The Topological Characteristics of Biological Ratio-Sensing Networks

Ratio sensing is a fundamental biological function observed in signal transduction and decision making. In the synthetic biology context, ratio sensing presents one of the elementary functions for cellular multi-signal computation. To investigate the mechanism of the ratio-sensing behavior, we explored the topological characteristics of biological ratio-sensing networks. With exhaustive enumeration of three-node enzymatic and transcriptional regulatory networks, we found that robust ratio sensing was highly dependent on network structure rather than network complexity. Specifically, a set of seven minimal core topological structures and four motifs were deduced to be capable of robust ratio sensing. Further investigations on the evolutionary space of robust ratio-sensing networks revealed highly clustered domains surrounding the core motifs which suggested their evolutionary plausibility. Our study revealed the network topological design principles of ratio-sensing behavior and provided a design scheme for constructing regulatory circuits with ratio-sensing behavior in synthetic biology.