Responses of metabolic systems to large changes in enzyme activities and effectors. 2. The linear treatment of branched pathways and metabolite concentrations. Assessment of the general non-linear case.

We extend the analysis of unbranched chains (preceding paper) to large parameter changes in branched systems using linear kinetic assumptions. More complex relationships between flux control coefficients and deviation indices are established. In particular, the deviation index in such systems depends on more than one control coefficient as well as on the magnitude of the enzyme change. Non-additivity of the indices is the general rule. Combined changes of groups of enzymes, whether co-ordinate or not, have also been formulated. Control coefficients can be estimated from a small number of independent large-change experiments. Alternatively, the amplification factors can be calculated given the knowledge of the control coefficients. A 'case study' using published data is presented. The movement of intermediate metabolites as a consequence of large parameter changes can be dealt with in a similar manner. Experimental methods for showing the admissibility of assuming the simplifying assumptions used are summarised. Some simulation studies show possible limits of the application of the approach and some aspects of the general, non-linear, case are discussed. It is concluded that, although metabolic systems are in principle non-linear, many behave, in practice, as quasi-linear systems. The relationships established between deviation indices and control coefficients therefore provide a practical way of predicting the effects of large-scale changes in parameters for many metabolic systems.