Abstract
We present a mean-field formalism able to predict the collective dynamics of large networks of conductance-based interacting spiking neurons. We apply this formalism to several neuronal models, from the simplest Adaptive Exponential Integrate-and-Fire model to the more complex Hodgkin–Huxley and Morris–Lecar models. We show that the resulting mean-field models are capable of predicting the correct spontaneous activity of both excitatory and inhibitory neurons in asynchronous irregular regimes, typical of cortical dynamics. Moreover, it is possible to quantitatively predict the population response to external stimuli in the form of external spike trains. This mean-field formalism therefore provides a paradigm to bridge the scale between population dynamics and the microscopic complexity of the individual cells physiology.NEW & NOTEWORTHY Population models are a powerful mathematical tool to study the dynamics of neuronal networks and to simulate the brain at macroscopic scales. We present a mean-field model capable of quantitatively predicting the temporal dynamics of a network of complex spiking neuronal models, from Integrate-and-Fire to Hodgkin–Huxley, thus linking population models to neurons electrophysiology. This opens a perspective on generating biologically realistic mean-field models from electrophysiological recordings.
Highlights
IntroductionBrain dynamics can be investigated at different scales, from the microscopic cellular scale, describing the voltage dynamics of neurons and synapses (Markram et al 2015), to the mesoscopic scale, characterizing the dynamics of whole populations of neurons (Wilson and Cowan 1972), up to the scale of the whole brain where several populations connect together (Bassett et al 2018; Deco et al 2015; Sanz Leon et al 2013)
Brain dynamics can be investigated at different scales, from the microscopic cellular scale, describing the voltage dynamics of neurons and synapses (Markram et al 2015), to the mesoscopic scale, characterizing the dynamics of whole populations of neurons (Wilson and Cowan 1972), up to the scale of the whole brain where several populations connect together (Bassett et al 2018; Deco et al 2015; Sanz Leon et al 2013).In their pioneering work (Wilson and Cowan 1972), Wilson and Cowan describe the dynamics of a population of neurons through a well-known differential equation where the inputoutput gain function is described by a sigmoid
We introduce mean-field equations describing population dynamics and the template to estimate the transfer function that we apply to all the neuronal models under consideration
Summary
Brain dynamics can be investigated at different scales, from the microscopic cellular scale, describing the voltage dynamics of neurons and synapses (Markram et al 2015), to the mesoscopic scale, characterizing the dynamics of whole populations of neurons (Wilson and Cowan 1972), up to the scale of the whole brain where several populations connect together (Bassett et al 2018; Deco et al 2015; Sanz Leon et al 2013) In their pioneering work (Wilson and Cowan 1972), Wilson and Cowan describe the dynamics of a population of neurons through a well-known differential equation where the inputoutput gain function is described by a sigmoid. They enable a direct comparison with imaging studies where the spatial resolution implies that the recorded field represents the average over a large population of neurons (i.e., a mean field) (Capone et al 2019b; Chemla et al 2019)
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