Myokit: A simple interface to cardiac cellular electrophysiology.

Myokit is a new powerful and versatile software tool for modeling and simulation of cardiac cellular electrophysiology. Myokit consists of an easy-to-read modeling language, a graphical user interface, single and multi-cell simulation engines and a library of advanced analysis tools accessible through a Python interface. Models can be loaded from Myokit's native file format or imported from CellML. Model export is provided to C, MATLAB, CellML, CUDA and OpenCL. Patch-clamp data can be imported and used to estimate model parameters. In this paper, we review existing tools to simulate the cardiac cellular action potential to find that current tools do not cater specifically to model development and that there is a gap between easy-to-use but limited software and powerful tools that require strong programming skills from their users. We then describe Myokit's capabilities, focusing on its model description language, simulation engines and import/export facilities in detail. Using three examples, we show how Myokit can be used for clinically relevant investigations, multi-model testing and parameter estimation in Markov models, all with minimal programming effort from the user. This way, Myokit bridges a gap between performance, versatility and user-friendliness.

Stochastic pacing reveals the propensity to cardiac action potential alternans and uncovers its underlying dynamics.

KEY POINTS: Beat-to-beat alternation (alternans) of the cardiac action potential duration is known to precipitate life-threatening arrhythmias and can be driven by the kinetics of voltage-gated membrane currents or by instabilities in intracellular calcium fluxes. To prevent alternans and associated arrhythmias, suitable markers must be developed to quantify the susceptibility to alternans; previous theoretical studies showed that the eigenvalue of the alternating eigenmode represents an ideal marker of alternans. Using rabbit ventricular myocytes, we show that this eigenvalue can be estimated in practice by pacing these cells at intervals varying stochastically. We also show that stochastic pacing permits the estimation of further markers distinguishing between voltage-driven and calcium-driven alternans. Our study opens the perspective to use stochastic pacing during clinical investigations and in patients with implanted pacing devices to determine the susceptibility to, and the type of alternans, which are both important to guide preventive or therapeutic measures. ABSTRACT: Alternans of the cardiac action potential (AP) duration (APD) is a well-known arrhythmogenic mechanism. APD depends on several preceding diastolic intervals (DIs) and APDs, which complicates the prediction of alternans. Previous theoretical studies pinpointed a marker called λalt that directly quantifies how an alternating perturbation persists over successive APs. When the propensity to alternans increases, λalt decreases from 0 to -1. Our aim was to quantify λalt experimentally using stochastic pacing and to examine whether stochastic pacing allows discriminating between voltage-driven and Ca(2+) -driven alternans. APs were recorded in rabbit ventricular myocytes paced at cycle lengths (CLs) decreasing progressively and incorporating stochastic variations. Fitting APD with a function of two previous APDs and CLs permitted us to estimate λalt along with additional markers characterizing whether the dependence of APD on previous DIs or CLs is strong (typical for voltage-driven alternans) or weak (Ca(2+) -driven alternans). During the recordings, λalt gradually decreased from around 0 towards -1. Intermittent alternans appeared when λalt reached -0.8 and was followed by sustained alternans. The additional markers detected that alternans was Ca(2+) driven in control experiments and voltage driven in the presence of ryanodine. This distinction could be made even before alternans was manifest (specificity/sensitivity >80% for -0.4 > λalt  > -0.5). These observations were confirmed in a mathematical model of a rabbit ventricular myocyte. In conclusion, stochastic pacing allows the practical estimation of λalt to reveal the onset of alternans and distinguishes between voltage-driven and Ca(2+) -driven mechanisms, which is important since these two mechanisms may precipitate arrhythmias in different manners.

Delayed afterdepolarizations generate both triggers and a vulnerable substrate promoting reentry in cardiac tissue.

