Fig 6. Regulation by intracellular substrate concentrations.

S_int can regulate either (A) transporter synthesis (α_T) or (B) transporter downregulation (γ_T). In both cases, we assume this regulation takes the form of a Hill equation with a 'saturation' constant of (A) K_syn or (B) K_deg. The saturation constant is the equivalent to the standard disassociation constant but represents the concentration where the system is half saturated for its regulatory potential. For (A) and (B) the diagram on the right uses a hill coefficient (n) of 3, (case of n = 1 is in S1 Appendix, section VII part b, S1 Fig). Higher n leads to more robustness, but global perfect homeostasis is not achievable by any finite value of n. For both (A) and (B), the saturation constants are normalized by $S_0=\frac{k_{act}{\alpha }_T}{k_{{\gamma }_S}{k}_{{\gamma }_T}^c}$.