Control analysis of transition times in metabolic systems

Abstract

The transition time, τ, of a metabolic system is defined as the ratio of the metabolite concentrations in the system, σ, to the steady-state flux, J. Its value reflects a temporal characteristic of the system as it relaxes towards the steady state. Like other systemic properties, the value of τ will be a function of the enzyme activities in the system. The influence of a particular enzyme activity on τ can be quantified by a Control Coefficient, C(ei)(τ). We show that it is possible to derive a Summation Theorem Σ(i=1)(n) C(ei)(τ) = -1 and a Connectivity Theorem Σ(i=1)(n) C(ei)(τ) · ε(Sk)(vi) = -S(k)/σ. We establish a 'sign rule' that predicts the order of positive and negative Control Coefficients in a sequence.