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Tai-Chia Lin
To describe ion transport through biological channels, we derive a new Poisson-Nernst-Planck (PNP) type model called the modified PNP_steric equations with derivative terms up to the fourth order using infinite expansion (in increasing order of derivatives) of the energy with the approximate Lennard-Jones (LJ) potential. A numerical scheme of the modified PNP_steric equations is developed to see the flow dynamics of charged particles, and the special feature of the scheme is that the numerical solutions satisfy a discrete energy law mimicking the energy law of the modified PNP_steric equations. The fourth-order derivative terms of the modified PNP_steric equations may stabilize the dynamics of the modified PNP_steric equations even though the coefficients of the second-order derivative terms are located in the symmetry breaking regime which may give multiple equilibriums of the original PNP_steric equations (with B. Eisenberg, Nonlinearity 28 (2015) 2053–2080). Our numerical results show that the energy of the modified PNP_steric equations may behave like a decreasing piecewise constant function of time. Such a model and computational method would be useful for the study of ion transport through channels. This is a joint work with Yi-Ping Lo and Chun-Hao Teng.
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Riccardo Sacco
In this communication we propose a multiphysics model for the simulation of biological ion channels using a continuum-based approach that self-consistently combines ion electrodiffusion, channel fluid motion, thermal self-heating and mechanical deformation. The mathematical formulation consists of a system of nonlinearly coupled partial differential equations in conservation form that includes: the thermo-velocity-extended Poisson-Nernst-Planck equations; the Stokes equations; the Navier-Lame' equations; and the heat equation.
Extensive computational examples are illustrated to provide a validation of models and methods in the simulation of two realistic channel geometries under quite different operation regimes. In the first case study we consider a cylindrical voltage operated ion nanochannel transporting K+ and Na+ ions. In the second case study we consider the interplay between the motion of K+, Na+, Cl- and HCO-_3 ions and the active secretion of aqueous humor across the (non-pigmented) epithelial cells of the ciliary body in the eye. Obtained results are in very good agreement with available experimental data and biophysical conjectures.
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Jan-Frederik Pietschmann
We introduce a class of non-linear variants of the well-known Poisson-Nernst-Planck Model and discuss its properties as well as possible applications to Ion channels and Nanopores. We will present a formal derivation based on a one-dimensional lattice model. We shall argue that our model is more well-suited for high densities in confined geometries.
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Heedeok Hong
Membrane proteins are assembled through balanced interactions among protein, lipids and water. Studying their folding while maintaining the native lipid environment is a necessary but challenging task. Here we present a set of methods for analyzing key elements in membrane protein folding, including thermodynamic stability, compactness of the unfolded state and unfolding cooperativity under native conditions. The methods are based on steric trapping which couples unfolding of a doubly-biotinylated protein to binding of monovalent streptavidin (mSA). We further advanced this technology for general application by developing versatile biotin probes possessing spectroscopic reporters that are sensitized by mSA binding or protein unfolding. By applying those methods to an intramembrane protease GlpG, we elucidated a widely unraveled unfolded state, subglobal unfolding of the region encompassing the active site, and a network of cooperative and localized interactions for maintaining the stability. These findings provide crucial insights into the folding energy landscape of membrane proteins.
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Emil Alexov
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Guowei Wei
We discuss adifferential geometry based multiscale and multiphysics paradigm for ion channel systems. We describe macromolecular systems by a number of approaches, including macroscopic electrostatics and elasticity and/or microscopic molecular mechanics (MM) and quantum mechanics; while treating the aqueous environment as a dielectric continuum or electrolytic fluids. We use differential geometry theory of surfaces to couple various microscopic and macroscopic domains on an equal footing. Based on the variational principle, we derive the coupled Poisson-Boltzmann, Nernst-Planck, Kohn-Sham, Laplace-Beltrami, and Newton equations for the structure, function, dynamics and transport of ion-channel systems. We employ homology modeling to construct mosquito sodium channels and combine MM and PNP type of approaches for the understanding of sodium channel gating.
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Heather Mayes
Proton transport via transmembrane transporters is vital to cellular function, yet many mechanistic questions remain unanswered. These mechanisms are difficult to study experimentally or computationally due to the involved complex interplay of dynamics on multiple length- and timescales, including chemical reactions (protonation/deprotonation events) that are coupled to solvation and biomolecular dynamics and conformational changes. Multistate reactive molecular mechanics (MS-RMD) describes reactive processes in a classical MD framework, thereby enabling the computational efficiency necessary to model transmembrane protein dynamics while still capturing the charge delocalization and fast bond-cleavage and bond-formation events of proton transfer (i.e., Grotthuss shuttling). This talk will introduce the MS-RMD mathematical formulation and explain how this framework can uncover key mechanistic insights into transmembrane proton transport. Three examples will describe how the method is applied and verified against experimental results.
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Chun Liu
The transport and distribution of charged particles in electrolyte solutions are crucial for many physical and biological processes. In this talk, I will go over various models of the transport of ions and charged particles in complicated environments. We will employ an energetic variational approach to derive governing systems for these general diffusion problems in non-ideal solutions.
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Huan-Xiang Zhou
Abstract not submitted.
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Perumal Nithiarasu
A simple approach that enables us to analyse the interrelationships between Ca2+ handling processes at the cellular level and the role of intercellular communication in the emergence of multicellular synchronization is presented. Individual cells are represented by a mathematical model of intracellular Ca2+ dynamics, and coupled via Ca2+ currents and membrane potential. Theoretical predictions successfully reproduce experimental findings and provide novel insights on the action of several pharmacological agents that modulate Ca2+ signalling pathways and intercellular communication via distinct mechanisms.
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Yongcheng Zhou
Abstract not submitted.
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Maria Kurnikova
Abstract not submitted.
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Weishi Liu
The talk will focus on applications from rigorous analysis of some Poisson-Nernst-Planck (PNP) type models for ion transport through membrane channels. Due to multi-variable and multi-scale features, and nonlinear interactions presented in the problem, the study demands a great deal of mathematical analysis efforts. The talk will start with a brief review of a geometric singular perturbation theory specified for analyzing PNP that has been developed based on modern geometric singular perturbation theory of nonlinear dynamical systems. The analysis allows one to track the nonlinear interplays between relevant physical quantities and to extract critical information on ionic flow properties, such as effects of ion sizes, permanent charges and channel geometry, at least, in simple settings.
