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

Abstract

International audienceWe 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

Principal process analysis of biological models

“…In a recent study, we also showed by other methods the robustness of PPA to initial conditions [ 21 ]. The latter were supposed to lie in rectangles contained in a region of the variable space varying by one order of magnitude in each coordinate.…”

“…We hence observed that the negative feedback loop controlling Per and Cry transcription through the formation of the large complex PER-CRY-CLOCK-BMAL1 is the main oscillator, in agreement with previous experimental and modelling studies [ 17 , 25 , 26 ]. Principal Process Analysis has been also applied with success to diverse biogeochemical and biochemical models in our group and elsewhere, see [ 14 , 21 , 28 , 29 ]. These case studies and the present one exemplify the applicability and scalability of the approach to models of diverse nature and and complexity.…”

“…Based on the behaviour of processes on the edges of the rectangles, it was then possible to determine the transitions between rectangles and deduce the evolution of process activities along the different transitions. The method has been applied on a small gene expression network containing a negative feedback loop [ 21 ]. The same principles could be applied to show the robustness of the model to larger variations of its parameters.…”

“…It may be questioned whether the uncertainty of their values influences the simplification of the model and thus, the analysis of the system dynamics. While we have shown PPA to be robust to variations of initial conditions in [ 21 ], the question remains open for parameter values.…”

Principal Process Analysis of dynamic GlucoCEST MRI data

“…This analysis allows designing a reduced model, dedicated to the fitting of experimental data, and quantification of physiological parameters. To do so we apply Principal Process Analysis (PPA) [3,4], a numerical method for the analysis and reduction of biological systems designed with ODE formalism. PPA allows associating a dynamic weight to all involved processes and inferring their importance during the acquisition time.…”