Drift-diffusion simulation of the ephaptic effect in the triad synapse of the retina

Finite-element modeling of neuromodulation via controlled delivery of potassium ions using conductive polymer-coated microelectrodes

Objective. The controlled delivery of potassium is an interesting neuromodulation modality, being potassium ions involved in shaping neuron excitability, synaptic transmission, network synchronization, and playing a key role in pathological conditions like epilepsy and spreading depression. Despite many successful examples of pre-clinical devices able to influence the extracellular potassium concentration, computational frameworks capturing the corresponding impact on neuronal activity are still missing.Approach. We present a finite-element model describing a PEDOT:PSS-coated microelectrode (herein, simplyionic actuator) able to release potassium and thus modulate the activity of a cortical neuron in anin-vitro-like setting. The dynamics of ions in the ionic actuator, the neural membrane, and the cellular fluids are solved self-consistently.Main results. We showcase the capability of the model to describe on a physical basis the modulation of the intrinsic excitability of the cell and of the synaptic transmission following the electro-ionic stimulation produced by the actuator. We consider three case studies for the ionic actuator with different levels of selectivity to potassium: ideal selectivity, no selectivity, and selectivity achieved by embedding ionophores in the polymer.Significance. This work is the first step toward a comprehensive computational framework aimed to investigate novel neuromodulation devices targeting specific ionic species, as well as to optimize their design and performance, in terms of the induced modulation of neural activity.

Cytoelectric Coupling: Electric fields sculpt neural activity and "tune" the brain's infrastructure

We propose and present converging evidence for the Cytoelectric Coupling Hypothesis: Electric fields generated by neurons are causal down to the level of the cytoskeleton. This could be achieved via electrodiffusion and mechanotransduction and exchanges between electrical, potential and chemical energy. Ephaptic coupling organizes neural activity, forming neural ensembles at the macroscale level. This information propagates to the neuron level, affecting spiking, and down to molecular level to stabilize the cytoskeleton, "tuning" it to process information more efficiently.

A multiscale continuum model of the vertebrate outer retina: The temporal dynamics of background-induced flicker enhancement

The retina is a part of the central nervous system that is accessible, well documented, and studied by researchers spanning the clinical, experimental, and theoretical sciences. Here, we mathematically model the subcircuits of the outer plexiform layer of the retina on two spatial scales: that of an individual synapse and that of the scale of the receptive field (hundreds to thousands of synapses). To this end we formulate a continuum spine model (a partial differential equation system) that incorporates the horizontal cell syncytium and its numerous processes (spines) within cone pedicles. With this multiscale modeling approach, detailed biophysical mechanisms at the synaptic level are retained while scaling up to the receptive field level. As an example of its utility, the model is applied to study background-induced flicker enhancement in which the onset of a dim background enhances the center flicker response of horizontal cells. Simulation results, in comparison with flicker enhancement data for square, slit, and disk test regions, suggest that feedback mechanisms that are voltage-axis modulators of cone calcium channels (for example, ephaptic and/or pH feedback) are robust in capturing the temporal dynamics of background-induced flicker enhancement. The value and potential of this continuum spine approach is that it provides a framework for mathematically modeling the input-output properties of the entire receptive field of the outer retina while implementing the latest models for transmission mechanisms at the synaptic level.

An electrodiffusive neuron-extracellular-glia model for exploring the genesis of slow potentials in the brain

