Recent advances in techniques for monitoring and perturbing neural populations have greatly enhanced our ability to study circuits in the brain. In particular, two-photon holographic optogenetics now enables precise photostimulation of experimenter-specified groups of individual neurons, while simultaneous two-photon calcium imaging enables the measurement of ongoing and induced activity across the neural population. Despite the enormous space of potential photostimulation patterns and the time-consuming nature of photostimulation experiments, very little algorithmic work has been done to determine the most effective photostimulation patterns for identifying the neural population dynamics. Here, we develop methods to efficiently select which neurons to stimulate such that the resulting neural responses will best inform a dynamical model of the neural population activity. Using neural population responses to photostimulation in mouse motor cortex, we demonstrate the efficacy of a low-rank linear dynamical systems model, and develop an active learning procedure which takes advantage of low-rank structure to determine informative photostimulation patterns. We demonstrate our approach on both real and synthetic data, obtaining in some cases as much as a two-fold reduction in the amount of data required to reach a given predictive power. Our active stimulation design method is based on a novel active learning procedure for low-rank regression, which may be of independent interest.

Calcium imaging with fluorescent protein sensors is widely used to record activity in neuronal populations. The transform between neural activity and calcium-related fluorescence involves nonlinearities and low-pass filtering, but the effects of the transformation on analyses of neural populations are not well understood. We compared neuronal spikes and fluorescence in matched neural populations in behaving mice. We report multiple discrepancies between analyses performed on the two types of data, including changes in single-neuron selectivity and population decoding. These were only partially resolved by spike inference algorithms applied to fluorescence. To model the relation between spiking and fluorescence we simultaneously recorded spikes and fluorescence from individual neurons. Using these recordings we developed a model transforming spike trains to synthetic-imaging data. The model recapitulated the differences in analyses. Our analysis highlights challenges in relating electrophysiology and imaging data, and suggests forward modeling as an effective way to understand differences between these data.