Time-course curves of enzyme reactions with dilute substrates can be determined from the reverse reactions

We present a novel and useful principle that can be applied to enzyme reactions with dilute substrates and enables to obtain the desired time-course curve from the reverse reaction when the latter can be measured more easily. Let us imagine an enzyme mixture that can catalyze the interconversion between substances A, B, C,.... If one substance (sufficiently dilute) is added to the mixture as the substrate and the time-course curve of the concentration of another substance is followed, then, "the time-course curve of A-->B" (which is the time-course curve of the concentration of substance B when substance A is added as the substrate) and that of the reverse reaction B-->A will coincide when plotted at appropriate scales of magnitude. Similar relation holds on any pair of substances even if they are widely separated in any type of reaction scheme. The principle was proved mathematically and holds on any first-order reaction network and can be applied on an enzyme reaction with a dilute substrate because it is reduced to a first-order reaction network. An example of experimental application of this principle is also given.