Decomposing the modulation of interactions between neuronal populations

Abstract

Identifying subpopulations of neurons that interact with each other from simultaneous recordings of populations of many neurons is key for understanding across-brain communication with cellular resolution. Recent work identified communication subspaces, which capture additive interactions between pairs of high-dimensional neural populations through a small number of source and target activity patterns. However, no current method captures how a third, potentially multivariate variable - such as behavioral state or the activity of a third population - modulates these interactions. Here we extend the communication subspace framework by parameterizing modulation as a low-rank tensor. This identifies multiplicative interaction channels (MICs), defined as triplets of source, target, and modulator activity patterns, in which the modulator pattern gates the source-target interaction. We derive MICs as a bilinear perturbation of reduced-rank regression. We develop a hierarchical fitting pipeline and provide a closed-form decomposition that quantifies whether modulation reshapes the modulator-averaged baseline interaction, recruits private dimensions of one population, or opens new interactions. In simulations, MICs reliably recover the presence and geometry of ground-truth modulation even in the high-dimensional, low-sample regime. Applying MICs to simultaneous calcium imaging of prefrontal axons and interneurons in the visual cortex revealed that behavioral state asymmetrically modulates top-down interactions, reconfiguring the patterns of prefrontal projections that interact with a stable set of visual interneuron activity patterns. By providing an efficient and compact characterization of modulatory interactions, MICs enable asking new questions about how potentially high-dimensional variables shape interactions between neural populations.