Electrostatic component of binding energy: Interpreting predictions from poisson–boltzmann equation and modeling protocols

Abstract

Macromolecular interactions are essential for understanding numerous biological processes and are typically characterized by the binding free energy. Important component of the binding free energy is the electrostatics, which is frequently modeled via the solutions of the Poisson-Boltzmann Equations (PBE). However, numerous works have shown that the electrostatic component (ΔΔGelec) of binding free energy is very sensitive to the parameters used and modeling protocol. This prompted some researchers to question the robustness of PBE in predicting ΔΔGelec. We argue that the sensitivity of the absolute ΔΔGelec calculated with PBE using different input parameters and definitions does not indicate PBE deficiency, rather this is what should be expected. We show how the apparent sensitivity should be interpreted in terms of the underlying changes in several numerous and physical parameters. We demonstrate that PBE approach is robust within each considered force field (CHARMM-27, AMBER-94 and OPLS-AA) once the corresponding structures are energy minimized. This observation holds despite of using two different molecular surface definitions, pointing again that PBE delivers consistent results within particular force field. The fact that PBE delivered ΔΔGelec values may differ if calculated with different modeling protocols is not a deficiency of PBE, but natural results of the differences of the force field parameters and potential functions for energy minimization. In addition, while the absolute ΔΔGelec values calculated with different force field differ, their ordering remains practically the same allowing for consistent ranking despite of the force field used.

What Are We Missing by Not Measuring the Net Charge of Proteins?

“…[1,4] Deoxyribonuclease and ovalbumin, for example, have identical isoelectricp oints of pI = 5.1, but the formal and measured net charge of both proteins differ by approximately 7u nits at pH 8.4. [4] The systematic absence of experimentally determinedv alues of Z has likely impeded ar igorous understanding of most chemicalp rocesses in which proteinsa re involved including aggregation and self-assembly, [20][21][22][23][24][25][26] ligand binding, [27][28][29][30][31][32][33][34] catalysis, [35][36][37][38][39] electron transfer, [3,6,[40][41][42][43][44][45][46][47] protein crystallization, [14,48] analytical separation, [49,50] and protein engineering. [51][52][53][54][55][56] It is tempting to assume that the formal net chargeo faprotein predicted from generalized residue pK a values (Z seq )issosimilar to the actual net charge that any difference is irrelevant, and the isoelectric point tells us all we need to know about ap rotein's net charge.…”

Combining the polarizable Drude force field with a continuum electrostatic Poisson–Boltzmann implicit solvation model

“…near the molecular boundary of the solute . Thus, results of continuum electrostatics models are especially sensitive to the location of the solute/solvent boundary and its functional form . In continuum models this boundary is defined on the basis of atomic Born‐like radii, which normally do not depend on the solute conformation, but may depend on the solute covalent structure.…”

Assessment of a Single Decoupling Alchemical Approach for the Calculation of the Absolute Binding Free Energies of Protein-Peptide Complexes

“…Implicit solvation models, based on the rigorous concept of the solvent potential of mean force (Roux and Simonson, 1999 ), are not intrinsically less accurate than other models. However, because they are asked to model a free energy rather than a potential energy, they are more difficult to design and parametrize than explicit models of solvation (Chakavorty et al, 2016 ). Some implicit solvent implementations, in particular, are known to overemphasize the formation of salt bridges between protein residues (Okur et al, 2008 ; Wickstrom et al, 2015 ).…”