Within the computational neuroscience community, there has been a focus on simulating the electrical activity of neurons, while other components of brain tissue, such as glia cells and the extracellular space, are often neglected. Standard models of extracellular potentials are based on a combination of multicompartmental models describing neural electrodynamics and volume conductor theory. Such models cannot be used to simulate the slow components of extracellular potentials, which depend on ion concentration dynamics, and the effect that this has on extracellular diffusion potentials and glial buffering currents. We here present the electrodiffusive neuron-extracellular-glia (edNEG) model, which we believe is the first model to combine compartmental neuron modeling with an electrodiffusive framework for intra- and extracellular ion concentration dynamics in a local piece of neuro-glial brain tissue. The edNEG model (i) keeps track of all intraneuronal, intraglial, and extracellular ion concentrations and electrical potentials, (ii) accounts for action potentials and dendritic calcium spikes in neurons, (iii) contains a neuronal and glial homeostatic machinery that gives physiologically realistic ion concentration dynamics, (iv) accounts for electrodiffusive transmembrane, intracellular, and extracellular ionic movements, and (v) accounts for glial and neuronal swelling caused by osmotic transmembrane pressure gradients. The edNEG model accounts for the concentration-dependent effects on ECS potentials that the standard models neglect. Using the edNEG model, we analyze these effects by splitting the extracellular potential into three components: one due to neural sink/source configurations, one due to glial sink/source configurations, and one due to extracellular diffusive currents. Through a series of simulations, we analyze the roles played by the various components and how they interact in generating the total slow potential. We conclude that the three components are of comparable magnitude and that the stimulus conditions determine which of the components that dominate.

Invaginating Structures in Synapses - Perspective

Invaginating structures are common in the synapses of most animals. However, the details of these invaginating structures remain understudied in part because they are not well resolved in light microscopy and were often misidentified in early electron microscope (EM) studies. Utilizing experimental techniques along with the latest advances in microscopy, such as focused ion beam-scanning EM (FIB-SEM), evidence is gradually building to suggest that the synaptic invaginating structures contribute to synapse development, maintenance, and plasticity. These invaginating structures are most elaborate in synapses mediating rapid integration of signals, such as muscle contraction, mechanoreception, and vision. Here we argue that the synaptic invaginations should be considered in future studies seeking to understand their role in sensory integration and coordination, learning, and memory. We review the various types of invaginating structures in the synapses and discuss their potential functions. We also present several new examples of invaginating structures from a variety of animals including Drosophila and mice, mainly using FIB-SEM, with which we trace the form and arrangement of these structures.

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

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.

Electrodiffusion with Calcium-Activated Potassium Channels in Dendritic Spine

We investigate calcium signaling feedback through calcium-activated potassium channels of a dendritic spine by applying the immersed boundary method with electrodiffusion. We simulate the stochastic gating of such ion channels and the resulting spatial distribution of concentration, current, and membrane voltage within the dendritic spine. In this simulation, the permeability to ionic flow across the membrane is regulated by the amplitude of chemical potential barriers. With spatially localized ion channels, chemical potential barriers are locally and stochastically regulated. This regulation represents the ion channel gating with multiple subunits, the open and closed states governed by a continuous-time Markov process. The model simulation recapitulates an inhibitory action on voltage-sensitive calcium channels by the calcium-activated potassium channels in a stochastic manner as a non-local feedback loop. The model predicts amplified calcium influx with more closely placed channel complexes, proposing a potential mechanism of differential calcium handling by channel distributions. This work provides a foundation for future computer simulation studies of dendritic spine motility and structural plasticity.

Simulating diffusion from a cluster of point sources using propagation integrals

A computational methodology to simulate the diffusion of ions from point sources (e.g., ion channels) is described. The outlined approach computes the ion concentration from a cluster of many ion channels at pre-specified locations as a function of time using the theory of propagation integrals. How the channels' open/closed states evolve in time does not need to be known at the start of the simulation, but can be updated on-the-fly as the simulation goes along. The technique uses analytic formulas for the solutions of the diffusion equation for three common geometries: (1) ions diffusing from a membrane (planar symmetry); (2) ions diffusing into a narrow cleft for effective two-dimensional diffusion (cylindrical symmetry); and (3) ions diffusing into open space like the cytosol (spherical symmetry). Because these formulas are exact solutions valid for arbitrarily long timesteps, no spatial or time discretizations are necessary. The only discrete locations are where the ion concentration is computed, and the only discrete timesteps are when the channels' open/closed states are updated. Beyond pure diffusion, the technique is generalized to the Excess Buffer Approximation of ion chelation to give an analytic solution of this approximation of the full reaction/diffusion system. Both the pure diffusion and the diffusion/buffering algorithms scale linearly with the number of channels and the number of ion concentration locations.

