Conductance-based Neuron Model Research Articles

Biorealistic Neuronal Temperature-Sensitive Dynamics within Threshold Switching Memristors: Toward Neuromorphic Thermosensation.

Neuromorphic nanoelectronic devices that can emulate the temperature-sensitive dynamics of biological neurons are of great interest for bioinspired robotics and advanced applications such as in silico neuroscience. In this work, we demonstrate the biomimetic thermosensitive properties of two-terminal V3O5 memristive devices and showcase their similarity to the firing characteristics of thermosensitive biological neurons. The temperature-dependent electrical characteristics of V3O5-based memristors are used to understand the spiking response of a simple relaxation oscillator. The temperature-dependent dynamics of these oscillators are then compared with those of biological neurons through numerical simulations of a conductance-based neuron model, the Morris-Lecar neuron model. Finally, we demonstrate a robust neuromorphic thermosensation system inspired by biological thermoreceptors for bioinspired thermal perception and representation. These results not only demonstrate the biorealistic emulative potential of threshold-switching memristors but also establish V3O5 as a functional material for realizing solid-state neurons for neuromorphic computing and sensing applications.

Coupled Memristor Oscillators for Neuromorphic Locomotion Control: Modeling and Analysis.

The recent surge of interest in brain-inspired architectures along with the development of nonlinear dynamical electronic devices and circuits has enabled energy-efficient hardware realizations of several important neurobiological systems and features. Central pattern generator (CPG) is one such neural system underlying the control of various rhythmic motor behaviors in animals. A CPG can produce spontaneous coordinated rhythmic output signals without any feedback mechanism, ideally realizable by a system of coupled oscillators. Bio-inspired robotics aims to use this approach to control the limb movement for synchronized locomotion. Hence, devising a compact and energy-efficient hardware platform to implement neuromorphic CPGs would be of great benefit for bio-inspired robotics. In this work, we demonstrate that four capacitively coupled vanadium dioxide (VO2) memristor-based oscillators can produce spatiotemporal patterns corresponding to the primary quadruped gaits. The phase relationships underlying the gait patterns are governed by four tunable bias voltages (or four coupling strengths) making the network programmable, reducing the complex problem of gait selection and dynamic interleg coordination to the choice of four control parameters. To this end, we first introduce a dynamical model for the VO2 memristive nanodevice, then perform analytical and bifurcation analysis of a single oscillator, and finally demonstrate the dynamics of coupled oscillators through extensive numerical simulations. We also show that adopting the presented model for a VO2 memristor reveals a striking resemblance between VO2 memristor oscillators and conductance-based biological neuron models such as the Morris-Lecar (ML) model. This can inspire and guide further research on implementation of neuromorphic memristor circuits that emulate neurobiological phenomena.

Computational modeling to study the impact of changes in Nav1.8 sodium channel on neuropathic pain.

Nav1.8 expression is restricted to sensory neurons; it was hypothesized that aberrant expression and function of this channel at the site of injury contributed to pathological pain. However, the specific contributions of Nav1.8 to neuropathic pain are not as clear as its role in inflammatory pain. The aim of this study is to understand how Nav1.8 present in peripheral sensory neurons regulate neuronal excitability and induce various electrophysiological features on neuropathic pain. To study the effect of changes in sodium channel Nav1.8 kinetics, Hodgkin-Huxley type conductance-based models of spiking neurons were constructed using the NEURON v8.2 simulation software. We constructed a single-compartment model of neuronal soma that contained Nav1.8 channels with the ionic mechanisms adapted from some existing small DRG neuron models. We then validated and compared the model with our experimental data from in vivo recordings on soma of small dorsal root ganglion (DRG) sensory neurons in animal models of neuropathic pain (NEP). We show that Nav1.8 is an important parameter for the generation and maintenance of abnormal neuronal electrogenesis and hyperexcitability. The typical increased excitability seen is dominated by a left shift in the steady state of activation of this channel and is further modulated by this channel's maximum conductance and steady state of inactivation. Therefore, modified action potential shape, decreased threshold, and increased repetitive firing of sensory neurons in our neuropathic animal models may be orchestrated by these modulations on Nav1.8. Computational modeling is a novel strategy to understand the generation of chronic pain. In this study, we highlight that changes to the channel functions of Nav1.8 within the small DRG neuron may contribute to neuropathic pain.

