A transport equation for confined structures applied to the OprP, Gramicidin A, and KcsA channels
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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.
KeywordsBoltzmann 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.
- 4.Berti, C., Furini, S., Cavalcanti, S., Sangiorgi, E., Fiegna, C.: Particle-based simulation of conductance of solid-state nanopores and ion channels. In: Proceedings of the International Conference on Simulation of Semiconductor Processes and Devices 2009 (SISPAD 2009), pp. 301–304. IEEE Operations Centers (NJ), San Diego, CA (2009)Google Scholar
- 7.Cronin, N.B., O’Reilly, A., Duclohier, H., Wallace, B.: Binding of the anticonvulsant drug lamotrigine and the neurotoxin batrachotoxin to voltage-gated sodium channels induces conformational changes associated with block and steady-state activation. J. Biol. Chem. 278(12), 10675–10682 (2003)CrossRefGoogle Scholar