Modeling Salt Dependence of Protein-Protein Association: Linear vs Non-Linear Poisson-Boltzmann Equation (Communications in Computational Physics, 2008)
Proteins perform various biological functions in the cell by interacting andbinding to other proteins, DNA, or other small molecules. These interactions occur incellular compartments with different salt concentrations, which may also vary underdifferent physiological conditions. The goal of this study is to investigate the effect ofsalt concentration on the electrostatic component of the binding free energy (hereafter,salt effect) based on a large set of 1482 protein-protein complexes, a task that has neverbeen done before. Since the proteins are irregularly shaped objects, the calculationshave been carried out by a means of finite-difference algorithm that solves Poisson-Boltzmann equation (PB) numerically. We performed simulations using both linearand non-linear PB equations and found that non-linearity, in general, does not havesignificant contribution into salt effect when the net charges of the protein monomersare of different polarity and are less than five electron units. However, for complexesmade of monomers carrying large net charges non-linearity is an important factor,especially for homo-complexes which are made of identical units carrying the samenet charge. A parameter reflecting the net charge of the monomers is proposed andused as a flag distinguishing between cases which should be treated with non-linearPoisson-Boltzmann equation and cases where linear PB produces sound results. It wasalso shown that the magnitude of the salt effect is not correlated with macroscopicparameters (such as net charge of the monomers, corresponding complexes, surfaceand number of interfacial residues) but rather is a complex phenomenon that dependson the shape and charge distribution of the molecules.