BACKGROUND: Delayed afterdepolarizations (DADs) have been well characterized as arrhythmia triggers, but their role in generating a tissue substrate vulnerable to reentry is not well understood. OBJECTIVE: The purpose of this study was to test the hypothesis that random DADs can self-organize to generate both an arrhythmia trigger and a vulnerable substrate simultaneously in cardiac tissue as a result of gap junction coupling. METHODS: Computer simulations in 1-dimensional cable and 2-dimensional tissue models were performed. The cellular DAD amplitude was varied by changing the strength of sarcoplasmic reticulum calcium release. Random DAD latency and amplitude in different cells were simulated using gaussian distributions. RESULTS: Depending on the strength of spontaneous sarcoplasmic reticulum calcium release and other conditions, random DADs in cardiac tissue resulted in the following behaviors: (1) triggered activity (TA); (2) a vulnerable tissue substrate causing unidirectional conduction block and reentry by inactivating sodium channels; (3) both triggers and a vulnerable substrate simultaneously by generating TA in regions next to regions with subthreshold DADs susceptible to unidirectional conduction block and reentry. The probability of the latter 2 behaviors was enhanced by reduced sodium channel availability, reduced gap junction coupling, increased tissue heterogeneity, and less synchronous DAD latency. CONCLUSION: DADs can self-organize in tissue to generate arrhythmia triggers, a vulnerable tissue substrate, and both simultaneously. Reduced sodium channel availability and gap junction coupling potentiate this mechanism of arrhythmias, which are relevant to a variety of heart disease conditions.

Computational tools to investigate genetic cardiac channelopathies.

The aim of this perspective article is to share with the community of ion channel scientists our thoughts and expectations regarding the increasing role that computational tools will play in the future of our field. The opinions and comments detailed here are the result of a 3-day long international exploratory workshop that took place in October 2013 and that was supported by the Swiss National Science Foundation.

Pro- and antiarrhythmic effects of ATP-sensitive potassium current activation on reentry during early afterdepolarization-mediated arrhythmias.

BACKGROUND: Under conditions promoting early afterdepolarizations (EADs), ventricular tissue can become bi-excitable, that is, capable of wave propagation mediated by either the Na current (INa) or the L-type calcium current (ICa,L), raising the possibility that ICa,L-mediated reentry may contribute to polymorphic ventricular tachycardia (PVT) and torsades de pointes. ATP-sensitive K current (IKATP) activation suppresses EADs, but the effects on ICa,L-mediated reentry are unknown. OBJECTIVE: To investigate the effects of IKATP activation on ICa,L-mediated reentry. METHODS: We performed optical voltage mapping in cultured neonatal rat ventricular myocyte monolayers exposed to BayK8644 and isoproterenol. The effects of pharmacologically activating IKATP with pinacidil were analyzed. RESULTS: In 13 monolayers with anatomic ICa,L-mediated reentry around a central obstacle, pinacidil (50 µM) converted ICa,L-mediated reentry to INa-mediated reentry. In 33 monolayers with functional ICa,L-mediated reentry (spiral waves), pinacidil terminated reentry in 17, converted reentry into more complex INa-mediated reentry resembling fibrillation in 12, and had no effect in 4. In simulated 2-dimensional bi-excitable tissue in which ICa,L- and INa-mediated wave fronts coexisted, slow IKATP activation (over minutes) reliably terminated rotors but rapid IKATP activation (over seconds) often converted ICa,L-mediated reentry to INa-mediated reentry resembling fibrillation. CONCLUSIONS: IKATP activation can have proarrhythmic effects on EAD-mediated arrhythmias if ICa,L-mediated reentry is present.

Loss of function of hNav1.5 by a ZASP1 mutation associated with intraventricular conduction disturbances in left ventricular noncompaction.

