Biochemical Systems Theory - Representation

Representation

The dynamics of a species is represented by a differential equation with the structure:

where X_i represents one of the n_d variables of the model (metabolite concentrations, protein concentrations or levels of gene expression). j represents the n_f biochemical processes affecting the dynamics of the species. On the other hand, _ij (stoichiometric coefficient), _j (rate constants) and f_jk (kinetic orders) are two different kinds of parameters defining the dynamics of the system.

The principal difference of power-law models with respect to other ODE models used in biochemical systems is that the kinetic orders can be non-integer numbers. A kinetic order can have even negative value when inhibition is modelled. In this way, power-law models have a higher flexibility to reproduce the non-linearity of biochemical systems.

Models using power-law expansions have been used during the last 35 years to model and analyse several kinds of biochemical systems including metabolic networks, genetic networks and recently in cell signalling.