Robust Modulation of Integrate-and-Fire Models.

By controlling the state of neuronal populations, neuromodulators ultimately affect behavior. A key neuromodulation mechanism is the alteration of neuronal excitability via the modulation of ion channel expression. This type of neuromodulation is normally studied with conductance-based models, but those models are computationally challenging for large-scale network simulations needed in population studies. This article studies the modulation properties of the multiquadratic integrate-and-fire model, a generalization of the classical quadratic integrate-and-fire model. The model is shown to combine the computational economy of integrate-and-fire modeling and the physiological interpretability of conductance-based modeling. It is therefore a good candidate for affordable computational studies of neuromodulation in large networks

Extracting non-linear integrate-and-fire models from experimental data using dynamic I–V curves

The dynamic I–V curve method was recently introduced for the efficient experimental generation of reduced neuron models. The method extracts the response properties of a neuron while it is subject to a naturalistic stimulus that mimics in vivo-like fluctuating synaptic drive. The resulting history-dependent, transmembrane current is then projected onto a one-dimensional current–voltage relation that provides the basis for a tractable non-linear integrate-and-fire model. An attractive feature of the method is that it can be used in spike-triggered mode to quantify the distinct patterns of post-spike refractoriness seen in different classes of cortical neuron. The method is first illustrated using a conductance-based model and is then applied experimentally to generate reduced models of cortical layer-5 pyramidal cells and interneurons, in injected-current and injected- conductance protocols. The resulting low-dimensional neuron models—of the refractory exponential integrate-and-fire type—provide highly accurate predictions for spike-times. The method therefore provides a useful tool for the construction of tractable models and rapid experimental classification of cortical neurons

Predicting spike times of a detailed conductance- based neuron model driven by stochastic spike arrival

Reduced models of neuronal activity such as Integrate-and-Fire models allow a description of neuronal dynamics in simple, intuitive terms and are easy to simulate numerically. We present a method to fit an Integrate-and-Fire-type model of neuronal activity, namely a modified version of the Spike Response Model, to a detailed Hodgkin-Huxley-type neuron model driven by stochastic spike arrival. In the Hogkin-Huxley model, spike arrival at the synapse is modeled by a change of synaptic conductance. For such conductance spike input, more than 70% of the postsynaptic action potentials can be predicted with the correct timing by the Integrate-and-Fire-type model. The modified Spike Response Model is based upon a linearized theory of conductance-driven Integrate-and-Fire neuron

Extracting non-linear integrate-and-fire models from experimental data using dynamic I - V curves

The dynamic I-V curve method was recently introduced for the efficient experimental generation of reduced neuron models. The method extracts the response properties of a neuron while it is subject to a naturalistic stimulus that mimics in vivo-like fluctuating synaptic drive. The resulting history-dependent, transmembrane current is then projected onto a one-dimensional current-voltage relation that provides the basis for a tractable non-linear integrate-and-fire model. An attractive feature of the method is that it can be used in spike-triggered mode to quantify the distinct patterns of post-spike refractoriness seen in different classes of cortical neuron. The method is first illustrated using a conductance-based model and is then applied experimentally to generate reduced models of cortical layer-5 pyramidal cells and interneurons, in injected-current and injected- conductance protocols. The resulting low-dimensional neuron models—of the refractory exponential integrate-and-fire type—provide highly accurate predictions for spike-times. The method therefore provides a useful tool for the construction of tractable models and rapid experimental classification of cortical neuron

Dynamics and spike trains statistics in conductance-based Integrate-and-Fire neural networks with chemical and electric synapses

We investigate the effect of electric synapses (gap junctions) on collective neuronal dynamics and spike statistics in a conductance-based Integrate-and-Fire neural network, driven by a Brownian noise, where conductances depend upon spike history. We compute explicitly the time evolution operator and show that, given the spike-history of the network and the membrane potentials at a given time, the further dynamical evolution can be written in a closed form. We show that spike train statistics is described by a Gibbs distribution whose potential can be approximated with an explicit formula, when the noise is weak. This potential form encompasses existing models for spike trains statistics analysis such as maximum entropy models or Generalized Linear Models (GLM). We also discuss the different types of correlations: those induced by a shared stimulus and those induced by neurons interactions.Comment: 42 pages, 1 figure, submitte

On Dynamics of Integrate-and-Fire Neural Networks with Conductance Based Synapses

