## Project-Team : modbio

## Section: New Results

**Keywords: ***metabolic networks*, *pathways*, *polyhedra*, *extreme rays*.

## Metabolic pathways analysis

**Participants:**Alexander Bockmayr, Stéphanie Bonne-Billaut, Abdelhalim Larhlimi.

Studying metabolic networks at steady state involves the computation
of special pathways that characterize all the possible fluxes in the
network. From a mathematical point of view, those pathways
correspond to the extreme rays of a polyhedral cone, which is
defined by all the fluxes verifying the stoechiometric constraints
of the system, together with some non-negativity constraints.
Several approaches have been recently proposed to compute such
extreme pathways [41].
However, due to the inherent algorithmic complexity of the problem,
their number may be very large even for small networks.
In [22], we propose an improved formalization of the
metabolic network, which reduces the number of variables and
constraints. This allows us to determine a minimal set of
characteristic pathways, which we call *generic* pathways. The
generic pathways form a proper subset of the extreme pathways, and
their number is typically much smaller. We use the double
description method [36] to compute those generic
pathways. We give also an algorithm that allows us to obtain all
the extreme pathways from the generic ones. This method is currently
being implemented.

In collaboration with ISA Beauvais (A. Chango), we have developed in [20] several models of the one-carbon metabolism. Anomalies in this system, depending on B group vitamins, play an important role in various diseases, such as cardiovascular diseases, Alzheimer etc. Experimental studies being difficult, an in silico analysis seemed promising. We studied the dynamics of the system starting from an ordinary differential equation model of the methionine cycle [43], and by applying the power-law formalism [49]. In a second step, a steady-state analysis of the one-carbon metabolism was performed, based on the method outlined before. The generic pathways that have been found are subject to further biological study.