Electrostatic potentials of proteins in water: a structured continuum approach (original) (raw)
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Multiscale models and approximation algorithms for protein electrostatics
arXiv (Cornell University), 2015
Electrostatic forces play many important roles in molecular biology, but are hard to model due to the complicated interactions between biomolecules and the surrounding solvent, a fluid composed of water and dissolved ions. Continuum model have been surprisingly successful for simple biological questions, but fail for important problems such as understanding the effects of protein mutations. In this paper we highlight the advantages of boundaryintegral methods for these problems, and our use of boundary integrals to design and test more accurate theories. Examples include a multiscale model based on nonlocal continuum theory, and a nonlinear boundary condition that captures atomic-scale effects at biomolecular surfaces.
Scientific reports, 2016
Interfacial waters are increasingly appreciated as playing a key role in protein-protein interactions. We report on a study of the prediction of interfacial water positions by both Molecular Dynamics and explicit solvent-continuum electrostatics based on the Dipolar Poisson-Boltzmann Langevin (DPBL) model, for three test cases: (i) the barnase/barstar complex (ii) the complex between the DNase domain of colicin E2 and its cognate Im2 immunity protein and (iii) the highly unusual anti-freeze protein Maxi which contains a large number of waters in its interior. We characterize the waters at the interface and in the core of the Maxi protein by the statistics of correctly predicted positions with respect to crystallographic water positions in the PDB files as well as the dynamic measures of diffusion constants and position lifetimes. Our approach provides a methodology for the evaluation of predicted interfacial water positions through an investigation of water-mediated inter-chain cont...
Work/Precision Tradeoffs in Continuum Models of Biomolecular Electrostatics
arXiv (Cornell University), 2015
The structure and function of biological molecules are strongly influenced by the water and dissolved ions that surround them. This aqueous solution (solvent) exerts significant electrostatic forces in response to the biomolecule's ubiquitous atomic charges and polar chemical groups. In this work, we investigate a simple approach to numerical calculation of this model using boundary-integral equation (BIE) methods and boundary-element methods (BEM). Traditional BEM discretizes the protein-solvent boundary into a set of boundary elements, or panels, and the approximate solution is defined as a weighted combination of basis functions with compact support. The resulting BEM matrix then requires integrating singular or near singular functions, which can be slow and challenging to compute. Here we investigate the accuracy and convergence of a simpler representation, namely modeling the unknown surface charge distribution as a set of discrete point charges on the surface. We find that at low resolution, point-based BEM is more accurate than panelbased methods, due to the fact that the protein surface is sampled directly, and can be of significant value for numerous important calculations that require only moderate accuracy, such as the preliminary stages of rational drug design and protein engineering
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Quarterly reviews of biophysics, 2012
An understanding of molecular interactions is essential for insight into biological systems at the molecular scale. Among the various components of molecular interactions, electrostatics are of special importance because of their long-range nature and their influence on polar or charged molecules, including water, aqueous ions, proteins, nucleic acids, carbohydrates, and membrane lipids. In particular, robust models of electrostatic interactions are essential for understanding the solvation properties of biomolecules and the effects of solvation upon biomolecular folding, binding, enzyme catalysis, and dynamics. Electrostatics, therefore, are of central importance to understanding biomolecular structure and modeling interactions within and among biological molecules. This review discusses the solvation of biomolecules with a computational biophysics view toward describing the phenomenon. While our main focus lies on the computational aspect of the models, we provide an overview of t...
A Nonlinear Boundary Condition for Continuum Models of Biomolecular Electrostatics
2015
Understanding the behavior of biomolecules such as proteins requires understanding the critical influence of the surrounding fluid (solvent) environment--water with mobile salt ions such as sodium. Unfortunately, for many studies, fully atomistic simulations of biomolecules, surrounded by thousands of water molecules and ions are too computationally slow. Continuum solvent models based on macroscopic dielectric theory (e.g. the Poisson equation) are popular alternatives, but their simplicity fails to capture well-known phenomena of functional significance. For example, standard theories predict that electrostatic response is symmetric with respect to the sign of an atomic charge, even though response is in fact strongly asymmetric if the charge is near the biomolecule surface. In this work, we present an asymmetric continuum theory that captures the essential physical mechanism--the finite size of solvent atoms--using a nonlinear boundary condition (NLBC) at the dielectric interface...
Molecular Based Mathematical Biology (Online), 2013
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. ...
Evaluation of Models of Electrostatic Interactions in Proteins
The conformations of proteins and protein-protein complexes observed in nature must be low in free energy relative to alternative (not observed) conformations, and it is plausible (but not absolutely necessary) that the electrostatic free energies of experimentally observed conformations are also low relative to other conformations. Starting from this assumption, we evaluate alternative models of electrostatic interactions in proteins by comparing the electrostatic free energies of native, nativelike, and non-native structures. We observe that the total electrostatic free energy computed using the Poisson-Boltzmann (PB) equation or the generalized Born (GB) model exhibits free energy gaps that are comparable to, or smaller than, the free energy gaps resulting from Coulomb interactions alone. Detailed characterization of the contributions of different atom types to the total electrostatic free energy showed that, although for most atoms unfavorable solvation energies associated with atom burial are more than compensated by attractive Coulomb interactions, Coulomb interactions do not become more favorable with burial for certain backbone atom types, suggesting inaccuracies in the treatment of backbone electrostatics. Sizable free energy gaps are obtained using simple distance-dependent dielectric models, suggesting their usefulness in approximating the attenuation of long range Coulomb interactions by induced polarization effects. Hydrogen bonding interactions appear to be better modeled with an explicitly orientation-dependent hydrogen bonding potential than with any of the purely electrostatic models of hydrogen bonds, as there are larger free energy gaps with the former. Finally, a combined electrostatics-hydrogen bonding potential is developed that appears to better capture the free energy differences between native, nativelike, and non-native proteins and protein-protein complexes than electrostatic or hydrogen bonding models alone.