Canonical sensitivities: a useful tool to deal with large perturbations in metabolic network modeling

The dynamic range of metabolic models can be extended to deal with large perturbations by introducing the related concepts of "generalized" kinetic order and "canonical" sensitivities. Generalized kinetic orders are built as a well-defined non linear combination of the canonical sensitivities coefficients, which in turn are obtained by a least-squares regression on central composite factorial design data. In a such way, the whole domain of the operating variables is mapped without need to determine locally neither the first nor the second order model derivatives. The method was validated through numerical simulations, its predictions being compared with those coming from a Michaelis-Menten formalism taken as reference. In parallel, two variants of the Power-law formalism (S-system, least-squares GMA) also were tested. The canonical sensitivities method produced the widest range to predict metabolite concentrations and metabolic fluxes at the steady states. In addition, the variation pattern for the logarithmic gains and for the characteristic eigenvalues have been accurately determined from a unique overall model, being both required to make realistic analysis in metabolic engineering. The achieved information also can be expressed in terms of those typical coefficients derived from the Metabolic Control Analysis (MCA). Even if current first order Power-law or MCA formalisms were used, the canonical sensitivities approach provides a significant advantage, since complete sets of homologous, accurate, locally valid metabolic coefficients can be simultaneously recovered from the array proposed, being representative of the whole range of the operating variables instead of a unique nominal condition as is usual.