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 neuron

Neuron models of the generic bifurcation type:network analysis and data modeling

Minimal nonlinear dynamic neuron models of the generic bifurcation type may provide the middle way between the detailed models favored by experimentalists and the simplified threshold and rate model of computational neuroscientists. This thesis investigates to which extent generic bifurcation type models grasp the essential dynamical features that may turn out play a role in cooperative neural behavior. The thesis considers two neuron models, of increasing complexity, and one model of synaptic interactions. The FitzHugh-Nagumo model is a simple two-dimensional model capable only of spiking behavior, and the Hindmarsh-Rose model is a three-dimensional model capable of more complex dynamics such as bursting and chaos. The model for synaptic interactions is a memory-less nonlinear function, known as fast threshold modulation (FTM). By means of a combination of nonlinear system theory and bifurcation analysis the dynamical features of the two models are extracted. The most important feature of the FitzHugh-Nagumo model is its dynamic threshold: the spike threshold does not only depend on the absolute value, but also on the amplitude of changes in the membrane potential. Part of the very complex, intriguing bifurcation structure of the Hindmarsh-Rose model is revealed. By considering basic networks of FTM-coupled FitzHugh-Nagumo (spiking) or Hindmarsh-Rose (bursting) neurons, two main cooperative phenomena, synchronization and coincidence detections, are addressed. In both cases it is illustrated that pulse coupling in combination with the intrinsic dynamics of the models provides robustness. In large scale networks of FTM-coupled bursting neurons, the stability of complete synchrony is independent from the network topology and depends only on the number of inputs to each neuron. The analytical results are obtained under very restrictive and biologically implausible hypotheses, but simulations show that the theoretical predictions hold in more realistic cases as well. Finally, the realism of the models is put to a test by identification of their parameters from in vitro measurements. The identification problem is addressed by resorting to standard techniques combined with heuristics based on the results of the reported mathematical analysis and on a priori knowledge from neuroscience. The FitzHugh-Nagumo model is only able to model pyramidal neurons and even then performs worse than simple threshold models; it should be used only when the advantages of the more realistic threshold mechanism are prevalent. The Hindmarsh-Rose model can model much of the diversity of neocortical neurons; it can be used as a model in the study of heterogeneous networks and as a realistic model of a pyramidal neuron

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

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

Analgosedation in paediatric severe traumatic brain injury (TBI): practice, pitfalls and possibilities

Analgosedation is a fundamental part of traumatic brain injury (TBI) treatment guidelines, encompassing both first and second tier supportive strategies. Worldwide analgosedation practices continue to be heterogeneous due to the low level of evidence in treatment guidelines (level III) and the choice of analgosedative drugs is made by the treating clinician. Current practice is thus empirical and may result in unfavourable (often hemodynamic) side effects. This article presents an overview of current analgosedation practices in the paediatric intensive care unit (PICU) and addresses pitfalls both in the short and long term. We discuss innovative (pre-)clinical research that can provide the framework for initiatives to improve our pharmacological understanding of analgesic and sedative drugs used in paediatric severe TBI and ultimately facilitate steps towards evidence-based and precision pharmacotherapy in this vulnerable patient group

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

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 Ca2+ 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 (λalt) of the dominant eigenmode of the cardiac system, which predicts that alternans occurs when λalt≤−1. For different BCLs, control values of λalt 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 λalt. 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 λalt. 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