Abstract
Brain neurons exhibit complex electroresponsive properties – including intrinsic subthreshold oscillations and pacemaking, resonance and phase-reset – which are thought to play a critical role in controlling neural network dynamics. Although these properties emerge from detailed representations of molecular-level mechanisms in “realistic” models, they cannot usually be generated by simplified neuronal models (although these may show spike-frequency adaptation and bursting). We report here that this whole set of properties can be generated by the extended generalized leaky integrate-and-fire (E-GLIF) neuron model. E-GLIF derives from the GLIF model family and is therefore mono-compartmental, keeps the limited computational load typical of a linear low-dimensional system, admits analytical solutions and can be tuned through gradient-descent algorithms. Importantly, E-GLIF is designed to maintain a correspondence between model parameters and neuronal membrane mechanisms through a minimum set of equations. In order to test its potential, E-GLIF was used to model a specific neuron showing rich and complex electroresponsiveness, the cerebellar Golgi cell, and was validated against experimental electrophysiological data recorded from Golgi cells in acute cerebellar slices. During simulations, E-GLIF was activated by stimulus patterns, including current steps and synaptic inputs, identical to those used for the experiments. The results demonstrate that E-GLIF can reproduce the whole set of complex neuronal dynamics typical of these neurons – including intensity-frequency curves, spike-frequency adaptation, post-inhibitory rebound bursting, spontaneous subthreshold oscillations, resonance, and phase-reset – providing a new effective tool to investigate brain dynamics in large-scale simulations.
Highlights
The causal relationship between components of the nervous system at different spatio-temporal scales, from subcellular mechanisms to behavior, still needs to be disclosed and this represents one of the main challenges of modern neuroscience
Specific advantages of extended generalized leaky integrate-and-fire (E-GLIF) are the second-order dynamics and the linearity: the model admits an oscillatory response to constant inputs and an analytical solution that allows to extend the theoretical analysis of complex firing dynamics
EGLIF keeps a correspondence between lumped model parameters and electrophysiological mechanisms, limiting black-box fitting and supporting the interpretation of neuronal physiological properties and their changes by neuromodulation and plasticity
Summary
The causal relationship between components of the nervous system at different spatio-temporal scales, from subcellular mechanisms to behavior, still needs to be disclosed and this represents one of the main challenges of modern neuroscience. To this aim, bottom-up modeling is an advanced strategy that allows to propagate low-level cellular phenomena into large-scale brain networks (Markram, 2013; Markram et al, 2015; D’Angelo and Gandini Wheeler-Kingshott, 2017). Simplified neuron models are fundamental for studying the emergent properties of neural circuits in large-scale simulations and for summarizing in a principled way the electrophysiological intrinsic neural properties that drive network dynamics and high-level behaviors (Gerstner et al, 2014). A critical issue is to obtain simplified neuronal models, that should be at the same time biologically meaningful and computationally efficient
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