Analysis of fast boundary-integral approximations for modeling electrostatic contributions of molecular binding

Amelia B Kreienkamp,Lucy Y Liu,Matthew G Knepley,Jaydeep P Bardhan,Mala L Radhakrishnan,Mona S Minkara

doi:10.2478/mlbmb-2013-0007

Amelia B Kreienkamp, Lucy Y Liu + Show 4 more

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https://doi.org/10.2478/mlbmb-2013-0007

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Abstract

We analyze and suggest improvements to a recently developed approximate continuum-electrostatic model for proteins. The model, called BIBEE/I (boundary-integral based electrostatics estimation with interpolation), was able to estimate electrostatic solvation free energies to within a mean unsigned error of 4% on a test set of more than 600 proteins-a significant improvement over previous BIBEE models. In this work, we tested the BIBEE/I model for its capability to predict residue-by-residue interactions in protein-protein binding, using the widely studied model system of trypsin and bovine pancreatic trypsin inhibitor (BPTI). Finding that the BIBEE/I model performs surprisingly less well in this task than simpler BIBEE models, we seek to explain this behavior in terms of the models' differing spectral approximations of the exact boundary-integral operator. Calculations of analytically solvable systems (spheres and tri-axial ellipsoids) suggest two possibilities for improvement. The first is a modified BIBEE/I approach that captures the asymptotic eigenvalue limit correctly, and the second involves the dipole and quadrupole modes for ellipsoidal approximations of protein geometries. Our analysis suggests that fast, rigorous approximate models derived from reduced-basis approximation of boundary-integral equations might reach unprecedented accuracy, if the dipole and quadrupole modes can be captured quickly for general shapes.

Highlights

Electrostatic interactions play central roles in molecular biophysics, mediating both the affinity and specificity of interactions between biological molecules
In this paper we investigate how several Boundary Integral-Based Electrostatic Estimation (BIBEE) variants perform for estimating the electrostatic contributions to three quantities that are often used in the analysis of biomolecular systems: solvation free energies, binding free energies, and relative binding free energies
The recently proposed BIBEE/I model [13] is able to predict protein solvation free energies to within 4% mean unsigned relative error over a large test set [32]. This represented a substantial improvement in accuracy over the original BIBEE models, which motivated us to test the viability of fast BIBEE models for component analysis

Summary

Introduction

Electrostatic interactions play central roles in molecular biophysics, mediating both the affinity and specificity of interactions between biological molecules. Relative binding free energies enable a valuable approach for biomolecular analysis called electrostatic component analysis [23], in which the contributions of individual protein residues or molecular moieties can be quantified, providing a systematic identification of residues or chemical groups that are critical for molecular recognition of binding partners. This approach has been used to identify crucial determinants of binding in protein–protein and drug–target [23, 35, 39, 50, 59, 61] systems.

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