Ion Channel Models Research Articles

Generalized polynomial chaos-based uncertainty quantification and propagation in multi-scale modeling of cardiac electrophysiology

Uncertainty and physiological variability are ubiquitous in cardiac electrical signaling. It is important to address the uncertainty and variability in cardiac modeling to provide reliable and realistic predictions of heart function, thus ensuring trustworthy computer-aided medical decision-making and treatment planning. Statistical techniques such as Monte Carlo (MC) simulations have been applied to uncertainty quantification and propagation in cardiac modeling. However, MC simulation-based methods are computationally prohibitive for complex cardiac models with a great number of parameters and governing equations. In this paper, we propose to use the Generalized Polynomial Chaos (gPC) expansion in combination with Galerkin projection to analytically quantify parametric uncertainty in ion channel models of mouse ventricular cell, and further propagate the uncertainty across different organizational levels of cell and tissue. To identify the most significant parametric uncertainty in cardiac ion channel and cell models, variance decomposition-based sensitivity analysis was first performed. Following this, gPC was integrated with deterministic cardiac models to propagate uncertainty through ion current, ventricular cell, 1D cable, and 2D tissue to account for the stochasticity and cell-to-cell variability. As compared to MC, the gPC in this work shows the superior performance in terms of computational efficiency. In addition, the gPC models can provide a measure of confidence in model predictions, which can improve the reliability of computer simulations of cardiac electrophysiology for clinical applications.

Towards systematic, data-driven validation of a collaborative, multi-scale model of Caenorhabditis elegans.

The OpenWorm Project is an international open-source collaboration to create a multi-scale model of the organism Caenorhabditis elegans At each scale, including subcellular, cellular, network and behaviour, this project employs one or more computational models that aim to recapitulate the corresponding biological system at that scale. This requires that the simulated behaviour of each model be compared with experimental data both as the model is continuously refined and as new experimental data become available. Here we report the use of SciUnit, a software framework for model validation, to attempt to achieve these goals. During project development, each model is continuously subjected to data-driven 'unit tests' that quantitatively summarize model-data agreement, identifying modelling progress and highlighting particular aspects of each model that fail to adequately reproduce known features of the biological organism and its components. This workflow is publicly visible via both GitHub and a web application and accepts community contributions to ensure that modelling goals are transparent and well-informed.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.

A biophysically constrained computational model of the action potential of mouse urinary bladder smooth muscle.

Urinary incontinence is associated with enhanced spontaneous phasic contractions of the detrusor smooth muscle (DSM). Although a complete understanding of the etiology of these spontaneous contractions is not yet established, it is suggested that the spontaneously evoked action potentials (sAPs) in DSM cells initiate and modulate the contractions. In order to further our understanding of the ionic mechanisms underlying sAP generation, we present here a biophysically detailed computational model of a single DSM cell. First, we constructed mathematical models for nine ion channels found in DSM cells based on published experimental data: two voltage gated Ca2+ ion channels, an hyperpolarization-activated ion channel, two voltage-gated K+ ion channels, three Ca2+-activated K+ ion channels and a non-specific background leak ion channel. The ion channels’ kinetics were characterized in terms of maximal conductances and differential equations based on voltage or calcium-dependent activation and inactivation. All ion channel models were validated by comparing the simulated currents and current-voltage relations with those reported in experimental work. Incorporating these channels, our DSM model is capable of reproducing experimentally recorded spike-type sAPs of varying configurations, ranging from sAPs displaying after-hyperpolarizations to sAPs displaying after-depolarizations. The contributions of the principal ion channels to spike generation and configuration were also investigated as a means of mimicking the effects of selected pharmacological agents on DSM cell excitability. Additionally, the features of propagation of an AP along a length of electrically continuous smooth muscle tissue were investigated. To date, a biophysically detailed computational model does not exist for DSM cells. Our model, constrained heavily by physiological data, provides a powerful tool to investigate the ionic mechanisms underlying the genesis of DSM electrical activity, which can further shed light on certain aspects of urinary bladder function and dysfunction.

