Comparison of Multi-Node Networks on Biological Properties

Exploring small network modules is important in systems biology. Based on three to five nodes network topologies, we have found a five-node motif with the special topological feature, i.e., the node activates its next node and restricts the one after the next simultaneously, exhibiting significant oscillation. In this paper we extend the study to multi-node (
$5 \leq n\leq 9$
) enzymatic regulatory networks and construct networks with these topological features, focusing on two important biological properties: oscillation and adaptation. We find a specific five-node and a nine-node network topologies exhibit more significant oscillation and stronger adaptation among all considered topologies, indicating that they have broader ranges of amplitude and period distributions and are capable to resist perturbations from the external input. Our approach shows that this specific five-node network is the structure with minimal nodes which exhibits excellent performance on oscillation and adaptation.