Well‐Posed Treatment of Space‐Charge Layers in the Electroneutral Limit of Electrodiffusion

Stinchcombe, Adam R.; Mori, Yoichiro; Peskin, Charles S.

doi:10.1002/cpa.21611

Cited by 6 publications

(5 citation statements)

References 17 publications

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“…In the situation we are considering here, in which (5.45) holds and the linearized space charge layer equations are therefore valid, the term c 1 i`0 is always greater in magnitude than i =.q´i /, with the result that an increase in the bulk concentration of any ion on either side of the membrane leads to an increase in the amount of that ion in the adjacent space charge layer. For analysis that supports this qualitative discussion, see Stinchcombe, Mori, and Peskin [83]. An alternative but somewhat less intuitive way of making the electroneutral model well-posed has been described by Mori [53].…”

Section: An Issue Of Ill-posedness and Its Resolutionmentioning

confidence: 95%

Electrophysiology

Griffith

Peskin

2013

Comm Pure Appl Math

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Electrical signaling is a fast mode of communication for cells within an organism. We are concerned here with the formulation and analysis of mathematical models that are used to describe this important class of physiological processes. These models generally take the form of partial differential equations that are descendants of those introduced by Hodgkin and Huxley to describe the propagation of an action potential along the squid giant axon. We review that work here and then go on to describe more recent variations on the Hodgkin-Huxley theme, including the three-dimensional bidomain (and monodomain) equations for cardiac electrophysiology, multiscale models for the heart that take cellular structure into account near the action potential wavefront, and finally a more detailed reformulation of electrophysiology in terms of electrodiffusion.

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Section: An Issue Of Ill-posedness and Its Resolutionmentioning

confidence: 95%

Electrophysiology

Griffith

Peskin

2013

Comm Pure Appl Math

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“…The reader will benefit from reading different approaches from ours in the work of several laboratories, including those of Mori, 55,354,[394][395][396][397][398][399][400][401][402][403][404] Ellingsrud, [405][406][407][408][409][410] Sacco, 411 and the many groups interested in glymphatics, sampled elsewhere. [47][48][49][50][51][52][53][54][55][56][57] While few if any of these papers deal with potassium accumulation in tridomain systems, no doubt their methods could be usefully applied to those issues.…”

Section: Ion Transportmentioning

confidence: 99%

Structural analysis of fluid flow in complex biological systems

Eisenberg

2023

MAIO

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Biology is about structure. Structures within structures. Organs within animals, tissues within organs, cells within tissues, and molecules, often proteins within cells. The structures are so complex that they can only be described by numbers. No numbers are of more importance than those that describe proteins. The numbers that describe coordinates of its atoms, often determined by Patterson functions (which are inverse Fourier Transforms of intensities) of crystal diffraction. Without these numbers, structural biology would hardly exist. Without numbers, engineering would not exist. Numbers are surely needed by the engineers who produce the x-rays diffracting from atoms of protein crystals. Devices of engineering have function. They are built to implement equations. Engineering devices use structures to implement equations, when power is supplied at the right places, that produces appropriate flows. Flows are the essence of life. Equilibrium means death in most living systems. Flows in biological structures are hard to analyze because we do not know input output equations in advance. Sometimes we do not know the function of the structures. Flows, forces, and structures of life (like those of engineering) are related by field equations of conservation laws, partial differential equations, constrained by location and properties of structures. Constraints are boundary conditions located on the complicated domain of biological structure. The hierarchy of structures allows a handful of atoms (in proteins and nucleic acids) to control macroscopic function. Dealing with this complexity is simplified if one systematically analyzes structure using the most general field theory known, electricity described by the Maxwell equations, without significant known error. Currents are involved because flows of biology usually involve migration of charges, convection of water and solutes, diffusion of ions that form the plasma of life, and their interactions. Interactions can dominate function. Here I show how a few complex structures can be understood in engineering detail. This approach may be useful in dealing with biological and medical issues in many other cases. In one limited case—the clearance of a toxic waste (potassium ions) from the optic nerve—this approach seems to have succeeded.

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“…1B). Using that the center of the branch is electroneutral (Stinchcombe et al, 2016), and hence the charges are all located at the membrane, the charge Q at the membrane is equal to the integrated charge over the section of the branch: 𝑄 = 𝜋 𝑎 2 ∑ 𝑖 𝑖𝑜𝑛𝑠 𝑐 𝑖 𝑧 𝑖 𝑁 𝑎 𝑒 where Na is the Avogadro number. Deriving eq.…”

Section: Mathematical Modelingmentioning

confidence: 99%

An Algorithm Based on a Cable-Nernst Planck Model Predicting Synaptic Activity throughout the Dendritic Arbor with Micron Specificity

Guerrier

Toth²,

Galtier³

et al. 2022

Neuroinform

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Recent technological advances have enabled the recording of neurons in intact circuits with a high spatial and temporal resolution, creating the need for modeling with the same precision. In particular, the development of ultra-fast two-photon microscopy combined with fluorescencebased genetically-encoded Ca 2+ -indicators allows capture of full-dendritic arbor and somatic responses associated with synaptic input and action potential output. The complexity of dendritic arbor structures and distributed patterns of activity over time results in the generation of incredibly rich 4D datasets that are challenging to analyze (Sakaki, 2020). Interpreting neural activity from fluorescence-based Ca 2+ biosensors is challenging due to non-linear interactions between several factors influencing intracellular calcium ion concentration and its binding to sensors, including the ionic dynamics driven by diffusion, electrical gradients and voltage-gated conductance. To investigate those dynamics, we designed a model based on a Cable-like equation coupled to the Nernst-Planck equations for ionic fluxes in electrolytes. We employ this model to simulate signal propagation and ionic electrodiffusion across a dendritic arbor. Using these simulation results, we then designed an algorithm to detect synapses from Ca 2+ imaging datasets. We finally apply this algorithm to experimental Ca 2+ -indicator datasets from neurons expressing jGCaMP7s (Dana et al., 2019), using full-dendritic arbor sampling in vivo in the Xenopus laevis optic tectum using fast random-access two-photon microscopy. Our model reproduces the dynamics of visual stimulus-evoked jGCaMP7s-mediated calcium signals observed experimentally, and the resulting algorithm allows prediction of the location of synapses across the dendritic arbor.Our study provides a way to predict synaptic activity and location on dendritic arbors, from fluorescence data in the full dendritic arbor of a neuron recorded in the intact and awake developing vertebrate brain.

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Well‐Posed Treatment of Space‐Charge Layers in the Electroneutral Limit of Electrodiffusion

Cited by 6 publications

References 17 publications

Electrophysiology

Electrophysiology

Structural analysis of fluid flow in complex biological systems

An Algorithm Based on a Cable-Nernst Planck Model Predicting Synaptic Activity throughout the Dendritic Arbor with Micron Specificity

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