Interlocked multi-node positive and negative feedback loops facilitate oscillations

Positive and negative feedback loops in biological regulatory networks appear often in a multi-node manner since regulatory processes are in general multi-step. Although it is well known that interlocked positive and negative feedback loops (iPNFLs) can generate sustained oscillations, how the number of nodes in each loop affects the oscillations remains elusive. By analyzing a model of iPNFLs with multiple nodes, we find that the node number of the negative loop mainly plays a role of amplifying oscillation amplitudes whereas that of the positive loop mainly plays a role of reducing oscillatory regions, both depending on the (competitive or noncompetitive) way of interaction between the two loops. We also find that given an iPNFL network of the same structure, the noncompetitive model is more likely to produce large-amplitude oscillations than the competitive model. These results not only indicate that multi-node iPNFLs are an effective mechanism of promoting oscillations but also are helpful for the design of synthetic oscillators.