Simulation of the Ephaptic Effect in the Cone--Horizontal Cell Synapse of the Retina

Gardner, Colin; Jones, Jeremiah R.; Baer, Steven; Chang, Shaojie

doi:10.1137/120878409

Cited by 6 publications

(4 citation statements)

References 14 publications

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“…Specifically, we point out three biological systems previously studied that could benefit from the electroneutral model: electrodiffusion in the node of Ranvier [10], horizontal cells of the retina [5], and the local field potential near a cylindrical axon with Hodgkin-Huxley transmembrane currents [17]. Careful consideration of the analysis of the space-charge layer and the other underlying assumptions of the electroneuronal model may permit the development of tractable models for a broader range of complex electrodiffusion phenomena.…”

Section: Resultsmentioning

confidence: 99%

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

Stinchcombe

Mori

Peskin

2015

Comm Pure Appl Math

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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.

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Section: Resultsmentioning

confidence: 99%

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

Stinchcombe

Mori

Peskin

2015

Comm Pure Appl Math

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“…The NPP models used for the description of neuronal compartments, presented in Section 3 of this review [5][6][7][8][9]41,42,72,[77][78][79], neglect the effects of ionic channels and the influence of the number, size, and distance between them. Instead, they treat the membrane as an inert and uniform boundary of the considered system and describe it using proper (Dirichlet or Neumann) boundary conditions.…”

Section: The Npp Description Of Ion Channelsmentioning

confidence: 99%

“…The visual information is translated into electric currents by photoreceptors through changes in their membrane potentials. The NPP was applied for the description of the triad synapse (a type of synapse in the outer plexiform layer formed by a cone, a horizontal cell, and a bipolar cell) in the goldfish retina in order to investigate the importance of ephaptic (electrical) effects [78,79]. These effects were demonstrated by calculating the shift in the current-potential curve for increasingly narrower openings between the cone and the horizontal cell.…”

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confidence: 99%

Electrodiffusion Phenomena in Neuroscience and the Nernst–Planck–Poisson Equations

Jasielec

2021

Electrochem

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This work is aimed to give an electrochemical insight into the ionic transport phenomena in the cellular environment of organized brain tissue. The Nernst–Planck–Poisson (NPP) model is presented, and its applications in the description of electrodiffusion phenomena relevant in nanoscale neurophysiology are reviewed. These phenomena include: the signal propagation in neurons, the liquid junction potential in extracellular space, electrochemical transport in ion channels, the electrical potential distortions invisible to patch-clamp technique, and calcium transport through mitochondrial membrane. The limitations, as well as the extensions of the NPP model that allow us to overcome these limitations, are also discussed.

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“…The coupling conditions on Γ cell and Γ sub are between different environments and typically give rise to the occurrence of boundary layers [4,18,33]. These latter are in the form of electrical double layers, of which we only account for the diffuse layer, neglecting the ions attached to the surfaces, as in the Gouy-Chapman approximation [21].…”

Section: Hierarchical Modelsmentioning

confidence: 99%

Hierarchical electrochemical modeling and simulation of bio-hybrid interfaces

Abbate

Porro

Nieus

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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Abstract. In this article we propose and investigate a hierarchy of mathematical models based on partial differential equations (PDE) and ordinary differential equations (ODE) for the simulation of the biophysical phenomena occurring in the electrolyte fluid that connects a biological component (a single cell or a system of cells) and a solid-state device (a single silicon transistor or an array of transistors). The three members of the hierarchy, ordered by decreasing complexity, are: (i) a 3D Poisson-Nernst-Planck (PNP) PDE system for ion concentrations and electric potential; (ii) a 2D reduced PNP system for the same dependent variables as in (i); (iii) a 2D area-contact PDE system for electric potential coupled with a system of ODEs for ion concentrations. The backward Euler method is adopted for temporal semi-discretization and a fixedpoint iteration based on Gummel's map is used to decouple system equations. Spatial discretization is performed using piecewise linear triangular finite elements stabilized via edge-based exponential fitting. Extensively conducted simulation results are in excellent agreement with existing analytical solutions of the PNP problem in radial coordinates and experimental and simulated data using simplified lumped parameter models.

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Simulation of the Ephaptic Effect in the Cone--Horizontal Cell Synapse of the Retina

Cited by 6 publications

References 14 publications

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

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

Electrodiffusion Phenomena in Neuroscience and the Nernst–Planck–Poisson Equations

Hierarchical electrochemical modeling and simulation of bio-hybrid interfaces

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