Abstract
Calculations of electrostatic properties of protein-protein complexes are usually done within framework of a model with a certain set of parameters. In this paper we present a comprehensive statistical analysis of the sensitivity of the electrostatic component of binding free energy (ΔΔGel) with respect with different force fields (Charmm, Amber, and OPLS), different values of the internal dielectric constant, and different presentations of molecular surface (different values of the probe radius). The study was done using the largest so far set of entries comprising 260 hetero and 2148 homo protein-protein complexes extracted from a previously developed database of protein complexes (ProtCom). To test the sensitivity of the energy calculations with respect to the structural details, all structures were energy minimized with corresponding force field, and the energies were recalculated. The results indicate that the absolute value of the electrostatic component of the binding free energy (ΔΔGel) is very sensitive to the force field parameters, the minimization procedure, the values of the internal dielectric constant, and the probe radius. Nevertheless our results indicate that certain trends in ΔΔGel behavior are much less sensitive to the calculation parameters. For instance, the fraction of the homo-complexes, for which the electrostatics was found to oppose binding, is 80% regardless of the force fields and parameters used. For the hetero-complexes, however, the percentage of the cases for which electrostatics opposed binding varied from 43% to 85%, depending on the protocol and parameters employed. A significant correlation was found between the effects caused by raising the internal dielectric constant and decreasing the probe radius. Correlations were also found among the results obtained with different force fields. However, despite of the correlations found, the absolute ΔΔGel calculated with different force field parameters could differ more than tens of kcal/mol in some cases. Set of rules of obtaining confident predictions of absolute ΔΔGel and ΔΔGel sign are provided in the conclusion section.PACS codes: 87.15.A-, 87.15. km
Highlights
Proteins are essential components of the living cell[1]
Since the electrostatic component of the binding free energy is the difference between two large and similar numbers, the calculations outcome inevitably depends on parameters of simulations such as the force field parameters, the choice of the internal dielectric constant of proteins, and the molecular surface representation
The analysis of the sensitivity of the Gel, calculated with different force fields, internal dielectric constants, probe radius value and minimization protocols, gives us the opportunity to suggest a set of rules of calculating (a) the absolute value of Gel and (b) the sign of Gel: (a1) if there is no prior knowledge what the effective value of both internal dielectric constant and probe radius are for a given protein complex and a particular protocol of calculating the Gel, the absolute value of calculated Gel is meaningless; (a2) provided that the effective value of both
Summary
Proteins are essential components of the living cell[1]. They function by interacting with other biological macromolecules, including other proteins. Protein-protein binding is a complex process mostly driven by the hydrophobic effect and van der Waals interactions, with significant contribution from entropy and electrostatics. While these energies can not be easy experimentally separated, the electrostatic energy is the energy mostly affected by pH and salt concentration. Since the electrostatic component of the binding free energy is the difference between two large and similar numbers (energy of pair-wise interactions and the desolvation penalty), the calculations outcome inevitably depends on parameters of simulations such as the force field parameters, the choice of the internal dielectric constant of proteins, and the molecular surface representation. Structural refinement affects the outcome of electrostatic calculations
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