Model-Free Reconstruction of Excitatory Neuronal Connectivity from Calcium Imaging Signals

Abstract

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically infeasible, even in simpler systems like dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct structural connectivity from network activity monitored through calcium imaging. We focus in this study on the inference of excitatory synaptic links. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the functional network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (bursting or non-bursting). Thus by conditioning with respect to the global mean activity, we improve the performance of our method. This allows us to focus the analysis to specific dynamical regimes of the network in which the inferred functional connectivity is shaped by monosynaptic excitatory connections, rather than by collective synchrony. Our method can discriminate between actual causal influences between neurons and spurious non-causal correlations due to light scattering artifacts, which inherently affect the quality of fluorescence imaging. Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good estimation of the excitatory network clustering coefficient, allowing for discrimination between weakly and strongly clustered topologies. Finally, we demonstrate the applicability of our method to analyses of real recordings of in vitro disinhibited cortical cultures where we suggest that excitatory connections are characterized by an elevated level of clustering compared to a random graph (although not extreme) and can be markedly non-local.

Fast algorithm for neural network reconstruction

“…In this section, we validate the proposed framework on a simulated calcium fluorescence dataset provided by [3]. This dataset has been the subject of the Kaggle connectomics challenge in which participants determine the connectivity of a 1,000 neuron network by using simulated calcium fluorescence data.…”

“…Similarly, some neurons can have larger connectivity scores than they should have, leading to more connections. In the network, however, neurons often have a similar number of connecting neurons [3]. It makes sense to apply a local threshold for each individual neuron.…”

“…Information theoretic metrics are common ways to measure the connection probabilities. A state-ofthe-art measure for measuring excitatory connectivity in calcium imaging neural network data is generalized transfer entropy [3]. Other standard information theoretic measures such as information gain can be used to measure the flow of information in the neural network.…”

“…Rather than standard transfer entropy, we use a modified form to improve results on calcium fluorescence neural network data introduced by [3], called generalized transfer entropy. The generalized transfer entropy from s i to s j , denoted GTE(s i , s j ), is calculated by ignoring network samples that occur during periods of high global fluorescence activity.…”

Efficient Combination of Pairwise Feature Networks

“…The data reproduces the dynamic behavior of real networks of cultured neurons. The simulator also includes the typical real defects of the calcium fluorescence technology: limited time resolution and light scattering artifacts (the activity of given neuron influences the measurements of nearby neurons) Stetter et al (2012).…”