BioSystems 45 (1998) 221 – 235 Effects of feedback inhibition on transit time in a linear pathway of Michaelis – Menten-type reactions Naoto Sakamoto 1 , Pedro de Atauri, Marta Cascante * Department of Biochemistry and Molecular Biology, Faculty of Chemistry, Uniersity of Barcelona, Martı ´ i Franque `s 1, 08028, Barcelona, Spain Received 5 April 1997; received in revised form 30 January 1998; accepted 3 February 1998 Abstract 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  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 M 1 (substrate of the pathway) or M 4 (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 M 1 concentration the transit time  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 M 4 concentration the transit time  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. © 1998 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Transit time; Relationship of steady-state behavior with flux; Linear pathway; Michaelis – Menten kinetics; Feedback inhibition 1. Introduction The transit time is a system variable that is suitable for the correlation of reaction mecha- nisms in a metabolic pathway with the character- istics of steady-state behavior of the flux and the metabolites in the pathway. It represents the time * Corresponding author. Tel.: +34 3 4021593; fax: +34 3 4021219; e-mail: marta@sun.bq.ub.es 1 On leave from the absence of the University of Tsukuba, Institute of Information Sciences and Electronics 0303-2647/98/$19.00 © 1998 Elsevier Science Ireland Ltd. All rights reserved. PII S0303-2647(98)00011-2