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Quantum Dynamics in Continuum for Proton Transport I: Basic Formulation

Published online by Cambridge University Press:  03 June 2015

Duan Chen  and
Guo-Wei Wei
Duan Chen
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
Guo-Wei Wei*
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA
*
*Corresponding author.Email:wei@math.msu.edu
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Abstract

Proton transport is one of the most important and interesting phenomena in living cells. The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins. We describe proton dynamics quantum mechanically via a density functional approach while implicitly model other solvent ions as a dielectric continuum to reduce the number of degrees of freedom. The densities of all other ions in the solvent are assumed to obey the Boltzmann distribution. The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly at the atomic level. We formulate a total free energy functional to put proton kinetic and potential energies as well as electrostatic energy of all ions on an equal footing. The variational principle is employed to derive nonlinear governing equations for the proton transport system. Generalized Poisson-Boltzmann equation and Kohn-Sham equation are obtained from the variational framework. Theoretical formulations for the proton density and proton conductance are constructed based on fundamental principles. The molecular surface of the channel protein is utilized to split the discrete protein domain and the continuum solvent domain, and facilitate the multiscale discrete/continuum/quantum descriptions. A number of mathematical algorithms, including the Dirichlet to Neumann mapping, matched interface and boundary method, Gummel iteration, and Krylov space techniques are utilized to implement the proposed model in a computationally efficient manner. The Gramicidin A (GA) channel is used to demonstrate the performance of the proposed proton transport model and validate the efficiency of proposed mathematical algorithms. The electrostatic characteristics of the GA channel is analyzed with a wide range of model parameters. The proton conductances are studied over a number of applied voltages and reference concentrations. A comparison with experimental data verifies the present model predictions and validates the proposed model.

Keywords

87.10.Ed87.15.hj87.16.VyProton transportquantum dynamics in continuummultiscale modelPoisson-Boltzmann equationgeneralized Kohn-Sham equationvariational principle
Type
Research Article
Information
Communications in Computational Physics , Volume 13 , Issue 1 , January 2013 , pp. 285 - 324
Copyright
Copyright © Global Science Press Limited 2013

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