Figures and data
Schematic of the two-stage recurrent circuit model.
Solid and dashed lines represent excitatory and inhibitory connections, respectively. Principal excitatory neurons are denoted by y, modulatory excitatory neurons by u, and modulatory inhibitory neurons by a and q. Subscripts 1 and 2 designate neurons in visual areas V1 and V2, respectively. z1 denotes the input drive from the LGN to V1, a weighted sum of the responses of LGN neurons. Parameters β1 and γ1 modulate the input and feedback gain to V1, respectively.
Comparison of theoretical predictions (left column) and experimental observations (right column) in V1 and V2.
All theoretical predictions are generated using the same baseline parameters (Table S1). a, Theoretical mean firing rates as a function of stimulus contrast (V1: dashed line, V2: solid line). b, Experimental mean firing rates of V1 and V2 (data from [24] and [25], replotted for comparison). The shaded area with a solid border indicates the 25th to 75th percentile range for V1, and the one with the dashed border indicates the same for V2. c, Theoretical V1 power spectra at various stimulus contrast levels. Power spectra were normalized using the equation 
Theoretical predictions: Modulating feedback (left) and input gain (right).
a,b, Firing rates as a function of contrast. Increasing either feedback gain or input gain enhances neural responses, with feedback gain showing a greater impact in the higher cortical area V2. c,d, V1 power spectra: 3% contrast. An alpha peak is observed for low feedback gain, but the peak diminishes with increasing feedback gain. The alpha peak is absent with input gain changes. e,f, V1 power spectra: 50% contrast. A consistent gamma peak is observed, which shifts toward higher frequencies with increasing feedback gain (e) and input gain (f). g,h, Coherence spectra: 3% contrast. A broad peak in the beta band is observed at low feedback gain, which vanishes at high feedback gain. No such peak is observed with changes in input gain. i,j, Coherence spectra: 50% contrast. A beta peak is observed for low feedback gain, which shifts toward higher (gamma) frequencies with increasing feedback gain. No beta peak is observed for changes in input gain, but the gamma peak shifts toward higher frequencies with increasing input gain. k,l, Communication subspaces. Increasing feedback gain enhances inter-areal (circles) communication while decreasing within-area (squares) communication. Conversely, increasing input gain decreases both inter- and within-area communication.
Theoretical prediction: Frequency-dependence of communication.
a, V1-V2 coherence spectra for different contrasts; same as in Fig. 2e. b, Prediction performance versus frequency at different contrasts, averaged across different subsets of the source and target populations. At low stimulus contrast (≈ 10 %), a peak in communication efficacy is observed around 20 Hz. As stimulus contrast increases, the preferred frequency of communication shifts towards higher frequencies (40 Hz). The magnitude of communication reaches a maximum around 40% contrast, before declining at higher contrast levels. Under conditions of very low contrast (< 10%), communication is mostly concentrated at very low frequencies. These frequency-specific trends in communication parallel the V1-V2 coherence patterns shown in panel a. c, Dimensionality of the communication subspace versus frequency, averaged across different subsets of the source and target populations. A notable dip in dimensionality occurs at frequencies corresponding to peaks in communication (panel b) and coherence (panel a). The shaded areas in panels b and c represent the standard error of the mean (SEM) across different subsets of the source and target populations.
Theoretical prediction: Feedback-dependent modulation of functional connectivity.
a, Feedback from V5 → V1 is stronger than feedback from V4 → V1, and V1 preferentially enhances communication with V5. b, Feedback from V4 → V1 is stronger than feedback from V5 → V1, and V1 preferentially enhances communication with V4. The plotted prediction performance is an average across different subsets of the source and target populations, and the shaded areas represent the standard error of the mean (SEM). These results demonstrate that top-down feedback can dynamically route information flow between cortical areas, i.e., modulating functional connectivity.
Hypothesized mapping of computational components in the model onto the dendritic compartments of a pyramidal cell.
The input drive is hypothesized to be the weighted sum of feedforward inputs arriving at the distal basal dendrites. This is modulated by an input gain, corresponding to inhibition at the proximal basal dendritic trunk. In the apical tuft, the feedback drive represents a weighted sum of feedback inputs from higher cortical areas. This signal is amplified by a feedback gain within the distal apical trunk. The recurrent drive corresponds to the sum of lateral inputs on the proximal apical dendrites. The combined recurrent and feedback signals are then modulated by a recurrent gain at the proximal apical trunk. The overall synaptic current is a combination of these gain-modulated drives. The pyramidal neuron cell shown is from [73].
Connectivity matrices in the hierarchical recurrent circuit model.
a, Orientation tuning curves corresponding to the V1 encoding matrix (Wzx). Each row represents the tuning curve of a V1 neuron. The weight matrix itself has positive and negative synaptic weights like standard models of orientation-selective receptive fields. b, The recurrent connectivity matrix for V1 (W11). The V2 recurrent connectivity matrix W22 has a similar structure. c, The Feedback connectivity matrix from V2 to V1 (W12). The corresponding feedforward matrix from V1 to V2, (W21), is its transpose. Since W21 is symmetric, the feedforward and feedback matrices are identical (W12 = W21).
