Neuronal variability is a reflection of recurrent circuitry and cellular physiology. The modulation of neuronal variability is a reliable signature of cognitive and processing state. A pervasive yet puzzling feature of cortical circuits is that despite their complex wiring, population-wide shared spiking variability is low dimensional with all neurons fluctuating en masse. We show that the spatiotemporal dynamics in a spatially structured network produce large population-wide shared variability. When the spatial and temporal scales of inhibitory coupling match known physiology, model spiking neurons naturally generate low dimensional shared variability that captures in vivo population recordings along the visual pathway. Further, we show that firing rate models with spatial coupling can also generate chaotic and low-dimensional rate dynamics. The chaotic parameter region expands when the network is driven by correlated noisy inputs, while being insensitive to the intensity of independent noise.

A wealth of experimental studies show that the trial-to-trial variability of neuronal activity is quenched during stimulus evoked responses. This fact has helped ground a popular view that the variability of spiking activity can be decomposed into two components. The first is due to irregular spike timing conditioned on the firing rate of a neuron (i.e. a Poisson process), and the second is the trial-to-trial variability of the firing rate itself. Quenching of the variability of the overall response is assumed to be a reflection of a suppression of firing rate variability. Network models have explained this phenomenon through a variety of circuit mechanisms. However, in all cases, from the vantage of a neuron embedded within the network, quenching of its response variability is inherited from its synaptic input. We analyze in vivo whole cell recordings from principal cells in layer (L) 2/3 of mouse visual cortex. While the variability of the membrane potential is quenched upon stimulation, the variability of excitatory and inhibitory currents afferent to the neuron are amplified. This discord complicates the simple inheritance assumption that underpins network models of neuronal variability. We propose and validate an alternative (yet not mutually exclusive) mechanism for the quenching of neuronal variability. We show how an increase in synaptic conductance in the evoked state shunts the transfer of current to the membrane potential, formally decoupling changes in their trial-to-trial variability. The ubiquity of conductance based neuronal transfer combined with the simplicity of our model, provides an appealing framework. In particular, it shows how the dependence of cellular properties upon neuronal state is a critical, yet often ignored, factor. Further, our mechanism does not require a decomposition of variability into spiking and firing rate components, thereby challenging a long held view of neuronal activity.

Cortical circuits receive multiple inputs from upstream populations with non-overlapping stimulus tuning preferences. Both the feedforward and recurrent architectures of the receiving cortical layer will reflect this diverse input tuning. We study how population-wide neuronal variability propagates through a hierarchical cortical network receiving multiple, independent, tuned inputs. We present new analysis of in vivo neural data from the primate visual system showing that the number of latent variables (dimension) needed to describe population shared variability is smaller in V4 populations compared to those of its downstream visual area PFC. We successfully reproduce this dimensionality expansion from our V4 to PFC neural data using a multi-layer spiking network with structured, feedforward projections and recurrent assemblies of multiple, tuned neuron populations. We show that tuning-structured connectivity generates attractor dynamics within the recurrent PFC current, where attractor competition is reflected in the high dimensional shared variability across the population. Indeed, restricting the dimensionality analysis to activity from one attractor state recovers the low-dimensional structure inherited from each of our tuned inputs. Our model thus introduces a framework where high-dimensional cortical variability is understood as ``time-sharing’’ between distinct low-dimensional, tuning-specific circuit dynamics.