Spontaneous action potentials in retinal horizontal cells of goldfish (Carassius auratus) are dependent upon L-type Ca2+ channels and ryanodine receptors

Horizontal cells (HCs) are interneurons of the outer retina that undergo graded changes in membrane potential during the light response and provide feedback to photoreceptors. We characterized spontaneous Ca²⁺-based action potentials (APs) in isolated goldfish (Carassius auratus) HCs with electrophysiological and intracellular imaging techniques. Transient changes in intracellular Ca²⁺ concentration ([Ca²⁺]_i) were observed with fura-2 and were abolished by removal of extracellular Ca²⁺ or by inhibition of Ca²⁺ channels by 50 µM Cd²⁺ or 100 µM nifedipine. Inhibition of Ca²⁺ release from stores with 20 µM ryanodine or 50 µM dantrolene abolished Ca²⁺ transients and increased baseline [Ca²⁺]_i. This increased baseline was prevented by blocking L-type Ca²⁺ channels with nifedipine, suggesting that Ca²⁺-induced Ca²⁺ release from stores may be needed to inactivate membrane Ca²⁺ channels. Caffeine (3 mM) increased the frequency of Ca²⁺ transients, and the store-operated channel antagonist 2-aminoethyldiphenylborinate (100 μM) counteracted this effect. APs were detected with voltage-sensitive dye imaging (FluoVolt) and current-clamp electrophysiology. In current-clamp recordings, regenerative APs were abolished by removal of extracellular Ca²⁺ or in the presence of 5 mM Co²⁺ or 100 µM nifedipine, and APs were amplified with 15 mM Ba²⁺. Collectively, our data suggest that during APs Ca²⁺ enters through L-type Ca²⁺ channels and that Ca²⁺ stores (gated by ryanodine receptors) contribute to the rise in [Ca²⁺]_i. This work may lead to further understanding of the possible role APs have in vision, such as transitioning from light to darkness or modulating feedback from HCs to photoreceptors.NEW & NOTEWORTHY Horizontal cells (HCs) are interneurons of the outer retina that provide inhibitory feedback onto photoreceptors. HCs respond to light via graded changes in membrane potential. We characterized spontaneous action potentials in HCs from goldfish and linked action potential generation to a rise in intracellular Ca²⁺ via plasma membrane channels and ryanodine receptors. Action potentials may play a role in vision, such as transitioning from light to darkness, or in modulating feedback from HCs to photoreceptors.

A Kirchhoff-Nernst-Planck framework for modeling large scale extracellular electrodiffusion surrounding morphologically detailed neurons

Many pathological conditions, such as seizures, stroke, and spreading depression, are associated with substantial changes in ion concentrations in the extracellular space (ECS) of the brain. An understanding of the mechanisms that govern ECS concentration dynamics may be a prerequisite for understanding such pathologies. To estimate the transport of ions due to electrodiffusive effects, one must keep track of both the ion concentrations and the electric potential simultaneously in the relevant regions of the brain. Although this is currently unfeasible experimentally, it is in principle achievable with computational models based on biophysical principles and constraints. Previous computational models of extracellular ion-concentration dynamics have required extensive computing power, and therefore have been limited to either phenomena on very small spatiotemporal scales (micrometers and milliseconds), or simplified and idealized 1-dimensional (1-D) transport processes on a larger scale. Here, we present the 3-D Kirchhoff-Nernst-Planck (KNP) framework, tailored to explore electrodiffusive effects on large spatiotemporal scales. By assuming electroneutrality, the KNP-framework circumvents charge-relaxation processes on the spatiotemporal scales of nanometers and nanoseconds, and makes it feasible to run simulations on the spatiotemporal scales of millimeters and seconds on a standard desktop computer. In the present work, we use the 3-D KNP framework to simulate the dynamics of ion concentrations and the electrical potential surrounding a morphologically detailed pyramidal cell. In addition to elucidating the single neuron contribution to electrodiffusive effects in the ECS, the simulation demonstrates the efficiency of the 3-D KNP framework. We envision that future applications of the framework to more complex and biologically realistic systems will be useful in exploring pathological conditions associated with large concentration variations in the ECS.

