Spatiotemporal expressions reflecting topological classes of repressor networks

A family of repressor networks is proposed as a simple model of gene regulatory networks. We analytically show three topological classes of the repressor networks, each of which exhibits distinctly growing complexity of spatiotemporal expressions starting from nearly homogeneous states. Further, by focusing on locally interacting cases such as chain networks, including a generalized repressilator, or feedforward(back)-loop networks, spatiotemporal expressions in the long time regime and elusive relationships between such different networks are discussed in detail.