Theory of interaction between untuned modulatory inputs and tuned sensory inputs

How does the brain integrate sensory inputs with non-feature-tuned signals, such as those arising from behavioral state changes or neuromodulation? Here, we show that the dynamics of disordered E/I networks with structured, feature-dependent connectivity can be well characterized by an effective model describing interactions between the responses of cells who prefer the current sensory stimulus ("matched" cells) and the responses of cells firing at the baseline. This effective network exhibits strong feedback from the baseline onto the matched responses but weak reverse projections. Thus, an untuned stimulus not only directly drives matched cells, but also indirectly drives them via modulation of the baseline. We demonstrate through a linear response analysis that the baseline effect on the matched response is suppressive if the network is strongly coupled and feedback-inhibition dominated. In particular, in this regime, feature-dependent networks produce "rate reshuffling", wherein untuned optogenetic excitation yields large changes in the individual responses of matched cells without significantly changing their overall firing rate distribution, as the optogenetically-induced baseline response suppresses the matched response. Finally, if multiple sensory stimuli are presented, yielding sublinear response summation ("normalization"), the influence of the baseline on the matched responses is weakened. Thus, an untuned (e.g., optogenetic) stimulus is less suppressive to multiple stimuli than to a single stimulus, making normalization effectively weaker in the presence of an untuned stimulus. Our framework provides the first theory of the interaction of untuned modulatory and tuned sensory inputs, reconciles prior experiments, and provides testable predictions about tuned-untuned interactions in cortical processing.