Pathogenic gating pore current conducted by autism-related mutations in the NaV1.2 brain sodium channel

Autism spectrum disorder (ASD) is a complex neurodevelopmental condition characterized by social and communication deficits and repetitive behaviors. The genetic heterogeneity of ASD presents a challenge to the development of an effective treatment targeting the underlying molecular defects. ASD gating charge mutations in the KCNQ/KV7 potassium channel cause gating pore currents (Igp) and impair action potential (AP) firing of dopaminergic neurons in brain slices. Here, we investigated ASD gating charge mutations of the voltage-gated SCN2A/NaV1.2 brain sodium channel, which ranked high among the ion channel genes with mutations in individuals with ASD. Our results show that ASD mutations in the gating charges R2 in Domain-II (R853Q), and R1 (R1626Q) and R2 (R1629H) in Domain-IV of NaV1.2 caused Igp in the resting state of ~0.1% of the amplitude of central pore current. The R1626Q mutant also caused significant changes in the voltage dependence of fast inactivation, and the R1629H mutant conducted proton-selective Igp. These potentially pathogenic Igp were exacerbated by the absence of the extracellular Mg2+ and Ca2+. In silico simulation of the effects of these mutations in a conductance-based single-compartment cortical neuron model suggests that the inward Igp reduces the time to peak for the first AP in a train, increases AP rates during a train of stimuli, and reduces the interstimulus interval between consecutive APs, consistent with increased neural excitability and altered input/output relationships. Understanding this common pathophysiological mechanism among different voltage-gated ion channels at the circuit level will give insights into the underlying mechanisms of ASD.

Exact Analysis of the Subthreshold Variability for Conductance-Based Neuronal Models with Synchronous Synaptic Inputs.

The spiking activity of neocortical neurons exhibits a striking level of variability, even when these networks are driven by identical stimuli. The approximately Poisson firing of neurons has led to the hypothesis that these neural networks operate in the asynchronous state. In the asynchronous state, neurons fire independently from one another, so that the probability that a neuron experience synchronous synaptic inputs is exceedingly low. While the models of asynchronous neurons lead to observed spiking variability, it is not clear whether the asynchronous state can also account for the level of subthreshold membrane potential variability. We propose a new analytical framework to rigorously quantify the subthreshold variability of a single conductance-based neuron in response to synaptic inputs with prescribed degrees of synchrony. Technically, we leverage the theory of exchangeability to model input synchrony via jump-process-based synaptic drives; we then perform a moment analysis of the stationary response of a neuronal model with all-or-none conductances that neglects postspiking reset. As a result, we produce exact, interpretable closed forms for the first two stationary moments of the membrane voltage, with explicit dependence on the input synaptic numbers, strengths, and synchrony. For biophysically relevant parameters, we find that the asynchronous regime yields realistic subthreshold variability (voltage variance ≃4-9 mV2) only when driven by a restricted number of large synapses, compatible with strong thalamic drive. By contrast, we find that achieving realistic subthreshold variability with dense cortico-cortical inputs requires including weak but nonzero input synchrony, consistent with measured pairwise spiking correlations. We also show that, without synchrony, the neural variability averages out to zero for all scaling limits with vanishing synaptic weights, independent of any balanced state hypothesis. This result challenges the theoretical basis for mean-field theories of the asynchronous state.

Rapid changes in synchronizability in conductance-based neuronal networks with conductance-based coupling.