Hodgkin–Huxley Neuron and FPAA Dynamics

We present the experimental silicon results on the dynamics of a Hodgkin-Huxley neuron implemented on a reconfigurable platform. The circuit has been inspired by the similarity between biology and silicon, by modeling ion channels and their time constants. Another significant motivation behind this paper is to make the system available to circuit designers as well as users in the neuroscience community. The open-source tool infrastructure and a remote system ease the accessibility of our system to a number of users. We demonstrate the reproducibility of the results by replicating the dynamics across different boards along with responses from different inputs and with different parameters. The reconfigurability enables one to make use of a single primary design to obtain a variety of results. The measurements are taken from the system compiled on a field programmable analog array fabricated on a 350-nm process.

Toward Realistic Large-Area Cell Membrane Mimics: Excluding Oil, Controlling Composition, and Including Ion Channels.

Capacitance measurements provide unique insights into the thickness, compressibility, and composition of large-area membrane bilayers and are used here in addition to demonstrate the successful incorporation of model ion channels. The simultaneous ability to control the bilayer size, manipulate tension, and optically monitor and electrically stimulate freestanding membranes enables precise determination of their specific capacitance and thickness across a wide range of areas. We confirm that membranes formed by this recently developed technique have capacitive properties similar to those formed by existing protocols, including solvent-free approaches, and discuss the effect using either hexadecane or squalene as the oil solvent. The results obtained here are relevant for other methods where lipid membranes are reconstituted from a bulk oil solvent. Because biological membranes have a diverse phospholipid profile, we show that the technique can successfully reconstitute membranes with binary composition mixtures. As an outlook, we show the capability of model membrane proteins, specifically α-hemolysin and alamethicin, to be incorporated into the formed bilayers and measure ion transport.

S62. Computational diagnosis of ion channel dysfunction in NMDA receptor antibody encephalitis

Introduction NMDA receptor (NMDAR) antibody encephalitis is an autoimmune disorder causing acute psychosis, confusion and seizures. Electroencephalography (EEG) findings are usually non-specific, with diagnosis confirmed by demonstration of serum/CSF autoantibodies. Improved clinical outcomes depend on early institution of immunotherapies. A non-invasive measure of NMDAR function could facilitate early treatment, and enable tracking of disease activity. Recent biophysical modeling advances allow inference of ion channel dynamics from macroscopic measures of brain activity. Here, we show that clinically relevant diagnoses of NMDAR ion channel dysfunction can be obtained using a microcircuit model fitted to individual human EEG data. Methods We compared resting state EEG cross-spectra from patients with NMDAR encephalitis, encephalopathy unrelated to NMDAR dysfunction, and non-encephalopathic controls. We fit biophysical models (dynamic causal models – DCMs) of connected neuronal ensembles, simulating post-synaptic membrane potentials and EEG spectra through lead field projection. We used canonical variate analysis (CVA) and an empirical Bayesian approach searching candidate models across the groups to reveal specific synaptic deficits. Results Clinical severity was matched between encephalopathic groups. However, there were clear differences in EEG cross-spectra at low (2–4 Hz) and high (28–40 Hz) frequencies, with increased beta-gamma power present in NMDAR antibody encephalitis patients. Subject-specific DCMs mapped model parameters representing dynamics at NMDA, AMPA and GABA receptors to spectral data features. Four inter-connected sources described delta-theta and beta-gamma cross-spectra observed at scalp sensors. Each source comprised a neural mass model with four neuronal subpopulations, with dynamics determined by intrinsic connections mediated via ionotropic receptors. Dynamics along intrinsic and extrinsic connections could reproduce scalp-based EEG recordings. Parameter estimate CVA showed significant differences between patients with and without NMDAR encephalitis in NMDAR parameters. A parametric empirical Bayes (PEB) analysis demonstrated that the group effects of NMDAR encephalitis were specific to NMDA model parameters, in contrast to other encephalopathies where differences were seen across receptor subtypes. Conclusion Neurological and psychiatric practice lack diagnostic probes to assess disease mechanisms at the neuronal level non-invasively in humans. We show that biophysical models of EEG applied to clinical EEG data identify abnormal NMDAR signaling in patients with NMDAR encephalitis but not in patients with other encephalopathies or neurological controls. By comparing model parameter estimates from these patient groups, we selectively identify NMDAR dysfunction in a multi ion-channel model. Given that EEG is ubiquitously available, our findings suggest the feasibility of EEG neuromodeling as a unique assay of brain dysfunction at the molecular-level.

