Unsupervised learning of control signals and their encodings in Caenorhabditis elegans whole-brain recordings

A major goal of computational neuroscience is to understand the relationship between synapse-level structure and network-level functionality. Caenorhabditis elegans is a model organism to probe this relationship due to the historic availability of the synaptic structure (connectome) and recent advances in whole brain calcium imaging techniques. Recent work has applied the concept of network controllability to neuronal networks, discovering some neurons that are able to drive the network to a certain state. However, previous work uses a linear model of the network dynamics, and it is unclear if the real neuronal network conforms to this assumption. Here, we propose a method to build a global, low-dimensional model of the dynamics, whereby an underlying global linear dynamical system is actuated by temporally sparse control signals. A key novelty of this method is discovering candidate control signals that the network uses to control itself. We analyse these control signals in two ways, showing they are interpretable and biologically plausible. First, these control signals are associated with transitions between behaviours, which were previously annotated via expert-generated features. Second, these signals can be predicted both from neurons previously implicated in behavioural transitions but also additional neurons previously unassociated with these behaviours. The proposed mathematical framework is generic and can be generalized to other neurosensory systems, potentially revealing transitions and their encodings in a completely unsupervised way.