Real neurons connect to each other non-randomly. These connectivity graphs can potentially impact the ability of networks to synchronize, along with the dynamics of neurons and the dynamics of their connections. How the connectivity of networks of conductance-based neuron models like the classical Hodgkin-Huxley model or the Morris-Lecar model impacts synchronizability remains unknown. One powerful tool to resolve the synchronizability of these networks is the master stability function (MSF). Here, we apply and extend the MSF approach to networks of Morris-Lecar neurons with conductance-based coupling to determine under which parameters and for which graphs the synchronous solutions are stable. We consider connectivity graphs with a constant non-zero row sum, where the MSF approach can be readily extended to conductance-based synapses rather than the more well-studied diffusive connectivity case, which primarily applies to gap junction connectivity. In this formulation, the synchronous solution is a single, self-coupled, or "autaptic" neuron. We find that the primary determining parameter for the stability of the synchronous solution is, unsurprisingly, the reversal potential, as it largely dictates the excitatory/inhibitory potential of a synaptic connection. However, the change between "excitatory" and "inhibitory" synapses is rapid, with only a few millivolts separating stability and instability of the synchronous state for most graphs. We also find that for specific coupling strengths (as measured by the global synaptic conductance), islands of synchronizability in the MSF can emerge for inhibitory connectivity. We verified the stability of these islands by direct simulation of pairs of neurons coupled with eigenvalues in the matching spectrum.

Heterogeneous off-target impact of ion-channel deletion on intrinsic properties of hippocampal model neurons that self-regulate calcium.

How do neurons that implement cell-autonomous self-regulation of calcium react to knockout of individual ion-channel conductances? To address this question, we used a heterogeneous population of 78 conductance-based models of hippocampal pyramidal neurons that maintained cell-autonomous calcium homeostasis while receiving theta-frequency inputs. At calcium steady-state, we individually deleted each of the 11 active ion-channel conductances from each model. We measured the acute impact of deleting each conductance (one at a time) by comparing intrinsic electrophysiological properties before and immediately after channel deletion. The acute impact of deleting individual conductances on physiological properties (including calcium homeostasis) was heterogeneous, depending on the property, the specific model, and the deleted channel. The underlying many-to-many mapping between ion channels and properties pointed to ion-channel degeneracy. Next, we allowed the other conductances (barring the deleted conductance) to evolve towards achieving calcium homeostasis during theta-frequency activity. When calcium homeostasis was perturbed by ion-channel deletion, post-knockout plasticity in other conductances ensured resilience of calcium homeostasis to ion-channel deletion. These results demonstrate degeneracy in calcium homeostasis, as calcium homeostasis in knockout models was implemented in the absence of a channel that was earlier involved in the homeostatic process. Importantly, in reacquiring homeostasis, ion-channel conductances and physiological properties underwent heterogenous plasticity (dependent on the model, the property, and the deleted channel), even introducing changes in properties that were not directly connected to the deleted channel. Together, post-knockout plasticity geared towards maintaining homeostasis introduced heterogenous off-target effects on several channels and properties, suggesting that extreme caution be exercised in interpreting experimental outcomes involving channel knockouts.

Loss or gain of function? Effects of ion channel mutations on neuronal firing depend on the neuron type.

Clinically relevant mutations to voltage-gated ion channels, called channelopathies, alter ion channel function, properties of ionic currents, and neuronal firing. The effects of ion channel mutations are routinely assessed and characterized as loss of function (LOF) or gain of function (GOF) at the level of ionic currents. However, emerging personalized medicine approaches based on LOF/GOF characterization have limited therapeutic success. Potential reasons are among others that the translation from this binary characterization to neuronal firing is currently not well-understood-especially when considering different neuronal cell types. In this study, we investigate the impact of neuronal cell type on the firing outcome of ion channel mutations. To this end, we simulated a diverse collection of single-compartment, conductance-based neuron models that differed in their composition of ionic currents. We systematically analyzed the effects of changes in ion current properties on firing in different neuronal types. Additionally, we simulated the effects of known mutations in KCNA1 gene encoding the KV1.1 potassium channel subtype associated with episodic ataxia type 1 (EA1). These simulations revealed that the outcome of a given change in ion channel properties on neuronal excitability depends on neuron type, i.e., the properties and expression levels of the unaffected ionic currents. Consequently, neuron-type specific effects are vital to a full understanding of the effects of channelopathies on neuronal excitability and are an important step toward improving the efficacy and precision of personalized medicine approaches.

