Cable theory in neurons with active, linearized membranes

Sliding mode control for uncertain fractional-order reaction-diffusion memristor neural networks with time delays

This paper investigates a sliding mode control method for a class of uncertain delayed fractional-order reaction-diffusion memristor neural networks. Different from most existing literature on sliding mode control for fractional-order reaction-diffusion systems, this study constructs a linear sliding mode switching function and designs the corresponding sliding mode control law. The sufficient theory for the globally asymptotic stability of the sliding mode dynamics are provided, and it is proven that the sliding mode surface is finite-time reachable under the proposed control law, with an estimate of the maximum reaching time. Finally, a numerical test is presented to validate the effectiveness of the theoretical analysis.

Perspective: an optoelectronic future for heterogeneous, dendritic computing

With the increasing number of applications reliant on large neural network models, the pursuit of more suitable computing architectures is becoming increasingly relevant. Progress toward co-integrated silicon photonic and CMOS circuits provides new opportunities for computing architectures with high bandwidth optical networks and high-speed computing. In this paper, we discuss trends in neuromorphic computing architecture and outline an optoelectronic future for heterogeneous, dendritic neuromorphic computing.

How neuronal morphology impacts the synchronisation state of neuronal networks

The biophysical properties of neurons not only affect how information is processed within cells, they can also impact the dynamical states of the network. Specifically, the cellular dynamics of action-potential generation have shown relevance for setting the (de)synchronisation state of the network. The dynamics of tonically spiking neurons typically fall into one of three qualitatively distinct types that arise from distinct mathematical bifurcations of voltage dynamics at the onset of spiking. Accordingly, changes in ion channel composition or even external factors, like temperature, have been demonstrated to switch network behaviour via changes in the spike onset bifurcation and hence its associated dynamical type. A thus far less addressed modulator of neuronal dynamics is cellular morphology. Based on simplified and anatomically realistic mathematical neuron models, we show here that the extent of dendritic arborisation has an influence on the neuronal dynamical spiking type and therefore on the (de)synchronisation state of the network. Specifically, larger dendritic trees prime neuronal dynamics for in-phase-synchronised or splayed-out activity in weakly coupled networks, in contrast to cells with otherwise identical properties yet smaller dendrites. Our biophysical insights hold for generic multicompartmental classes of spiking neuron models (from ball-and-stick-type to anatomically reconstructed models) and establish a connection between neuronal morphology and the susceptibility of neural tissue to synchronisation in health and disease.

The enigmatic HCN channels: A cellular neurophysiology perspective

What physiological role does a slow hyperpolarization-activated ion channel with mixed cation selectivity play in the fast world of neuronal action potentials that are driven by depolarization? That puzzling question has piqued the curiosity of physiology enthusiasts about the hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, which are widely expressed across the body and especially in neurons. In this review, we emphasize the need to assess HCN channels from the perspective of how they respond to time-varying signals, while also accounting for their interactions with other co-expressing channels and receptors. First, we illustrate how the unique structural and functional characteristics of HCN channels allow them to mediate a slow negative feedback loop in the neurons that they express in. We present the several physiological implications of this negative feedback loop to neuronal response characteristics including neuronal gain, voltage sag and rebound, temporal summation, membrane potential resonance, inductive phase lead, spike triggered average, and coincidence detection. Next, we argue that the overall impact of HCN channels on neuronal physiology critically relies on their interactions with other co-expressing channels and receptors. Interactions with other channels allow HCN channels to mediate intrinsic oscillations, earning them the "pacemaker channel" moniker, and to regulate spike frequency adaptation, plateau potentials, neurotransmitter release from presynaptic terminals, and spike initiation at the axonal initial segment. We also explore the impact of spatially non-homogeneous subcellular distributions of HCN channels in different neuronal subtypes and their interactions with other channels and receptors. Finally, we discuss how plasticity in HCN channels is widely prevalent and can mediate different encoding, homeostatic, and neuroprotective functions in a neuron. In summary, we argue that HCN channels form an important class of channels that mediate a diversity of neuronal functions owing to their unique gating kinetics that made them a puzzle in the first place.

Saturated and asymmetric saturated control for projective synchronization of inertial neural networks with delays and discontinuous activations through matrix measure method

The projective synchronization work presented in this article is focused on a class of nonlinear discontinuous coupled inertial neural networks with mixed time-varying delays and a cluster topological structure. The synchronization problem for discontinuous coupled inertial neural networks with clustering topology is examined in consideration with the mismatched parameters and the mutual influence among various clusters. To determine the required conditions for network convergence under the influence of an extensive range of impulses, the matrix measure technique and the average impulsive intervals are employed. To illustrate the effectiveness of the theoretical findings, graphical representation of varied impulsive ranges for multiple cases are provided using numerical simulations.

Finite/fixed-time synchronization of inertial memristive neural networks by interval matrix method for secure communication

This paper investigates the finite/fixed-time synchronization problem of delayed inertial memristive neural networks (DIMNNs) using interval matrix-based methods within a unified control framework. By employing set-valued mapping and differential inclusion theory, two distinct methods are applied to handle the switching behavior of memristor parameters: the maximum absolute value method and the interval matrix method. Based on these different approaches, two control strategies are proposed to select appropriate control parameters, enabling the system to achieve finite and fixed-time synchronization, respectively. Additionally, the resulting theoretical criteria differ based on the chosen control strategy, with one expressed in algebraic form and the other in the form of linear matrix inequalities (LMIs). Numerical simulations demonstrate that the interval matrix method outperforms the maximum absolute value method in terms of handling memristor parameter switching, achieving faster finite/fixed-time synchronization. Furthermore, the theoretical results are extended to the field of image encryption, where the response system is utilized for decryption and expanding the keyspace.

