Equivalence oftranspaths in ion channels

Encyclopedia of Computational Neuroscience, 2013

Kinetic schemes; Markov chains Definition A Markov model is a simplified phenomenological representation of (bio)physical, chemical, or biological process dynamics, described quantitatively as a set of discrete states and by the ease of transition through time from one state to another.

Biophysical Chemistry, 1983

We treat the transport of univalent cations through pore-like protein channels in biological membranes anaigtic;IIIy. using two models (A + B) for the channel and the ion-channei interaction. A Lennnrd-Jones-type repulsion between Ihe ions and the pore wafl is introduced. We also incfude Van der Waals-and coulomb-type interactions between polar ligands of the pore-forming protein (e.g.. carbonyl groups directed towards the axis of the channel) and the migrating particles. In model A. the polar groups are assumed 10 occur in pairs of dipoles pointing in opposite directions (as in the gramicidin A channel). while in model B the channel is treated as a pore with a radially isotropic charge distribution. In both models the ion-channel interaction leads to the occurrence of periodic potentiais. corresponding to quasi-equitihrium and transition stafe sites of rhe ion in the pore. The diffusion rate can be calculated employing rare-thcore&al concepts on the basis of microscopic parameters. It is demonstrated that the anomaly (inversion of the normai mass effect) for the transport rates of different ions can he related to differences in the activaGon entropy. The latter quantity is estimated ;InaIyticnlIy for both models. As a test. we performed numerical calculations with parameters based on the gramicidin A model. The results are in good agreement with experimental data and data from computer simulations. This shows that simple analytic expressions are well suited for predicting trends in the ionic conductivity of protein channels on the basis of microscopic intrmctions. the channel interior. In particular, the inffuence oC structural inhomogeneities of the channel on the migration rate of different ions '3 studied. In ger,eral. real protein channels have a highly complicated structure and a detailed analysis of the infiuence of microscopic interaction between the 0301-4622/83/oooO-oooO/503.00

Ion channels are of major interest and form an area of intensive research in the fields of biophysics and medicine, since they control many vital physiological functions. The aim of this work is on one hand to propose a fully stochastic and discrete model describing the main characteristics of a multiple channel system. The movement of the ions is coupled, as usual, with a Poisson equation for the electrical field; we have considered in addition the influence of exclusion forces. On the other hand, we have discussed about the nondimensionalization of the stochastic system by using real physical parameters, all supported by numerical simulations. The specific features of both cases of micro and nano channels have been have been taken in due consideration with particular attention to the latter case in order to show that it is necessary to consider inside the channels a discrete and stochastic model for ions movement.

We discuss various models of ion transport through cell membrane channels.

Multiscale Modeling & Simulation, 2016

Ion channels are of major interest and form an area of intensive research in the fields of biophysics and medicine since they control many vital physiological functions. The aim of this work is on one hand to propose a fully stochastic and discrete model describing the main characteristics of a multiple channel system. The movement of the ions is coupled, as usual, with a Poisson equation for the electrical field; we have considered, in addition, the influence of exclusion forces. On the other hand, we have discussed about the nondimensionalization of the stochastic system by using real physical parameters, all supported by numerical simulations. The specific features of both cases of micro-and nanochannels have been taken in due consideration with particular attention to the latter case in order to show that it is necessary to consider a discrete and stochastic model for ions movement inside the channels.

Journal of Mathematical Chemistry, 2012

Mass action type deterministic kinetic models of ion channels are usually constructed in such a way as to obey the principle of detailed balance (or, microscopic reversibility) for two reasons: first, the authors aspire to have models harmonizing with thermodynamics, second, the conditions to ensure detailed balance reduce the number of reaction rate coefficients to be measured. We investigate a series of ion channel models which are asserted to obey detailed balance, however, these models violate mass conservation and in their case only the necessary conditions (the so-called circuit conditions) are taken into account. We show that ion channel models have a very specific structure which makes the consequences true in spite of the imprecise arguments. First, we transform the models into mass conserving ones, second, we show that the full set of conditions ensuring detailed balance (formulated by Feinberg) leads to the same relations for the reaction rate constants in these special cases, both for the original models and the transformed ones.

