Linking metabolic network features to phenotypes using sparse group lasso.

Motivation: Integration of metabolic networks with '-omics' data has been a subject of recent research in order to better understand the behaviour of such networks with respect to differences between biological and clinical phenotypes. Under the conditions of steady state of the reaction network and the non-negativity of fluxes, metabolic networks can be algebraically decomposed into a set of sub-pathways often referred to as extreme currents (ECs). Our objective is to find the statistical association of such sub-pathways with given clinical outcomes, resulting in a particular instance of a self-contained gene set analysis method.

Geometric analysis of pathways dynamics: Application to versatility of TGF-β receptors.

We propose a new geometric approach to describe the qualitative dynamics of chemical reactions networks. By this method we identify metastable regimes, defined as low dimensional regions of the phase space close to which the dynamics is much slower compared to the rest of the phase space. These metastable regimes depend on the network topology and on the orders of magnitude of the kinetic parameters.

A Geometric Method for Model Reduction of Biochemical Networks with Polynomial Rate Functions.

Model reduction of biochemical networks relies on the knowledge of slow and fast variables. We provide a geometric method, based on the Newton polytope, to identify slow variables of a biochemical network with polynomial rate functions. The gist of the method is the notion of tropical equilibration that provides approximate descriptions of slow invariant manifolds.