Spatial gradients and multidimensional dynamics in a neural integrator circuit

In a neural integrator, the variability and topographical organization of neuronal firing rate persistence can provide information about the circuit’s functional architecture. Here we use optical recording to measure the time constant of decay of persistent firing (“persistence time”) across a population of neurons comprising the larval zebrafish oculomotor velocity-to-position neural integrator. We find extensive persistence time variation (10-fold; coefficients of variation 0.58–1.20) across cells within individual larvae. We also find that the similarity in firing between two neurons decreased as the distance between them increased and that a gradient in persistence time was mapped along the rostrocaudal and dorsoventral axes. This topography is consistent with the emergence of persistence time heterogeneity from a circuit architecture in which nearby neurons are more strongly interconnected than distant ones. Collectively, our results can be accounted for by integrator circuit models characterized by multiple dimensions of slow firing rate dynamics.