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This paper uses mathematical modeling to study the mechanisms of surround suppression in the primate visual cortex. We present a large-scale neural circuit model consisting of three interconnected components: LGN and two input layers (Layer 4Ca and Layer 6) of the primary visual cortex V1, covering several hundred hypercolumns. Anatomical structures are incorporated and physiological parameters from realistic modeling work are used. The remaining parameters are chosen to produce model outputs that emulate experimentally observed size-tuning curves. Our two main results are: (i) we discovered the character of the long-range connections in Layer 6 responsible for surround effects in the input layers; and (ii) we showed that a net-inhibitory feedback, i.e., feedback that excites I-cells more than E-cells, from Layer 6 to Layer 4 is conducive to producing surround properties consis- tent with experimental data. These results are obtained through parameter selection and model analysis. The effects of nonlinear recurrent excitation and inhibition are also dis- cussed. A feature that distinguishes our model from previous modeling work on surround suppression is that we have tried to reproduce realistic lengthscales that are crucial for quantitative comparison with data. Due to its size and the large number of unknown parame- ters, the model is computationally challenging. We demonstrate a strategy that involves first locating baseline values for relevant parameters using a linear model, followed by the intro- duction of nonlinearities where needed. We find such a methodology effective, and propose it as a possibility in the modeling of complex biological systems. 

Neuroscience models come in a wide range of scales and specificity, from mean-field rate models to large-scale networks of spiking neurons. There are potential trade-offs between simplicity and realism, versatility and computational speed. This paper is about large-scale cortical network models, and the question we address is one of scalability: would scaling down cell density impact a network’s ability to reproduce cortical dynamics and function? We investigated this problem using a previously constructed realistic model of the monkey visual cortex that is true to size. Reducing cell density gradually up to 50-fold, we studied changes in model behavior. Size reduction without parameter adjustment was catastrophic. Surprisingly, relatively minor compensation in synaptic weights guided by a theoretical algo- rithm restored mean firing rates and basic function such as orientation selectivity to models 10-20 times smaller than the real cortex. Not all was normal in the reduced model cortices: intracellular dynamics acquired a character different from that of real neurons, and while the ability to relay feedforward inputs remained intact, reduced models showed signs of defi- ciency in functions that required dynamical interaction among cortical neurons. These findings are not confined to models of the visual cortex, and modelers should be aware of potential issues that accompany size reduction. Broader implications of this study include the importance of homeostatic maintenance of firing rates, and the functional consequences of feedforward versus recurrent dynamics, ideas that may shed light on other species and on systems suffering cell loss.