TY - JOUR T1 - Structure and variability of optogenetic responses identify the operating regime of cortex JF - bioRxiv DO - 10.1101/2020.11.11.378729 SP - 2020.11.11.378729 AU - Agostina Palmigiano AU - Francesco Fumarola AU - Daniel P. Mossing AU - Nataliya Kraynyukova AU - Hillel Adesnik AU - Kenneth D. Miller Y1 - 2020/01/01 UR - http://biorxiv.org/content/early/2020/11/11/2020.11.11.378729.abstract N2 - Identifying the regime in which the cortical microcircuit operates is a prerequisite to determine the mechanisms that mediate its response to stimulus. Classic modeling work has started to characterize this regime through the study of perturbations, but an encompassing perspective that links the full ensemble of the network’s response to appropriate descriptors of the cortical operating regime is still lacking. Here we develop a class of mathematically tractable models that exactly describe the modulation of the distribution of cell-type-specific calcium-imaging activity with the contrast of a visual stimulus. The model’s fit recovers signatures of the connectivity structure found in mouse visual cortex. Analysis of this structure subsequently reveal parameter-independent relations between the responses of different cell types to perturbations and each interneuron’s role in circuit-stabilization. Leveraging recent theoretical approaches, we derive explicit expressions for the distribution of responses to partial perturbations which reveal a novel, counter-intuitive effect in the sign of response functions.Competing Interest StatementThe authors have declared no competing interest.αiShort for population to which cell i belongsχLinear response matrix of the low-dimensional circuitΔαVariance of the input to population ακ and νlow rank vectors that compose σVariance in the population αωLow-dimensional connectivity matrixΠLDiagonal matrix with entries κΠRDiagonal matrix with entries vΣOptogenetic targeting matrixσαβmatrix of the standard deviations of the weight matrix WτTime constantξPower in a threshold power law input-output functionADiagonal matrix with factors to transform calcium to ratesBMeasuring matrixcContrast value, usually normalized to 1EError functionFDiagonal matrix with the derivatives of f at the fixed point of the high-dimensional circuitfInput-output function /nonlinearityf′Derivative of fhExternal inputs to the networkJJacobiankNormalized entries of the low-dimensional linear response matrix χmαMean firing rate in population α for high-D modelNNumber of neurons in the high-D systemnNumber of populations (different cell-types) in the networkNαNumber of neurons in population αPαDistribution of activity over population αqαFraction of cells in population α : Nα /NRLinear response of the high-D systemrActivity, rα is the activity in population αR0Linear response of the high-D system in the absence of disorderTDiagonal matrix of time constantsuαMean input to population αvαSecond moment of the activity distributions in population αWWeight matrix of the high-dimensional modelwαβMean connection strength form population β to population αWeight connecting neuron j in population β to neuron i in population αW0matrix of entries wαβzInput currentf′Diagonal matrix with the derivatives of f at the fixed point of the low-dimensional circuitHFPHomogeneous fixed pointhigh-DHigh-dimensional (i.e. N dimensional) model, with 4 populationslow-DLow-dimensional (i.e. 4-dimensional) model ER -