native state and the average of non-native states versus the roughness measured by the variance of the free energy landscape around its mean. The intrinsic specificity obeys a Gaussian distribution near the mean and an exponential distribution near the tail. Furthermore, the kinetics of binding follows a log-normal distribution near the mean and a power law distribution at the tail. Our study provides new insights into the statistical nature of thermodynamics, kinetics and function from different ligands binding with a specific receptor or equivalently specific ligand binding with different receptors. The elucidation of distributions of the kinetics and free energy has guiding roles in studying biomolecular recognition and function through small-molecule evolution and chemical genetics.

Partial Text: Molecular recognition has been a long standing issue of molecular biology [1, 2]. On the practical side, it is also under intensive investigations in drug discovery and pharmaceutical industry [3]. There are two major issues in biomolecular binding. One is the affinity which is responsible for the driving force and the stability of the binding complex. The other one is the specificity [4, 5] which is crucial for molecular recognition measuring discriminations of “good” binding against “bad” binding. Using microscopic atomistic descriptions to quantitatively study binding is rather difficult [6, 7]. Further more, the accurate estimates of the physical relevant quantities are limited by the delicate balance between hydrophobic interactions, electrostatic interactions, solvation effects and conformational entropy.

We will first present the analytical results and then the simulation results. For analytical studies, since we are mostly interested in the general laws governing the biomolecular binding, the task here is to obtain the universal features. We can use the coarse grained level description instead of the microscopic detailed one to characterize the system.