BACKGROUND: Defects of cytoarchitectural proteins can cause left ventricular noncompaction, which is often associated with conduction system diseases. We have previously identified a p.D117N mutation in the LIM domain-binding protein 3-encoding Z-band alternatively spliced PDZ motif gene (ZASP) in a patient with left ventricular noncompaction and conduction disturbances. We sought to investigate the role of p.D117N mutation in the LBD3 NM_001080114.1 isoform (ZASP1-D117N) for the regulation of cardiac sodium channel (Na(v)1.5) that plays an important role in the cardiac conduction system. METHODS AND RESULTS: Effects of ZASP1-wild-type and ZASP1-D117N on Na(v)1.5 were studied in human embryonic kidney-293 cells and neonatal rat cardiomyocytes. Patch-clamp study demonstrated that ZASP1-D117N significantly attenuated I(Na) by 27% in human embryonic kidney-293 cells and by 32% in neonatal rat cardiomyocytes. In addition, ZASP1-D117N rightward shifted the voltage-dependent activation and inactivation in both systems. In silico simulation using Luo-Rudy phase 1 model demonstrated that altered Na(v)1.5 function can reduce cardiac conduction velocity by 28% compared with control. Pull-down assays showed that both wild-type and ZASP1-D117N can complex with Na(v)1.5 and telethonin/T-Cap, which required intact PDZ domains. Immunohistochemical staining in neonatal rat cardiomyocytes demonstrates that ZASP1-D117N did not significantly disturb the Z-line structure. Disruption of cytoskeletal networks with 5-iodonaphthalene-1-sulfonyl homopiperazine and cytochalasin D abolished the effects of ZASP1-D117N on Na(v)1.5. CONCLUSIONS: ZASP1 can form protein complex with telethonin/T-Cap and Na(v)1.5. The left ventricular noncompaction-specific ZASP1 mutation can cause loss of function of Na(v)1.5, without significant alteration of the cytoskeletal protein complex. Our study suggests that electric remodeling can occur in left ventricular noncompaction subject because of a direct effect of mutant ZASP on Na(v)1.5.

Synchronization of early afterdepolarizations and arrhythmogenesis in heterogeneous cardiac tissue models.

Early afterdepolarizations (EADs) are linked to both triggered arrhythmias and reentrant arrhythmias by causing premature ventricular complexes (PVCs), focal excitations, or heterogeneous tissue substrates for reentry formation. However, a critical number of cells that synchronously exhibit EADs are needed to result in arrhythmia triggers and substrates in tissue. In this study, we use mathematical modeling and computer simulations to investigate EAD synchronization and arrhythmia induction in tissue models with random cell-to-cell variations. Our major observations are as follows. Random cell-to-cell variations in action potential duration without EAD presence do not cause large dispersion of refractoriness in well-coupled tissue. In the presence of phase-2 EADs, the cells may synchronously exhibit the same number of EADs or no EADs with a very small dispersion of refractoriness, or synchronize regionally to result in large dispersion of refractoriness. In the presence of phase-3 EADs, regional synchronization leads to propagating EADs, forming PVCs in tissue. Interestingly, even though the uncoupled cells exhibit either no EAD or only a single EAD, when these cells are coupled to form a tissue, more than one PVC can occur. When the PVCs occur at different locations and time, multifocal arrhythmias are triggered, with the foci shifting in space and time in an irregular manner. The focal arrhythmias either spontaneously terminate or degenerate into reentrant arrhythmias due to heterogeneities and spatiotemporal chaotic dynamics of the foci.

Dynamics of early afterdepolarization-mediated triggered activity in cardiac monolayers.

Early afterdepolarizations (EADs) are voltage oscillations that occur during the repolarizing phase of the cardiac action potential and cause cardiac arrhythmias in a variety of clinical settings. EADs occur in the setting of reduced repolarization reserve and increased inward-over-outward currents, which intuitively explains the repolarization delay but does not mechanistically explain the time-dependent voltage oscillations that are characteristic of EADs. In a recent theoretical study, we identified a dual Hopf-homoclinic bifurcation as a dynamical mechanism that causes voltage oscillations during EADs, depending on the amplitude and kinetics of the L-type Ca(2+) channel (LTCC) current relative to the repolarizing K(+) currents. Here we demonstrate this mechanism experimentally. We show that cardiac monolayers exposed to the LTCC agonists BayK8644 and isoproterenol produce EAD bursts that are suppressed by the LTCC blocker nitrendipine but not by the Na(+) current blocker tetrodoxin, depletion of intracellular Ca(2+) stores with thapsigargin and caffeine, or buffering of intracellular Ca(2+) with BAPTA-AM. These EAD bursts exhibited a key dynamical signature of the dual Hopf-homoclinic bifurcation mechanism, namely, a gradual slowing in the frequency of oscillations before burst termination. A detailed cardiac action potential model reproduced the experimental observations, and identified intracellular Na(+) accumulation as the likely mechanism for terminating EAD bursts. Our findings in cardiac monolayers provide direct support for the Hopf-homoclinic bifurcation mechanism of EAD-mediated triggered activity, and raise the possibility that this mechanism may also contribute to EAD formation in clinical settings such as long QT syndromes, heart failure, and increased sympathetic output.

