A Map about power-law models in biochemical systems

The following figure shows how the different power-law models can be derived from the very general equation that describe all the kinetic models used to model biochemical systems.

From the original equation, we obtain Detailed power-law models if we allow positive non-integer kinetic orders. We notice that Conventional kinetic models are obtained from the same equation if only positive integer kinetic orders are allowed (g=1 for simple interaction and g=2 for dimerisation). In detailed power-law models all the biochemical processes in the investigated biological system are considered, which lead to the use of positive non-integer (higher than one) kinetic orders; they encode the effect of the non-homogeneous intracellular medium.

If we simplify the model aggregating some processes into simple rate equations, we obtain Simplified power-law models. In this case, kinetic orders can have any non-integer value, even non-integer negative numbers when inhibitory processes are considered with simplified equations.

Finally, if we apply a generalised rate aggregation in which all positive input (or production) fluxes are aggregated into a unique input flux and negative output (or degradation) fluxes are aggregated into a unique negative flux, we obtain S-system models.