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 - 2021/01/01
UR - http://biorxiv.org/content/early/2021/02/23/2020.11.11.378729.abstract
N2 - Predicting the response of the cortical microcircuit to perturbations is a prerequisite to determine the mechanisms that mediate its response to stimulus; yet, an encompassing perspective that describes the full ensemble of the network’s response in models that accurately recapitulate recorded data 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 inferred parameters recover signatures of the connectivity structure found in mouse visual cortex. Analysis of this structure subsequently reveals 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. Finally applying the theory to inferring feedback to V1 during locomotion, we find that it is predominantly mediated by both SOM and VIP modulation.Competing Interest StatementThe authors have declared no competing interest.“iShort for population to which cell i belongsχLinear response matrix of the Low-dimensional circuitΔαVariance of the input to population ακ and vlow 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 HD modelNNumber of neurons in the HD 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 HD systemrActivity, rα is the activity in population αR0Linear response of the HD 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 circuitHDhigh-dimensional (i.e. N dimensional) model, with 4 populationsHFPHomogeneous fixed pointLDLow-dimensional (i.e. 4-dimensional) model
ER -