A general pattern of non-spiking neuron dynamics under the effect of potassium and calcium channel modifications.

Electrical activity of excitable cells results from ion exchanges through cell membranes, so that genetic or epigenetic changes in genes encoding ion channels are likely to affect neuronal electrical signaling throughout the brain. There is a large literature on the effect of variations in ion channels on the dynamics of spiking neurons that represent the main type of neurons found in the vertebrate nervous systems. Nevertheless, non-spiking neurons are also ubiquitous in many nervous tissues and play a critical role in the processing of some sensory systems. To our knowledge, however, how conductance variations affect the dynamics of non-spiking neurons has never been assessed. Based on experimental observations reported in the biological literature and on mathematical considerations, we first propose a phenotypic classification of non-spiking neurons. Then, we determine a general pattern of the phenotypic evolution of non-spiking neurons as a function of changes in calcium and potassium conductances. Furthermore, we study the homeostatic compensatory mechanisms of ion channels in a well-posed non-spiking retinal cone model. We show that there is a restricted range of ion conductance values for which the behavior and phenotype of the neuron are maintained. Finally, we discuss the implications of the phenotypic changes of individual cells at the level of neuronal network functioning of the C. elegans worm and the retina, which are two non-spiking nervous tissues composed of neurons with various phenotypes.

Conductance-Based Phenomenological Nonspiking Model: A Dimensionless and Simple Model That Reliably Predicts the Effects of Conductance Variations on Nonspiking Neuronal Dynamics.

The modeling of single neurons has proven to be an indispensable tool in deciphering the mechanisms underlying neural dynamics and signal processing. In that sense, two types of single-neuron models are extensively used: the conductance-based models (CBMs) and the so-called phenomenological models, which are often opposed in their objectives and their use. Indeed, the first type aims to describe the biophysical properties of the neuron cell membrane that underlie the evolution of its potential, while the second one describes the macroscopic behavior of the neuron without taking into account all of its underlying physiological processes. Therefore, CBMs are often used to study "low-level" functions of neural systems, while phenomenological models are limited to the description of "high-level" functions. In this letter, we develop a numerical procedure to endow a dimensionless and simple phenomenological nonspiking model with the capability to describe the effect of conductance variations on nonspiking neuronal dynamics with high accuracy. The procedure allows determining a relationship between the dimensionless parameters of the phenomenological model and the maximal conductances of CBMs. In this way, the simple model combines the biological plausibility of CBMs with the high computational efficiency of phenomenological models, and thus may serve as a building block for studying both high-level and low-level functions of nonspiking neural networks. We also demonstrate this capability in an abstract neural network inspired by the retina and C. elegans networks, two important nonspiking nervous tissues.

Cell to network computational model of the epileptic human hippocampus suggests specific roles of network and channel dysfunctions in the ictal and interictal oscillations.

The mechanisms underlying the generation of hippocampal epileptic seizures and interictal events and their interactions with the sleep-wake cycle are not yet fully understood. Indeed, medial temporal lobe epilepsy is associated with hippocampal abnormalities both at the neuronal (channelopathies, impaired potassium and chloride dynamics) and network level (neuronal and axonal loss, mossy fiber sprouting), with more frequent seizures during wakefulness compared with slow-wave sleep. In this article, starting from our previous computational modeling work of the hippocampal formation based on realistic topology and synaptic connectivity, we study the role of micro- and mesoscale pathological conditions of the epileptic hippocampus in the generation and maintenance of seizure-like theta and interictal oscillations. We show, through the simulations of hippocampal activity during slow-wave sleep and wakefulness that: (i) both mossy fiber sprouting and sclerosis account for seizure-like theta activity, (ii) but they have antagonist effects (seizure-like activity occurrence increases with sprouting but decreases with sclerosis), (iii) though impaired potassium and chloride dynamics have little influence on the generation of seizure-like activity, they do play a role on the generation of interictal patterns, and (iv) seizure-like activity and fast ripples are more likely to occur during wakefulness and interictal spikes during sleep.

A detailed anatomical and mathematical model of the hippocampal formation for the generation of sharp-wave ripples and theta-nested gamma oscillations.

The mechanisms underlying the broad variety of oscillatory rhythms measured in the hippocampus during the sleep-wake cycle are not yet fully understood. In this article, we propose a computational model of the hippocampal formation based on a realistic topology and synaptic connectivity, and we analyze the effect of different changes on the network, namely the variation of synaptic conductances, the variations of the CAN channel conductance and the variation of inputs. By using a detailed simulation of intracerebral recordings, we show that this is able to reproduce both the theta-nested gamma oscillations that are seen in awake brains and the sharp-wave ripple complexes measured during slow-wave sleep. The results of our simulations support the idea that the functional connectivity of the hippocampus, modulated by the sleep-wake variations in Acetylcholine concentration, is a key factor in controlling its rhythms.

The CAN-In network: A biologically inspired model for self-sustained theta oscillations and memory maintenance in the hippocampus.