Frequency-domain analysis of membrane polarization in two-compartment model neurons with weak alternating electric fields.

Transcranial alternating current stimulation (tACS) is widely used in studying brain functions and the treatment of neuropsychiatric diseases in a frequency-specific manner. However, how tACS works on neuronal activity has been poorly understood. In this paper, we use linear system analysis to investigate how weak alternating electric fields (EFs) affect the membrane polarization of neurons in the frequency domain. Two biophysically realistic conductance-based two-compartment models of cortical pyramidal neurons are developed to simulate subthreshold membrane polarization with weak alternating EFs. We linearize the original nonlinear models at the stable equilibrium points and further simplify them to the two- or three-dimensional linear systems. Thus, we calculate the transfer functions of the low-dimensional linear models to model neuronal polarization patterns. Based on the transfer functions, we compute the amplitude- and phase-frequency characteristics to describe the relationship between weak EFs and membrane polarization. We also computed the parameters (gain, zeros, and poles) and structures (the number of zeros and poles) of transfer functions to reveal how neuronal intrinsic properties affect the parameters and structure of transfer functions and thus the frequency-dependent membrane polarization with alternating EFs. We find that the amplitude and phase of membrane polarization both strongly depended on EF frequency, and these frequency responses are modulated by the intrinsic properties of neurons. The compartment geometry, internal coupling conductance, and ionic currents (except Ih) affect the frequency-dependent polarization by mainly changing the gain and pole of transfer functions. Larger gain contributes to larger amplitude-frequency characteristics. The closer the pole is to the imaginary axis, the lower phase-frequency characteristics. However, Ih changes the structure of transfer function in the dendrite by introducing a new pair of zero-pole points, which decrease the amplitude at low frequencies and thus lead to a visible resonance. These results highlight the effects of passive properties and active ion currents on subthreshold membrane polarization with alternating EFs in the frequency domain, which provide an explainable connection of how intrinsic properties of neurons modulate the neuronal input-output functions with weak EF stimulation.

Synchrony-Division Neural Multiplexing: An Encoding Model

Cortical neurons receive mixed information from the collective spiking activities of primary sensory neurons in response to a sensory stimulus. A recent study demonstrated an abrupt increase or decrease in stimulus intensity and the stimulus intensity itself can be respectively represented by the synchronous and asynchronous spikes of S1 neurons in rats. This evidence capitalized on the ability of an ensemble of homogeneous neurons to multiplex, a coding strategy that was referred to as synchrony-division multiplexing (SDM). Although neural multiplexing can be conceived by distinct functions of individual neurons in a heterogeneous neural ensemble, the extent to which nearly identical neurons in a homogeneous neural ensemble encode multiple features of a mixed stimulus remains unknown. Here, we present a computational framework to provide a system-level understanding on how an ensemble of homogeneous neurons enable SDM. First, we simulate SDM with an ensemble of homogeneous conductance-based model neurons receiving a mixed stimulus comprising slow and fast features. Using feature-estimation techniques, we show that both features of the stimulus can be inferred from the generated spikes. Second, we utilize linear nonlinear (LNL) cascade models and calculate temporal filters and static nonlinearities of differentially synchronized spikes. We demonstrate that these filters and nonlinearities are distinct for synchronous and asynchronous spikes. Finally, we develop an augmented LNL cascade model as an encoding model for the SDM by combining individual LNLs calculated for each type of spike. The augmented LNL model reveals that a homogeneous neural ensemble model can perform two different functions, namely, temporal- and rate-coding, simultaneously.

Adaptive unscented Kalman filter for neuronal state and parameter estimation.

