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R S Eisenberg - One of the best experts on this subject based on the ideXlab platform.
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optic nerve microcirculation fluid flow and Electrodiffusion
2021Co-Authors: Yi Zhu, R S Eisenberg, Huaxiong HuangAbstract:Complex fluids flow in complex ways in complex structures. Transport of water and various organic and inorganic molecules in the central nervous system are important in a wide range of biological and medical processes [C. Nicholson, and S. Hrabětova, Biophysical Journal, 113(10), 2133(2017)]. However, the exact driving mechanisms are often not known. In this paper, we investigate flows induced by action potentials in an optic nerve as a prototype of the central nervous system (CNS). Different from traditional fluid dynamics problems, flows in biological tissues such as the CNS are coupled with ion transport. It is driven by osmosis created by concentration gradient of ionic solutions, which in term influence the transport of ions. Our mathematical model is based on the known structural and biophysical properties of the experimental system used by the Harvard group Orkand et al [R.K. Orkand, J.G. Nicholls, S.W. Kuffler, Journal of Neurophysiology, 29(4), 788(1966)]. Asymptotic analysis and numerical computation show the significant role of water in convective ion transport. The full model (including water) and the Electrodiffusion model (excluding water) are compared in detail to reveal an interesting interplay between water and ion transport. In the full model, convection due to water flow dominates inside the glial domain. This water flow in the glia contributes significantly to the spatial buffering of potassium in the extracellular space. Convection in the extracellular domain does not contribute significantly to spatial buffering. Electrodiffusion is the dominant mechanism for flows confined to the extracellular domain.
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a model of Electrodiffusion and osmotic water flow and its energetic structure
2011Co-Authors: Yoichiro Mori, Chun Liu, R S EisenbergAbstract:We introduce a model for ionic Electrodiffusion and osmotic water flow through cells and tissues. The model consists of a system of partial differential equations for ionic concentration and fluid flow with interface conditions at deforming membrane boundaries. The model satisfies a natural energy equality, in which the sum of the entropic, elastic and electrostatic free energies are dissipated through viscous, electrodiffusive and osmotic flows. We discuss limiting models when certain dimensionless parameters are small. Finally, we develop a numerical scheme for the one-dimensional case and present some simple applications of our model to cell volume control.
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Electrodiffusion and osmotic water flow and its variational structure
2011Co-Authors: Yoichiro Mori, Chun Liu, R S EisenbergAbstract:We propose a system of partial differential equations (PDE) that describe Electrodiffusion and osmotic water flow. From a physical standpoint, this is a far-reaching generalization of the standard treatment of osmosis and Electrodiffusion in irreversible thermodynamics to spatially extended systems. As far as we know, this is the first mechanically and thermodynamically consistent model of osmotic water flow and Electrodiffusion in systems with deformable cells and membranes with capacitance and conductance. We use an energetic variational approach to enforce consistency and derive a field theory describing the flow, diffusion, and migration of ions, water, and the solution itself. The variational approach is particularly useful because it treats interactions automatically and consistently with a minimal number of arbitrary parameters. Electrodiffusion and osmotic water flow are involved in a wide range of biological functions of organs, tissues, cells, and organelles, including the homeostasis of ions in the brain, fluid secretion by epithelial systems, electrolyte regulation in the kidney, fluid circulation in ocular systems, gastric protection, water uptake by plants, etc. The field equations can be written with boundary conditions and parameters appropriate for the anatomy of each system. The field equations then form a physically and anatomically consistent model of biological function in the variational framework of modern field theory. The variational approach deals naturally with the many ionic solutions (containing a multitude of interacting components in a wide range of concentrations) and the wide range of conditions and forces used in experiments. Solving the PDEs will help suggest and interpret new experiments to understand the interaction of components, conditions, structure, and forces. In the view of classical physiology and biophysics, these interactions are the essence of biological function.
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a multidomain model for Electrodiffusion and water flow
2010Co-Authors: Yoichiro Mori, R S EisenbergAbstract:Fluid flow and its coupling to Electrodiffusion is involved in many physiological systems from the kidney to the lens of the eye, where it has been studied in some detail (Journal of Membrane Biology (2007) 216:1-16). We formulate a mathematical model that describes Electrodiffusion and water flow in three dimensions with resolution and scale appropriate for analysis of tissues. The mathematical model presented can be seen as a coarse-grained version of a model used in (PNAS(2008) 105:6463-6468) to model cellular and subcellular Electrodiffusion. We shall discuss the relationship of the general model to other macroscopic models in electrophysiology, and show preliminary computations and applications.
