Effects of feedback inhibition on transit time in a linear pathway of Michaelis-Menten-type reactions

An analysis of the effects of external and internal metabolites on the steady-state behavior of linear pathways comprising a sequence of three Michaelis-Menten-type reactions with and without a simple feedback inhibition (i.e. an interaction of an internal metabolite with the pathway) is performed with respect to the transit time tau by its formulation as rectangular-hyperbolic functions of the flux J, instead of direct expressions in terms of the external metabolite concentrations. For a given concentration of the external metabolite M1 (substrate of the pathway) or M4 (product of the pathway), the flux J has a lower value in the pathway with feedback inhibition than in the pathway without feedback inhibition. With variation in the M1 concentration the transit time tau shows a concave relationship with the flux J which is virtually identical for both pathways, yielding a minimum at a certain value of J. With variation in the M4 concentration the transit time tau monotonously decreases with higher value of J, and for a given value of J the feedback inhibition allows a lower transit time. This effect is enhanced with stronger feedback inhibition, and is in turn greatly reduced with higher values of total concentration and rate constants for the first enzyme in the pathway.