Sinusoidal voltage protocols for rapid characterisation of ion channel kinetics.

Key points Ion current kinetics are commonly represented by current–voltage relationships, time constant–voltage relationships and subsequently mathematical models fitted to these. These experiments take substantial time, which means they are rarely performed in the same cell.Rather than traditional square‐wave voltage clamps, we fitted a model to the current evoked by a novel sum‐of‐sinusoids voltage clamp that was only 8 s long.Short protocols that can be performed multiple times within a single cell will offer many new opportunities to measure how ion current kinetics are affected by changing conditions.The new model predicts the current under traditional square‐wave protocols well, with better predictions of underlying currents than literature models. The current under a novel physiologically relevant series of action potential clamps is predicted extremely well.The short sinusoidal protocols allow a model to be fully fitted to individual cells, allowing us to examine cell–cell variability in current kinetics for the first time. Understanding the roles of ion currents is crucial to predict the action of pharmaceuticals and mutations in different scenarios, and thereby to guide clinical interventions in the heart, brain and other electrophysiological systems. Our ability to predict how ion currents contribute to cellular electrophysiology is in turn critically dependent on our characterisation of ion channel kinetics – the voltage‐dependent rates of transition between open, closed and inactivated channel states. We present a new method for rapidly exploring and characterising ion channel kinetics, applying it to the hERG potassium channel as an example, with the aim of generating a quantitatively predictive representation of the ion current. We fitted a mathematical model to currents evoked by a novel 8 second sinusoidal voltage clamp in CHO cells overexpressing hERG1a. The model was then used to predict over 5 minutes of recordings in the same cell in response to further protocols: a series of traditional square step voltage clamps, and also a novel voltage clamp comprising a collection of physiologically relevant action potentials. We demonstrate that we can make predictive cell‐specific models that outperform the use of averaged data from a number of different cells, and thereby examine which changes in gating are responsible for cell–cell variability in current kinetics. Our technique allows rapid collection of consistent and high quality data, from single cells, and produces more predictive mathematical ion channel models than traditional approaches.

Makaluvamine G from the Marine Sponge Zyzzia fuliginosa Inhibits Muscle nAChR by Binding at the Orthosteric and Allosteric Sites.

Diverse ligands of the muscle nicotinic acetylcholine receptor (nAChR) are used as muscle relaxants during surgery. Although a plethora of such molecules exists in the market, there is still a need for new drugs with rapid on/off-set, increased selectivity, and so forth. We found that pyrroloiminoquinone alkaloid Makaluvamine G (MG) inhibits several subtypes of nicotinic receptors and ionotropic γ-aminobutiric acid receptors, showing a higher affinity and moderate selectivity toward muscle nAChR. The action of MG on the latter was studied by a combination of electrophysiology, radioligand assay, fluorescent microscopy, and computer modeling. MG reveals a combination of competitive and un-competitive inhibition and caused an increase in the apparent desensitization rate of the murine muscle nAChR. Modeling ion channel kinetics provided evidence for MG binding in both orthosteric and allosteric sites. We also demonstrated that theα1 (G153S) mutant of the receptor, associated with the myasthenic syndrome, is more prone to inhibition by MG. Thus, MG appears to be a perspective hit molecule for the design of allosteric drugs targeting muscle nAChR, especially for treating slow-channel congenital myasthenic syndromes.

Peptides with regularly alternating enantiomeric sequence: From ion channel models to bioinspired nanotechnological applications

AbstractPeptides are versatile building blocks that have been extensively used as peptide‐based organizers to generate bioinspired hybrid materials. Among them, those peptides characterized by regularly alternating enantiomeric sequences (l,d‐peptides) have attracted much interest. Their structures, which are not accessible to the corresponding homochiral peptides, have been exploited to achieve hybrid conjugates, the chemical and structural properties of which can be predetermined by correct design. Molecules that self‐assemble into hollow tubular architectures with side chains on the outer surface can form, allowing the introduction of new functionalities on amino acid residues containing reactive side chains. This provides an effective strategy to develop engineered nanotubes with the surface suitably tuned for applications in different fields, spanning from electronics to medicine.