Beyond rhythm - a framework for understanding the frequency spectrum of neural activity

Cognitive and behavioral processes are often accompanied by changes within well-defined frequency bands of the local field potential (LFP i.e., the voltage induced by neuronal activity). These changes are detectable in the frequency domain using the Fourier transform and are often interpreted as neuronal oscillations. However, aside some well-known exceptions, the processes underlying such changes are difficult to track in time, making their oscillatory nature hard to verify. In addition, many non-periodic neural processes can also have spectra that emphasize specific frequencies. Thus, the notion that spectral changes reflect oscillations is likely too restrictive. In this study, we use a simple yet versatile framework to understand the frequency spectra of neural recordings. Using simulations, we derive the Fourier spectra of periodic, quasi-periodic and non-periodic neural processes having diverse waveforms, illustrating how these attributes shape their spectral signatures. We then show how neural processes sum their energy in the local field potential in simulated and real-world recording scenarios. We find that the spectral power of neural processes is essentially determined by two aspects: (1) the distribution of neural events in time and (2) the waveform of the voltage induced by single neural events. Taken together, this work guides the interpretation of the Fourier spectrum of neural recordings and indicates that power increases in specific frequency bands do not necessarily reflect periodic neural activity.

Simulations of cortical networks using spatially extended conductance-based neuronal models

The Hodgkin-Huxley model of action potential generation and propagation, published in the Journal of Physiology in 1952, initiated the field of biophysically detailed computational modelling in neuroscience, which has expanded to encompass a variety of species and components of the nervous system. Here we review the developments in this area with a focus on efforts in the community towards modelling the mammalian neocortex using spatially extended conductance-based neuronal models. The Hodgkin-Huxley formalism and related foundational contributions, such as Rall's cable theory, remain widely used in these efforts to the current day. We argue that at present the field is undergoing a qualitative change due to new very rich datasets describing the composition, connectivity and functional activity of cortical circuits, which are being integrated systematically into large-scale network models. This trend, combined with the accelerating development of convenient software tools supporting such complex modelling projects, is giving rise to highly detailed models of the cortex that are extensively constrained by the data, enabling computational investigation of a multitude of questions about cortical structure and function.

Beyond rhythm - A framework for understanding the frequency spectrum of neural activity

Cognitive and behavioral processes are often accompanied by changes within well-defined frequency bands of the local field potential (LFP i.e., the voltage induced by neuronal activity). These changes are detectable in the frequency domain using the Fourier transform and are often interpreted as neuronal oscillations. However, aside some well-known exceptions, the processes underlying such changes are difficult to track in time, making their oscillatory nature hard to verify. In addition, many non-periodic neural processes can also have spectra that emphasize specific frequencies. Thus, the notion that spectral changes reflect oscillations is likely too restrictive. In this study, we propose a simple yet versatile framework to understand the frequency spectra of neural recordings. Using simulations, we derive the Fourier spectra of periodic, quasi-periodic and non-periodic neural processes having diverse waveforms, illustrating how these attributes shape their spectral signatures. We then show how neural processes sum their energy in the local field potential in simulated and real-world recording scenarios. We find that the spectral power of neural processes is essentially determined by two aspects: 1) the distribution of neural events in time and 2) the waveform of the voltage induced by single neural events. Taken together, this work guides the interpretation of the Fourier spectrum of neural recordings and indicates that power increases in specific frequency bands do not necessarily reflect periodic neural activity.

The effect of the subthreshold oscillation induced by the neurons' resonance upon the electrical stimulation-dependent instability

Repetitive electrical nerve stimulation can induce a long-lasting perturbation of the axon's membrane potential, resulting in unstable stimulus-response relationships. Despite being observed in electrophysiology, the precise mechanism underlying electrical stimulation-dependent (ES-dependent) instability is still an open question. This study proposes a model to reveal a facet of this problem: how threshold fluctuation affects electrical nerve stimulations. This study proposes a new method based on a Circuit-Probability theory (C-P theory) to reveal the interlinkages between the subthreshold oscillation induced by neurons' resonance and ES-dependent instability of neural response. Supported by in-vivo studies, this new model predicts several key characteristics of ES-dependent instability and proposes a stimulation method to minimize the instability. This model provides a powerful tool to improve our understanding of the interaction between the external electric field and the complexity of the biophysical characteristics of axons.

Computational models of neurotransmission at cerebellar synapses unveil the impact on network computation

The neuroscientific field benefits from the conjoint evolution of experimental and computational techniques, allowing for the reconstruction and simulation of complex models of neurons and synapses. Chemical synapses are characterized by presynaptic vesicle cycling, neurotransmitter diffusion, and postsynaptic receptor activation, which eventually lead to postsynaptic currents and subsequent membrane potential changes. These mechanisms have been accurately modeled for different synapses and receptor types (AMPA, NMDA, and GABA) of the cerebellar cortical network, allowing simulation of their impact on computation. Of special relevance is short-term synaptic plasticity, which generates spatiotemporal filtering in local microcircuits and controls burst transmission and information flow through the network. Here, we present how data-driven computational models recapitulate the properties of neurotransmission at cerebellar synapses. The simulation of microcircuit models is starting to reveal how diverse synaptic mechanisms shape the spatiotemporal profiles of circuit activity and computation.

