A phase diagram structure determines the optimal sensitivity-precision trade-off in signaling systems

Abstract

Signal transduction is crucial for many biological functions. However, it is still unclear how signaling systems function accurately under noisy situations. More specifically, such systems operate in a regime of low response noise, while maintaining high sensitivity to signals. To gain further insight on this regime, here we derive a fundamental trade-off between response sensitivity and precision in biological signaling processes under the static noise condition. We find that the optimal trade-off in signaling networks can be better characterized by a phase diagram structure rather than topological structures. We confirm that the patterning network of early Drosophila embryos agrees with our derived relationship, and apply the optimal phase diagram structure to quantitatively predict the patterning position shifts of the downstream genes, including hunchback, Krüppel, giant, knirps and even-skipped, upon the dosage perturbation of the morphogen Bicoid.