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Figure 6 | BMC Systems Biology

Figure 6

From: (Im)Perfect robustness and adaptation of metabolic networks subject to metabolic and gene-expression regulation: marrying control engineering with metabolic control analysis

Figure 6

The closed-loop control structure of a metabolic pathway subject to various types of regulation. There are three types of feedback control mechanisms: i) proportional or nonlinear control that is related to the substrate or allosteric effects; ii) derivative control that can be related with signalling, e.g. phyosphocreatine buffering; and iii) integral control introduced by gene-expression regulation because protein synthesis requires time integration. The former two control loops i) and ii) are often modelled together with the dynamics of the metabolic process. Here, metabolite concentration X is the output of a metabolic process and is the controlled variable of different control loops. Reaction rates v(X,E) are the manipulated variables because they are functions of both enzyme concentration E, i.e. the output of integral control loop (gene-expression regulation), and metabolic process (f(X)), i.e. the outputs of proportional/nonlinear and derivative control loops (metabolic regulation or signalling). Here, the integral control input q(t) is a function of the controlled variable (q(t) = φ(X(t)) or the difference (or error) between the controlled variable and a reference signal (r).

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