A Geometric Approach for the Study of Functional Connectivity Dynamics

Functional connectivity has been the focus of many research groups aiming to study the interaction between cells and brain regions. A standard method for analyzing connectivity is to statistically compare pairwise interactions between cells or brain regions across behavioral states or conditions. This methodology ignores the intrinsic properties of functional connectivity as a multivariate and dynamic signal, expressing the correlational configuration of the network. In this talk, I will present a geometric approach, combining Graph Theory and Riemannian Geometry to build "a graph of graphs" and extract the latent dynamics of the overall correlational structure. Using this approach, we formulate the statistical relations between network dynamics and spontaneous behavior as a second-order Taylor’s expansion. Our analysis shows that fast fluctuations in functional connectivity of large-scale cortical networks are closely linked to variations in behavioral metrics related to the arousal state. We further expand this methodology to longer time scales to study the effect of dopamine on network dynamics in the primary motor cortex (M1) during learning. We developed a series of analysis methods indicating that as animals learn to perform a motor task, the network of pyramidal neurons in layer 2-3 gradually and monotonically reorganizes toward an "expert" configuration. Our results highlight the critical role of dopamine in driving synaptic plasticity: Blocking dopaminergic neurotransmission locally in M1 prevented motor learning at the behavioral level and concomitantly halted plasticity changes in network activity and in functional connectivity.