We present a mathematical analysis of a networks with Integrate-and-Fire neurons and adaptive conductances. Taking into account the realistic fact that the spike time is only known within some \textit{finite} precision, we propose a model where spikes are effective at times multiple of a characteristic time scale $\delta$, where $\delta$ can be \textit{arbitrary} small (in particular, well beyond the numerical precision). We make a complete mathematical characterization of the model-dynamics and obtain the following results. The asymptotic dynamics is composed by finitely many stable periodic orbits, whose number and period can be arbitrary large and can diverge in a region of the synaptic weights space, traditionally called the "edge of chaos", a notion mathematically well defined in the present paper. Furthermore, except at the edge of chaos, there is a one-to-one correspondence between the membrane potential trajectories and the raster plot. This shows that the neural code is entirely "in the spikes" in this case. As a key tool, we introduce an order parameter, easy to compute numerically, and closely related to a natural notion of entropy, providing a relevant characterization of the computational capabilities of the network. This allows us to compare the computational capabilities of leaky and Integrate-and-Fire models and conductance based models. The present study considers networks with constant input, and without time-dependent plasticity, but the framework has been designed for both extensions.Comment: 36 pages, 9 figure

Spike Train Statistics from Empirical Facts to Theory: The Case of the Retina

International audienceThis chapter focuses on methods from statistical physics and probability theory allowing the analysis of spike trains in neural networks. Taking as an example the retina we present recent works attempting to understand how retina ganglion cells encode the information transmitted to the visual cortex via the optical nerve, by analyzing their spike train statistics. We compare the maximal entropy models used in the literature of retina spike train analysis to rigorous results establishing the exact form of spike train statistics in conductance-based Integrate-and-Fire neural networks

KInNeSS: A Modular Framework for Computational Neuroscience

Making use of very detailed neurophysiological, anatomical, and behavioral data to build biological-realistic computational models of animal behavior is often a difficult task. Until recently, many software packages have tried to resolve this mismatched granularity with different approaches. This paper presents KInNeSS, the KDE Integrated NeuroSimulation Software environment, as an alternative solution to bridge the gap between data and model behavior. This open source neural simulation software package provides an expandable framework incorporating features such as ease of use, scalabiltiy, an XML based schema, and multiple levels of granularity within a modern object oriented programming design. KInNeSS is best suited to simulate networks of hundreds to thousands of branched multu-compartmental neurons with biophysical properties such as membrane potential, voltage-gated and ligand-gated channels, the presence of gap junctions of ionic diffusion, neuromodulation channel gating, the mechanism for habituative or depressive synapses, axonal delays, and synaptic plasticity. KInNeSS outputs include compartment membrane voltage, spikes, local-field potentials, and current source densities, as well as visualization of the behavior of a simulated agent. An explanation of the modeling philosophy and plug-in development is also presented. Further developement of KInNeSS is ongoing with the ultimate goal of creating a modular framework that will help researchers across different disciplines to effecitively collaborate using a modern neural simulation platform.Center for Excellence for Learning Education, Science, and Technology (SBE-0354378); Air Force Office of Scientific Research (F49620-01-1-0397); Office of Naval Research (N00014-01-1-0624

Fast Simulations of Highly-Connected Spiking Cortical Models Using GPUs

Over the past decade there has been a growing interest in the development of parallel hardware systems for simulating large-scale networks of spiking neurons. Compared to other highly-parallel systems, GPU-accelerated solutions have the advantage of a relatively low cost and a great versatility, thanks also to the possibility of using the CUDA-C/C++ programming languages. NeuronGPU is a GPU library for large-scale simulations of spiking neural network models, written in the C++ and CUDA-C++ programming languages, based on a novel spike-delivery algorithm. This library includes simple LIF (leaky-integrate-and-fire) neuron models as well as several multisynapse AdEx (adaptive-exponential-integrate-and-fire) neuron models with current or conductance based synapses, different types of spike generators, tools for recording spikes, state variables and parameters, and it supports user-definable models. The numerical solution of the differential equations of the dynamics of the AdEx models is performed through a parallel implementation, written in CUDA-C++, of the fifth-order Runge-Kutta method with adaptive step-size control. In this work we evaluate the performance of this library on the simulation of a cortical microcircuit model, based on LIF neurons and current-based synapses, and on balanced networks of excitatory and inhibitory neurons, using AdEx or Izhikevich neuron models and conductance-based or current-based synapses. On these models, we will show that the proposed library achieves state-of-the-art performance in terms of simulation time per second of biological activity. In particular, using a single NVIDIA GeForce RTX 2080 Ti GPU board, the full-scale cortical-microcircuit model, which includes about 77,000 neurons and 3 · 108 connections, can be simulated at a speed very close to real time, while the simulation time of a balanced network of 1,000,000 AdEx neurons with 1,000 connections per neuron was about 70 s per second of biological activity