scholarly journals Quantum dynamics in continuum for proton transport—Generalized correlation

2012 ◽  
Vol 136 (13) ◽  
pp. 134109 ◽  
Author(s):  
Duan Chen ◽  
Guo-Wei Wei
2013 ◽  
Vol 13 (1) ◽  
pp. 285-324 ◽  
Author(s):  
Duan Chen ◽  
Guo-Wei Wei

AbstractProton 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.


1992 ◽  
Vol 86 (1) ◽  
pp. 63-70 ◽  
Author(s):  
David Brauer ◽  
DeNea Conner ◽  
Shu-I Tu

2016 ◽  
Vol 12 (1) ◽  
pp. 4172-4177
Author(s):  
Abdul Malek

The denial of the existence of contradiction is at the root of all idealism in epistemology and the cause for alienations.  This alienation has become a hindrance for the understanding of the nature and the historical evolution mathematics itself and its role as an instrument in the enquiry of the physical universe (1). A dialectical materialist approach incorporating  the role of the contradiction of the unity of the opposites, chance and necessity etc., can provide a proper understanding of the historical evolution of mathematics and  may ameliorate  the negative effect of the alienation in modern theoretical physics and cosmology. The dialectical view also offers a more plausible materialist interpretation of the bewildering wave-particle duality in quantum dynamics (2).


Author(s):  
Walter Dittrich ◽  
Martin Reuter
Keyword(s):  

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