Eliminating Warrantless Assumptions Facilitates Consideration of an Electrostatic Model of Ion-Channel Activation

Models of voltage-sensitive ion channels (VSICs) that don’t specify the way reduction in electric field at threshold activation leads to observed outward S4 motions don’t provide satisfactory explanations of voltage sensing [Bezanilla F (2008) Neuron50:456-468]. Current models depend on unrealistic assumptions: screening of charges by a putative water-filled pore, and simple mechanical devices. A gate, screw, paddle or other everyday device cannot physically explain activation of the highly energetic resting channel, a far-from-equilibrium macromolecular system: The α-helix's hydrogen bonds are too weak to support such rigid structures. The energy required to lengthen the H-bonds is provided when the capacitive energy lost in the voltage reduction to threshold does mechanical work on the channel. Similarities exist between excitable membranes and ferroelectrics [Leuchtag HR (1987) J Theor Biol 127:321-340; 127:341-359; (2008) Voltage-Sensitive Ion Channels, Springer]. The ferroelectricity of excitable membranes must originate in the channels, since VSICs are their active components. In ferroelectrics, the dielectric coefficient ε is a function of the electric field. Electrostatic forces are inversely proportional to ε. Evidence from molecules with the sidechains of the branched-chain amino acids isoleucine, leucine and valine shows that their ε becomes remarkably large in a high electric field [Yoshino K, Sakurai T (1991) in: Goodby JW et al. Ferroelectric Liquid Crystals:317-363], comparable to that in a resting channel. According to the Channel Activation by Electrostatic Repulsion (CAbER) model, ε is high at rest potential and drops on depolarization. The consequently increased electrostatic repulsion between positively charged arginine and lysine residues at activation expands the S4 segments. This outward motion reconfigures the VSIC into an “open” structure with pore-domain sites wide enough to accommodate unhydrated permeant ions that hop stochastically across the channel [Leuchtag HR (2016) Biophys. J. 112(3):544a; 112(3):543a-544a].

Sinusoidal Voltage Protocols for Rapid Characterisation of Ion Channel Kinetics

Rationale: Understanding the roles of ion currents is crucial to predict the action of pharmaceuticals and mutations in different scenarios, and thereby to guide clinical interventions in the heart, brain and other electrophysiological systems. Our ability to predict how ion currents contribute to cellular electrophysiology is in turn critically dependent on our characterization of ion channel kinetics - the voltage-dependent rates of transition between open, closed and inactivated channel states. Objective: The hERG potassium channel plays a fundamental role in controlling electrical activity in the heart and many other tissues. There is a well-established link between hERG mutations, or block by pharmaceuticals, and increased arrhythmic risk. We present a new method for rapidly exploring and characterizing ion channel kinetics, applying it to the hERG channel as an example, with the aim of generating a quantitatively predictive representation of the ion current. Methods & Results: We fit a mathematical model to currents evoked by a novel 8 second sinusoidal voltage clamp in CHO cells over-expressing hERG1a. The model is then used to predict over 5 minutes of recordings in the same cell in response to further protocols: a series of traditional square step voltage clamps, and also a novel voltage clamp comprised of a collection of physiologically-relevant action potentials. We demonstrate that we can make predictive cell-specfic models that outperform the use of averaged data from a number of different cells, and thereby examine which changes in gating are responsible for cell-cell variability in current kinetics. Conclusions: Our technique allows rapid collection of consistent and high quality data, from single cells, and produces more predictive mathematical ion channel models than traditional approaches. The approach will be widely applicable to other voltage-gated ion currents both in the heart and other electrophysiological systems.

Divide-and-conquer strategy for large-scale Eulerian solvent excluded surface.

