Ionic Flow through Membrane Channels

Tuesday, June 15 at 05:45pm (PDT)
Wednesday, June 16 at 01:45am (BST)
Wednesday, June 16 09:45am (KST)

SMB2021 SMB2021 Follow Monday (Tuesday) during the "MS09" time block.
Note: this minisymposia has multiple sessions. The second session is MS03-NEUR (click here).

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Peter Bates (Michigan State University), Weishi Liu (Mathematics, U. Kansas, USA), Mingji Zhang (Mathematics, New Mexico Tech., USA)


A fundamental concern of physiology is the function of ion channels, these being essential to most cellular processes. Ion channels are cylindrical proteins with hollow cores that provide a controllable path for electro-diffusion of ions through membranes. Thus, they establish communication among cells and the external environment and affect the cell membrane potential. This way, ion channels control a wide range of biological functions. The study of ion channels consists of two related major topics: The structures of the different ion channels and the ionic flow properties within those channels. This session will focus on the latter. With the structure of an open channel given, there are many important aspects to its electro-diffusion properties. Beyond general electro-diffusion phenomena for electrolytic solutions in bulk or near charged walls, the study of ionic flows through channels should take into consideration boundary conditions in the concentration of ion species, the effective sizes and valences of the different ions, and the structure of the channel, including the distribution of permanent charge. One would like to gain an understanding of selectivity and the values of reversal potentials for the separate flows of the ionic species in a given channel. This session will explore those issues.

Tom DeCoursey

(Department of Physiology & Biophysics Rush University Medical Center, USA)
"Proton Selective Conduction Through hHV1, the Human Voltage-gated Proton Channel"
Voltage-gated proton channels are unique ion channels, because the molecule is a free-standing voltage-sensing domain with an intrinsic proton conduction pathway. An exquisite proton selectivity mechanism excludes all other ions. How proton channels achieve this selectivity will be discussed. An essential element is an aspartic acid residue located within a narrow region at the center of the membrane. The aspartate is likely hydrogen-bonded to one of the three arginine residues. An approaching hydronium ion breaks the hydrogen bonds to allow proton conduction. When the channel is closed, a hydrophobic region prevents proton leakage through the pore.

Mingji Zhang

(Mathematics, New Mexico Tech., USA)
"Competition between Cations via Classical Poisson–Nernst–Planck Models with Small Permanent Charges"
We study a one-dimensional Poisson–Nernst–Planck system for ionic flow through a membrane channel. Nonzero but small permanent charge, the major structural quantity of an ion channel, is included in the model. Two cations with the same valences and one anion are included in the model, which provides more rich and complicated correlations or interactions between ions. The cross-section area of the channel is included in the system, providing important information on the geometry of the three-dimensional channel, which is critical for our analysis. Geometric singular perturbation analysis is employed to establish the existence and local uniqueness of solutions to the system for small permanent charges. Treating the permanent charge as a small parameter, through regular perturbation analysis, we are able to derive approximations of the individual fluxes explicitly, and this allows us to study the competition between two cations, which is related to the selectivity phenomena of ion channels. Numerical simulations are performed to provide a more intuitive illustration of our analytical results, and they are consistent.

Hamid Mofidi

(Mathematics, U. Iowa, USA)
"Effects of ion size on current and fluxes via hard-sphere PNP models"
This reports on studies of a one-dimensional version of a Poisson-Nernst-Planck-type system with a local hard-sphere potential model for ionic flow through a membrane channel with fixed boundary ion concentrations (charges) and electric potentials. The research is directed to set up a simple structure defined by permanent charges with two mobile ion species. A local hard-sphere potential that depends pointwise on ion concentrations is incorporated in the model to evaluate ion-size influences on the ionic flow. The model problem is treated as a boundary value problem of a singularly perturbed differential system, and the analysis is based on the geometric singular perturbation theory. We examine ion size effects on the flow rate of matter through a cross-section by treating the ion sizes as small parameters.

Weishi Liu

(Mathematics, U. Kansas, USA)
"Permanent charge effects on ionic flow"
Permanent charge is the most important structure of an ion channel.   In this talk, we will report our studies toward an understanding of permanent charges on ionic flow via a quasi-one-dimensional Poisson-Nernst-Planck (PNP) model.    The permanent charges are limited to a special case of piecewise constant with one non-zero portion. For ionic mixtures with one cation species and one anion species, a fairly rich behavior of permanent charge effects is revealed from rigorous analyses based on a geometric framework for PNP and from numerical simulations guided by the analytical results.   For ionic mixtures with two cation species and one anion species, richer behavior is expected and our preliminary analytical results identify a number of these, including some not-so-intuitive ones.

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Virtual conference of the Society for Mathematical Biology, 2021.