Reliable Inference of Functional Connectivity Measures from Two-Photon Calcium Imaging Data

Abstract

Two-photon (2P) calcium imaging enables cellular-resolution recordings from large neural populations, yet recovering both the timing of directed interactions and the spatial organization of cortical activity remains difficult. This dissertation develops and applies statistical methods that operate directly on 2P fluorescence data to infer directed interactions and spatial structure in the brain.

First, a latent-variable framework is developed to estimate Granger causal (GC) links directly from fluorescence traces, avoiding explicit spike deconvolution while conditioning on stimulus and behavior. In simulations with known ground truth, the method recovers stimulus-to-neuron, neuron-to-neuron, and neuron-to-behavior influences and correctly identifies, in the sense of Granger, populations of neurons with stimulus-encoding (GS), behavior-decoding (GB), and intersection (GI) roles. Applied to the mouse primary auditory cortex (A1) during tone-discrimination experiments, the analysis reveals task-dependent reconfiguration of directed connectivity and shows that GI neurons bridge sensory encoding and behavioral readout.

Second, Gaussian Processes with Zernike means (GPRZ) are used to reconstruct smooth, uncertainty-aware two-dimensional maps of signal correlation from irregularly sampled fields of view. The maps come with region-level summaries (peak coordinate, average radius, contour level, effect size) and are robust to perturbations such as subsampling, rotation, and occlusion. Using two-tone stimuli, these correlation maps uncover a harmonicity-dependent structure: harmonic pairs suppress short-range correlations yet increase correlations at specific long-range locations along the tonotopic axis, whereas non-harmonic pairs result in broad correlation increases. A circuit model with lateral inhibition and cross-frequency excitation reproduces these patterns, consistent with the observed data from mouse A1.

Finally, we consider the spatial maps of directed interactions in dual-plane (L4 and L2/3) recordings combined with holographic optogenetic stimulation of mouse A1. Directed links (estimated with a Monte Carlo GC procedure) are mapped using GPRZ to produce connection maps and region-level statistics. We find that sound-evoked networks are denser, with fewer but larger subnetworks, than optogenetically driven networks; laminar composition is consistent with columnar organization; and patchy intra- and interlaminar patterns emerge within and between layers.

Together, these results provide a coherent account of when information flows, where it concentrates, and how laminar architecture supports patchy, stimulus-dependent organization in A1. The developed tools operate directly on fluorescence data, quantify uncertainty, and are applicable to other 2P datasets, stimuli settings, and behavioral contexts.