@Article{CiCP-13-1,
author = {},
title = {Quantum Dynamics in Continuum for Proton Transport I: Basic Formulation},
journal = {Communications in Computational Physics},
year = {2013},
volume = {13},
number = {1},
pages = {285--324},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.050511.050811s},
url = {https://global-sci.com/article/80621/quantum-dynamics-in-continuum-for-proton-transport-i-basic-formulation}
}