Gradient models in molecular biophysics: progress, challenges, opportunities

Abstract

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.

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators

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Communication: Modeling charge-sign asymmetric solvation free energies with nonlinear boundary conditions

“…Importantly, the latter could distinguish between smallmagnitude charges near the surface, and larger charges further away 16 . Fourth, water's length-scale-dependent dielectric behavior might be included using nonlocal electrostatics 7,20,[64][65][66] . The new model also does not necessarily capture specific hydrogen-bonding effects like AGBNP2 does ?…”

Calcium Chloride (CaCl2) : Characteristics and Molecular Interaction in Solution

“…Dinamika molekuler (30)(31)(32)(33)(34)(35)(36)(37)(38) merupakan suatu metode untuk menyelidiki struktur dari zat padat (41) , cair dan gas. Dinamika molekuler (42) pada umumnya menggunakan teknik persamaan hukum newton (43)(44)(45)(46)(47) dan mekanika klasik.…”