Geometric analysis of pathways dynamics: application to versatility of TGF-{\beta} receptors

TL;DR

This paper introduces a geometric method to analyze the dynamics of chemical reaction networks, identifying metastable regimes and modeling pathway transitions, with applications to TGF-β signaling and tumor cell line differentiation.

Contribution

The authors develop a novel geometric framework for understanding pathway dynamics and metastable states in chemical networks, applied to signaling pathways and cancer cell differentiation.

Findings

Metastable regimes can be identified using geometric analysis.

The TGFβ receptor ratio discriminates metastable regimes.

Tumor cell lines differ in their metastable pathway regimes.

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.