A Modified Nonlocal Continuum Electrostatic Model for Protein in Water and Its Analytical Solutions for Ionic Born Models

A nonlocal continuum electrostatic model, defined as integro-differential equations, can significantly improve the classic Poisson dielectric model, but is too costly to be applied to large protein simulations. To sharply reduce the model's com- plexity, a modified nonlocal continuum electrostatic model is presented in this paper for a protein immersed in water solvent, and then transformed equivalently as a sys- tem of partial differential equations. By using this new differential equation system, analytical solutions are derived for three different nonlocal ionic Born models, where a monoatomic ion is treated as a dielectric continuum ball with point charge either in the center or uniformly distributed on the surface of the ball. These solutions are analyt- ically verified to satisfy the original integro-differential equations, thereby, validating the new differential equation system. AMS subject classifications: 92-08, 65N30

[1]  D. Griffiths.  Introduction to Electrodynamics , 2017 .

[2]  Thomas Simonson,et al.  Electrostatics and dynamics of proteins , 2003 .

[3]  C. Brooks,et al.  Recent advances in the development and application of implicit solvent models in biomolecule simulations. , 2004, Current opinion in structural biology.

[4]  Nathan A. Baker,et al.  Improving implicit solvent simulations: a Poisson-centric view. , 2005, Current opinion in structural biology.

[5]  M. A. Vorotyntsev,et al.  Model non-local electrostatics. III. Cylindrical interface , 1979 .

[6]  Hans-Peter Lenhof,et al.  Electrostatic potentials of proteins in water: a structured continuum approach , 2007, Bioinform..

[7]  D. Davidson,et al.  Dielectric Properties of Ices II, III, V, and VI , 1965 .

[8]  B. Roux,et al.  Implicit solvent models. , 1999, Biophysical chemistry.

[9]  Godehard Sutmann,et al.  NONLOCAL DIELECTRIC SATURATION IN LIQUID WATER , 1997 .

[10]  Bopp,et al.  Static nonlocal dielectric function of liquid water. , 1996, Physical review letters.

[11]  Andreas Hildebrandt,et al.  A new numerical method for nonlocal electrostatics in biomolecular simulations , 2010, J. Comput. Phys..

[12]  S. Cohn,et al.  Ooce Note Series on Global Modeling and Data Assimilation Construction of Correlation Functions in Two and Three Dimensions and Convolution Covariance Functions , 2022 .

[13]  Mikhail V. Basilevsky,et al.  NONLOCAL CONTINUUM SOLVATION MODEL WITH OSCILLATING SUSCEPTIBILITY KERNELS: A NONRIGID CAVITY MODEL , 1998 .

[14]  Andreas Hildebrandt,et al.  Biomolecules in a structured solvent : a novel formulation of nonlocal electrostatics and its numerical solution , 2005 .

[15]  Maria Teresa Neves-Petersen,et al.  Protein electrostatics: a review of the equations and methods used to model electrostatic equations in biomolecules--applications in biotechnology. , 2003, Biotechnology annual review.

[16]  Yi Jiang,et al.  A Fast Solver for a Nonlocal Dielectric Continuum Model , 2012, SIAM J. Sci. Comput..

[17]  Jacopo Tomasi,et al.  Quantum Mechanical Continuum Solvation Models , 2005 .

[18]  M. A. Vorotyntsev,et al.  Model nonlocal electrostatics. I , 1978 .

[19]  D. A. Dunnett.  Classical Electrodynamics , 2020, Nature.

[20]  Olaf Steinbach,et al.  A Boundary Integral Formulation for Nonlocal Electrostatics , 2008 .

[21]  G. Sutmann,et al.  NONLOCAL DIELECTRIC FUNCTION OF WATER : HOW STRONG ARE THE EFFECTS OF INTRAMOLECULAR CHARGE FORM FACTORS ? , 1999 .

[22]  J. H. Robertson,et al.  The chemical physics of solvation. Part A: Theory of solvation edited by R. R. Dogonadze, E. Kalman, A. A. Kornyshev and J. Ulstrup , 1986 .

[23]  Ariel Fernández,et al.  Continuum equations for dielectric response to macro-molecular assemblies at the nano scale , 2004 .

[24]  R Blossey,et al.  Novel formulation of nonlocal electrostatics. , 2004, Physical review letters.

[25]  Mikhail V. Basilevsky,et al.  An advanced continuum medium model for treating solvation effects: Nonlocal electrostatics with a cavity , 1996 .

[26]  Mikhail V. Basilevsky,et al.  Nonlocal continuum solvation model with exponential susceptibility kernels , 1998 .

[27]  R. Blossey,et al.  Slits, plates, and Poisson-Boltzmann theory in a local formulation of nonlocal electrostatics. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  P. Koehl.  Electrostatics calculations: latest methodological advances. , 2006, Current opinion in structural biology.

[29]  B. Mennucci,et al.  Comprar Continuum Solvation Models in Chemical Physics: Theory and Applications | Benedetta Mennucci | 9780470029381 | Wiley , 2007 .

[30]  H. Römer.  The Electrodynamics of Continuous Media , 2005 .

[31]  M. A. Vorotyntsev,et al.  Model nonlocal electrostatics. II. Spherical interface , 1978 .