Brain signal predictions from multi-scale networks using a linearized framework

Simulations of neural activity at different levels of detail are ubiquitous in modern neurosciences, aiding the interpretation of experimental data and underlying neural mechanisms at the level of cells and circuits. Extracellular measurements of brain signals reflecting transmembrane currents throughout the neural tissue remain commonplace. The lower frequencies (≲ 300Hz) of measured signals generally stem from synaptic activity driven by recurrent interactions among neural populations and computational models should also incorporate accurate predictions of such signals. Due to limited computational resources, large-scale neuronal network models (≳ 10⁶ neurons or so) often require reducing the level of biophysical detail and account mainly for times of action potentials (‘spikes’) or spike rates. Corresponding extracellular signal predictions have thus poorly accounted for their biophysical origin.

Here we propose a computational framework for predicting spatiotemporal filter kernels for such extracellular signals stemming from synaptic activity, accounting for the biophysics of neurons, populations, and recurrent connections. Signals are obtained by convolving population spike rates by appropriate kernels for each connection pathway and summing the contributions. Our main results are that kernels derived via linearized synapse and membrane dynamics, distributions of cells, conduction delay, and volume conductor model allow for accurately capturing the spatiotemporal dynamics of ground truth extracellular signals from conductance-based multicompartment neuron networks. One particular observation is that changes in the effective membrane time constants caused by persistent synapse activation must be accounted for.

The work also constitutes a major advance in computational efficiency of accurate, biophysics-based signal predictions from large-scale spike and rate-based neuron network models drastically reducing signal prediction times compared to biophysically detailed network models. This work also provides insight into how experimentally recorded low-frequency extracellular signals of neuronal activity may be approximately linearly dependent on spiking activity. A new software tool LFPykernels serves as a reference implementation of the framework.

Understanding the brain’s function and activity in healthy and pathological states across spatial scales and times spanning entire lives is one of humanity’s great undertakings. In experimental and clinical work probing the brain’s activity, a variety of electric and magnetic measurement techniques are routinely applied. However interpreting the extracellularly measured signals remains arduous due to multiple factors, mainly the large number of neurons contributing to the signals and complex interactions occurring in recurrently connected neuronal circuits. To understand how neurons give rise to such signals, mechanistic modeling combined with forward models derived using volume conductor theory has proven to be successful, but this approach currently does not scale to the systems level (encompassing millions of neurons or more) where simplified or abstract neuron representations typically are used. Motivated by experimental findings implying approximately linear relationships between times of neuronal action potentials and extracellular population signals, we provide a biophysics-based method for computing causal filters relating spikes and extracellular signals that can be applied with spike times or rates of large-scale neuronal network models for predictions of population signals without relying on ad hoc approximations.

Non-uniform distribution of dendritic nonlinearities differentially engages thalamostriatal and corticostriatal inputs onto cholinergic interneurons

The tonic activity of striatal cholinergic interneurons (CINs) is modified differentially by their afferent inputs. Although their unitary synaptic currents are identical, in most CINs cortical inputs onto distal dendrites only weakly entrain them, whereas proximal thalamic inputs trigger abrupt pauses in discharge in response to salient external stimuli. To test whether the dendritic expression of the active conductances that drive autonomous discharge contribute to the CINs’ capacity to dissociate cortical from thalamic inputs, we used an optogenetics-based method to quantify dendritic excitability in mouse CINs. We found that the persistent sodium (NaP) current gave rise to dendritic boosting, and that the hyperpolarization-activated cyclic nucleotide-gated (HCN) current gave rise to a subhertz membrane resonance. This resonance may underlie our novel finding of an association between CIN pauses and internally-generated slow wave events in sleeping non-human primates. Moreover, our method indicated that dendritic NaP and HCN currents were preferentially expressed in proximal dendrites. We validated the non-uniform distribution of NaP currents: pharmacologically; with two-photon imaging of dendritic back-propagating action potentials; and by demonstrating boosting of thalamic, but not cortical, inputs by NaP currents. Thus, the localization of active dendritic conductances in CIN dendrites mirrors the spatial distribution of afferent terminals and may promote their differential responses to thalamic vs. cortical inputs.

Nonfragile H∞ Synchronization of BAM Inertial Neural Networks Subject to Persistent Dwell-Time Switching Regularity

This article concentrates on the synchronization of discrete-time persistent dwell-time (PDT) switched bidirectional associative memory inertial neural networks with time-varying delays. Through the use of the switched system theory related to the PDT, the convex optimization technique together with some straightforward decoupling methods, an appropriate mode-dependent controller with nonfragility is developed to acclimatize itself to some practical circumstances. Simultaneously, sufficient conditions of ensuring the H_∞ performance and exponential stability for the resulting switched synchronization error system are derived. Finally, a numerical example is utilized to show the validity of the model constructed and the influence of the PDT on the H_∞ performance. In addition, an image encryption example is employed to show the potential application prospect of the investigated system.