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Electrodiffusion model simulation of ionic channels 1d simulations
2004Co-Authors: Carl L Gardner, Wolfgang Nonner, R S EisenbergAbstract:The drift-diffusion (Poisson-Nernst-Planck) model is applied to ionic channels in biological membranes plus surrounding solution baths. Simulations of the K channel in KCl solutions using the TRBDF2 method are presented which show significant boundary layers at the ends of the channel. The computed current-voltage curve for the K channel shows excellent agreement with experimental measurements.
Yoichiro Mori - One of the best experts on this subject based on the ideXlab platform.
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from Electrodiffusion theory to the electrohydrodynamics of leaky dielectrics through the weak electrolyte limit
2018Co-Authors: Yoichiro Mori, Yuannan YoungAbstract:The Taylor–Melcher (TM) model is the standard model for describing the dynamics of poorly conducting leaky dielectric fluids under an electric field. The TM model treats the fluids as ohmic conductors, without modelling the underlying ion dynamics. On the other hand, Electrodiffusion models, which have been successful in describing electrokinetic phenomena, incorporate ionic concentration dynamics. Mathematical reconciliation of the Electrodiffusion picture and the TM model has been a major issue for electrohydrodynamic theory. Here, we derive the TM model from an Electrodiffusion model in which we explicitly model the electrochemistry of ion dissociation. We introduce salt dissociation reaction terms in the bulk Electrodiffusion equations and take the limit in which the salt dissociation is weak; the assumption of weak dissociation corresponds to the fact that the TM model describes poor conductors. Together with the assumption that the Debye length is small, we derive the TM model with or without the surface charge convection term depending upon the scaling of relevant dimensionless parameters. An important quantity that emerges is the Galvani potential (GP), the jump in voltage across the liquid–liquid interface between the two leaky dielectric media; the GP arises as a natural consequence of the interfacial boundary conditions for the ionic concentrations, and is absent under certain parametric conditions. When the GP is absent, we recover the TM model. Our analysis also reveals the structure of the Debye layer at the liquid–liquid interface, which suggests how interfacial singularities may arise under strong imposed electric fields. In the presence of a non-zero GP, our model predicts that the liquid droplet will drift under an imposed electric field, the velocity of which is computed explicitly to leading order.
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Well-Posed Treatment of Space-Charge Layers in the Electroneutral Limit of Electrodiffusion
2015Co-Authors: Adam R. Stinchcombe, Yoichiro Mori, Charles S. PeskinAbstract:The electroneutral model describes cellular electrical activity, accounting for ionic concentration dynamics without resolution of the fine spatial scales of the space-charge layer. This is done by asserting that the ionic solution is electrically neutral at each point in space. However, electroneutrality is inconsistent with the original boundary conditions at cell membranes. We consider three separate methods of resolving this inconsistency that result in well-posed models that are accurate approximations to a detailed model in which the space-charge layer is fully resolved. A particular Electrodiffusion problem is utilized to make the discussion specific. © 2015 Wiley Periodicals, Inc.
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A Multidomain Model for Ionic Electrodiffusion and Osmosis with an Application to Cortical Spreading Depression
2014Co-Authors: Yoichiro MoriAbstract:Ionic Electrodiffusion and osmotic water flow are central processes in many physiological systems. We formulate a system of partial differential equations that governs ion movement and water flow in biological tissue. A salient feature of this model is that it satisfies a free energy identity, ensuring the thermodynamic consistency of the model. A numerical scheme is developed for the model in one spatial dimension and is applied to a model of cortical spreading depression, a propagating breakdown of ionic and cell volume homeostasis in the brain.
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a model of Electrodiffusion and osmotic water flow and its energetic structure
2011Co-Authors: Yoichiro Mori, Chun Liu, R S EisenbergAbstract:We introduce a model for ionic Electrodiffusion and osmotic water flow through cells and tissues. The model consists of a system of partial differential equations for ionic concentration and fluid flow with interface conditions at deforming membrane boundaries. The model satisfies a natural energy equality, in which the sum of the entropic, elastic and electrostatic free energies are dissipated through viscous, electrodiffusive and osmotic flows. We discuss limiting models when certain dimensionless parameters are small. Finally, we develop a numerical scheme for the one-dimensional case and present some simple applications of our model to cell volume control.
