Deterministic and stochastic models of enzymatic networks—applications to pharmaceutical research

The intracellular transducing device consists of complex networks of enzymatic reactions. Unfortunately, the mathematical models commonly used to describe them are still unsatisfactory and unreliable, even at the level of reproducing simple reaction schemes. The improvement of mathematical models is necessary and can follow different approaches still poorly employed, such as the modeling of spatial structures and phenomena, time delays, stochastic perturbations, only to cite the most relevant ones. In this paper we show some recent results related to the total quasi-steady-state approximation (tQSSA), in a deterministic scenario. Moreover, we show some possible applications of the tQSSA in a stochastic scheme.