Dina Obeid^{1,2}, Kenneth D. Miller^{1,3}
^{1}Center for Theoretical Neuroscience, Columbia University, New York, NY 10027
^{2}Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138
^{3}Department of Neuroscience, Columbia University, New York, NY 10027
Abstract: This study presents a cortical circuit model based on the Stabilized Supralinear Network (SSN) to explain center-surround interactions in primary visual cortex (V1). The model reproduces three key phenomena: reduction of excitatory and inhibitory currents during surround suppression, maximal suppression when the surround orientation matches that of the center, and specific suppression of plaid stimulus components. Using a two-dimensional network of layer 2/3 of V1, with biologically plausible connectivity, the model was tested in both rate- and firing-rate-based versions. The results also replicate the fast decay dynamics (~10 ms) observed experimentally, suggesting that the SSN is a robust mechanism for cortical computations.
Introduction
Interactions between stimuli in the classical receptive field (center) and the surrounding region (surround) in primary visual cortex (V1) are fundamental to visual processing. These interactions, known as surround suppression, modulate neuronal responses based on factors such as orientation, contrast, and distance. This study develops an SSN model to explain three observed phenomena: (1) reduced excitatory and inhibitory currents during surround suppression; (2) stronger suppression when the surround orientation matches that of the center, even for non-preferred orientations; and (3) specific suppression of plaid stimulus components. Furthermore, the model addresses the fast decay dynamics of cortical activity (~10 ms) after thalamic silencing, challenging the expectation of slow decays in networks with strong recurrent excitation.
Materials and Methods
The model consists of a two-dimensional grid of 75×75 points, representing 16×16 degrees of visual space and 8×8 mm of cortex, with a cortical magnification factor of 0.5 mm/degree. Each point contains one excitatory (E) and one inhibitory (I) cell, totaling 5,625 of each type. Connectivity depends on cortical distance and preferred orientation difference, with E cells forming short- and long-range connections and I cells limited to short-range. Connection strengths are defined by Gaussian functions fitted to biological data.
The rate-based version uses a supralinear transfer function (power 2.2), while the firing version, implemented in the Brian simulator, uses conductance equations. The external input is modeled as a function of stimulus contrast, and the dynamics follow differential equations for rates or membrane potentials. Simulations evaluated: (1) surround suppression with reduction of E and I currents; (2) dependence on surround orientation; (3) suppression in plaid stimuli; and (4) decay after thalamic silencing. Parameters were adjusted to ensure stability (Ω_E < 0) and alignment with experimental data.
Results
The SSN model reproduced the three surround suppression phenomena:
Surround suppression reduced both excitatory and inhibitory currents, consistent with experimental data. This required strong local connectivity, stabilized by feedback inhibition, with stronger E→I connections at longer distances.
Suppression was maximal when the surround orientation matched that of the center, even for non-preferred orientations, requiring broadly tuned local connectivity for orientation.
In plaid stimuli, surround selectively suppressed the corresponding component, without requiring broadly tuned connectivity, suggesting independence between mechanisms.
The model also replicated the rapid decay of activity (~10 ms for E cells, ~6.67 ms for I cells) after thalamic silencing, despite strong recurrent excitation, due to the balance between excitation and inhibition. In the triggering version, suppression indices were 0.45–0.65 for E cells and 0.098–0.14 for I cells, varying with contrast.
Discussion
The SSN model demonstrates that a cortical circuit with biologically plausible connectivity can explain complex surround suppression phenomena in V1. The robustness of the results to firing rate models suggests that the SSN is a general mechanism for cortical computations such as discontinuity detection and object recognition. The fast decay dynamics indicate that long cortical autocorrelation times may depend on thalamic inputs or thalamocortical loops rather than intrinsic cortical circuits. The model predicts that E→I connections should be stronger at longer distances, a hypothesis that is experimentally testable.
Conclusion
This study establishes the SSN as a robust model for center-surround interactions in V1, integrating multiple observed phenomena and fast dynamics. The findings advance the understanding of cortical circuits and provide predictions for future experimental investigations.
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