Microcircuits in cortex consist of populations of neurons that produce coordinated computations to interpret a sensory input. Such coordinated computations are achieved by the relative rates at which the neurons in the circuit fire action potentials. The dimensionality of the population firing dynamics is important because it provides information on which subsets of neurons in the circuit have similar firing profiles for a given stimulus. As even a single cortical microcircuit consists of tens of thousands of neurons, it is a central goal of theoretical neuroscience to develop rules for how the wiring between neurons in a circuit 1) contributes to the dimensionality of firing activity in the population and 2) supports specific sensory computations. We examine a visual working-memory microcircuit in prefrontal cortex (PFC) which is able to preserve knowledge of a visual cue - even during a delay period in which that cue is removed - using the persistent firing activity of neurons that are selective for the spatial properties of the cue. Using a novel task in which primates had to recall not only the orientation of a visual cue after a delay period but also its radial distance from the central fixation point, we demonstrate that PFC neurons are preferentially tuned to a two-dimensional location in polar space. The likelihood that a pair of neurons has correlated firing activity is fairly constant as a function of the difference in their radial tuning preferences, but is generally inversely proportional to their angular tuning preferences. However, neurons that prefer stimuli in opposite visual hemifields have uncorrelated firing activity, even when the angular difference between their preferred stimuli is small. Furthermore, we analyze simultaneous recordings of neurons in the final microcircuit of visual cortex (V4), which serves as the input layer to the studied PFC microcircuit. We show that population firing has low-dimensional dynamics of approximately rank 1 in V4, which get filtered to produce high-dimensional dynamics at the level of PFC. We develop a two-layer biophysical model of spiking neurons that explains how clustered subnetwork architectures arising from simple, probabilistic wiring rules based on the spatial tuning preferences of V4 and PFC neurons give rise to the observed firing dynamics in V4 and PFC. Thus, we formalize the relationship between the ability of the primate to hold a visual stimulus in working memory and the graph architecture of the microcircuits that produce said computation.
