Principal Process Analysis and reduction of biological models with order of magnitude

We present a simple method that allows to analyze the biological processes of a dynamical model and classify them. Along the system trajectories, we decompose the model into biological meaningful processes and then study their activity or inactivity during the time evolution of the system. The structure of the model is then reduced to the core mechanisms involving only the active processes. The initial conditions are supposed to lie in some rectangle, that could represent one order of magnitude for the variables. Keeping only the active processes, we obtain the principal processes in the rectangle and then in the adjacent rectangles where the trajectories may have a transition. Finally we obtain a partition of the space with a reduced model within each rectangle. We apply these techniques to a classical model of gene expression with protein and messenger RNA.