Mathematical modelling of negative feedback regulation by carboxyltransferase.

Acetyl-CoA carboxylase catalyses the first committed step in fatty acid synthesis in all organisms. The chemistry is accomplished in two half-reactions: activation of biotin via carboxylation by biotin carboxylase, followed by the carboxyltransferase-catalysed transfer of the carboxyl moiety from carboxybiotin to acetyl-CoA to generate malonyl-CoA. The Escherichia coli form of the carboxyltransferase subunit was recently found to regulate its own activity and expression by binding its own mRNA. By binding acetyl-CoA or the mRNA encoding its own subunits, carboxyltransferase is able to sense the metabolic state of the cell and attenuate its own translation and enzymatic activity using a negative feedback mechanism. Here, the network of these interactions is modelled mathematically with a set of non-linear differential equations. Numerical simulations of the model show that it qualitatively and quantitatively agrees with the experimental results for both inhibition of carboxyltransferase by mRNA and attenuation of translation. The modelling of the autoregulatory function of carboxyltransferase confirms that it is more than isolated interactions, but functions as a single dynamic system.