The kinetics of protein-protein recognition

Abstract

We examine a simple kinetic model for association that incorporates the basic features of protein-protein recognition within the rigid body approximation, that is, when no large conformation change occurs. Association starts with random collision at the rate k(coll) predicted by the Einstein-Smoluchowski equation. This creates an encounter pair that can evolve into a stable complex if and only if the two molecules are correctly oriented and positioned, which has a probability p(r). In the absence of long-range interactions, the bimolecular rate of association is p(r) k(coll). Long-range electrostatic interactions affect both k(coll) and p(r). The collision rate is multiplied by q(t), a factor larger than 1 when the molecules carry net charges of opposite sign as coulombic attraction makes collisions more frequent, and less than 1 in the opposite case. The probability p(r) is multiplied by a factor q(r) that represents the steering effect of electric dipoles, which preorient the molecules before they collide. The model is applied to experimental data obtained by Schreiber and Fersht (Nat. Struct. Biol. 3:427-431, 1996) on the kinetics of barnase-barstar association. When long-range electrostatic interactions are fully screened or mutated away, q(t)q(r) approximately 1, and the observed rate of productive collision is p(r) k(coll) approximately 10(5) M(-1) x s(-1). Under these conditions, p(r) approximately 1.5 x 10(-5) is determined by geometric constraints corresponding to a loss of rotational freedom. Its value is compatible with computer docking simulations and implies a rotational entropy loss deltaS(rot) approximately 22 e.u. in the transition state. At low ionic strength, long-range electrostatic interactions accelerate barnase-barstar association by a factor q(t)q(r) of up to 10(5) as favorable charge-charge and charge-dipole interactions work together to make it much faster than free diffusion would allow.