Commun. Comput. Phys.,
Modeling Salt Dependence of Protein-Protein Association: Linear vs Non-Linear Poisson-Boltzmann Equation
Kemper Talley 1, Petras Kundrotas 1, Emil Alexov 1*1 Computational Biophysics and Bioinformatics, Department of Physics, Clemson University, Clemson, SC 29634, USA.
Received 30 September 2007; Accepted (in revised version) 5 January 2008
Available online 25 January 2008
Proteins perform various biological functions in the cell by interacting and binding to other proteins, DNA, or other small molecules. These interactions occur in cellular compartments with different salt concentrations, which may also vary under different physiological conditions. The goal of this study is to investigate the effect of salt 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 never been done before. Since the proteins are irregularly shaped objects, the calculations have been carried out by a means of finite-difference algorithm that solves Poisson-Boltzmann equation (PB) numerically. We performed simulations using both linear and non-linear PB equations and found that non-linearity, in general, does not have significant contribution into salt effect when the net charges of the protein monomers are of different polarity and are less than five electron units. However, for complexes made of monomers carrying large net charges non-linearity is an important factor, especially for homo-complexes which are made of identical units carrying the same net charge. A parameter reflecting the net charge of the monomers is proposed and used as a flag distinguishing between cases which should be treated with non-linear Poisson-Boltzmann equation and cases where linear PB produces sound results. It was also shown that the magnitude of the salt effect is not correlated with macroscopic parameters (such as net charge of the monomers, corresponding complexes, surface and number of interfacial residues) but rather is a complex phenomenon that depends on the shape and charge distribution of the molecules.
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PACS: 82.20.wt, 87.15.km
Key words: Poisson-Boltzmann equation, electrostatics, protein-protein complexes, salt-dependence of binding energy, finite-difference Poisson-Boltzmann method.
Email: firstname.lastname@example.org (K. Talley), email@example.com (P. Kundrotas), firstname.lastname@example.org (E. Alexov)