Effect of overall feedback inhibition in unbranched biosynthetic pathways

We have determined the effects of control by overall feedback inhibition on the systemic behavior of unbranched metabolic pathways with an arbitrary pattern of other feedback inhibitions by using a recently developed numerical generalization of Mathematically Controlled Comparisons, a method for comparing the function of alternative molecular designs. This method allows the rigorous determination of the changes in systemic properties that can be exclusively attributed to overall feedback inhibition. Analytical results show that the unbranched pathway can achieve the same steady-state flux, concentrations, and logarithmic gains with respect to changes in substrate, with or without overall feedback inhibition. The analytical approach also shows that control by overall feedback inhibition amplifies the regulation of flux by the demand for end product while attenuating the sensitivity of the concentrations to the same demand. This approach does not provide a clear answer regarding the effect of overall feedback inhibition on the robustness, stability, and transient time of the pathway. However, the generalized numerical method we have used does clarify the answers to these questions. On average, an unbranched pathway with control by overall feedback inhibition is less sensitive to perturbations in the values of the parameters that define the system. The difference in robustness can range from a few percent to fifty percent or more, depending on the length of the pathway and on the metabolite one considers. On average, overall feedback inhibition decreases the stability margins by a minimal amount (typically less than 5%). Finally, and again on average, stable systems with overall feedback inhibition respond faster to fluctuations in the metabolite concentrations. Taken together, these results show that control by overall feedback inhibition confers several functional advantages upon unbranched pathways. These advantages provide a rationale for the prevalence of this control mechanism in unbranched metabolic pathways in vivo.