Mathematical models of ion transport through cell membrane channels

• Autorzy: Miękisz J. , Gomułkiewicz J. , Miękisz S.

Identyfikatory

DOI

10.14708/ma.v42i1.469

Warianty tytułu

PL

Matematyczne modele transportu jonów w kanałach komórkowych

• Języki publikacji: EN

Abstrakty

EN

We discuss various models of ion transport through cell membrane channels. Recent experimental data shows that sizes of some ion channels are compared to those of ions and that only few ions may be simultaneously in any single channel. Theoretical description of ion transport in such channels should therefore take into account stochastic fluctuations and interactions between ions and between ions and channel proteins. This is not satisfied by macroscopic continuum models based on the Poisson-Nernst-Planck equations. More realistic descriptions of ion transport are offered by microscopic molecular and Brownian dynamics. We present a derivation of the Poisson-Nernst-Planck equations. We also review some recent models such as single-file diffusion and Markov chains of interacting ions (boundary driven lattice gases). Such models take into account discrete and stochastic nature of ion transport and specifically interactions between ions in ion channels.

PL

W naszej pracy przeglądowej przedstawiamy różne modele transportu jonów w kanałach komórkowych. Rozmiary niektórych kanałów jonowych są rzędu średnicy jonów, a więc tylko kilka jonów może jednocześnie znajdować się w danym kanale. Opis transporu w tak wąskich kanałach powinien brać pod uwagę stochastyczne fluktuacje liczby jonów oraz oddziaływania między nimi. Ciagłe modele makrosko powe oparte na równaniach Poissona-Nernsta-Plancka nie spełniają tych warunków. Bardziej realistyczne modele, takie jak dynamika molekularna i dynamika brownowska, uwzględniają mikroskopową dyskretną strukturę kanałów jonowych. Przed stawiamy wyprowadzenie równań Poissona-Nernsta-Plancka. Przedyskutowujemy również modele łańcuchów Markowa oddziałujących jonów. Modele takie biorą pod uwagę dyskretny charakter transportu jonów i oddziaływania między nimi.

Słowa kluczowe

EN

ion channels; ion transport; Poisson–Nernst–Planck equations; non-equilibrium statistical mechanics; Kawasaki dynamics; driven lattice gases

PL

kanały jonowe; transport jonów; równanie Poissona-Nernsta-Plancka; dynamika Kawasaki

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2014
• Tom: Vol. 42, No. 1
• Strony: 39--62
• Opis fizyczny: Bibliogr. 121 poz., rys.

Twórcy

autor

Miękisz J.

• University of Warsaw Institute of Applied Mathematics and Mechanics Banacha 2, 02-097 Warsaw, Poland

autor

Gomułkiewicz J.

• Wrocław Technical University Institute of Physics Wrocław, Poland

autor

Miękisz S.

• Medical University of Wrocław Department of Biophysics Wrocław, Poland

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