Biophysical Journal, 1993

A novel way to model permeation through ionic channels is formulated. Our method does not require that equilibrium exists in the channel or at the channel interfaces. In addition, the potential profile does not need to be specified and the assumption of constant field across the membrane does not need to be made. Our formulation relies on statistical rate theory for its development and uses a form of the electrochemical potential which assumes that the ions are in solution.

Fluctuation and Noise Letters, 2012

We present a nonequilibrium reaction rate model of the ionic transition through an 28 open ion channel, taking account of the interaction between an ion at the entrance of 29 the channel and an ion at the binding site in a self-consistent way. The electrostatic 30 potential is calculated by solution of the Poisson equation for a channel modeled as a 31 cylindrical tube. The transition rate, and the binding site occupancy as a function of 32 the left bulk concentration are compared to 1D Brownian dynamics simulations. The 33 analysis is performed for a single binding site of high-affinity, with the exit rate influenced 34 by barrier fluctuations at the channel exit. The results are compared with experimental 35 data for the permeation of the Na + ion through the Gramicidin A channel, with which 36 they are shown to be in good agreement. 37 Ion channels are pathways down the centres of proteins embedded into the mem-2 branes of biological cells [1, 2], facilitating the diffusion of ions across the mem-3 branes. They are complicated devices [3], built of thousands of atoms, flexible, and 4 filled with ions and water dipoles that coordinate their movements to allow ions 5 to pass one by one across the membrane. To support life, channels have to be pre-6 cise often selecting between similar ions with an accuracy of 1:1000 [4], yet able to 7 deliver millions of ions per second, i.e., almost at the rate of free diffusion. In recent 8 years impressive progress has been achieved both in understanding the structure 9 of ion channels [3] and in modeling their properties [5]. Yet the mechanism that 10 enables channels to be highly selective while still passing millions of ions per second 11 remains a tantalizing paradox. 12 Channels displaying counter-intuitive behavior of this kind often have one singly 13 occupied selectivity site [6] with a high affinity for a specific type of ion. The fact 14 that a satisfactory explanation of the paradox has yet to be found, even in the 15 most clearly characterized cases [7] of channel conduction, suggests that some basic 16 physical phenomenon has been overlooked. The difficulties in modeling the system 17 stem from the presence of the long-range Coulomb interaction and regions with 18 low-and high-dielectric constants. The stochastic dynamics of ionic motion needs 19 to be solved simultaneously with the Poisson equation for all the charges, which 20 often results in strongly nonequilibrium stochastic dynamics. Therefore, only an 21 approximate semi-analytic treatment of the problem is possible.

2015

Abstract. We discuss various models of ion transport through cell membrane channels. Recent experimental data shows that sizes of 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 interactions between ions and between ions and channel proteins. This is not satisfied by macroscopic continuum models based on Poisson-Nernst-Planck equations. More realistic descriptions of ion transport are offered by microscopic Brownian and molecular dynamics. One should also take into account a dynamical character of the channel structure. This is not yet addressed in the literature.

arXiv: Soft Condensed Matter, 2019

In this work, the dependence of reversal potentials and zero-current fluxes on diffusion coefficients are examined for ionic flows through membrane channels. The study is conducted for the setup of a simple structure defined by the profile of permanent charges with two mobile ion species, one positively charged (cation) and one negatively charged (anion). Numerical observations are obtained from analytical results established using geometric singular perturbation analysis of classical Poisson-Nernst-Planck models. For 1:1 ionic mixtures with arbitrary diffusion coefficients, Mofidi and Liu [arXiv:1909.01192] conducted a rigorous mathematical analysis and derived an equation for reversal potentials that, in its particular case, can be compared to Goldman-Hodgkin-Katz equation. We summarize and extend these results with numerical observations for biological relevant situations. The numerical investigations on profiles of the electrochemical potentials, ion concentrations, and electric...