Understanding the dynamical behavior of biological networks is complicated due to their large number of components and interactions. We present a method to analyse key processes for the system behavior, based on the a priori knowledge of the system trajectory and the simplification of mathematical models of these networks. The method consists of the model decomposition into biologically meaningful processes, whose activity or inactivity is evaluated during the time evolution of the system. The structure of the model is reduced to the core mechanisms involving active processes only. We assess the quality of the reduction by means of global relative errors and apply our method to two models of the circadian rhythm in Drosophila and the influence of RKIP on the ERK signaling pathway.

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.

The aim of this paper is to analyze the dynamical behavior of gene transcription-translation models, in particular the system of synthesis of RNA polymerase in a cell. Because RNA polymerase is needed to transcribe its own gene, it is an example of a positive feedback loop. We write a full model of high dimension based on mass-action laws. Using monotone system theory and time-scale arguments, we reduce it to a model with two variables (RNA polymerase protein and its mRNA) and we show (again by techniques from monotone systems) that it has either a single globally stable trivial equilibrium in (0; 0), or it has an unstable zero equilibrium and a globally stable positive one. Moreover, we give generalizations of this model, in particular with a variable growth rate. The dynamical behaviour can be related to biological observations on the bacterium Escherichia coli that raise important questions in biology.

Understanding the dynamical behavior of biological systems is challenged by their large number of components and interactions. We design a method for dealing with this complexity, based on the reduction of dynamical models by means of Principal Process Analysis. In this paper, we applied the method to a well-known model of circadian rhythms in Mammals [1]. The knowledge of the system trajectories allowed us to decompose the system dynamics into processes that were active or inactive with respect to a certain threshold value. We eliminated from the model processes that were always inactive, and inactive in one or several time windows. This reduced the complex dynamics of the original model to the much simpler dynamics of the core processes, in a succession of sub-models that were easier to analyze. We used global relative errors to assess the quality of the model reduction and applied global sensitivity analysis to test the influence of model parameters on the errors. Results proved the robustness of our method. In addition we showed for our example that in each reversible reaction of the system, the direct reaction was generally active and the reverse reaction inactive. Such a simple method could be a supplementary tool to analyze the dynamical behavior of complex biological systems.