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Electrodiffusion and osmotic water flow and its variational structure
2011Co-Authors: Yoichiro Mori, Chun Liu, R S EisenbergAbstract:We propose a system of partial differential equations (PDE) that describe Electrodiffusion and osmotic water flow. From a physical standpoint, this is a far-reaching generalization of the standard treatment of osmosis and Electrodiffusion in irreversible thermodynamics to spatially extended systems. As far as we know, this is the first mechanically and thermodynamically consistent model of osmotic water flow and Electrodiffusion in systems with deformable cells and membranes with capacitance and conductance. We use an energetic variational approach to enforce consistency and derive a field theory describing the flow, diffusion, and migration of ions, water, and the solution itself. The variational approach is particularly useful because it treats interactions automatically and consistently with a minimal number of arbitrary parameters. Electrodiffusion and osmotic water flow are involved in a wide range of biological functions of organs, tissues, cells, and organelles, including the homeostasis of ions in the brain, fluid secretion by epithelial systems, electrolyte regulation in the kidney, fluid circulation in ocular systems, gastric protection, water uptake by plants, etc. The field equations can be written with boundary conditions and parameters appropriate for the anatomy of each system. The field equations then form a physically and anatomically consistent model of biological function in the variational framework of modern field theory. The variational approach deals naturally with the many ionic solutions (containing a multitude of interacting components in a wide range of concentrations) and the wide range of conditions and forces used in experiments. Solving the PDEs will help suggest and interpret new experiments to understand the interaction of components, conditions, structure, and forces. In the view of classical physiology and biophysics, these interactions are the essence of biological function.
Andrew Pohorille - One of the best experts on this subject based on the ideXlab platform.
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computational electrophysiology from a single molecular dynamics simulation and the Electrodiffusion model
2021Co-Authors: Michael A Wilson, Andrew PohorilleAbstract:The availability of high-resolution structures of ion channels opens the doors to reliable computations of electrophysiological properties, such as the dependence of ionic currents and selectivities on applied voltage. We develop two theoretical approaches for calculating these properties from molecular dynamics simulations at a single voltage, or even in the absence of voltage, combined with the Electrodiffusion model in which ion motion in the channel is represented as one-dimensional diffusion in the potential of mean force exerted by other components of the system and the applied electric field. No knowledge of diffusivity or ion densities at other voltages is needed. Instead, in one approach, one-sided ion fluxes and density profiles are used to determine the free energy profile. In the other approach, committor probabilities for ions transported at the selected voltage are used for this purpose. Both approaches have been validated in an example of a simple ion channel formed by trichotoxin. The potentials of mean force calculated by way of the proposed approaches and obtained from traditional methods are in excellent agreement. Furthermore, the current-voltage dependence agrees very well with results obtained by way of computationally more demanding methods. We also have readily calculated the reversal potential, a computationally challenging electrophysiological property. The key assumptions of the Electrodiffusion model, such as the independence of crossing events or the insensitivity of the potential of mean force to applied voltage, have been found to be satisfied. We also show that the voltage changes linearly in the hydrophobic core of the membrane and is constant elsewhere.
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combining molecular dynamics and an Electrodiffusion model to calculate ion channel conductance
2014Co-Authors: Michael A Wilson, Thuy Hien Nguyen, Andrew PohorilleAbstract:Establishing the relation between the structures and functions of protein ion channels, which are protein assemblies that facilitate transmembrane ion transport through water-filled pores, is at the forefront of biological and medical sciences. A reliable way to determine whether our understanding of this relation is satisfactory is to reproduce the measured ionic conductance over a broad range of applied voltages. This can be done in molecular dynamics simulations by way of applying an external electric field to the system and counting the number of ions that traverse the channel per unit time. Since this approach is computationally very expensive we develop a markedly more efficient alternative in which molecular dynamics is combined with an Electrodiffusion equation. This alternative approach applies if steady-state ion transport through channels can be described with sufficient accuracy by the one-dimensional diffusion equation in the potential given by the free energy profile and applied voltage. The theory refers only to line densities of ions in the channel and, therefore, avoids ambiguities related to determining the surface area of the channel near its endpoints or other procedures connecting the line and bulk ion densities. We apply the theory to a simple, model system based on the trichotoxin channel. We test the assumptions of the Electrodiffusion equation, and determine the precision and consistency of the calculated conductance. We demonstrate that it is possible to calculate current/voltage dependence and accurately reconstruct the underlying (equilibrium) free energy profile, all from molecular dynamics simulations at a single voltage. The approach developed here applies to other channels that satisfy the conditions of the Electrodiffusion equation.
Michael A Wilson - One of the best experts on this subject based on the ideXlab platform.
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computational electrophysiology from a single molecular dynamics simulation and the Electrodiffusion model
2021Co-Authors: Michael A Wilson, Andrew PohorilleAbstract:The availability of high-resolution structures of ion channels opens the doors to reliable computations of electrophysiological properties, such as the dependence of ionic currents and selectivities on applied voltage. We develop two theoretical approaches for calculating these properties from molecular dynamics simulations at a single voltage, or even in the absence of voltage, combined with the Electrodiffusion model in which ion motion in the channel is represented as one-dimensional diffusion in the potential of mean force exerted by other components of the system and the applied electric field. No knowledge of diffusivity or ion densities at other voltages is needed. Instead, in one approach, one-sided ion fluxes and density profiles are used to determine the free energy profile. In the other approach, committor probabilities for ions transported at the selected voltage are used for this purpose. Both approaches have been validated in an example of a simple ion channel formed by trichotoxin. The potentials of mean force calculated by way of the proposed approaches and obtained from traditional methods are in excellent agreement. Furthermore, the current-voltage dependence agrees very well with results obtained by way of computationally more demanding methods. We also have readily calculated the reversal potential, a computationally challenging electrophysiological property. The key assumptions of the Electrodiffusion model, such as the independence of crossing events or the insensitivity of the potential of mean force to applied voltage, have been found to be satisfied. We also show that the voltage changes linearly in the hydrophobic core of the membrane and is constant elsewhere.