Activity-dependent modulation of NMDA receptors by endogenous zinc shapes dendritic function in cortical neurons

NMDA receptors (NMDARs) have been proposed to control single-neuron computations in vivo. However, whether specific mechanisms regulate the function of such receptors and modulate input-output transformations performed by cortical neurons under in vivo-like conditions is understudied. Here, we report that in layer 2/3 pyramidal neurons (L2/3 PNs), repeated synaptic stimulation results in an activity-dependent decrease in NMDAR function by vesicular zinc. Such a mechanism shifts the threshold for dendritic non-linearities and strongly reduces LTP. Modulation of NMDARs is cell and pathway specific, being present selectively in L2/3-L2/3 connections but absent in inputs originating from L4 neurons. Numerical simulations highlight that activity-dependent modulation of NMDARs influences dendritic computations, endowing L2/3 PN dendrites with the ability to sustain non-linear integrations constant across different regimes of synaptic activity like those found in vivo. Our results unveil vesicular zinc as an important endogenous modulator of dendritic function in cortical PNs.

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Vesicular zinc release downregulates function of synaptic NMDARs in cortical neurons

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Zinc modulation of NMDARs is activity dependent, pathway and cell specific

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Endogenous zinc controls dendritic non-linearities and synaptic plasticity in L2/3 PNs

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Modulation of NMDARs normalizes dendritic function during ongoing synaptic activity

Path-dependent dynamics induced by rewiring networks of inertial oscillators

In networks of coupled oscillators, it is of interest to understand how interaction topology affects synchronization. Many studies have gained key insights into this question by studying the classic Kuramoto oscillator model on static networks. However, new questions arise when the network structure is time varying or when the oscillator system is multistable, the latter of which can occur when an inertial term is added to the Kuramoto model. While the consequences of evolving topology and multistability on collective behavior have been examined separately, real-world systems such as gene regulatory networks and the brain may exhibit these properties simultaneously. It is thus relevant to ask how time-varying network connectivity impacts synchronization in systems that can exhibit multistability. To address this question, we study how the dynamics of coupled Kuramoto oscillators with inertia are affected when the topology of the underlying network changes in time. We show that hysteretic synchronization behavior in networks of coupled inertial oscillators can be driven by changes in connection topology alone. Moreover, we find that certain fixed-density rewiring schemes induce significant changes to the level of global synchrony that remain even after the network returns to its initial configuration, and we show that these changes are robust to a wide range of network perturbations. Our findings highlight that the specific progression of network topology over time, in addition to its initial or final static structure, can play a considerable role in modulating the collective behavior of systems evolving on complex networks.

GABA B Receptor-Mediated Regulation of Dendro-Somatic Synergy in Layer 5 Pyramidal Neurons

Synergistic interactions between independent synaptic input streams may fundamentally change the action potential (AP) output. Using partial information decomposition, we demonstrate here a substantial contribution of synergy between somatic and apical dendritic inputs to the information in the AP output of L5b pyramidal neurons. Activation of dendritic GABA_B receptors (GABA_BRs), known to decrease APs in vivo, potently decreased synergy and increased somatic control of AP output. Synergy was the result of the voltage-dependence of the transfer resistance between dendrite and soma, which showed a two-fold increase per 28.7 mV dendritic depolarization. GIRK channels activated by dendritic GABA_BRs decreased voltage-dependent transfer resistances and AP output. In contrast, inhibition of dendritic L-type Ca²⁺ channels prevented high-frequency bursts of APs, but did not affect dendro-somatic synergy. Finally, we show that NDNF-positive neurogliaform cells effectively control somatic AP via synaptic activation of dendritic GIRK channels. These results uncover a novel inhibitory mechanism that powerfully gates cellular information flow in the cortex.

Post-stroke epileptogenesis is associated with altered intrinsic properties of hippocampal pyramidal neurons leading to increased theta resonance

Brain insults like stroke, trauma or infections often lead to blood-brain barrier-dysfunction (BBBd) frequently resulting into epileptogenesis. Affected patients suffer from seizures and cognitive comorbidities that are potentially linked to altered network oscillations. It has been shown that a hippocampal BBBd in rats leads to in vivo seizures and increased power at theta (3-8 Hz), an important type of network oscillations. However, the underlying cellular mechanisms remain poorly understood. At membrane potentials close to the threshold for action potentials (APs) a subpopulation of CA1 pyramidal cells (PCs) displays intrinsic resonant properties due to an interplay of the muscarine-sensitive K⁺-current (I_M) and the persistent Na⁺-current (I_NaP). Such resonant neurons are more excitable and generate more APs when stimulated at theta frequencies, being strong candidates for contributing to hippocampal theta oscillations during epileptogenesis. We tested this hypothesis by characterizing changes in intrinsic properties of hippocampal PCs one week after post-stroke epileptogenesis, a model associated with BBBd, using slice electrophysiology and computer modeling. We find a higher proportion of resonant neurons in BBBd compared to sham animals (47 vs. 29%), accompanied by an increase in their excitability. In contrast, BBBd non-resonant neurons showed a reduced excitability, presented with lower impedance and more positive AP threshold. We identify an increase in I_M combined with either a reduction in I_NaP or an increase in I_Leak as possible mechanisms underlying the observed changes. Our results support the hypothesis that a higher proportion of more excitable resonant neurons in the hippocampus contributes to increased theta oscillations and an increased likelihood of seizures in a model of post-stroke epileptogenesis.

