Quantum mechanics

lac operon

Brownian motion

Biochemistry

Lac repressor

Electrostatics

Physical chemistry

Physics

Molecular physics

Molecular dynamics

Poisson–Boltzmann equation

Computational chemistry

Brownian dynamics

Crystallography

Chemistry

Plasmid

The Journal of Physical Chemistry B

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.

Free Energy of Nonspecific Binding of Cro Repressor Protein to DNA