Journal of Computational Electronics

, Volume 14, Issue 2, pp 524–532 | Cite as

A transport equation for confined structures applied to the OprP, Gramicidin A, and KcsA channels

  • Amirreza Khodadadian
  • Clemens Heitzinger


A transport equation for confined structures is used to calculate the ionic currents through various transmembrane proteins. The transport equation is a diffusion-type equation where the concentration of the particles depends on the one-dimensional position in the confined structure and on the local energy. The computational significance of this continuum model is that the (6 + 1)-dimensional Boltzmann equation is reduced to a (2 + 1)-dimensional diffusion-type equation that can be solved with small computational effort so that ionic currents through confined structures can be calculated quickly. The applications here are three channels, namely OprP, Gramicidin A, and KcsA. In each case, the confinement potential is estimated from the known molecular structure of the channel. Then the confinement potentials are used to calculate ionic currents and to study the effect of parameters such as the potential of mean force, the ionic bath concentration, and the applied voltage. The simulated currents are compared with measurements, and very good agreement is found in each case. Finally, virtual potassium channels with selectivity filters of varying length are simulated in order to discuss the optimality of the filter.


Boltzmann equation Confined structures Ionic transport 



The authors acknowledge support by FWF (Austrian Science Fund) START Project No. Y660 PDE Models for Nanotechnology. The authors also acknowledge interesting discussions with Ulrich Kleinekathöfer (Bremen), who also provided the experimental data for the OprP pore.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institute for Analysis and Scientific ComputingVienna University of Technology (TU Vienna)ViennaAustria
  2. 2.School of Mathematical and Statistical SciencesArizona State University (ASU)TempeUSA

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