Surface generation and visualization are some of the most important tasks in biomolecular modeling and computation. Eulerian solvent excluded surface (ESES) software provides analytical solvent excluded surface (SES) in the Cartesian grid, which is necessary for simulating many biomolecular electrostatic and ion channel models. However, large biomolecules and/or fine grid resolutions give rise to excessively large memory requirements in ESES construction. We introduce an out-of-core and parallel algorithm to improve the ESES software. The present approach drastically improves the spatial and temporal efficiency of ESES. The memory footprint and time complexity are analyzed and empirically verified through extensive tests with a large collection of biomolecule examples. Our results show that our algorithm can successfully reduce memory footprint through a straightforward divide-and-conquer strategy to perform the calculation of arbitrarily large proteins on a typical commodity personal computer. On multi-core computers or clusters, our algorithm can reduce the execution time by parallelizing most of the calculation as disjoint subproblems. Various comparisons with the state-of-the-art Cartesian grid based SES calculation were done to validate the present method and show the improved efficiency. This approach makes ESES a robust software for the construction of analytical solvent excluded surfaces. http://weilab.math.msu.edu/ESES.

Integrated microfluidic biosensing platform for simultaneous confocal microscopy and electrophysiological measurements on bilayer lipid membranes and ion channels.

Combining high-resolution imaging and electrophysiological recordings is key for various types of experimentation on lipid bilayers and ion channels. Here, we propose an integrated biosensing platform consisting of a microfluidic cartridge and a dedicated chip-holder to conduct such dual measurements on suspended lipid bilayers, in a user-friendly manner. To illustrate the potential of the integrated platform, we characterize lipid bilayers in terms of thickness and fluidity while simultaneously monitoring single ion channel currents. For that purpose, POPC lipid bilayers are supplemented with a fluorescently-tagged phospholipid (NBD-PE, 1% mol) for Fluorescence Recovery After Photobleaching (FRAP) measurements and a model ion channel (gramicidin, 1 nM). These combined measurements reveal that NBD-PE has no effect on the lipid bilayer thickness while gramicidin induces thinning of the membrane. Furthermore, the presence of gramicidin does not alter the lipid bilayer fluidity. Surprisingly, in lipid bilayers supplemented with both probes, a reduction in gramicidin open probability and lifetime is observed compared to lipid bilayers with gramicidin only, suggesting an influence of NBD-PE on the gramicidin ion function. Altogether, our proposed microfluidic biosensing platform in combination with the herein presented multi-parametric measurement scheme paves the way to explore the interdependent relationship between lipid bilayer properties and ion channel function.

Modeling pathogenesis and treatment response in childhood absence epilepsy.

Childhood absence epilepsy (CAE) is a genetic generalized epilepsy syndrome with polygenic inheritance, with genes for γ-aminobutyric acid (GABA) receptors and T-type calcium channels implicated in the disorder. Previous studies of T-type calcium channel electrophysiology have shown genetic changes and medications have multiple effects. The aim of this study was to use an established thalamocortical computer model to determine how T-type calcium channels work in concert with cortical excitability to contribute to pathogenesis and treatment response in CAE. The model is comprised of cortical pyramidal, cortical inhibitory, thalamocortical relay, and thalamic reticular single-compartment neurons, implemented with Hodgkin-Huxley model ion channels and connected by AMPA, GABAA , and GABAB synapses. Network behavior was simulated for different combinations of T-type calcium channel conductance, inactivation time, steady state activation/inactivation shift, and cortical GABAA conductance. Decreasing cortical GABAA conductance and increasing T-type calcium channel conductance converted spindle to spike and wave oscillations; smaller changes were required if both were changed in concert. In contrast, left shift of steady state voltage activation/inactivation did not lead to spike and wave oscillations, whereas right shift reduced network propensity for oscillations of any type. These results provide a window into mechanisms underlying polygenic inheritance in CAE, as well as a mechanism for treatment effects and failures mediated by these channels. Although the model is a simplification of the human thalamocortical network, it serves as a useful starting point for predicting the implications of ion channel electrophysiology in polygenic epilepsy such as CAE.

