Generalization of the theory of transition times in metabolic pathways: a geometrical approach

Cell metabolism is able to respond to changes in both internal parameters and boundary constraints. The time any system variable takes to make this response has relevant implications for understanding the evolutionary optimization of metabolism as well as for biotechnological applications. This work is focused on estimating the magnitude of the average time taken by any observable of the system to reach a new state when either a perturbation or a persistent variation occurs. With this aim, a new variable, called characteristic time, based on geometric considerations, is introduced. It is stressed that this new definition is completely general, being useful for evaluating the response time, even in complex transitions involving periodic behavior. It is shown that, in some particular situations, this magnitude coincides with previously defined transition times but differs drastically in others. Finally, to illustrate the applicability of this approach, a model of a reaction mediated by an allosteric enzyme is analyzed.