Data assimilation techniques for state and parameter estimation are frequently applied in the context of computational neuroscience. In this work, we show how an adaptive variant of the unscented Kalman filter (UKF) performs on the tracking of a conductance-based neuron model. Unlike standard recursive filter implementations, the robust adaptive unscented Kalman filter (RAUKF) jointly estimates the states and parameters of the neuronal model while adjusting noise covariance matrices online based on innovation and residual information. We benchmark the adaptive filter's performance against existing nonlinear Kalman filters and explore the sensitivity of the filter parameters to the system being modelled. To evaluate the robustness of the proposed solution, we simulate practical settings that challenge tracking performance, such as a model mismatch and measurement faults. Compared to standard variants of the Kalman filter the adaptive variant implemented here is more accurate and robust to faults.

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.

Effect of propagation noise on the network dynamics of a flux coupled conductance-based neuron model

Effect of propagation noise on the network dynamics of a flux coupled conductance-based neuron model

Switching from active to non-active states in a birhythmic conductance-based neuronal model under electromagnetic induction

Switching from active to non-active states in a birhythmic conductance-based neuronal model under electromagnetic induction

A Simple Model of Nonspiking Neurons.

Due to the ubiquity of spiking neurons in neuronal processes, various simple spiking neuron models have been proposed as an alternative to conductance-based models (a.k.a. Hodgkin-Huxley-type models), known to be computationally expensive and difficult to treat mathematically. However, to the best of our knowledge, there is no equivalent in the literature of a simple and lightweight model for describing the voltage behavior of nonspiking neurons, which also are ubiquitous in a large variety of nervous tissues in both vertebrate and invertebrate species and play a central role in information processing. This letter proposes a simple model that reproduces the experimental qualitative behavior of known types of nonspiking neurons. The proposed model, which differs fundamentally from classic simple spiking models unable to characterize nonspiking dynamics due to their intrinsic structure, is derived from the bifurcation study of conductance-based models of nonspiking neurons. Since such neurons display a high sensitivity to noise, the model aims at capturing the experimental distribution of single-neuron responses rather than perfectly replicating a single given experimental voltage trace. We show that such a model can be used as a building block for realistic simulations of large nonspiking neuronal networks and is endowed with generalization capabilities, granted by design.

Delay-dependent transitions of phase synchronization and coupling symmetry between neurons shaped by spike-timing-dependent plasticity.

Synchronization plays a key role in learning and memory by facilitating the communication between neurons promoted by synaptic plasticity. Spike-timing-dependent plasticity (STDP) is a form of synaptic plasticity that modifies the strength of synaptic connections between neurons based on the coincidence of pre- and postsynaptic spikes. In this way, STDP simultaneously shapes the neuronal activity and synaptic connectivity in a feedback loop. However, transmission delays due to the physical distance between neurons affect neuronal synchronization and the symmetry of synaptic coupling. To address the question that how transmission delays and STDP can jointly determine the emergent pairwise activity-connectivity patterns, we studied phase synchronization properties and coupling symmetry between two bidirectionally coupled neurons using both phase oscillator and conductance-based neuron models. We show that depending on the range of transmission delays, the activity of the two-neuron motif can achieve an in-phase/anti-phase synchronized state and its connectivity can attain a symmetric/asymmetric coupling regime. The coevolutionary dynamics of the neuronal system and the synaptic weights due to STDP stabilizes the motif in either one of these states by transitions between in-phase/anti-phase synchronization states and symmetric/asymmetric coupling regimes at particular transmission delays. These transitions crucially depend on the phase response curve (PRC) of the neurons, but they are relatively robust to the heterogeneity of transmission delays and potentiation-depression imbalance of the STDP profile.

Birhythmic oscillations and global stability analysis of a conductance-based neuronal model under ion channel fluctuations

By drawing inspiration from existing polynomial models for neurons, we make use of the Moris Lecar system to derive a new two dimensional birhythmic conductance-based neuronal model for nerves. The analysis of fixed points and their stability indicates that its dynamics strongly depends on the parameters of the newly nonlinear terms introduced. Using Lindsted's method, it is observed that the neuronal system can exhibit coexistence of attractors. These coexisting attractors are on the one hand the subthreshold oscillation and on the other hand the spike generation well known in neuronal systems. After introducing the effects of the channel fluctuations in the form of a Gaussian white noise, the global stability of the attractors is analyzed. The effective active energy barrier also called threshold potential is obtained. This threshold potential is the one needed by neuron to switch from one attractor to another. The probability distribution is also studied analytically and numerically, using the Fokker–Planck type equation derived from the new model and the Monte Carlo methods. It is observed that the system physiological parameters and the intensity of the noise plays an important role in the probability of neuron to switch from the subthreshold attractor to the spiking one and vice versa.

