Quantum dynamics in continuum for proton channel transport
Duan Chen, Mathematics, Michigan State University (April 27, 2011)
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Proton transport across membranes is one of the most important and interesting phenomena in living cells. The present work proposes a multiscale/multiphysical model for the understanding of atomic level mechanism of proton transport in transmembrane proteins. We describe proton dynamics quantum mechanically via a density functional approach while implicitly model numerous solvent molecules as a dielectric continuum to reduce the number of degrees of freedom. The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly in atomic level. 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. 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. Generalized Poisson-Boltzmann equation and Kohn-Sham equation are obtained from the variational framework. 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 channel model and validate the efficiency of the proposed mathematical algorithms. The electrostatic characteristics and proton conductance of the GA channel are analyzed with a wide range of model parameters. A comparison with experimental data verifies the present model predictions and validates the proposed model.