Measuring amount of computation done by C.elegans using whole brain neural activity

Many dynamical systems found in biology, ranging from genetic circuits to the human brain to human social systems, are inherently computational. Although extensive research has explored their resulting functions and behaviors, the underlying computations often remain elusive. Even the fundamental task of quantifying the \textit{amount} of computation performed by a dynamical system remains under-investigated. In this study we address this challenge by introducing a novel framework to estimate the amount of computation implemented by an arbitrary physical system based on empirical time-series of its dynamics. This framework works by forming a statistical reconstruction of that dynamics, and then defining the amount of computation in terms of both the complexity and fidelity of this reconstruction. We validate our framework by showing that it appropriately distinguishes the relative amount of computation across different regimes of Lorenz dynamics and various computation classes of cellular automata. We then apply this framework to neural activity in \textit{Caenorhabditis elegans}, as captured by calcium imaging. By analyzing time-series neural data obtained from the fluorescent intensity of the calcium indicator GCaMP, we find that high and low amounts of computation are required, respectively, in the neural dynamics of freely moving and immobile worms. Our analysis further sheds light on the amount of computation performed when the system is in various locomotion states. In sum, our study refines the definition of computational amount from time-series data and highlights neural computation in a simple organism across distinct behavioral states.