Convolutional neural networks (CNNs) have been shown to be the state-of-the-art approach for modeling the transfer functions of visual cortical neurons. Cortical neurons in the primary visual cortex are are sensitive to contextual information mediated by extensive horizontal and feedback connections. Standard CNNs can integrate global spatial image information to model such contextual modulation via two mechanisms: successive rounds of convolutions and a fully connected readout layer. In this paper, we find that non-local networks or self-attention (SA) mechanisms, theoretically related to context-dependent flexible gating mechanisms observed in the primary visual cortex, improve neural response predictions over parameter-matched CNNs in two key metrics: tuning curve correlation and tuning peak. We factorize networks to determine the relative contribution of each context mechanism. This reveals that information in the local receptive field is most important for modeling the overall tuning curve, but surround information is critically necessary for characterizing the tuning peak. We find that self-attention can replace subsequent spatial-integration convolutions when learned in an incremental manner, and is further enhanced in the presence of a fully connected readout layer, suggesting that the two context mechanisms are complementary. Finally, we find that learning a receptive-field-centric model with self-attention, before incrementally learning a fully connected readout, yields a more biologically realistic model in terms of center-surround contributions.