During working memory tasks, the hippocampus exhibits synchronous theta-band activity, which is thought to be correlated with the short-term memory maintenance of salient stimuli. Recent studies indicate that the hippocampus contains the necessary circuitry allowing it to generate and sustain theta oscillations without the need of extrinsic drive. However, the cellular and network mechanisms supporting synchronous rhythmic activity are far from being fully understood. Based on electrophysiological recordings from hippocampal pyramidal CA1 cells, we present a possible mechanism for the maintenance of such rhythmic theta-band activity in the isolated hippocampus. Our model network, based on the Hodgkin-Huxley formalism, comprising pyramidal neurons equipped with calcium-activated nonspecific cationic (CAN) ion channels, is able to generate and sustain synchronized theta oscillations (4-12 Hz), following a transient stimulation. The synchronous network activity is maintained by an intrinsic CAN current (ICAN ), in the absence of constant external input. When connecting the pyramidal-CAN network to fast-spiking inhibitory interneurons, the dynamics of the model reveal that feedback inhibition improves the robustness of fast theta oscillations, by tightening the synchronization of the pyramidal CAN neurons. The frequency and power of the theta oscillations are both modulated by the intensity of the ICAN , which allows for a wide range of oscillation rates within the theta band. This biologically plausible mechanism for the maintenance of synchronous theta oscillations in the hippocampus aims at extending the traditional models of septum-driven hippocampal rhythmic activity. © 2017 Wiley Periodicals, Inc.

Study of GABAergic extra-synaptic tonic inhibition in single neurons and neural populations by traversing neural scales: application to propofol-induced anaesthesia.

Anaesthetic agents are known to affect extra-synaptic GABAergic receptors, which induce tonic inhibitory currents. Since these receptors are very sensitive to small concentrations of agents, they are supposed to play an important role in the underlying neural mechanism of general anaesthesia. Moreover anaesthetic agents modulate the encephalographic activity (EEG) of subjects and hence show an effect on neural populations. To understand better the tonic inhibition effect in single neurons on neural populations and hence how it affects the EEG, the work considers single neurons and neural populations in a steady-state and studies numerically and analytically the modulation of their firing rate and nonlinear gain with respect to different levels of tonic inhibition. We consider populations of both type-I (Leaky Integrate-and-Fire model) and type-II (Morris-Lecar model) neurons. To bridge the single neuron description to the population description analytically, a recently proposed statistical approach is employed which allows to derive new analytical expressions for the population firing rate for type-I neurons. In addition, the work shows the derivation of a novel transfer function for type-I neurons as considered in neural mass models and studies briefly the interaction of synaptic and extra-synaptic inhibition. We reveal a strong subtractive and divisive effect of tonic inhibition in type-I neurons, i.e. a shift of the firing rate to higher excitation levels accompanied by a change of the nonlinear gain. Tonic inhibition shortens the excitation window of type-II neurons and their populations while maintaining the nonlinear gain. The gained results are interpreted in the context of recent experimental findings under propofol-induced anaesthesia.

Automated parameter estimation of the Hodgkin-Huxley model using the differential evolution algorithm: application to neuromimetic analog integrated circuits.

We propose a new estimation method for the characterization of the Hodgkin-Huxley formalism. This method is an alternative technique to the classical estimation methods associated with voltage clamp measurements. It uses voltage clamp type recordings, but is based on the differential evolution algorithm. The parameters of an ionic channel are estimated simultaneously, such that the usual approximations of classical methods are avoided and all the parameters of the model, including the time constant, can be correctly optimized. In a second step, this new estimation technique is applied to the automated tuning of neuromimetic analog integrated circuits designed by our research group. We present a tuning example of a fast spiking neuron, which reproduces the frequency-current characteristics of the reference data, as well as the membrane voltage behavior. The final goal of this tuning is to interconnect neuromimetic chips as neural networks, with specific cellular properties, for future theoretical studies in neuroscience.

Reactivation, replay, and preplay: how it might all fit together.

Sequential activation of neurons that occurs during "offline" states, such as sleep or awake rest, is correlated with neural sequences recorded during preceding exploration phases. This so-called reactivation, or replay, has been observed in a number of different brain regions such as the striatum, prefrontal cortex, primary visual cortex and, most prominently, the hippocampus. Reactivation largely co-occurs together with hippocampal sharp-waves/ripples, brief high-frequency bursts in the local field potential. Here, we first review the mounting evidence for the hypothesis that reactivation is the neural mechanism for memory consolidation during sleep. We then discuss recent results that suggest that offline sequential activity in the waking state might not be simple repetitions of previously experienced sequences. Some offline sequential activity occurs before animals are exposed to a novel environment for the first time, and some sequences activated offline correspond to trajectories never experienced by the animal. We propose a conceptual framework for the dynamics of offline sequential activity that can parsimoniously describe a broad spectrum of experimental results. These results point to a potentially broader role of offline sequential activity in cognitive functions such as maintenance of spatial representation, learning, or planning.

Design of Experiments and Sobol' sensitivity analysis of a hippocampus computational model.

