Relating Divisive Normalization to Modulation of Correlated Variability in Primary Visual Cortex

Correlated fluctuations of neural activity, termed noise correlations (NCs), are widespread in cortex
and affected by sensory and non-sensory variables. Past work suggests that divisive normalization (DN), a
cortical computation responsible for coordinating neural activity, could explain those modulations of neuronal
covariability. However, quantifying the relation between DN and NCs remains challenging, as most successful
descriptive models of neural variability do not account for DN. We propose a pairwise stochastic DN model
that accounts for the effect of DN on covariability. In the model, the numerators (representing excitatory input
drive) and denominators (normalization signals) of two neurons are correlated random variables. Therefore,
the model partitions NCs into two main sources of correlated fluctuations. We show analytically and with
simulations that the effects of DN on NCs depends qualitatively on whether normalization signals are
correlated, highlighting the importance of understanding the sharing of normalization between neurons to
fully understand DN’s influences on covariability. By fitting the model to simulated pairwise responses, we
study the regimes of parameter identifiability: importantly, the denominators’ correlation parameter is best
recovered when the numerators contribution to NCs is small. Furthermore, we find that the pairwise model
can improve both predictive power and inference of single-trial normalization strength, relative to
independent stochastic DN. Lastly, we demonstrate that the model fits accurately Ca2+ imaging data in mouse
primary visual cortex (V1) and captures the modulation of NCs by contrast. Our descriptive model can be used
to characterize NCs in neural data and quantitatively measure the modulation of NCs by stimulus and state
variables. This will enable researchers to study mechanisms underlying DN, test predictions made by
normative models about how the structure of population variability affects information coding, and quantify
the effects of DN and neural variability on behavior.