# Differential Algebra and Chemical Reaction Networks

This informal workshop on differential algebra and chemical reaction networks is partially funded by a Procope project and the CFHP team.

### Monday November 7th, 2016 (M3 226)

- Morning, 9h30. Informal discussion.
- Afternoon. Working group on Kolchin's proof of [1, IV, 17, Proposition 10, page 200].

[1] Ellis R. Kolchin.*Differential Algebra and Algebraic Groups*. Academic Press, 1973

### Tuesday November 8th, 2016 (M3 324)

The Tuesday is dedicated to the visit of Julien Sebag (univ. Rennes I).

- 10h00-18h30. Julien Sebag. Seminar/Lecture on the "schéma des arcs", its relationship with differential algebra, and a geometric proof of the irreductibility theorem of Kolchin [1, IV, 17, Proposition 10, page 200]. Talk in French, with lecture notes in English.
- Evening. Restaurant

### Wednesday November 9th, 2016 (M3 226)

- Morning, 10h00. Matthias Seis. An introduction to the differential Galois theory.
- Afternoon. François Lemaire. Title to be precised.

### Thursday November 10th, 2016 (M3 336 PM)

- Morning, 10h30 (M3 226). Talk of the Biocomputing Working Group by Émilie Allart. Elementary flux modes improve changes prediction of reaction networks with partial kinetic information.

Elementary flux mode analysis, consisting in finding non decomposable steady state pathways in metabolic networks, has been proven to be a valuable approach in gaining understanding of cellular metabolism. In our previous work, we wanted to predict which influx changes and reaction knockouts lead to an overproduction of metabolite of interest within a reaction networks with partial kinetic information, based on abstract interpretation that allows qualitative reasoning about changes on the reaction network at steady state. Nevertheless, abstract interpretation over-approximates the solution space. To make up this problem, we enhance our knowledge of the reaction network by finding a minimal set of equations representing all consequences of the elementary modes.