Effect of the ordered interfacial water layer in protein complex formation: A nonlocal electrostatic approach

Rubinstein, Alexander; Sabirianov, Renat; Mei, Wai Ning; Namavar, F.; Khoynezhad, A.

doi:10.1103/physreve.82.021915

Cited by 19 publications

(53 citation statements)

References 52 publications

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“…Rubinstein et al have used this model to study numerous biomolecular processes, using geometries with high symmetry to simplify calculations [33, 165, 166]. Similarly, Paillusson et al solved one-dimensional problems with a nonlocal Poisson–Boltzmann equation, and extended their model to higher-order theories [167].…”

Section: Nonlocal Dielectric Modelsmentioning

confidence: 99%

Gradient models in molecular biophysics: progress, challenges, opportunities

Bardhan

2013

Journal of the Mechanical Behavior of Materials

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In the interest of developing a bridge between researchers modeling materials and those modeling biological molecules, we survey recent progress in developing nonlocal-dielectric continuum models for studying the behavior of proteins and nucleic acids. As in other areas of science, continuum models are essential tools when atomistic simulations (e.g. molecular dynamics) are too expensive. Because biological molecules are essentially all nanoscale systems, the standard continuum model, involving local dielectric response, has basically always been dubious at best. The advanced continuum theories discussed here aim to remedy these shortcomings by adding features such as nonlocal dielectric response, and nonlinearities resulting from dielectric saturation. We begin by describing the central role of electrostatic interactions in biology at the molecular scale, and motivate the development of computationally tractable continuum models using applications in science and engineering. For context, we highlight some of the most important challenges that remain and survey the diverse theoretical formalisms for their treatment, highlighting the rigorous statistical mechanics that support the use and improvement of continuum models. We then address the development and implementation of nonlocal dielectric models, an approach pioneered by Dogonadze, Kornyshev, and their collaborators almost forty years ago. The simplest of these models is just a scalar form of gradient elasticity, and here we use ideas from gradient-based modeling to extend the electrostatic model to include additional length scales. The paper concludes with a discussion of open questions for model development, highlighting the many opportunities for the materials community to leverage its physical, mathematical, and computational expertise to help solve one of the most challenging questions in molecular biology and biophysics.

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Section: Nonlocal Dielectric Modelsmentioning

confidence: 99%

Gradient models in molecular biophysics: progress, challenges, opportunities

Bardhan

2013

Journal of the Mechanical Behavior of Materials

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“…This is a mean-field approach to account for solvent structure that Hildebrandt has referred to as structured continuum model. 22 Nonlocal models may, therefore, offer new insights into molecular binding, 24 a process for which electrostatic contributions are commonly conceived as a balance between favorable interactions gained on binding and the unfavorable desolvation penalty. Our study here reports on a model geometry of charge burial in a spherical solute.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal continuum electrostatic theory predicts surprisingly small energetic penalties for charge burial in proteins

Bardhan

2011

The Journal of Chemical Physics

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We study the energetics of burying charges, ion pairs, and ionizable groups in a simple protein model using nonlocal continuum electrostatics. Our primary finding is that the nonlocal response leads to markedly reduced solvent screening, comparable to the use of application-specific protein dielectric constants. Employing the same parameters as used in other nonlocal studies, we find that for a sphere of radius 13.4 Å containing a single +1e charge, the nonlocal solvation free energy varies less than 18 kcal/mol as the charge moves from the surface to the center, whereas the difference in the local Poisson model is ∼35 kcal/mol. Because an ion pair (salt bridge) generates a comparatively more rapidly varying Coulomb potential, energetics for salt bridges are even more significantly reduced in the nonlocal model. By varying the central parameter in nonlocal theory, which is an effective length scale associated with correlations between solvent molecules, nonlocal-model energetics can be varied from the standard local results to essentially zero; however, the existence of the reduction in charge-burial penalties is quite robust to variations in the protein dielectric constant and the correlation length. Finally, as a simple exploratory test of the implications of nonlocal response, we calculate glutamate pK(a) shifts and find that using standard protein parameters (ε(protein) = 2-4), nonlocal results match local-model predictions with much higher dielectric constants. Nonlocality may, therefore, be one factor in resolving discrepancies between measured protein dielectric constants and the model parameters often used to match titration experiments. Nonlocal models may hold significant promise to deepen our understanding of macromolecular electrostatics without substantially increasing computational complexity.

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“…The nonlocal dielectric approach has been studied for more than thirty years for the purpose of improving the quality of the classic Poisson dielectric approach [1][2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Analytical solutions of nonlocal Poisson dielectric models with multiple point charges inside a dielectric sphere

2016

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The nonlocal dielectric approach has led to new models and solvers for predicting electrostatics of proteins (or other biomolecules), but how to validate and compare them remains a challenge. To promote such a study, in this paper, two typical nonlocal dielectric models are revisited. Their analytical solutions are then found in the expressions of simple series for a dielectric sphere containing any number of point charges. As a special case, the analytical solution of the corresponding Poisson dielectric model is also derived in simple series, which significantly improves the well known Kirkwood's double series expansion. Furthermore, a convolution of one nonlocal dielectric solution with a commonly-used nonlocal kernel function is obtained, along with the reaction parts of these local and nonlocal solutions. To turn these new series solutions into a valuable research tool, they are programmed as a free Fortran software package, which can input point charge data directly from a protein data bank file. Consequently, different validation tests can be quickly done on different proteins. Finally, a test example for a protein with 488 atomic charges is reported to demonstrate the differences between the local and nonlocal models as well as the importance of using the reaction parts to develop local and nonlocal dielectric solvers.

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Effect of the ordered interfacial water layer in protein complex formation: A nonlocal electrostatic approach

Cited by 19 publications

References 52 publications

Gradient models in molecular biophysics: progress, challenges, opportunities

Gradient models in molecular biophysics: progress, challenges, opportunities

Nonlocal continuum electrostatic theory predicts surprisingly small energetic penalties for charge burial in proteins

Analytical solutions of nonlocal Poisson dielectric models with multiple point charges inside a dielectric sphere

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