State dependence of neural networks on past history and stimulus presentation in Caenorhabditis elegans

Neurons represent changes in external and internal environments by altering their activity patterns. While coherent brain-wide patterns of neural activity have been observed in neuronal populations, very little is known about their dimensionality, geometry, and how they are correlated with sensory inputs. Here, we recorded the activity of most head neurons in Caenorhabditis elegans experiencing changes in bacterial or control buffer stimuli around their nose. We first classified active neurons into six functional clusters: two sensory neuron clusters (ON and OFF responding to addition and removal of stimuli, respectively) and four motor/command neuron clusters (AVA, RME, SMDD and SMDV). Next, we estimated stimulus selectivity for each cluster and found that while sensory neurons exhibit their maximal responses within 15 seconds, changes in bacterial stimuli drive maximal responses in command and motor neuron clusters after tens of seconds. Furthermore, we show that bacterial stimuli induce neural dynamics that are best described by a hyperbolic, not Euclidean, space, of dimensionality eight. The hyperbolic space provided a better description of neural activity than the standard Euclidean space. This space can be separated into three components - one sensory, and two motor directions (forward-backward and dorsal-ventral). Collectively, we show that C. elegans neural activity can be effectively represented in low-dimensional hyperbolic space to describe a sensorimotor transformation. Significance statementA major function of a nervous system is to transform sensory information into behavioral outputs. As the first receiver of sensory input, sensory neuronal activity is often most correlated with stimulus features. However, this sensory activity is modified as it travels to other neurons, where it integrates with network activity before altering motor neurons and driving corresponding behavior. Activity in non-sensory neurons is driven by ongoing network activity and sensory input, but distinguishing between their relative contributions is often difficult. Here, we identify two sensory and four command/motor neuron clusters in the C. elegans neural network responding to bacterial stimuli and define their receptive fields. We then use a hyperbolic embedding to identify how these clusters interact with each other and identify the relevant dimensions that might alter behavior. Our method is fully scalable to other systems, including those without neuronal identities, and allows us to attribute neural activity to network states and behavioral outputs.