This first paper in a series investigates the problem of predicting and analysing the effects of large changes in enzyme activities or external nutrients/effectors on metabolic fluxes. We introduce the concept of a deviation index, D, which gives a measure of the relative change in a metabolic variable (e.g. flux) due to a large (non-infinitesimal) relative change in a parameter (e.g. enzyme). Using simplifying kinetic assumptions we have found, for an unbranched metabolic chain, a direct relationship between deviation indices and flux control coefficients. This relationship provides a method to estimate flux control coefficients using a single large change in enzyme activity. We also provide a method of predicting the effects of, for example, DNA manipulation or other techniques for enzyme activity/concentration changes on metabolic fluxes. Up-modulations of single enzymes rarely produce significant changes in fluxes. We show that combined changes of activity of a group of enzymes will produce a more than 'additive' response. We provide a method of predicting the effects of these combined changes, given either the flux control coefficients of the group of enzymes or the effects on the flux of changing the enzymes individually. A similar analysis is carried out for large changes in external nutrients or effectors. These amplification factors, f, give experimentally accessible estimates of the expected changes in metabolic variables. We provide three 'case studies' to illustrate our results.