Fig. 2: A network model of interacting cortical columns.
a The network consists of two parallel two-dimensional lattices corresponding to superficial and deep cortical layers. Each unit represents a local population of neurons within one layer of a cortical column. The units transition between the On (yellow) and Off (blue) phases. Bottom-up inputs from visual stimuli (gray shading) and top-down attentional inputs (red shading) target local groups of columns in the model. Each network layer receives different attentional inputs to account for differences in noise-correlation changes between superficial versus deep cortical layers. b Dynamical system modeling On-Off dynamics in single columns (left panel). The mean firing-rate variable r(t) receives a recurrent self-coupling F(r) and a negative feedback from the adaptation variable a(t). The dynamical system is driven by a white noise ξ(t), recurrent inputs from the neighboring columns Irec(t), and external inputs \({I}_{{{{{{{{\rm{stim}}}}}}}}}(t)\) and Iatt(t). On the phase plane (right panel), the r-nulcline (gray) and a-nullcline (black) cross at the On (yellow) and Off (blue) stable fixed points. The attentional input shifts the r-nulcline (red) modulating the stability of the On and Off fixed points. c In single columns, the model generates stochastic On-Off transitions (left panel). The durations of On (yellow) and Off (blue) episodes are irregular and exponentially distributed (right panel). The average duration (dashed lines) of On-episodes is longer in attention (Iatt > 0, lower row, average \({\bar{\tau }}_{{{{{{{{\rm{on}}}}}}}}}=113\) ms, \({\bar{\tau }}_{{{{{{{{\rm{off}}}}}}}}}=88\) ms) relative to the control condition (Iatt = 0, upper row, average \({\bar{\tau }}_{{{{{{{{\rm{on}}}}}}}}}=102\) ms, \({\bar{\tau }}_{{{{{{{{\rm{off}}}}}}}}}=98\) ms). d The network generates spatiotemporal On-Off dynamics, where the On and Off phases form local spatial clusters (a single snapshot of simulated activity in the dynamical-system network is shown). The spatiotemporal pattern differs between attention (red square) and control (black square) conditions. e Spikes of individual neurons are modeled as inhomogeneous Poisson processes with different mean rates during the On (yellow) and Off (blue) phases generated by the network. All neurons represented by a single network unit follow the same shared On-Off sequence. f Model parameters are estimated by fitting the experimental data with the HMM, which provides the On-Off transition rates (α1 and α2, top) and the On and Off firing rates (ron and roff) for each MU and SU in each recording session and task condition. Histograms show the On (yellow) and Off (blue) firing rates for MUs for an example HMM fit. Source data are provided as a Source Data file.
