The original Convolutional Neural Networks (CNNs) and their modern updates such as the ResNet are heavily inspired by the mammalian visual system. These models include afferent connections (retina and LGN to the visual cortex) and long-range projections (connections across different visual cortical areas). However, in the mammalian visual system, there are connections within each visual cortical area, known as lateral (or horizontal) connections. These would roughly correspond to connections within CNN feature maps, and this important architectural feature is missing in current CNN models. In this paper, we present how such lateral connections can be modeled within the standard CNN framework, and test its benefits and analyze its emergent properties in relation to the biological visual system. We will focus on two main architectural features of lateral connections: (1) recurrent activation and (2) separation of excitatory and inhibitory connections. We show that recurrent CNN using weight sharing is equivalent to lateral connections, and propose a custom loss function to separate excitatory and inhibitory weights. The addition of these two leads to increased classification accuracy, and importantly, the activation properties and connection properties of the resulting model show properties similar to those observed in the biological visual system. We expect our approach to help align CNN closer to its biological counterpart and better understand the principles of visual cortical computation.