Quantum Dynamics in Continuum for Proton Transport I: Basic Formulation (Communications in Computational Physics, 2013)
Proton transport is one of the most important and interesting phenomena inliving 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 functionalapproach 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 solventare assumed to obey the Boltzmann distribution. The impact of protein molecularstructure and its charge polarization on the proton transport is considered explicitlyat the atomic level. We formulate a total free energy functional to put proton kineticand 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 theproton transport system. Generalized Poisson-Boltzmann equation and Kohn-Shamequation are obtained from the variational framework. Theoretical formulations forthe proton density and proton conductance are constructed based on fundamentalprinciples. The molecular surface of the channel protein is utilized to split the discreteprotein 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) channelis used to demonstrate the performance of the proposed proton transport model andvalidate the efficiency of proposed mathematical algorithms. The electrostatic characteristics of the GA channel is analyzed with a wide range of model parameters. Theproton 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.