Inferring synaptic connectivity from spatio-temporal spike patterns

Abstract

Networks of well-known dynamical units but unknown interaction topology arise across various fields of biology, including genetics, ecology, and neuroscience. The collective dynamics of such networks is often sensitive to the presence (or absence) of individual interactions, but there is usually no direct way to probe for their existence. Here we present an explicit method for reconstructing interaction networks of leaky integrate-and-fire neurons from the spike patterns they exhibit in response to external driving. Given the dynamical parameters are known, the approach works well for networks in simple collective states but is also applicable to networks exhibiting complex spatio-temporal spike patterns. In particular, stationarity of spiking time series is not required.

Network Dynamics as an Inverse Problem

“…Here, similarly to previous works [4,34,35,64,69, 100], we also exploit the sparsityinducing nature of the L 1 -norm for selecting a particular solution from a family of possible solutions for g i Γ i . The underlying reasoning for choosing a sparse-inducing norm is that if a network is sparse then many entries in g i Γ i are zero due to the non-existing explicit dependencies in Λ i .…”

“…Whether one studies gene regulatory networks, metabolic networks or neural networks, sometimes we may have no means of directly measuring the network connectivity [20,21,[33][34][35][36][37][38][39]. Instead, one is forced to resort to indirect approaches to estimate the network connections from available data.…”

“…Instead, one is forced to resort to indirect approaches to estimate the network connections from available data. For instance, spike trains of neural networks may be used ti reveal network connections between spiking neurons [34,35,40]. Moreover, gene expression levels may also reveal the regulatory features of gene regulatory networks [4,7,9,20,21,33,37].…”

“…In particular, knowing the actual parameters and functions generating the network dynamics reduces the problem of inferring network structural connections to just fitting a collection of unknown parameters (in this case the connections) to measured data [34,35,40,[68][69][70][71][72][73]. Such approaches are especially reliable when estimating connections from time series [68][69][70][71][72][73][74], even in the presence of challenging dynamics (e.g.…”

“…chaotic and noisy dynamics) [69]. Furthermore, such approaches may also reveal the structural connectivity of hybrid systems [75] where the coupling dynamics occurs at discrete events in times, such as in networks of spiking neurons [34,35,40].…”