FREE-ENERGY OF NONSPECIFIC-BINDING OF CRO REPRESSOR PROTEIN TO DNA

The Brownian dynamics (ED) simulation method has been employed to stud y the energetics of nonspecific binding of lambda Cro repressor protei n (Cro) to model B-DNA. BD simulates the diffusional dynamics as the p rotein encounters the DNA surface and describes (i) the steric effects of encounter between the irregular surfaces of the protein and DNA mo lecules based on crystallographic coordinates and (ii) the electrostat ic effects of encounter based on finite difference numerical solutions of the Poisson-Boltzmann (PB) equation. Using ED as a means of genera ting a statistical ensemble of docked complexes in a Boltzmann distrib ution, a direct calculation of the free energy and entropy of the enco unter is performed as a function of the radial distance from the DNA h elix axis to the protein center. During the simulation electrostatic e nergies of protein interaction with DNA are taken from prior solutions of the PB equation stored on a cubic lattice. The PB equation is solv ed in three different forms: (i) the linearized form (LPB), (ii) the f ull nonlinear form (FPB), and (iii) the full form with periodic bounda ry conditions implemented (FPBBC). All three methods give qualitativel y similar free energy curves, but different depths for the minima. For example, with FPBBC electrostatics a free energy well-depth of -5.2 /- 0.5 kcal/mol was obtained. The LPB method yielded a well-depth of - 6.1 +/- 0.5 kcal/mol. Using the free energy profile of nonspecific doc king predicted with FPBBC electrostatics and assuming free one-dimensi onal lateral diffusion (sliding) of docked pairs, we estimated the lif etime of a nonspecifically docked state to be 5 mu s. The protein shou ld be able to slide laterally approximately 50 base pairs before becom ing detached.