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 a nd boundary constraints. The time any system variable takes to make this re sponse has relevant implications for understanding the evolutionary optimiz ation of metabolism as well as for biotechnological applications. This work is focused on estimating the magnitude of the average time taken by any ob servable of the system to reach a new state when either a perturbation or a persistent variation occurs. With this aim, a new variable, called charact eristic time, based on geometric considerations, is introduced. It is stres sed that this new definition is completely general, being useful for evalua ting the response time, even in complex transitions involving periodic beha vior. It is shown that, in some particular situations, this magnitude coinc ides with previously defined transition times but differs drastically in ot hers. Finally, to illustrate the applicability of this approach, a model of a reaction mediated by an allosteric enzyme is analyzed.