Computational modeling and numerical methods for spatiotemporal calcium cycling in ventricular myocytes.

Intracellular calcium (Ca) cycling dynamics in cardiac myocytes is regulated by a complex network of spatially distributed organelles, such as sarcoplasmic reticulum (SR), mitochondria, and myofibrils. In this study, we present a mathematical model of intracellular Ca cycling and numerical and computational methods for computer simulations. The model consists of a coupled Ca release unit (CRU) network, which includes a SR domain and a myoplasm domain. Each CRU contains 10 L-type Ca channels and 100 ryanodine receptor channels, with individual channels simulated stochastically using a variant of Gillespie's method, modified here to handle time-dependent transition rates. Both the SR domain and the myoplasm domain in each CRU are modeled by 5 × 5 × 5 voxels to maintain proper Ca diffusion. Advanced numerical algorithms implemented on graphical processing units were used for fast computational simulations. For a myocyte containing 100 × 20 × 10 CRUs, a 1-s heart time simulation takes about 10 min of machine time on a single NVIDIA Tesla C2050. Examples of simulated Ca cycling dynamics, such as Ca sparks, Ca waves, and Ca alternans, are shown.

Uncovering the dynamics of cardiac systems using stochastic pacing and frequency domain analyses.

Alternans of cardiac action potential duration (APD) is a well-known arrhythmogenic mechanism which results from dynamical instabilities. The propensity to alternans is classically investigated by examining APD restitution and by deriving APD restitution slopes as predictive markers. However, experiments have shown that such markers are not always accurate for the prediction of alternans. Using a mathematical ventricular cell model known to exhibit unstable dynamics of both membrane potential and Ca²âº cycling, we demonstrate that an accurate marker can be obtained by pacing at cycle lengths (CLs) varying randomly around a basic CL (BCL) and by evaluating the transfer function between the time series of CLs and APDs using an autoregressive-moving-average (ARMA) model. The first pole of this transfer function corresponds to the eigenvalue (λ(alt)) of the dominant eigenmode of the cardiac system, which predicts that alternans occurs when λ(alt) ≤ -1. For different BCLs, control values of λ(alt) were obtained using eigenmode analysis and compared to the first pole of the transfer function estimated using ARMA model fitting in simulations of random pacing protocols. In all versions of the cell model, this pole provided an accurate estimation of λ(alt). Furthermore, during slow ramp decreases of BCL or simulated drug application, this approach predicted the onset of alternans by extrapolating the time course of the estimated λ(alt). In conclusion, stochastic pacing and ARMA model identification represents a novel approach to predict alternans without making any assumptions about its ionic mechanisms. It should therefore be applicable experimentally for any type of myocardial cell.

Spontaneous ventricular fibrillation in right ventricular failure secondary to chronic pulmonary hypertension.

