Free Energy of Nonspecific Binding of Cro Repressor Protein to DNA

Abstract

The Brownian dynamics (BD) simulation method has been employed to study the energetics of nonspecific binding of λ Cro repressor protein (Cro) to model B-DNA. BD simulates the diffusional dynamics as the protein encounters the DNA surface and describes (i) the steric effects of encounter between the irregular surfaces of the protein and DNA molecules based on crystallograhpic coordinates and (ii) the electrostatic effects of encounter based on finite difference numerical solutions of the Poisson−Boltzmann (PB) equation. Using BD as a means of generating a statistical ensemble of docked complexes in a Boltzmann distribution, a direct calculation of the free energy and entropy of the encounter is performed as a function of the radial distance from the DNA helix axis to the protein center. During the simulation electrostatic energies of protein interaction with DNA are taken from prior solutions of the PB equation stored on a cubic lattice. The PB equation is solved in three different forms: (i) the linearized form (LPB), (ii) the full nonlinear form (FPB), and (iii) the full form with periodic boundary conditions implemented (FPBBC). All three methods give qualitatively 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 docking predicted with FPBBC electrostatics and assuming free one-dimensional lateral diffusion (sliding) of docked pairs, we estimated the lifetime of a nonspecifically docked state to be 5 μs. The protein should be able to slide laterally approximately 50 base pairs before becoming detached.

Brownian dynamics of interactions between aldolase mutants and F‐actin

“…It is possible for BD to see multiple minima, as in the case of nonspecific binding (e.g. BD simulations of 434 Cro repessor binding DNA show two wells where different orientations contributed to the nonspecific interaction; Thomasson et al, 1997;Yang et al, 2001). The large electrostatic attraction between F-actin and aldolase is somewhat similar to that observed for barnase and barstar (Camacho et al, 1999) because the electrostatics both steers and orients the docking of the two proteins.…”

Calculation of Weak Protein-Protein Interactions: The pH Dependence of the Second Virial Coefficient

“…Finally, it is worth noting that the model developed here lends itself naturally to inclusion in BD simulations of the type that have been used extensively (Gabdoulline and Wade, 1997;Elcock et al, 1999;Northrup et al, 1988). BD simulations have been used to provide considerable insight into the factors governing the kinetics of macromolecular association events, but have up to now been used only sparingly in applications that depend on thermodynamics (Thomasson et al, 1997). This has been the case simply because it has not been certain that the models used (which typically model only electrostatic interactions) reproduce the thermodynamics correctly.…”

Ionic strength dependence of F‐actin and glycolytic enzyme associations: A Brownian dynamics simulations approach

“…BD is also capable of providing other information concerning macromolecular associations, including: the prediction of relative free energies of interaction and the dynamics of nonspecific binding for protein‐protein or protein‐DNA interactions20 and the prediction of specific encounter complexes 21, 22. BD has also been able to reproduce the ionic strength dependence of a variety of processes including the interaction of 464 Cro repressor and B‐DNA 23.…”