Effects of Ih and TASK-like shunting current on dendritic impedance in layer 5 pyramidal-tract neurons

Pyramidal neurons in neocortex have complex input-output relationships that depend on their morphologies, ion channel distributions, and the nature of their inputs, but which cannot be replicated by simple integrate-and-fire models. The impedance properties of their dendritic arbors, such as resonance and phase shift, shape neuronal responses to synaptic inputs and provide intraneuronal functional maps reflecting their intrinsic dynamics and excitability. Experimental studies of dendritic impedance have shown that neocortical pyramidal tract neurons exhibit distance-dependent changes in resonance and impedance phase with respect to the soma. We, therefore, investigated how well several biophysically detailed multicompartment models of neocortical layer 5 pyramidal tract neurons reproduce the location-dependent impedance profiles observed experimentally. Each model tested here exhibited location-dependent impedance profiles, but most captured either the observed impedance amplitude or phase, not both. The only model that captured features from both incorporates hyperpolarization-activated cyclic nucleotide-gated (HCN) channels and a shunting current, such as that produced by Twik-related acid-sensitive K+ (TASK) channels. TASK-like channel density in this model was proportional to local HCN channel density. We found that although this shunting current alone is insufficient to produce resonance or realistic phase response, it modulates all features of dendritic impedance, including resonance frequencies, resonance strength, synchronous frequencies, and total inductive phase. We also explored how the interaction of HCN channel current (Ih) and a TASK-like shunting current shape synaptic potentials and produce degeneracy in dendritic impedance profiles, wherein different combinations of Ih and shunting current can produce the same impedance profile.NEW & NOTEWORTHY We simulated chirp current stimulation in the apical dendrites of 5 biophysically detailed multicompartment models of neocortical pyramidal tract neurons and found that a combination of HCN channels and TASK-like channels produced the best fit to experimental measurements of dendritic impedance. We then explored how HCN and TASK-like channels can shape the dendritic impedance as well as the voltage response to synaptic currents.

A shape-adjusted ellipse approach corrects for varied axonal dispersion angles and myelination in primate nerve roots

Segmentation of axons in light and electron micrographs allows for quantitative high-resolution analysis of nervous tissues, but varied axonal dispersion angles result in over-estimates of fiber sizes. To overcome this technical challenge, we developed a novel shape-adjusted ellipse (SAE) determination of axonal size and myelination as an all-inclusive and non-biased tool to correct for oblique nerve fiber presentations. Our new resource was validated by light and electron microscopy against traditional methods of determining nerve fiber size and myelination in rhesus macaques as a model system. We performed detailed segmental mapping and characterized the morphological signatures of autonomic and motor fibers in primate lumbosacral ventral roots (VRs). An en bloc inter-subject variability for the preganglionic parasympathetic fibers within the L7-S2 VRs was determined. The SAE approach allows for morphological ground truth data collection and assignment of individual axons to functional phenotypes with direct implications for fiber mapping and neuromodulation studies.

Stability of delayed inertial neural networks on time scales: A unified matrix-measure approach

This note introduces a unified matrix-measure concept to study the stability of a class of inertial neural networks with bounded time delays on time scales. The novel matrix-measure concept unifies the classic matrix-measure and the generalized matrix-measure concept. One sufficient global exponential stability criterion is obtained based on this key matrix-measure and no Lyapunov function is required. To make the stability performance better, another stability criterion in which more detailed information is involved has been acquired. The theoretical results in this note contain and extend some existing continuous-time and discrete-time works. A numerical example is given to show the validity of the results.

Theoretical Aspects of Resting-State Cardiomyocyte Communication for Multi-Nodal Nano-Actuator Pacemakers

The heart consists of billions of cardiac muscle cells-cardiomyocytes-that work in a coordinated fashion to supply oxygen and nutrients to the body. Inter-connected specialized cardiomyocytes form signaling channels through which the electrical signals are propagated throughout the heart, controlling the heart's beat to beat function of the other cardiac cells. In this paper, we study to what extent it is possible to use ordinary cardiomyocytes as communication channels between components of a recently proposed multi-nodal leadless pacemaker, to transmit data encoded in subthreshold membrane potentials. We analyze signal propagation in the cardiac infrastructure considering noise in the communication channel by performing numerical simulations based on the Luo-Rudy computational model. The Luo-Rudy model is an action potential model but describes the potential changes with time including membrane potential and action potential stages, separated by the thresholding mechanism. Demonstrating system performance, we show that cardiomyocytes can be used to establish an artificial communication system where data are reliably transmitted between 10 s of cells. The proposed subthreshold cardiac communication lays the foundation for a new intra-cardiac communication technique.

Global exponential stabilization and lag synchronization control of inertial neural networks with time delays

The global exponential stabilization and lag synchronization control of delayed inertial neural networks (INNs) are investigated. By constructing nonnegative function and employing inequality techniques, several new results about exponential stabilization and exponential lag synchronization are derived via adaptive control. And the theoretical outcomes are developed directly from the INNs themselves without variable substitution. In addition, the synchronization results are also applied to image encryption and decryption. Finally, an example is presented to illustrate the validity of the derived results.

