Abstract
Understanding the computational capabilities of the nervous system means to “identify” its emergent multiscale dynamics. For this purpose, we propose a novel model-driven identification procedure and apply it to sparsely connected populations of excitatory integrate-and-fire neurons with spike frequency adaptation (SFA). Our method does not characterize the system from its microscopic elements in a bottom-up fashion, and does not resort to any linearization. We investigate networks as a whole, inferring their properties from the response dynamics of the instantaneous discharge rate to brief and aspecific supra-threshold stimulations. While several available methods assume generic expressions for the system as a black box, we adopt a mean-field theory for the evolution of the network transparently parameterized by identified elements (such as dynamic timescales), which are in turn non-trivially related to single-neuron properties. In particular, from the elicited transient responses, the input–output gain function of the neurons in the network is extracted and direct links to the microscopic level are made available: indeed, we show how to extract the decay time constant of the SFA, the absolute refractory period and the average synaptic efficacy. In addition and contrary to previous attempts, our method captures the system dynamics across bifurcations separating qualitatively different dynamical regimes. The robustness and the generality of the methodology is tested on controlled simulations, reporting a good agreement between theoretically expected and identified values. The assumptions behind the underlying theoretical framework make the method readily applicable to biological preparations like cultured neuron networks and in vitro brain slices.
Highlights
Brain functions rely on complex dynamics both at the microscopic level of neurons and synapses and at the“mesoscopic”resolution of local cell assemblies, eventually expressed as the concerted activity of macroscopic cortical and sub-cortical areas (Nunez, 2000; Deco et al, 2008)
A natural choice of microscopic computational unit is the single nervous cell described as a “black box,” whose output is the discharge rate of spikes or the neuron membrane potential in response to an incoming ionic current induced by the synaptic bombardment
Complexity reduction in single-neuron modeling is the result of a trade-off between the tractability of the description and the capability of mimicking almost all the behaviors exhibited by isolated nervous cells
Summary
Brain functions rely on complex dynamics both at the microscopic level of neurons and synapses and at the“mesoscopic”resolution of local cell assemblies, eventually expressed as the concerted activity of macroscopic cortical and sub-cortical areas (Nunez, 2000; Deco et al, 2008). A natural choice of microscopic computational unit is the single nervous cell described as a “black box,” whose output is the discharge rate of spikes or the neuron membrane potential in response to an incoming ionic current induced by the synaptic bombardment. Even though neurons described as linear systems might seem a rather rude approximation, a reliable non-linear response to an arbitrary incoming current can be obtained by rectifying the input and/or the output of the linear black box with a threshold-linear function in cascade (Sakai, 1992; Poliakov et al, 1997; Köndgen et al, 2008). Direct identification of the non-linear relationship between afferent currents and the membrane voltage has been proposed, further improving the prediction ability of the detailed timing of emitted spikes by in vitro maintained neurons (Badel et al, 2008)
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