Adapting Poisson-Boltzmann to the self-consistent mean field theory: Application to protein side-chain modeling

Abstract

We present an extension of the self-consistent mean field theory for protein side-chain modeling in which solvation effects are included based on the Poisson-Boltzmann (PB) theory. In this approach, the protein is represented with multiple copies of its side chains. Each copy is assigned a weight that is refined iteratively based on the mean field energy generated by the rest of the protein, until self-consistency is reached. At each cycle, the variational free energy of the multi-copy system is computed; this free energy includes the internal energy of the protein that accounts for vdW and electrostatics interactions and a solvation free energy term that is computed using the PB equation. The method converges in only a few cycles and takes only minutes of central processing unit time on a commodity personal computer. The predicted conformation of each residue is then set to be its copy with the highest weight after convergence. We have tested this method on a database of hundred highly refined NMR structures to circumvent the problems of crystal packing inherent to x-ray structures. The use of the PB-derived solvation free energy significantly improves prediction accuracy for surface side chains. For example, the prediction accuracies for χ 1 for surface cysteine, serine, and threonine residues improve from 68%, 35%, and 43% to 80%, 53%, and 57%, respectively. A comparison with other side-chain prediction algorithms demonstrates that our approach is consistently better in predicting the conformations of exposed side chains.

Protein side chain conformation predictions with an MMGBSA energy function

“…A GB variant called SGB gave improvements (compared to a distance‐dependent dielectric) of 5% for χ 1 of surface side chains in single‐position predictions . A PB term gave an improvement of 4% for χ 1 and 3% for χ 1 + 2 of surface residues; the improvement was obtained for polar residues; hydrophobic residues were unaffected.…”

“…Most side chain prediction studies take the minimum energy structure as their target, and make no attempt to predict thermal fluctuations (mean field theory studies are an exception). In reality, many protein side chains, especially at the surface, spend a significant fraction of their time in more than one rotamer .…”

Capturing protein sequence–structure specificity using computational sequence design

“…Our side‐chain placement method, for example, includes only a vdW potential and a basic Coulomb potential for electrostatics with a distance‐dependent dielectric constant. We have recently shown that it can be expanded to account for the solvent, at a minimal cost. We are currently implementing this idea into our sequence design procedure.…”

Analytical solutions of nonlinear Poisson–Boltzmann equation for colloidal particles immersed in a general electrolyte solution by homotopy perturbation technique

“…The approximations introduced by the PB theory include omitting finite ion size and ion-ion correlation effects, which prohibit its application to systems where these effects become pronounced such as ionic layering, overcharging, or charge inversion, like-charge attraction, and ion selectivity inversion, all of which are associated with highly charged macroions, usually under high-salt conditions or in the presence of multivalent ions [4][5][6]. However, because of its simplicity and ability to satisfactorily predict many thermodynamic properties, the nonlinear PB theory has been extensively used to model the ionic solvent environment of biomolecules [7][8][9][10][11]. Extensive research suggests that the PB approximation remains a good reference theory for describing the essential features of electrolyte solutions at thermal equilibrium.…”