Neuroprotective effects of inhibitors of Acid-Sensing ion channels (ASICs) in optic nerve crush model in rodents

ABSTRACTPurpose: The purpose of the current study was to assess the potential involvement of acid-sensing ion channel 1 (ASIC1) in retinal ganglion cell (RGC) death and investigate the neuroprotective effects of inhibitors of ASICs in promoting RGC survival following optic nerve crush (ONC).Results: ASIC1 protein was significantly increased in optic nerve extracts at day 7 following ONC in rats. Activated calpain-1 increased at 2 and 7 days following ONC as evidenced by increased degradation of α-fodrin, known substrate of calpain. Glial fibrillary acidic protein levels increased significantly at 2 and 7 days post-injury. By contrast, glutamine synthetase increased at 2 days while decreased at 7 days. The inhibition of ASICs with amiloride and psalmotoxin-1 significantly increased RGC survival in rats following ONC (p < 0.05, one-way ANOVA). The mean number of surviving RGCs in rats (n = 6) treated with amiloride (100 µM) following ONC was 1477 ± 98 cells/mm2 compared with ONC (1126 ± 101 cells/mm2), where psalmotoxin-1 (1 μM) treated rats (n = 6) and subjected to ONC had 1441 ± 63 RGCs/mm2 compared with ONC (1065 ± 76 RGCs/mm2). Average number of RGCs in control rats (n = 12) was 2092 ± 46 cells/mm2. Blocking of ASICs also significantly increased RGC survival from ischemic-like insult from 473 ± 80 to 842 ± 49 RGCs/mm2 (for psalmotoxin-1) and from 628 ± 53 RGCs/mm2 to 890 ± 55 RGCs/mm2 (for amiloride) with p ≤ 0.05, using one-way ANOVA. Acidification (a known activator of ASIC1) increased intracellular Ca2+ ([Ca2+]i) in rat primary RGCs, which was statistically blocked by pretreatment with 100 nM psalmotoxin-1.Conclusions: ASIC1 up-regulation-induced influx of extracellular calcium may be responsible for activation of calcium-sensitive calpain-1 in the retina. Calpain-1 induced degradation of α-fodrin and leads to morphological changes and eventually neuronal death. Therefore, blockers of ASIC1 can be used as potential therapeutics in the treatment of optic nerve degeneration.Abbreviations: 4-(2-Aminoethyl) benzenesulfonyl fluoride hydrochloride (AEBSF); acid-sensing ion channels (ASICs); analysis of variance (ANOVA); bicinchoninic acid (BCA); brain-derived neurotrophic factor (BDNF); central nervous system (CNS); ciliary neurotrophic factor (CNTF); dimethyl sulfoxide (DMSO); endoplasmic reticulum (ER); ethylene glycol-bis(β-aminoethyl ether)-N,N,N’,N’-tetraacetic acid (EGTA); ethylenediaminetetraacetic acid (EDTA); Food and Drug Administration (FDA); glial fibrillary acidic protein (GFAP); glutamine synthetase (GS); intraocular pressure (IOP); kilodalton (kDa); Krebs-Ringer Buffer (KRB); optic nerve crush (ONC); phosphate-buffered saline (PBS); plasma membrane (PM); polymerase chain reaction (PCR); retinal ganglion cell (RGC); RNA Binding Protein With Multiple Splicing (RBPMS); room temperature (RT); standard error of the mean (SEM).

Conservation and variability of the pore-lining helices in P-loop channels

ABSTRACTThe family of P-loop channels, which play key roles in the cell physiology, is characterized by four membrane re-entering extracellular P-loops that connect eight transmembrane helices of the pore-forming domain. The X-ray and cryo-EM structures of the open- and closed-state channels show conserved state-dependent folding despite the sequences are very diverse. In sodium, calcium, TRPV and two-pore channels, the pore-lining helices contain conserved asparagines and may or may not include π-helix bulges. Comparison of the sequence- and 3D-alignemnts suggests that the asparagines appeared in evolution as insertions that are accommodated in two ways: by π-helix bulges, which preserve most of inter-segment contacts, or by twists of the C-terminal thirds and switch of inter-segment contacts. The two possibilities should be considered in homology modeling of ion channels and in structure-based interpretations of numerous experimental data on physiology, pathophysiology, pharmacology and toxicology of the channels.

