Dynamics and Computation Theory Lab

What are the principles that govern the responses of cortical networks to their inputs and the emergence of these responses from recurrent connectivity? Recent experiments have probed these questions by measuring cortical responses to two-photon optogenetic perturbations of single cells in the mouse primary visual cortex. A robust theoretical framework is needed to determine the implications of these responses for cortical recurrence. Here we propose a novel analytical approach: a formulation of the dependence of cell-type-specific connectivity on spatial distance that yields an exact solution for the linear perturbation response of a model with multiple cell types and space- and feature-dependent connectivity. Importantly and unlike previous approaches, the solution is valid in regimes of strong as well as weak intra-cortical coupling. Analysis reveals the structure of connectivity implied by various features of single-cell perturbation responses, such as the surprisingly narrow spatial radius of nearby excitation beyond which inhibition dominates, the number of transitions between mean excitation and inhibition thereafter, and the dependence of these responses on feature preferences. Comparison of these results to existing optogenetic perturbation data yields constraints on cell-type-specific connection strengths and their tuning dependence. Finally, we provide experimental predictions regarding the response of inhibitory neurons to single-cell perturbations and the modulation of perturbation response by neuronal gain; the latter can explain observed differences in the feature-tuning of perturbation responses in the presence vs. absence of visual stimuli.

The ability to optogenetically perturb neural circuits opens an unprecedented window into mechanisms governing circuit function. We analyzed and theoretically modeled neuronal responses to visual and optogenetic inputs in mouse and monkey V1. In both species, optogenetic stimulation of excitatory neurons strongly modulated the activity of single neurons yet had weak or no effects on the distribution of firing rates across the population. Thus, the optogenetic inputs reshuffled firing rates across the network. Key statistics of mouse and monkey responses lay on a continuum, with mice/monkeys occupying the low-/high-rate regions, respectively. We show that neuronal reshuffling emerges generically in randomly connected excitatory/inhibitory networks, provided the coupling strength (combination of recurrent coupling and external input) is sufficient that powerful inhibitory feedback cancels the mean optogenetic input. A more realistic model, distinguishing tuned visual vs. untuned optogenetic input in a structured network, reduces the coupling strength needed to explain reshuffling.

Neuronal spiking activity in cortical circuits is often temporally structured by collective rhythms. Rhythmic activity has been hypothesized to regulate temporal coding and to mediate the flexible routing of information flow across the cortex. Spiking neuronal circuits, however, are non-linear systems that, through chaotic dynamics, can amplify insignificant microscopic fluctuations into network-scale response variability. In nonlinear systems in general, rhythmic oscillatory drive can induce chaotic behavior or boost the intensity of chaos. Thus, neuronal oscillations could rather disrupt than facilitate cortical coding functions by flooding the finite population bandwidth with chaotically-boosted noise. Here we tackle a fundamental mathematical challenge to characterize the dynamics on the attractor of effectively delayed network models. We find that delays introduce a transition to collective oscillations, below which ergodic theory measures have a stereotypical dependence on the delay so far only described in scalar systems and low-dimensional maps. We demonstrate that the emergence of internally generated oscillations induces a complete dynamical reconfiguration, by increasing the dimensionality of the chaotic attractor, the speed at which nearby trajectories separate from one another, and the rate at which the network produces entropy. We find that periodic input drive leads to a dramatic increase of chaotic measures at a the resonance frequency of the recurrent network. However, transient oscillatory input only has a moderate role on the collective dynamics. Our results suggest that simple temporal dynamics of the mean activity can have a profound effect on the structure of the spiking patterns and therefore on the information processing capability of neuronal networks.

The visual cortex receives non-sensory inputs containing behavioral and brain state information. Here we propose a parallel between optogenetic and behavioral modulations of activity and characterize their impact on cell-type-specific V1 processing under a common theoretical framework. We infer cell-type-specific circuitry from large-scale V1 recordings and demonstrate that, given strong recurrent excitation, the cell-type-specific responses imply key aspects of the known connectivity. In the inferred models, parvalbumin-expressing (PV), but not other, interneurons have responses to perturbations that we show theoretically imply that their activity stabilizes the circuit. We infer inputs that explain locomotion-induced changes in firing rates and find that, contrary to hypotheses of simple disinhibition, locomotory drive to VIP cells and to SOM cells largely cancel, with enhancement of excitatory-cell visual responses likely due to direct locomotory drive to them. We show that this SOM/VIP cancellation is a property emerging from V1 connectivity structure. 2 (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission. The copyright holder for this preprint this version posted January 22, 2023. ; https://doi.

Perception, cognition and behavior rely on flexible communication between microcircuits in distinct cortical regions. The mechanisms underlying rapid information rerouting between such microcircuits are still unknown. It has been proposed that changing patterns of coherence between local gamma rhythms support flexible information rerouting. The stochastic and transient nature of gamma oscillations in vivo, however, is hard to reconcile with such a function. Here we show that models of cortical circuits near the onset of oscillatory synchrony selectively route input signals despite the short duration of gamma bursts and the irregularity of neuronal firing. In canonical multiarea circuits, we find that gamma bursts spontaneously arise with matched timing and frequency and that they organize information flow by large-scale routing states. Specific self-organized routing states can be induced by minor modulations of background activity.