BACKGROUND: Right ventricular failure (RVF) in pulmonary hypertension (PH) is associated with increased incidence of sudden death by a poorly explored mechanism. We test the hypothesis that PH promotes spontaneous ventricular fibrillation (VF) during a critical post-PH onset period characterized by a sudden increase in mortality. METHODS AND RESULTS: Rats received either a single subcutaneous dose of monocrotaline (MCT, 60 mg/kg) to induce PH-associated RVF (PH, n=24) or saline (control, n=17). Activation pattern of the RV-epicardial surface was mapped using voltage-sensitive dye in isolated Langendorff-perfused hearts along with single glass-microelectrode and ECG-recordings. MCT-injected rats developed severe PH by day 21 and progressed to RVF by approximately day 30. Rats manifested increased mortality, and ≈30% rats died suddenly and precipitously during 23-32 days after MCT. This fatal period was associated with the initiation of spontaneous VF by a focal mechanism in the RV, which was subsequently maintained by both focal and incomplete reentrant wave fronts. Microelectrode recordings from the RV-epicardium at the onset of focal activity showed early afterdepolarization-mediated triggered activity that led to VF. The onset of the RV cellular triggered beats preceded left ventricular depolarizations by 23±8 ms. The RV but not the left ventricular cardiomyocytes isolated during this fatal period manifested significant action potential duration prolongation, dispersion, and an increased susceptibility to depolarization-induced repetitive activity. No spontaneous VF was observed in any of the control hearts. RVF was associated with significantly reduced RV ejection fraction (P<0.001), RV hypertrophy (P<0.001), and RV fibrosis (P<0.01). The hemodynamic function of the LV and its structure were preserved. CONCLUSIONS: PH-induced RVF is associated with a distinct phase of increased mortality characterized by spontaneous VF arising from the RV by an early afterdepolarization-mediated triggered activity.

Differential conditions for early after-depolarizations and triggered activity in cardiomyocytes derived from transgenic LQT1 and LQT2 rabbits.

Early after-depolarization (EAD), or abnormal depolarization during the plateau phase of action potentials, is a hallmark of long-QT syndrome (LQTS). More than 13 genes have been identified as responsible for LQTS, and elevated risks for EADs may depend on genotypes, such as exercise in LQT1 vs. sudden arousal in LQT2 patients. We investigated mechanisms underlying different high-risk conditions that trigger EADs using transgenic rabbit models of LQT1 and LQT2, which lack I(Ks) and I(Kr) (slow and fast components of delayed rectifying K(+) current), respectively. Single-cell patch-clamp studies show that prolongation of action potential duration (APD) can be further enhanced by lowering extracellular potassium concentration ([K(+)](o)) from 5.4 to 3.6 mm. However, only LQT2 myocytes developed spontaneous EADs following perfusion with lower [K(+)](o), while there was no EAD formation in littermate control (LMC) or LQT1 myocytes, although APDs were also prolonged in LMC myocytes and LQT1 myocytes. Isoprenaline (ISO) prolonged APDs and triggered EADs in LQT1 myocytes in the presence of lower [K(+)](o). In contrast, continuous ISO perfusion diminished APD prolongation and reduced the incidence of EADs in LQT2 myocytes. These different effects of ISO on LQT1 and LQT2 were verified by optical mapping of the whole heart, suggesting that ISO-induced EADs are genotype specific. Further voltage-clamp studies revealed that ISO increases L-type calcium current (I(Ca)) faster than I(Ks) (time constant 9.2 s for I(Ca) and 43.6 s for I(Ks)), and computer simulation demonstrated a high-risk window of EADs in LQT2 during ISO perfusion owing to mismatch in the time courses of I(Ca) and I(Ks), which may explain why a sympathetic surge rather than high sympathetic tone can be an effective trigger of EADs in LQT2 perfused hearts. In summary, EAD formation is genotype specific, such that EADs can be elicited in LQT2 myocytes simply by lowering [K(+)](o), while LQT1 myocytes require sympathetic stimulation. Slower activation of I(Ks) than of I(Ca) by ISO may explain why different sympathetic modes, i.e. sympathetic surge vs. high sympathetic tone, are associated with polymorphic ventricular tachycardia in LQTS patients.

Bi-stable wave propagation and early afterdepolarization-mediated cardiac arrhythmias.

