Fig. 1.

Modular representation of the chemotaxis system. (A) Transmembrane receptors bind the ligand (L) and control the activity of histidine kinases CheA (A). The kinase CheA phosphorylates the response regulator CheY (Y) into the active form CheY-P (Y_p). CheY-P diffuses throughout the cell and interacts with the flagellar motors to induce clockwise rotation (tumble). The phosphatase CheZ (Z) dephosphorylates CheY-P (42). A sudden increase of ligands ΔL causes the kinase activity to decrease by ΔA*. The chemotaxis system is equipped with an adaptation module in which two antagonistic enzymes regulate the activity of the kinase-receptor complexes. The methyltransferase CheR (R) catalyzes the autophosphorylation of CheA by methylating the receptors. The active kinase A* phosphorylates the methylesterase CheB in CheB-P (B_p). CheB-P removes methyl groups from active receptor complexes, which catalyzes kinase deactivation. (B) The adaptation module consists of a series of slow (de)methylation reactions that modulate the activity of the receptor complexes. We use a two-state model where the probability a_m of a receptor complex to be in active conformation depends on the occupancy of its ligand binding sites and on the level of methylation of the receptors that ranges within m = 0, …, m_max (7, 17–19). m_max is the total number of methylation sites. We assume that CheR only methylates inactive complexes (43), whereas CheB-P only demethylates active complexes (44) (details on the model and alternative hypotheses in Sect. 4 of SI Appendix).