Slow-Fast Systems in Cellular Biology

Informations projet

SFSysCellBio

N° de convention de subvention: 661650

DOI

10.3030/661650

Projet clôturé

Date de signature de la CE 31 Août 2015

Date de début 30 Août 2016

Date de fin 29 Août 2019

Financé au titre de

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Coût total

€ 178 156,80

Contribution de l’UE

€ 178 156,80

Coordonné par

TECHNISCHE UNIVERSITAET WIEN
Austria

Periodic Reporting for period 1 - SFSysCellBio (Slow-Fast Systems in Cellular Biology)

Période du rapport: 2016-08-30 au 2018-08-29

Résumé du contexte et des objectifs généraux du projet

Biologists have identified a wealth of molecular components and regulatory mechanisms underlying the
control of the fundamental cellular processes such as cell differentiation, cell cycle, and cell death. A
multitude of signalling pathways controlling the response of cells to environmental variability or stimuli is
critical for these processes. Mathematical modelling has emerged as an important tool to handle the overwhelmingly structural
complexity of cellular processes and to gain better understanding of their functioning and dynamics.

This project was devoted to the mathematical analysis of ODE models arising in cell biology. Pertinent mathematical questions of
biological interest are: existence and stability of equilibria, periodic oscillations, switching phenomena, and bifurcations, i.e. changes
of these dynamical properties as key parameter vary. The approach in this project relied strongly on novel dynamical systems
methods for systems with multiple time scale dynamics, known as geometric singular perturbation theory (GSPT). These methods
have been successfully used in many areas of mathematical physiology, e.g. mathematical neuroscience and calcium signaling.
However, slow-fast analysis and GSPT of mathematical models of the cell cycle and for signaling pathways is much less established.

Travail effectué depuis le début du projet jusqu’à la fin de la période considérée dans le rapport et principaux résultats atteints jusqu’à présent

We have focused on several models based on Michaelis-Menten type kinetics. Interestingly, the models under investigation do not have the standard form of slow-fast systems and were not covered by the existing theory. It turns out that such systems have a specific hidden multi-scale structures caused by the occurrence of very large or very small parameters in important types of nonlinearities commonly found in such models, e.g. Michaelis-Menten-type terms and Hill functions.
In this project an extended version of GSPT was adopted to singular perturbation problems of general type arising in these contexts, in order to analyze the induced dynamics, in particular switching phenomena and oscillatory behavior. The research generated novel mathematical results and led to considerable advances in the field of GSPT.
The methods were applied to specific signalling problems in collaboration with our project partner from systems biology.
A visualization tool, which supports our geometric approach, has been developed in collaboration with partners from computer science working in visualization.

Progrès au-delà de l’état des connaissances et impact potentiel prévu (y compris l’impact socio-économique et les conséquences sociétales plus larges du projet jusqu’à présent)

Impact on mathematics and modelling in cell biology.

The project advanced multidisciplinary research at the boundary of mathematics and modelling in cell biology.
New geometric techniques and dynamical systems methods for the analysis of medium sized models with complicated slow-fast dynamics have been developed which
considerably extend the scope and applicability of GSPT. Systematic mathematical analysis of biological models supports simulation and interpretation of
results. This leads to better understanding of the cellular processes and their dynamics. The techniques and tools used and developed in the project are applicable in the analysis of other important signaling and control pathways.

visualization by manylands