BACKGROUND: In normal atrial and ventricular tissue, the electrical wavefronts are mediated by the fast sodium current (I(Na)), whereas in sinoatrial and atrioventricular nodal tissue, conduction is mediated by the slow L-type calcium current (I(Ca,L)). However, it has not been shown whether the same tissue can exhibit both the I(Na)-mediated and the I(Ca,L)-mediated conduction. OBJECTIVE: This study sought to test the hypothesis that bi-stable cardiac wave conduction, mediated by I(Na) and I(Ca,L), respectively, can occur in the same tissue under conditions promoting early afterdepolarizations (EADs), and to study how this novel wave dynamics is related to the mechanisms of EAD-mediated arrhythmias. METHODS: Computer models of two-dimensional (2D) tissue with a physiologically detailed action potential model were used to study the bi-stable wave dynamics. Theoretical predictions were tested experimentally by optical mapping in neonatal rat ventricular myocyte monolayers. RESULTS: In the same 2D homogeneous tissue, we could induce spiral waves that are mediated by either I(Na) or I(Ca,L) under conditions in which the action potential model exhibited EADs. This bi-stable wave propagation behavior was similar to bi-stability shown in many other nonlinear systems. Because the bi-stable states are also excitable, we call this novel behavior bi-excitability. In a 2D heterogeneous tissue, the I(Ca,L)-mediated spiral wave meanders, giving rise to a twisting electrocardiographic QRS axis, resembling torsades de pointes, whereas the coexistence and interplay between the I(Na)-mediated wavefronts and I(Ca,L)-mediated wavefronts give rise to polymorphic ventricular tachycardia. We also present experimental evidence for bi-excitability under EAD-promoting conditions in neonatal rat ventricular myocyte monolayers exposed to BayK8644 and isoproterenol. CONCLUSION: Under EAD-prone conditions, both I(Na)-mediated conduction and I(Ca,L)-mediated conduction can occur in the same tissue. These novel wave dynamics may be responsible for certain EAD-mediated arrhythmias, such as torsades de pointes and polymorphic ventricular tachycardia.

Effects of stochastic channel gating and distribution on the cardiac action potential.

Ion channels exhibit stochastic conformational changes determining their gating behavior. In addition, the process of protein turnover leads to a natural variability of the number of membrane and gap junctional channels. Nevertheless, in computational models, these two aspects are scarcely considered and their impacts are largely unknown. We investigated the effects of stochastic current fluctuations and channel distributions on action potential duration (APD), intercellular conduction delays (ICDs) and conduction blocks using a modified ventricular cell model (Rudy et al.) with Markovian formulations of the principal ion currents (to simulate their stochastic open-close gating behavior) and with channel counts drawn from Poisson distributions (to simulate their natural variability). In single cells, APD variability (coefficient of variation: 1.6% at BCL=1000ms) was essentially caused by stochastic channel gating of I(Ks), persistent I(Na) and I(Ca,L). In cell strands, ICD variability induced by stochastic channel gating and Poissonian channel distributions was low under normal conditions. Nonetheless, at low intercellular coupling levels, Poissonian gap junctional channel distribution resulted in a large ICD variability (coefficient of variation >20%), highly heterogeneous conduction patterns and conduction blocks. Therefore, the stochastic behavior of current fluctuations and channel distributions can contribute to the heterogeneity of conduction patterns and to conduction block, as observed previously in experiments in cardiac tissue with altered intercellular coupling.

Alternans resonance and propagation block during supernormal conduction in cardiac tissue with decreased [K(+)](o).

Cardiac restitution is an important factor in arrhythmogenesis. Steep positive action potential duration and conduction velocity (CV) restitution slopes promote alternans and reentrant arrhythmias. We examined the consequences of supernormal conduction (characterized by a negative CV restitution slope) on patterns of conduction and alternans in strands of Luo-Rudy model cells and in cultured cardiac cell strands. Interbeat intervals (IBIs) were analyzed as a function of distance during S1S2 protocols and during pacing at alternating cycle lengths. Supernormal conduction was induced by decreasing [K(+)](o). In control [K(+)](o) simulations, S1S2 intervals converged toward basic cycle length with a length constant determined by both CV and the CV restitution slope. During alternant pacing, the amplitude of IBI alternans converged with a shorter length constant, determined also by the action potential duration restitution slope. In contrast, during supernormal conduction, S1S2 intervals and the amplitude of alternans diverged. This amplification (resonance) led to phase-locked or more complex alternans patterns, and then to distal conduction block. The convergence/divergence of IBIs was verified in the cultured strands, in which naturally occurring tissue heterogeneities resulted in prominent discontinuities of the spatial IBI profiles. We conclude that supernormal conduction potentiates alternans and spatial analysis of IBIs represents a powerful method to locate tissue heterogeneities.

