Distinctive topologies of partner-switching signaling networks correlate with their physiological roles

Regulatory networks controlling bacterial gene expression often evolve from common origins and share homologous proteins and similar network motifs. However, when functioning in different physiological contexts, these motifs may be re-arranged with different topologies that significantly affect network performance. Here we analyze two related signaling networks in the bacterium Bacillus subtilis in order to assess the consequences of their different topologies, with the aim of formulating design principles applicable to other systems. These two networks control the activities of the general stress response factor sigma(B) and the first sporulation-specific factor sigma(F). Both networks have at their core a "partner-switching" mechanism, in which an anti-sigma factor forms alternate complexes either with the sigma factor, holding it inactive, or with an anti-anti-sigma factor, thereby freeing sigma. However, clear differences in network structure are apparent: the anti-sigma factor for sigma(F) forms a long-lived, "dead-end" complex with its anti-anti-sigma factor and ADP, whereas the genes encoding sigma(B) and its network partners lie in a sigma(B)-controlled operon, resulting in positive and negative feedback loops. We constructed mathematical models of both networks and examined which features were critical for the performance of each design. The sigma(F) model predicts that the self-enhancing formation of the dead-end complex transforms the network into a largely irreversible hysteretic switch; the simulations reported here also demonstrate that hysteresis and slow turn off kinetics are the only two system properties associated with this complex formation. By contrast, the sigma(B) model predicts that the positive and negative feedback loops produce graded, reversible behavior with high regulatory capacity and fast response time. Our models demonstrate how alterations in network design result in different system properties that correlate with regulatory demands. These design principles agree with the known or suspected roles of similar networks in diverse bacteria.