From functional to structural connectivity using partial correlation in neuronal assemblies

Objective. Our goal is to re-introduce an optimized version of the partial correlation to infer structural connections from functional-effective ones in dissociated neuronal cultures coupled to microelectrode arrays. Approach. We first validate our partialization procedure on in silico networks, mimicking different experimental conditions (i.e., different connectivity degrees and number of nodes) and comparing the partial correlation's performance with two gold-standard methods: cross-correlation and transfer entropy. Afterwards, to infer the structural connections in in vitro neuronal networks where the ground truth is unknown, we propose a thresholding heuristic approach. Then, to validate whether the partialization process correctly reconstructs macroscopic features of the network structure, we extract a modularity index from segregated in silico and in vitro models. Finally, as a case study, we apply our partialization procedure to analyze connectivity and topology on spontaneous developing and electrically stimulated in vitro cultures. Main results. In simulated networks, partial correlation outperforms cross-correlation and transfer entropy at low and medium connectivity degrees, not only in relatively small (60 nodes) but also in larger (120-240 nodes) assemblies. Furthermore, partial correlation correctly identifies interconnected neuronal sub-populations and allows one to derive network topology in in vitro cortical networks. Significance. Our results support the idea that partial correlation is a good method for connectivity studies and can be applied to derive topological and structural features of neuronal assemblies.