The average enzyme principle

The Michaelis-Menten equation for an irreversible enzymatic reaction depends linearly on the enzyme concentration. Even if the enzyme concentration changes in time, this linearity implies that the amount of substrate depleted during a given time interval depends only on the average enzyme concentration. Here, we use a time re-scaling approach to generalize this result to a broad category of multi-reaction systems, whose constituent enzymes have the same dependence on time, e.g. they belong to the same regulon. This “average enzyme principle” provides a natural methodology for jointly studying metabolism and its regulation.