Theoretical Studies of Protein-Protein and Protein-DNA Binding Rates

Proteins are folded chains of amino acids. Some of the amino acids (e.g. Lys, Arg, His, Asp, and Glu) carry charges under physiological conditions. Proteins almost always function through binding to other proteins or ligands, for example barnase is a ribonuclease protein, found in the bacterium Bacil lus amyloliquefaceus. Barnase degrades RNA by hydrolysis. For the bacterium to inhibit the potentially lethal action of Barnase within its own cell it co-produces another protein called barstar which binds quickly, and tightly, to barnase. The biological function of this binding is to block the active site of barnase. The speeds (rates) at which proteins associate are vital to many biological processes. They span a wide range (from less than 103 to 108 M-1 s-1 ). Rates greater than ~106 M -1s-1 are typically found to be manifestations of enhancements by long-range electrostatic interactions between the associating proteins. A different paradigm appears in the case of protein binding to DNA. The rate in this case is enhanced through attractive surface potential that effectively reduces the dimensionality of the available search space for the diffusing protein. This thesis presents computational and theoretical models on the rate of association of ligands/proteins to other proteins or DNA. For protein-protein association we present a general strategy for computing protein-protein rates of association. The main achievements of this strategy is the ability to obtain a stringent reaction criteria based on the landscape of short-range interactions between the associating proteins, and the ability to compute the effect of the electrostatic interactions on the rates of association accurately using the best known solvers for Poisson-Boltzmann equation presently available. For protein-DNA association we present a mathematical model for proteins targeting specific sites on a circular DNA topology. The main achievements are the realization that a linear DNA with reflecting ends and specific site in the middle of the chain is kinetically indistinguishable from its circularized topology, and the ability to predict the effect of the dissociation via the ends of linear DNA on the rate of association which is to reduce the rate.