Ionic Flow through Membrane Channels

Monday, June 14 at 5:45pm (PDT)
Tuesday, June 15 at 01:45am (BST)
Tuesday, June 15 09:45am (KST)

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

Bob Eisenberg

(Molecular Biophysics & Physiology, Rush University, USA)
"Maxwell’s Core Equations Exact, Universal, and Scary"
When the Maxwell equations are written without a dielectric constant, they are universal and exact, for biological and technological applications, from inside atoms to between stars. Dielectric and polarization phenomena need then to be described by stress strain relations for charge, that show how charge redistributes when the electric field is changed, in each system of interest. Conservation of total current (including the ethereal displacement current ε_0  ∂E∕∂t) is then as exact as the Maxwell equations themselves and independent of any property of matter. It is a consequence of the Lorentz invariance of the elementary charge, a property of all locally inertial systems, described by the theory of relativity. Exact Conservation of Total Current allows a redefinition of Kirchhoff’s current law that is itself exact. In unbranched systems like circuit components or ion channels, conservation of total current becomes equality. Spatial dependence of total current disappears in that case. Hopping phenomena disappear. Spatial Brownian motion disappears. The infinite variation of a Brownian model of thermal noise becomes the zero spatial variation of total current. Maxwell’s Core Equations become a perfect (spatial) low pass filter. An Exact and Universal theory of Electrodynamics is a scary challenge to scientists like me, trained to be skeptical of all sweeping claims to perfection.

Jianing Chen

(Mathematics, New Mexico Tech., USA)
"Effects on zero-current ionic flows from ion sizes via PNP system with boundary layers"
We study the qualitative properties of zero-current ionic flows via Poisson-Nernst-Planck systems for two oppositely charged particles with boundary layers. Local Bikerman’s hard-sphere model is included in the system to account for finite ion size effects. Of particular interest is to examine the effects on the zero-current ionic flows from finite ion sizes, diffusion coefficients, ion valences and boundary layers due to the violation of electroneutrality boundary conditions. The nonlinear interplays among those system parameters are characterized in detail, which provides better understandings of the internal dynamics of ionic flows through membrane channels.

Francisco Bezanilla

(Biochemistry and Molecular Biology and Institute for Biophysical Dynamics, University of Chicago and CINV, University of Valparaiso, Chile., USA)
"Voltage sensors and ion channel opening"
The generation of the nerve impulse (action potential) depends on voltage-dependent sodium channels that must open before voltage-dependent potassium channels. We will briefly explain the voltage sensors that give voltage dependence of the ion channels. The voltage sensors have intrinsic charges in the channel protein which move in the cell membrane electric field and generate gating currents. Experiments with voltage clamp and site-directed fluorescence describe molecular details of the voltage sensor operation indicating the paths followed by the charged arginine residues within the protein core. A detailed study of the residues in the core show that the nature of the side chains determine that Na channels are faster than K channels. The canonical coupling of the voltage sensor to the conduction pore is via the linker between transmembrane segments S3 and S4. We will describe that the proximity of the S4 segment of the voltage sensor and the S5 segment of the pore region makes another noncanonical coupling pathway. The molecular basis of this pathway will be described.

Pei Liu

(Mathematics, U. Minnesota, USA)
"Ion-dependent DNA Configuration in Bacteriophage Capsids"
Bacteriophages densely pack their long dsDNA genome inside a protein capsid. The conformation of the viral genome inside the capsid is consistent with a hexagonal liquid crystalline structure, and experimental results have confirmed that it depends on environmental ionic conditions. In this work, we propose a biophysical model to describe the dependence of DNA configurations inside bacteriophage capsids on ions types and concentrations. The total free energy of the system combines the liquid crystal free energy, the electrostatic energy and the Lennard--Jones energy. The equilibrium points of this energy solve a highly nonlinear, second order partial differential equation (PDE) that defines the distributions of DNA and the ions inside the capsid. We develop a computational approach to simulate predictions of our model. The numerical results show good agreement with existing experiments and molecular dynamics simulations.

Hosted by SMB2021 Follow
Virtual conference of the Society for Mathematical Biology, 2021.