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combining molecular dynamics and an Electrodiffusion model to calculate ion channel conductance
2014Co-Authors: Michael A Wilson, Thuy Hien Nguyen, Andrew PohorilleAbstract:Establishing the relation between the structures and functions of protein ion channels, which are protein assemblies that facilitate transmembrane ion transport through water-filled pores, is at the forefront of biological and medical sciences. A reliable way to determine whether our understanding of this relation is satisfactory is to reproduce the measured ionic conductance over a broad range of applied voltages. This can be done in molecular dynamics simulations by way of applying an external electric field to the system and counting the number of ions that traverse the channel per unit time. Since this approach is computationally very expensive we develop a markedly more efficient alternative in which molecular dynamics is combined with an Electrodiffusion equation. This alternative approach applies if steady-state ion transport through channels can be described with sufficient accuracy by the one-dimensional diffusion equation in the potential given by the free energy profile and applied voltage. The theory refers only to line densities of ions in the channel and, therefore, avoids ambiguities related to determining the surface area of the channel near its endpoints or other procedures connecting the line and bulk ion densities. We apply the theory to a simple, model system based on the trichotoxin channel. We test the assumptions of the Electrodiffusion equation, and determine the precision and consistency of the calculated conductance. We demonstrate that it is possible to calculate current/voltage dependence and accurately reconstruct the underlying (equilibrium) free energy profile, all from molecular dynamics simulations at a single voltage. The approach developed here applies to other channels that satisfy the conditions of the Electrodiffusion equation.
Y. C. Zhou - One of the best experts on this subject based on the ideXlab platform.
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Electrodiffusion of Lipids on Membrane Surfaces
2012Co-Authors: Y. C. ZhouAbstract:Random lateral translocation of lipids and proteins is a universal process on membrane surfaces. Local aggregation or organization of lipids and proteins can be induced when this lateral random diffusion is mediated by the electrostatic interactions and membrane curvature. Though the lateral diffusion rates of lipids on membrane of various compositions are measured and the electrostatic free energies of predetermined protein-membrane-lipid systems can be computed, the process of the aggregation and the evolution to the electrostatically favorable states remain undetermined. Here we propose an Electrodiffusion model, based on the variational principle of free energy functional, for the self-consistent lateral drift-diffusion of multiple species of charged lipids on membrane surfaces. Finite sizes of lipids are modeled to enforce the geometrical constraint of the lipid concentration on membrane surfaces. A surface finite element method is developed to appropriate the Laplace-Beltrami operators in the partial differential equations (PDEs) of the model. Our model properly describes the saturation of lipids on membrane surface, and correctly predicts that the MARCKS peptide can consistently sequester three multivalent phosphatidylinositol 4,5-bisphosphate (\pip2) lipids through its basic amino acid residues, even there is a large fraction of monovalent phosphatidylserine (PS) in the membrane. Solutions of the PDEs also show the salt-dependence of the lipid sequestration.
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Electrodiffusion of lipids on membrane surfaces
2012Co-Authors: Y. C. ZhouAbstract:Lateral translocation of lipids and proteins is a universal process on membrane surfaces. Local aggregation or organization of lipids and proteins can be induced when the random lateral motion is mediated by the electrostatic interactions and membrane curvature. Although the lateral diffusion rates of lipids on membranes of various compositions are measured and the electrostatic free energies of predetermined protein-membrane-lipid systems can be computed, the process of the aggregation and the evolution to the electrostatically favorable states remain largely undetermined. Here we propose an Electrodiffusion model, based on the variational principle of the free energy functional, for the self-consistent lateral drift-diffusion of multiple species of charged lipids on membrane surfaces. Finite sizes of lipids are modeled to enforce the geometrical constraint of the lipid concentration on membrane surfaces. A surface finite element method is developed to appropriate the Laplace-Beltrami operators in the partial differential equations of the model. Our model properly describes the saturation of lipids on membrane surfaces, and correctly predicts that the MARCKS peptide can consistently sequester three multivalent phosphatidylinositol 4,5-bisphosphate lipids through its basic amino acid residues, regardless of a wide range of the percentage of monovalent phosphatidylserine in the membrane.