Fig. 1: Conceptual illustration of sigmoidal response by dual self-controlling system.

a Modulator in the relay of biological information. b Chemical responses for the target concentration in conventional responses. c Dual self-controlling responses (this work) (S: substrate, T: target, and P: product). d Schematic strategies for self-activation based on random depolymerization. e Self-regulation based on a switch in the rate-determining step (c1 and c2 are the threshold concentrations).