The hippocampus is a brain area involved in many memory processes. This structure can also be affected in neurological diseases such as mesial temporal lobe epilepsy. A better understanding of its electrophysiological activity could benefit both the neuroscientific and clinical communities. We proposed, in a previous paper, a detailed bio-realistic conductance-based mathematical model of more than thirty thousand neurons to reproduce the main oscillatory features of the healthy hippocampus during slow-wave sleep and wakefulness, from slow to very fast frequencies. One big challenge of this model is its parametrization. The aim of the present work is to combine neuroscientific expertise and systematic yet efficient exploration of the highly dimensional parameter space using well defined identification methods, namely the design of experiments and the Sobol's sensitivity analysis.

Simulation of Large Scale Neural Models With Event-Driven Connectivity Generation.

Accurate simulations of brain structures is a major problem in neuroscience. Many works are dedicated to design better models or to develop more efficient simulation schemes. In this paper, we propose a hybrid simulation scheme that combines time-stepping second-order integration of Hodgkin-Huxley (HH) type neurons with event-driven updating of the synaptic currents. As the HH model is a continuous model, there is no explicit spike events. Thus, in order to preserve the accuracy of the integration method, a spike detection algorithm is developed that accurately determines spike times. This approach allows us to regenerate the outgoing connections at each event, thereby avoiding the storage of the connectivity. Consequently, memory consumption is significantly reduced while preserving execution time and accuracy of the simulations, especially the spike times of detailed point neuron models. The efficiency of the method, implemented in the SiReNe software, is demonstrated by the simulation of a striatum model which consists of more than 106 neurons and 108 synapses (each neuron has a fan-out of 504 post-synaptic neurons), under normal and Parkinson's conditions.

Optimal Model Parameter Estimation from EEG Power Spectrum Features Observed during General Anesthesia.

Mathematical modeling is a powerful tool that enables researchers to describe the experimentally observed dynamics of complex systems. Starting with a robust model including model parameters, it is necessary to choose an appropriate set of model parameters to reproduce experimental data. However, estimating an optimal solution of the inverse problem, i.e., finding a set of model parameters that yields the best possible fit to the experimental data, is a very challenging problem. In the present work, we use different optimization algorithms based on a frequentist approach, as well as Monte Carlo Markov Chain methods based on Bayesian inference techniques to solve the considered inverse problems. We first probe two case studies with synthetic data and study models described by a stochastic non-delayed linear second-order differential equation and a stochastic linear delay differential equation. In a third case study, a thalamo-cortical neural mass model is fitted to the EEG spectral power measured during general anesthesia induced by anesthetics propofol and desflurane. We show that the proposed neural mass model fits very well to the observed EEG power spectra, particularly to the power spectral peaks within δ - (0 - 4 Hz) and α - (8 - 13 Hz) frequency ranges. Furthermore, for each case study, we perform a practical identifiability analysis by estimating the confidence regions of the parameter estimates and interpret the corresponding correlation and sensitivity matrices. Our results indicate that estimating the model parameters from analytically computed spectral power, we are able to accurately estimate the unknown parameters while avoiding the computational costs due to numerical integration of the model equations.

Tunable neuromimetic integrated system for emulating cortical neuron models.

Nowadays, many software solutions are currently available for simulating neuron models. Less conventional than software-based systems, hardware-based solutions generally combine digital and analog forms of computation. In previous work, we designed several neuromimetic chips, including the Galway chip that we used for this paper. These silicon neurons are based on the Hodgkin-Huxley formalism and they are optimized for reproducing a large variety of neuron behaviors thanks to tunable parameters. Due to process variation and device mismatch in analog chips, we use a full-custom fitting method in voltage-clamp mode to tune our neuromimetic integrated circuits. By comparing them with experimental electrophysiological data of these cells, we show that the circuits can reproduce the main firing features of cortical cell types. In this paper, we present the experimental measurements of our system which mimic the four most prominent biological cells: fast spiking, regular spiking, intrinsically bursting, and low-threshold spiking neurons into analog neuromimetic integrated circuit dedicated to cortical neuron simulations. This hardware and software platform will allow to improve the hybrid technique, also called "dynamic-clamp," that consists of connecting artificial and biological neurons to study the function of neuronal circuits.

Real-time simulation of biologically realistic stochastic neurons in VLSI.

Neuronal variability has been thought to play an important role in the brain. As the variability mainly comes from the uncertainty in biophysical mechanisms, stochastic neuron models have been proposed for studying how neurons compute with noise. However, most papers are limited to simulating stochastic neurons in a digital computer. The speed and the efficiency are thus limited especially when a large neuronal network is of concern. This brief explores the feasibility of simulating the stochastic behavior of biological neurons in a very large scale integrated (VLSI) system, which implements a programmable and configurable Hodgkin-Huxley model. By simply injecting noise to the VLSI neuron, various stochastic behaviors observed in biological neurons are reproduced realistically in VLSI. The noise-induced variability is further shown to enhance the signal modulation of a neuron. These results point toward the development of analog VLSI systems for exploring the stochastic behaviors of biological neuronal networks in large scale.