Invaginating Structures in Mammalian Synapses

Invaginating structures at chemical synapses in the mammalian nervous system exist in presynaptic axon terminals, postsynaptic spines or dendrites, and glial processes. These invaginating structures can be divided into three categories. The first category includes slender protrusions invaginating into axonal terminals, postsynaptic spines, or glial processes. Best known examples of this category are spinules extending from postsynaptic spines into presynaptic terminals in forebrain synapses. Another example of this category are protrusions from inhibitory presynaptic terminals invaginating into postsynaptic neuronal somas. Regardless of the direction and location, the invaginating structures of the first category do not have synaptic active zones within the invagination. The second category includes postsynaptic spines invaginating into presynaptic terminals, whereas the third category includes presynaptic terminals invaginating into postsynaptic spines or dendrites. Unlike the first category, the second and third categories have active zones within the invagination. An example of the second category are mossy terminal synapses of the hippocampal CA3 region, in which enlarged spine-like structures invaginate partly or entirely into mossy terminals. An example of the third category is the neuromuscular junction (NMJ) where substantial invaginations of the presynaptic terminals invaginate into the muscle fibers. In the retina, rod and cone synapses have invaginating processes from horizontal and bipolar cells. Because horizontal cells act both as post and presynaptic structures, their invaginating processes represent both the second and third category. These invaginating structures likely play broad yet specialized roles in modulating neuronal cell signaling.

Invaginating Presynaptic Terminals in Neuromuscular Junctions, Photoreceptor Terminals, and Other Synapses of Animals

Typically, presynaptic terminals form a synapse directly on the surface of postsynaptic processes such as dendrite shafts and spines. However, some presynaptic terminals invaginate-entirely or partially-into postsynaptic processes. We survey these invaginating presynaptic terminals in all animals and describe several examples from the central nervous system, including giant fiber systems in invertebrates, and cup-shaped spines, electroreceptor synapses, and some specialized auditory and vestibular nerve terminals in vertebrates. We then examine mechanoreceptors and photoreceptors, concentrating on the complex of pre- and postsynaptic processes found in basal invaginations of the cell. We discuss in detail the role of vertebrate invaginating horizontal cell processes in both chemical and electrical feedback mechanisms. We also discuss the common presence of indenting or invaginating terminals in neuromuscular junctions on muscles of most kinds of animals, and especially discuss those of Drosophila and vertebrates. Finally, we consider broad questions about the advantages of possessing invaginating presynaptic terminals and describe some effects of aging and disease, especially on neuromuscular junctions. We suggest that the invagination is a mechanism that can enhance both chemical and electrical interactions at the synapse.

How do horizontal cells 'talk' to cone photoreceptors? Different levels of complexity at the cone-horizontal cell synapse

The first synapse of the retina plays a fundamental role in the visual system. Due to its importance, it is critical that it encodes information from the outside world with the greatest accuracy and precision possible. Cone photoreceptor axon terminals contain many individual synaptic sites, each represented by a presynaptic structure called a 'ribbon'. These synapses are both highly sophisticated and conserved. Each ribbon relays the light signal to one ON cone bipolar cell and several OFF cone bipolar cells, while two dendritic processes from a GABAergic interneuron, the horizontal cell, modulate the cone output via parallel feedback mechanisms. The presence of these three partners within a single synapse has raised numerous questions, and its anatomical and functional complexity is still only partially understood. However, the understanding of this synapse has recently evolved, as a consequence of progress in understanding dendritic signal processing and its role in facilitating global versus local signalling. Indeed, for the downstream retinal network, dendritic processing in horizontal cells may be essential, as they must support important functional operations such as contrast enhancement, which requires spatial averaging of the photoreceptor array, while at the same time preserving accurate spatial information. Here, we review recent progress made towards a better understanding of the cone synapse, with an emphasis on horizontal cell function, and discuss why such complexity might be necessary for early visual processing.