A Discrete Time Framework for Spike Transfer Process in a Cortical Neuron With Asynchronous EPSP, IPSP, and Variable Threshold

Interpretation of high level cognitive behavior of human brain requires comprehensive understanding of spike transfer process at neuronal level. Synapses play major role in spike transfer process from one neuron to another. An expanded leaky integrate and fire model of a neuron in multiple input and single output configuration with threshold variability for spike transfer process is proposed in this paper. Asynchronous generation of post synaptic potential is considered. Multiple types of excitatory and inhibitory post-synaptic potentials are also included in the model. An analytical expression of membrane potential including threshold variability and activity dependant noise process has been developed. The model captures several important features of a spiking neuron through a set of well defined parameters. Simulation results are provided to explain various aspects of the proposed model. A functionally scaled version of the model has also been compared with limited experimental data, available from the Allen Institute of Brain Science.

Exact solutions to cable equations in branching neurons with tapering dendrites

Neurons are biological cells with uniquely complex dendritic morphologies that are not present in other cell types. Electrical signals in a neuron with branching dendrites can be studied by cable theory which provides a general mathematical modelling framework of spatio-temporal voltage dynamics. Typically such models need to be solved numerically unless the cell membrane is modelled either by passive or quasi-active dynamics, in which cases analytical solutions can be reduced to calculation of the Green's function describing the fundamental input-output relationship in a given morphology. Such analytically tractable models often assume individual dendritic segments to be cylinders. However, it is known that dendritic segments in many types of neurons taper, i.e. their radii decline from proximal to distal ends. Here we consider a generalised form of cable theory which takes into account both branching and tapering structures of dendritic trees. We demonstrate that analytical solutions can be found in compact algebraic forms in an arbitrary branching neuron with a class of tapering dendrites studied earlier in the context of single neuronal cables by Poznanski (Bull. Math. Biol. 53(3):457-467, 1991). We apply this extended framework to a number of simplified neuronal models and contrast their output dynamics in the presence of tapering versus cylindrical segments.

Electrodiffusion models of synaptic potentials in dendritic spines

The biophysical properties of dendritic spines play a critical role in neuronal integration but are still poorly understood, due to experimental difficulties in accessing them. Spine biophysics has been traditionally explored using theoretical models based on cable theory. However, cable theory generally assumes that concentration changes associated with ionic currents are negligible and, therefore, ignores electrodiffusion, i.e. the interaction between electric fields and ionic diffusion. This assumption, while true for large neuronal compartments, could be incorrect when applied to femto-liter size structures such as dendritic spines. To extend cable theory and explore electrodiffusion effects, we use here the Poisson (P) and Nernst-Planck (NP) equations, which relate electric field to charge and Fick's law of diffusion, to model ion concentration dynamics in spines receiving excitatory synaptic potentials (EPSPs). We use experimentally measured voltage transients from spines with nanoelectrodes to explore these dynamics with realistic parameters. We find that (i) passive diffusion and electrodiffusion jointly affect the dynamics of spine EPSPs; (ii) spine geometry plays a key role in shaping EPSPs; and, (iii) the spine-neck resistance dynamically decreases during EPSPs, leading to short-term synaptic facilitation. Our formulation, which complements and extends cable theory, can be easily adapted to model ionic biophysics in other nanoscale bio-compartments.

Classes of dendritic information processing

Dendrites are much more than passive neuronal components. Mounting experimental evidence and decades of computational work have decisively shown that dendrites leverage a host of nonlinear biophysical phenomena and actively participate in sophisticated computations, at the level of the single neuron and at the level of the network. However, a coherent view of their processing power is still lacking and dendrites are largely neglected in neural network models. Here, we describe four classes of dendritic information processing and delineate their implications at the algorithmic level. We propose that beyond the well-known spatiotemporal filtering of their inputs, dendrites are capable of selecting, routing and multiplexing information. By separating dendritic processing from axonal outputs, neuron networks gain a degree of freedom with implications for perception and learning.

Theoretical Modeling and Experimental Detection of the Extracellular Phasic Impedance Modulation in Rabbit Hearts

Theoretical cardiac electrophysiology focuses on the dynamics of the membrane and sarcoplasmic reticulum ion currents; however, passive (e.g., membrane capacitance) and quasi-active (response to small signals) properties of the cardiac sarcolemma, which are quantified by impedance, are also important in determining the behavior of cardiac tissue. Theoretically, impedance varies in the different phases of a cardiac cycle. Our goal in this study was to numerically predict and experimentally validate these phasic changes. We calculated the expected impedance signal using analytic methods (for generic ionic models) and numerical computation (for a rabbit ventricular ionic model). Cardiac impedance is dependent on the phase of the action potential, with multiple deflections caused by a sequential activation and inactivation of various membrane channels. The two main channels shaping the impedance signal are the sodium channel causing a sharp and transient drop at the onset of action potential and the inward rectifying potassium channel causing an increase in impedance during the plateau phase. This dip and dome pattern was confirmed in an ex-vivo rabbit heart model using high-frequency sampling through a monophasic action potential electrode. The hearts were immobilized using a myosin-inhibitor to minimize motion artifacts. We observed phasic impedance changes in three out of four hearts with a dome amplitude of 2 − 4Ω. Measurement of phasic impedance modulation using an extracellular electrode is feasible and provides a non-invasive way to gain insight into the state of cardiac cells and membrane ionic channels. The observed impedance recordings are consistent with the dip and dome pattern predicted analytically.

