Susceptibility of non-linear systems as an approach to metabolic responses

Abstract

http://bbm1.ucm.es/torralba/funder/

Susceptibilities of an Irreversible Michaelis – Menten Enzyme

“…The finite response of a metabolic system, F , can be obtained from a functional Taylor expansion (Torralba, 2003) of the form…”

“…A susceptibility is a special kind of derivative, a functional derivative, because it is taken with respect to a function, not to a scalar variable (cf. Torralba, 2003). Thus, it has greater generality than the usual definition.…”

“…In other words, they are expected to depend on time differences, rather than on absolute times. The procedure for computing the enzyme susceptibilities involves several steps (an algorithm was presented by Torralba, 2003; additional details will be published elsewhere): (1) to determine the progress curve (decay) of the rate (or concentration) as a function of the initial substrate concentration; (2) to find the sensitivities (derivatives) of the progress curve with respect to the initial concentration;…”

“…In a previous paper (Torralba, 2003), it was shown that a possible solution is to express the nonlinear response of the metabolic network as a transformation of variable inputs into variable outputs, by means of a sensitivity analysis, in the line of CCT. The original application showed the potential of the method for small-and medium-sized networks.…”

“…First, to adapt the method presented in Torralba (2003) so that decays (responses to only one impulse) can be used to characterize the response of a metabolic system to arbitrary timedependent fluxes, and second, to illustrate the approach by means of an analytically workable example. For that, the simplest Michaelis-Menten enzyme will be considered.…”