# Geometric analysis of pathways dynamics: application to versatility of TGF-β receptors

Satya Samal, Aurélien Naldi, Dima Grigoriev, Andreas Weber, Nathalie Thèret, and Ovidiu Radulescu
In: Biosystems (July 2016)

## Abstract

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. Given the network topology and the orders of magnitude of kinetic parameters, the number of such metastable regimes is finite. The dynamics of the network can be described as a sequence of jumps from one metastable regime to another. We show that a geometrically computed connectivity graph restricts the set of possible jumps. We also provide finite state machine (Markov chain) models for such dynamic changes. Applied to signal transduction models, our approach unravels dynamical and functional capacities of signaling pathways, as well as parameters responsible for specificity of the pathway response. In particular, for a model of TGF\beta signalling, we find that the ratio of TGFBR1 to TGFBR2 concentrations can be used to discriminate between metastable regimes. Using expression data from the NCI60 panel of human tumor cell lines, we show that aggressive and non-aggressive tumour cell lines function in different metastable regimes and can be distinguished by measuring the relative concentrations of receptors of the two types.

## Bibtex

@ARTICLE{Samal2015c,
author = {Samal, Satya and Naldi, Aur{\'e}lien and Grigoriev, Dima and Weber, Andreas and Th{\`e}ret, Nathalie and
title = {Geometric analysis of pathways dynamics: application to versatility of TGF-β receptors},
journal = {Biosystems},
year = {2016},
month = jul,
abstract = {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.
Given the network topology and the orders of magnitude of kinetic parameters, the number of such
metastable regimes is finite. The dynamics of the network can be described as a sequence of jumps
from one metastable regime to another. We show that a geometrically computed connectivity graph
restricts the set of possible jumps. We also provide finite state machine (Markov chain) models for
such dynamic changes. Applied to signal transduction models, our approach unravels dynamical and
functional capacities of signaling pathways, as well as parameters responsible for specificity of
the pathway response. In particular, for a model of TGF$\beta$ signalling, we find that the ratio of
TGFBR1 to TGFBR2 concentrations can be used to discriminate between metastable regimes. Using
expression data from the NCI60 panel of human tumor cell lines, we show that aggressive and
non-aggressive tumour cell lines function in different metastable regimes and can be distinguished
by measuring the relative concentrations of receptors of the two types.},
doi = {10.1016/j.biosystems.2016.07.004}
}