Active membrane conductances and morphology of a collision detection neuron broaden its impedance profile and improve discrimination of input synchrony

How neurons filter and integrate their complex patterns of synaptic inputs is central to their role in neural information processing. Synaptic filtering and integration are shaped by the frequency-dependent neuronal membrane impedance. Using single and dual dendritic recordings in vivo, pharmacology, and computational modeling, we characterized the membrane impedance of a collision detection neuron in the grasshopper Schistocerca americana. This neuron, the lobula giant movement detector (LGMD), exhibits consistent impedance properties across frequencies and membrane potentials. Two common active conductances g_H and g_M, mediated respectively by hyperpolarization-activated cyclic nucleotide-gated (HCN) channels and by muscarine-sensitive M-type K⁺ channels, promote broadband integration with high temporal precision over the LGMD's natural range of membrane potentials and synaptic input frequencies. Additionally, we found that a model based on the LGMD's branching morphology increased the gain and decreased the delay associated with the mapping of synaptic input currents to membrane potential. More generally, this was true for a wide range of model neuron morphologies, including those of neocortical pyramidal neurons and cerebellar Purkinje cells. These findings show the unexpected role played by two widespread active conductances and by dendritic morphology in shaping synaptic integration.NEW & NOTEWORTHY Neuronal filtering and integration of synaptic input patterns depend on the electrochemical properties of dendrites. We used an identified collision detection neuron in grasshoppers to examine how its morphology and two conductances affect its membrane impedance in relation to the computations it performs. The neuronal properties examined are ubiquitous and therefore promote a general understanding of neuronal computations, including those in the human brain.

Linking demyelination to compound action potential dispersion with a spike-diffuse-spike approach

To establish and exploit novel biomarkers of demyelinating diseases requires a mechanistic understanding of axonal propagation. Here, we present a novel computational framework called the stochastic spike-diffuse-spike (SSDS) model for assessing the effects of demyelination on axonal transmission. It models transmission through nodal and internodal compartments with two types of operations: a stochastic integrate-and-fire operation captures nodal excitability and a linear filtering operation describes internodal propagation. The effects of demyelinated segments on the probability of transmission, transmission delay and spike time jitter are explored. We argue that demyelination-induced impedance mismatch prevents propagation mostly when the action potential leaves a demyelinated region, not when it enters a demyelinated region. In addition, we model sodium channel remodeling as a homeostatic control of nodal excitability. We find that the effects of mild demyelination on transmission probability and delay can be largely counterbalanced by an increase in excitability at the nodes surrounding the demyelination. The spike timing jitter, however, reflects the level of demyelination whether excitability is fixed or is allowed to change in compensation. This jitter can accumulate over long axons and leads to a broadening of the compound action potential, linking microscopic defects to a mesoscopic observable. Our findings articulate why action potential jitter and compound action potential dispersion can serve as potential markers of weak and sporadic demyelination.

Modulation of voltage-dependent K+ conductances in photoreceptors trades off investment in contrast gain for bandwidth

Modulation is essential for adjusting neurons to prevailing conditions and differing demands. Yet understanding how modulators adjust neuronal properties to alter information processing remains unclear, as is the impact of neuromodulation on energy consumption. Here we combine two computational models, one Hodgkin-Huxley type and the other analytic, to investigate the effects of neuromodulation upon Drosophila melanogaster photoreceptors. Voltage-dependent K⁺ conductances in these photoreceptors: (i) activate upon depolarisation to reduce membrane resistance and adjust bandwidth to functional requirements; (ii) produce negative feedback to increase bandwidth in an energy efficient way; (iii) produce shunt-peaking thereby increasing the membrane gain bandwidth product; and (iv) inactivate to amplify low frequencies. Through their effects on the voltage-dependent K⁺ conductances, three modulators, serotonin, calmodulin and PIP2, trade-off contrast gain against membrane bandwidth. Serotonin shifts the photoreceptor performance towards higher contrast gains and lower membrane bandwidths, whereas PIP2 and calmodulin shift performance towards lower contrast gains and higher membrane bandwidths. These neuromodulators have little effect upon the overall energy consumed by photoreceptors, instead they redistribute the energy invested in gain versus bandwidth. This demonstrates how modulators can shift neuronal information processing within the limitations of biophysics and energy consumption.

The properties of neurons and neural circuits can be adjusted by neuromodulators, molecules that alter their ability to respond to future activity. Many neuromodulators target voltage-dependent ion channels, molecular components of cell membranes that influence the electrical activity of neurons. Because of their importance, the action of neuromodulators upon voltage-dependent ion channels and the subsequent changes in neural activity has been studied extensively. However, the properties of voltage-dependent ion channels also influence the energy that neural signalling consumes. Here we assess the impact of neuromodulators upon neuronal energy consumption. We use analytical and computational models to determine the impact of different neuromodulators upon the signalling properties and energy consumption of fly photoreceptors. Our models uncover previously unknown properties of voltage-dependent ion channels in fly photoreceptors, showing how they adjust the membrane properties, gain and bandwidth, to prevailing light levels. Neuromodulators alter voltage-dependent ion channel properties, adjusting the gain and bandwidth. Although neuromodulators do not substantially alter the overall energy consumption of photoreceptors, they redistribute energy investment in gain and bandwidth. Hence, our models provide novel insights into the functions that neuromodulators play in neurons and neural circuits.

h-Channels Contribute to Divergent Intrinsic Membrane Properties of Supragranular Pyramidal Neurons in Human versus Mouse Cerebral Cortex