Calcium dynamics and regulation in horizontal cells of the vertebrate retina: lessons from teleosts

Horizontal cells (HCs) are inhibitory interneurons of the vertebrate retina. Unlike typical neurons, HCs are chronically depolarized in the dark, leading to a constant influx of Ca2+ Therefore, mechanisms of Ca2+ homeostasis in HCs must differ from neurons elsewhere in the central nervous system, which undergo excitotoxicity when they are chronically depolarized or stressed with Ca2+ HCs are especially well characterized in teleost fish and have been used to unlock mysteries of the vertebrate retina for over one century. More recently, mammalian models of the retina have been increasingly informative for HC physiology. We draw from both teleost and mammalian models in this review, using a comparative approach to examine what is known about Ca2+ pathways in vertebrate HCs. We begin with a survey of Ca2+-permeable ion channels, exchangers, and pumps and summarize Ca2+ influx and efflux pathways, buffering, and intracellular stores. This includes evidence for Ca2+-permeable α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors and N-methyl-d-aspartate receptors and for voltage-gated Ca2+ channels. Special attention is given to interactions between ion channels, to differences among species, and in which subtypes of HCs these channels have been found. We then discuss a number of unresolved issues pertaining to Ca2+ dynamics in HCs, including a potential role for Ca2+ in feedback to photoreceptors, the role for Ca2+-induced Ca2+ release, and the properties and functions of Ca2+-based action potentials. This review aims to highlight the unique Ca2+ dynamics in HCs, as these are inextricably tied to retinal function.

The Diversity of Spine Synapses in Animals

Here we examine the structure of the various types of spine synapses throughout the animal kingdom. Based on available evidence, we suggest that there are two major categories of spine synapses: invaginating and non-invaginating, with distributions that vary among different groups of animals. In the simplest living animals with definitive nerve cells and synapses, the cnidarians and ctenophores, most chemical synapses do not form spine synapses. But some cnidarians have invaginating spine synapses, especially in photoreceptor terminals of motile cnidarians with highly complex visual organs, and also in some mainly sessile cnidarians with rapid prey capture reflexes. This association of invaginating spine synapses with complex sensory inputs is retained in the evolution of higher animals in photoreceptor terminals and some mechanoreceptor synapses. In contrast to invaginating spine synapse, non-invaginating spine synapses have been described only in animals with bilateral symmetry, heads and brains, associated with greater complexity in neural connections. This is apparent already in the simplest bilaterians, the flatworms, which can have well-developed non-invaginating spine synapses in some cases. Non-invaginating spine synapses diversify in higher animal groups. We also discuss the functional advantages of having synapses on spines and more specifically, on invaginating spines. And finally we discuss pathologies associated with spine synapses, concentrating on those systems and diseases where invaginating spine synapses are involved.

Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue

Recorded potentials in the extracellular space (ECS) of the brain is a standard measure of population activity in neural tissue. Computational models that simulate the relationship between the ECS potential and its underlying neurophysiological processes are commonly used in the interpretation of such measurements. Standard methods, such as volume-conductor theory and current-source density theory, assume that diffusion has a negligible effect on the ECS potential, at least in the range of frequencies picked up by most recording systems. This assumption remains to be verified. We here present a hybrid simulation framework that accounts for diffusive effects on the ECS potential. The framework uses (1) the NEURON simulator to compute the activity and ionic output currents from multicompartmental neuron models, and (2) the electrodiffusive Kirchhoff-Nernst-Planck framework to simulate the resulting dynamics of the potential and ion concentrations in the ECS, accounting for the effect of electrical migration as well as diffusion. Using this framework, we explore the effect that ECS diffusion has on the electrical potential surrounding a small population of 10 pyramidal neurons. The neural model was tuned so that simulations over ∼100 seconds of biological time led to shifts in ECS concentrations by a few millimolars, similar to what has been seen in experiments. By comparing simulations where ECS diffusion was absent with simulations where ECS diffusion was included, we made the following key findings: (i) ECS diffusion shifted the local potential by up to ∼0.2 mV. (ii) The power spectral density (PSD) of the diffusion-evoked potential shifts followed a 1/f2 power law. (iii) Diffusion effects dominated the PSD of the ECS potential for frequencies up to several hertz. In scenarios with large, but physiologically realistic ECS concentration gradients, diffusion was thus found to affect the ECS potential well within the frequency range picked up in experimental recordings.