Control analysis of metabolic networks

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Abstract
The summation theorem C1J + ... + CnJ = 1 for flux control coefficients CiJ is shown to be equivalent to the assumption that flux J is a homogeneous function of degree 1 of enzyme concentrations E1,..., En, that is to the assumption J (tE1,...,tEn) = tJ(E1,...,En) for any t .noteq. 0. Likewise, the summation theorem C1Xj + ... + CnXj=0 for concentration control coefficients CiXj is equivalent to homogeneity of degree 0 of steady-state metabolite concentrations Xj, or to Xj(tE1,...,tEn) = Xj(E1,...,En). From this equivalence it is obvious that metabolic control analysis applies only to homogeneous systems. The summation theorem for flux control coefficients is shown to be equivalent to that for concentration control coefficients, provided all reaction rates vi are homogeneous functions of enzyme concentrations Ei. The equivalence between homogeneity of flux J and the summation theorem for flux control coefficients is used to analyse branching of fluxes in metabolic pathways in terms of flux control coefficients.