Gene expression studies suggest that differential ion channel expression contributes to differences in rodent versus human neuronal physiology. We tested whether h-channels more prominently contribute to the physiological properties of human compared to mouse supragranular pyramidal neurons. Single-cell/nucleus RNA sequencing revealed ubiquitous HCN1-subunit expression in excitatory neurons in human, but not mouse, supragranular layers. Using patch-clamp recordings, we found stronger h-channel-related membrane properties in supragranular pyramidal neurons in human temporal cortex, compared to mouse supragranular pyramidal neurons in temporal association area. The magnitude of these differences depended upon cortical depth and was largest in pyramidal neurons in deep L3. Additionally, pharmacologically blocking h-channels produced a larger change in membrane properties in human compared to mouse neurons. Finally, using biophysical modeling, we provide evidence that h-channels promote the transfer of theta frequencies from dendrite-to-soma in human L3 pyramidal neurons. Thus, h-channels contribute to between-species differences in a fundamental neuronal property.

h-Type Membrane Current Shapes the Local Field Potential from Populations of Pyramidal Neurons

In cortex, the local field potential (LFP) is thought to mainly stem from correlated synaptic input to populations of geometrically aligned neurons. Computer models of single cortical pyramidal neurons showed that subthreshold voltage-dependent membrane conductances can also shape the LFP signal, in particular the hyperpolarization-activated cation current (I_h; h-type). This ion channel is prominent in various types of pyramidal neurons, typically showing an increasing density gradient along the apical dendrites. Here, we investigate how I_h affects the LFP generated by a model of a population of cortical pyramidal neurons. We find that the LFP from populations of neurons that receive uncorrelated synaptic input can be well predicted by the LFP from single neurons. In this case, when input impinges on the distal dendrites, where most h-type channels are located, a strong resonance in the LFP was measured near the soma, whereas the opposite configuration does not reveal an I_h contribution to the LFP. Introducing correlations in the synaptic inputs to the pyramidal cells strongly amplifies the LFP, while maintaining the differential effects of I_h for distal dendritic versus perisomatic input. Previous theoretical work showed that input correlations do not amplify LFP power when neurons receive synaptic input uniformly across the cell. We find that this crucially depends on the membrane conductance distribution: the asymmetric distribution of I_h results in a strong amplification of the LFP when synaptic inputs to the cell population are correlated. In conclusion, we find that the h-type current is particularly suited to shape the LFP signal in cortical populations.SIGNIFICANCE STATEMENT The local field potential (LFP), the low-frequency part of extracellular potentials recorded in neural tissue, is often used for probing neural circuit activity. While the cortical LFP is thought to mainly reflect synaptic inputs onto pyramidal neurons, little is known about the role of subthreshold active conductances in shaping the LFP. By means of biophysical modeling we obtain a comprehensive, qualitative understanding of how LFPs generated by populations of cortical pyramidal neurons depend on active subthreshold currents, and identify the key importance of the h-type channel. Our results show that LFPs can give information about the active properties of neurons and that preferred frequencies in the LFP can result from those cellular properties instead of, for example, network dynamics.

Differential polarization of cortical pyramidal neuron dendrites through weak extracellular fields

The rise of transcranial current stimulation (tCS) techniques have sparked an increasing interest in the effects of weak extracellular electric fields on neural activity. These fields modulate ongoing neural activity through polarization of the neuronal membrane. While the somatic polarization has been investigated experimentally, the frequency-dependent polarization of the dendritic trees in the presence of alternating (AC) fields has received little attention yet. Using a biophysically detailed model with experimentally constrained active conductances, we analyze the subthreshold response of cortical pyramidal cells to weak AC fields, as induced during tCS. We observe a strong frequency resonance around 10-20 Hz in the apical dendrites sensitivity to polarize in response to electric fields but not in the basal dendrites nor the soma. To disentangle the relative roles of the cell morphology and active and passive membrane properties in this resonance, we perform a thorough analysis using simplified models, e.g. a passive pyramidal neuron model, simple passive cables and reconstructed cell model with simplified ion channels. We attribute the origin of the resonance in the apical dendrites to (i) a locally increased sensitivity due to the morphology and to (ii) the high density of h-type channels. Our systematic study provides an improved understanding of the subthreshold response of cortical cells to weak electric fields and, importantly, allows for an improved design of tCS stimuli.

Nerve conduction models in myelinated and unmyelinated nerves based on three-dimensional electrostatic interaction

Until now, nerve conduction has been described on the basis of equivalent circuit model and cable theory, both of which supposed closed electric circuits spreading inside and outside the axoplasm. With these conventional models, we can simulate the propagating pattern of action potential along the axonal membrane based on Ohm’s law and Kirchhoff’s law. However, we could not fully explain the different conductive patterns in unmyelinated and myelinated nerves with these theories. Also, whether we can really suppose closed electrical circuits in the actual site of the nerves or not has not been fully discussed yet. In this report, a recently introduced new theoretical model of nerve conduction based on electrostatic molecular interactions within the axoplsm will be reviewed. With this new approach, we can explain the different conductive patterns in unmyelinated and myelinated nerves. This new mathematical conductive model based on electrostatic compressional wave in the intracellular fluid may also be able to explain the signal integration in the neuronal cell body and the back-propagation mechanism from the axons to the dendrites. With this new mathematical nerve conduction model based on electrostatic molecular interactions within the intracellular fluid, we may be able to achieve an integrated explanation for the physiological phenomena taking place in the nervous system.