The transfer functions of cardiac tissue during stochastic pacing.

The restitution properties of cardiac action potential duration (APD) and conduction velocity (CV) are important factors in arrhythmogenesis. They determine alternans, wavebreak, and the patterns of reentrant arrhythmias. We developed a novel approach to characterize restitution using transfer functions. Transfer functions relate an input and an output quantity in terms of gain and phase shift in the complex frequency domain. We derived an analytical expression for the transfer function of interbeat intervals (IBIs) during conduction from one site (input) to another site downstream (output). Transfer functions can be efficiently obtained using a stochastic pacing protocol. Using simulations of conduction and extracellular mapping of strands of neonatal rat ventricular myocytes, we show that transfer functions permit the quantification of APD and CV restitution slopes when it is difficult to measure APD directly. We find that the normally positive CV restitution slope attenuates IBI variations. In contrast, a negative CV restitution slope (induced by decreasing extracellular [K(+)]) amplifies IBI variations with a maximum at the frequency of alternans. Hence, it potentiates alternans and renders conduction unstable, even in the absence of APD restitution. Thus, stochastic pacing and transfer function analysis represent a powerful strategy to evaluate restitution and the stability of conduction.

The Hindmarsh-Rose neuron model: bifurcation analysis and piecewise-linear approximations.

This paper provides a global picture of the bifurcation scenario of the Hindmarsh-Rose model. A combination between simulations and numerical continuations is used to unfold the complex bifurcation structure. The bifurcation analysis is carried out by varying two bifurcation parameters and evidence is given that the structure that is found is universal and appears for all combinations of bifurcation parameters. The information about the organizing principles and bifurcation diagrams are then used to compare the dynamics of the model with that of a piecewise-linear approximation, customized for circuit implementation. A good match between the dynamical behaviors of the models is found. These results can be used both to design a circuit implementation of the Hindmarsh-Rose model mimicking the diversity of neural response and as guidelines to predict the behavior of the model as well as its circuit implementation as a function of parameters.

Predicting single spikes and spike patterns with the Hindmarsh-Rose model.

Most simple neuron models are only able to model traditional spiking behavior. As physiologists discover and classify different electrical phenotypes, computational neuroscientists become interested in using simple phenomenological models that can exhibit these different types of spiking patterns. The Hindmarsh-Rose model is a three-dimensional relaxation oscillator which can show both spiking and bursting patterns and has a chaotic regime. We test the predictive powers of the Hindmarsh-Rose model on two different test databases. We show that the Hindmarsh-Rose model can predict the spiking response of rat layer 5 neocortical pyramidal neurons on a stochastic input signal with a precision comparable to the best known spiking models. We also show that the Hindmarsh-Rose model can capture qualitatively the electrical footprints in a database of different types of neocortical interneurons. When the model parameters are fit from sub-threshold measurements only, the model still captures well the electrical phenotype, which suggests that the sub-threshold signals contain information about the firing patterns of the different neurons.

Synchronization of bursting neurons: what matters in the network topology.

We study the influence of coupling strength and network topology on synchronization behavior in pulse-coupled networks of bursting Hindmarsh-Rose neurons. Surprisingly, we find that the stability of the completely synchronous state in such networks only depends on the number of signals each neuron receives, independent of all other details of the network topology. This is in contrast with linearly coupled bursting neurons where complete synchrony strongly depends on the network structure and number of cells. Through analysis and numerics, we show that the onset of synchrony in a network with any coupling topology admitting complete synchronization is ensured by one single condition.