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Measuring the activity of neuronal populations with calcium imaging can capture emergent functional properties of neuronal circuits with single cell resolution. However, the motion of freely behaving animals, together with the intermittent detectability of calcium sensors, can hinder automatic monitoring of neuronal activity and their subsequent functional characterization. We report the development and open-source implementation of a multi-step cellular tracking algorithm (Elastic Motion Correction and Concatenation or EMC 2 ) that compensates for the intermittent disappearance of moving neurons by integrating local deformation information from detectable neurons. We demonstrate the accuracy and versatility of our algorithm using calcium imaging data from two-photon volumetric microscopy in visual cortex of awake mice, and from confocal microscopy in behaving Hydra , which experiences major body deformation during its contractions. We quantify the performance of our algorithm using ground truth manual tracking of neurons, along with synthetic time-lapse sequences, covering a wide range of particle motions and detectability parameters. As a demonstration of the utility of the algorithm, we monitor for several days calcium activity of the same neurons in layer 2/3 of mouse visual cortex in vivo , finding significant turnover within the active neurons across days, with only few neurons that remained active across days. Also, combining automatic tracking of single neuron activity with statistical clustering, we characterize and map neuronal ensembles in behaving Hydra , finding three major non-overlapping ensembles of neurons (CB, RP1 and RP2) whose activity correlates with contractions and elongations. Our results show that the EMC 2 algorithm can be used as a robust and versatile platform for neuronal tracking in behaving animals. 

Mathematical and statistical models have played important roles in neuroscience, especially by describing the electrical activity of neurons recorded individually, or collectively across large networks. As the field moves forward rapidly, new challenges are emerging. For maximal effectiveness, those working to advance computational neuroscience will need to appreciate and exploit the complementary strengths of mechanistic theory and the statistical paradigm.