An Analytic Framework for Inferring Population Dynamics from Aggregated Calcium Fluorescence

Capturing and inferring brain-wide neural activity remains a significant challenge. Wide-field imaging techniques offer a solution in the shape of simultaneous recording of neural activity across large cortical surfaces at high temporal resolution. Nevertheless, the broad field of view introduced by wide-field imaging limits its spatial resolution, as each camera pixel in a wide-field setup integrates calcium-dependent fluorescence signals from many neurons. Furthermore, calcium indicators that convert neural activity into light emissions distort the neural activity by their dynamics. The inherent noise in recordings, combined with the low spatial resolution and the distorted dynamics introduced by the calcium indicators, makes it particularly challenging to infer underlying neural activity from wide-field fluorescence data. Despite its importance, a rigorously studied analytic solution for this inference problem in the wide-field context has not yet been established. In this study, we present an analytic solution to the inference problem posed by wide-field imaging. We formulate an optimization problem that establishes a relationship between the biological quantities and the properties of the inferred solution, thereby elucidating biologically interpretable results. The analytic solution we find provides significant advantages, including rapid and accurate inference. Furthermore, we introduce a novel approach to parameter tuning within the optimization framework, which leverages the extensive datasets typical of wide-field imaging. The results demonstrate that our solution surpasses a previously used method for this inference in both accuracy and efficiency. We rigorously validate our solution through comprehensive simulations, large-scale biophysical modeling, and parallel recordings of fluorescence and spiking activity. Collectively, these analyses provide a robust foundation for future applications of our proposed analytical inference.