Fractional Poisson-Nernst-Planck Model for Ion Channels I: Basic Formulations and Algorithms.

In this work, we propose a fractional Poisson-Nernst-Planck model to describe ion permeation in gated ion channels. Due to the intrinsic conformational changes, crowdedness in narrow channel pores, binding and trapping introduced by functioning units of channel proteins, ionic transport in the channel exhibits a power-law-like anomalous diffusion dynamics. We start from continuous-time random walk model for a single ion and use a long-tailed density distribution function for the particle jump waiting time, to derive the fractional Fokker-Planck equation. Then, it is generalized to the macroscopic fractional Poisson-Nernst-Planck model for ionic concentrations. Necessary computational algorithms are designed to implement numerical simulations for the proposed model, and the dynamics of gating current is investigated. Numerical simulations show that the fractional PNP model provides a more qualitatively reasonable match to the profile of gating currents from experimental observations. Meanwhile, the proposed model motivates new challenges in terms of mathematical modeling and computations.

Noise in Neuronal and Electronic Circuits: A General Modeling Framework and Non-Monte Carlo Simulation Techniques.

The brain is extremely energy efficient and remarkably robust in what it does despite the considerable variability and noise caused by the stochastic mechanisms in neurons and synapses. Computational modeling is a powerful tool that can help us gain insight into this important aspect of brain mechanism. A deep understanding and computational design tools can help develop robust neuromorphic electronic circuits and hybrid neuroelectronic systems. In this paper, we present a general modeling framework for biological neuronal circuits that systematically captures the nonstationary stochastic behavior of ion channels and synaptic processes. In this framework, fine-grained, discrete-state, continuous-time Markov chain models of both ion channels and synaptic processes are treated in a unified manner. Our modeling framework features a mechanism for the automatic generation of the corresponding coarse-grained, continuous-state, continuous-time stochastic differential equation models for neuronal variability and noise. Furthermore, we repurpose non-Monte Carlo noise analysis techniques, which were previously developed for analog electronic circuits, for the stochastic characterization of neuronal circuits both in time and frequency domain. We verify that the fast non-Monte Carlo analysis methods produce results with the same accuracy as computationally expensive Monte Carlo simulations. We have implemented the proposed techniques in a prototype simulator, where both biological neuronal and analog electronic circuits can be simulated together in a coupled manner.

Development of Neuron Ion Channel Model using Colored Noise Terms in the Conductance

The aim of this study is the ion channel model with noise variance as approximations to the Hodgkin-Huxley model proposed, due to the Hodgkin-Huxley model affected when inserting some colored noise terms inside the conductances, where those effects captured by colored noise because of the gate multiplicity. Firstly, it introduces the comparison of ion channel based on Fox, Lu and Linaro models. Additionally, in order to overcome the limitations of other parameter estimation methods, the proposed method fully constrains their models and obtains all model's capabilities of reproducing the data. Finally, the relationship between the sequence of colored noise and the spike frequency are simulated efficiently each gate compared with microscopic simulations of the stochastic Markov process method. In simulation results, the spiking rate generated from the proposed model very close to microscopic simulations and doesn’t effect by the membrane size.

Modeling and analysis for multi-state systems with discrete-time Markov regime-switching

The main focus of this paper is on the development of reliability measures for a repairable multi-state system which operates under dynamic regimes under the discrete-time hypothesis. The switching process of regimes is governed by a Markov chain, and the functioning process of the system follows another Markov chain with different transition probability matrices under different regimes. In terms of two chains as above, a new Markov chain is constructed to depict the evolution process of the dynamic system. For the regime consideration, some novel reliability indices are essential and firstly introduced in this paper. By means of hierarchical partitions for the new state space, Ion-Channel modeling theory and discrete-time Markov chain, the traditional and novel reliability and availability functions for the system under random regimes are easily obtained with the closed form solutions, such as two types of system reliabilities, two types of system point availabilities, two types of system multiple-point availabilities and the associated system multi-interval availabilities and so on. In addition, some probability distributions of sojourn times we are interested in are discussed and computed here. Finally, a numerical example is given to illustrate the results obtained in the paper.