Multiscale Computer Model of the Spinal Dorsal Horn Reveals Changes in Network Processing Associated with Chronic Pain.

Pain-related sensory input is processed in the spinal dorsal horn (SDH) before being relayed to the brain. That processing profoundly influences whether stimuli are correctly or incorrectly perceived as painful. Significant advances have been made in identifying the types of excitatory and inhibitory neurons that comprise the SDH, and there is some information about how neuron types are connected, but it remains unclear how the overall circuit processes sensory input or how that processing is disrupted under chronic pain conditions. To explore SDH function, we developed a computational model of the circuit that is tightly constrained by experimental data. Our model comprises conductance-based neuron models that reproduce the characteristic firing patterns of spinal neurons. Excitatory and inhibitory neuron populations, defined by their expression of genetic markers, spiking pattern, or morphology, were synaptically connected according to available qualitative data. Using a genetic algorithm, synaptic weights were tuned to reproduce projection neuron firing rates (model output) based on primary afferent firing rates (model input) across a range of mechanical stimulus intensities. Disparate synaptic weight combinations could produce equivalent circuit function, revealing degeneracy that may underlie heterogeneous responses of different circuits to perturbations or pathologic insults. To validate our model, we verified that it responded to the reduction of inhibition (i.e., disinhibition) and ablation of specific neuron types in a manner consistent with experiments. Thus validated, our model offers a valuable resource for interpreting experimental results and testing hypotheses in silico to plan experiments for examining normal and pathologic SDH circuit function.SIGNIFICANCE STATEMENT We developed a multiscale computer model of the posterior part of spinal cord gray matter (spinal dorsal horn), which is involved in perceiving touch and pain. The model reproduces several experimental observations and makes predictions about how specific types of spinal neurons and synapses influence projection neurons that send information to the brain. Misfiring of these projection neurons can produce anomalous sensations associated with chronic pain. Our computer model will not only assist in planning future experiments, but will also be useful for developing new pharmacotherapy for chronic pain disorders, connecting the effect of drugs acting at the molecular scale with emergent properties of neurons and circuits that shape the pain experience.

Adaptive conductance control

Neuromodulation is central to the adaptation and robustness of animal nervous systems. This paper explores the classical paradigm of indirect adaptive control to design neuromodulatory controllers in conductance-based neuronal models. The adaptive control of maximal conductance parameters is shown to provide a methodology aligned with the central concepts of neuromodulation in physiology and of impedance control in robotics.

Analysis of the Neuron Dynamics in Thalamic Reticular Nucleus by a Reduced Model.

Strategically located between the thalamus and the cortex, the inhibitory thalamic reticular nucleus (TRN) is a hub to regulate selective attention during wakefulness and control the thalamic and cortical oscillations during sleep. A salient feature of TRN neurons contributing to these functions is their characteristic firing patterns, ranging in a continuum from tonic spiking to bursting spiking. However, the dynamical mechanism under these firing behaviors is not well understood. In this study, by applying a reduction method to a full conductance-based neuron model, we construct a reduced three-variable model to investigate the dynamics of TRN neurons. We show that the reduced model can effectively reproduce the spiking patterns of TRN neurons as observed in vivo and in vitro experiments, and meanwhile allow us to perform bifurcation analysis of the spiking dynamics. Specifically, we demonstrate that the rebound bursting of a TRN neuron is a type of “fold/homo-clinic” bifurcation, and the tonic spiking is the fold cycle bifurcation. Further one-parameter bifurcation analysis reveals that the transition between these discharge patterns can be controlled by the external current. We expect that this reduced neuron model will help us to further study the complicated dynamics and functions of the TRN network.