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250115 VO Mathematical models of chemical and metabolic networks (2021W)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik
ON-SITE

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

max. 25 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

Wednesday 13.10. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 20.10. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 27.10. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 03.11. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 10.11. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 17.11. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 24.11. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 01.12. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 15.12. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 12.01. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 19.01. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Wednesday 26.01. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

Aims

Fundamental cellular functions including signaling, gene regulation, and metabolism involve numerous molecular species interacting via chemical reactions. More than one century of biochemistry and several decades of molecular biology have provided an unprecedented window into the complexity of such chemical reaction networks in living cells. Recent experimental techniques even allow real-time observations of complex dynamical behaviour such as hysteresis, oscillations, and stochastic fluctuations.

Mathematics has played a pivotal role in coping with the complexity of chemical reaction networks and is a cornerstone of current systems biology. In this lecture, we will consider two modeling frameworks in more detail.

Contents

Chemical networks: Many cellular systems can be modeled as networks of chemical reactions, often with mass-action kinetics (leading to ordinary differential equations with polynomial right-hand sides). Interestingly, for large classes of networks, the qualitative behaviour of the dynamical systems is independent of the system parameters.

In this lecture, we will prove a classical result that guarantees existence, uniqueness, and stability of positive equilibria independently of the rate constants (for networks with deficiency zero). Moreover, we will study extensions of the theory to systems with generalized mass-action kinetics.

Metabolic networks: As a particular cellular system, metabolism is modeled as a network of enzymatic reactions, often without exact knowledge of the kinetics. Since cellular organisms survive and reproduce in complex environments under permanent evolutionary pressure, metabolic pathways are assumed to be highly adapted, and optimality principles are used to study the organization of metabolism. Traditionally, the analysis of genome-scale metabolic models is based on stoichiometric data, leading to linear programs for fluxes (steady-state reaction rates).

In this lecture, we will also consider kinetic data and study optimal enzyme allocation, leading to nonlinear problems. Importantly, optimal solutions are (combinations of) elementary flux modes (elementary vectors of the flux cone), representing minimal metabolic pathways.

Methods

For the study of chemical and metabolic networks, we combine concepts and methods from graph theory, dynamical systems, polyhedral geometry, and oriented matroids (such as Laplacian matrices, Lyapunov functions, polyhedral cones, and elementary vectors).

Assessment and permitted materials

Minimum requirements and assessment criteria

Examination topics

Reading list


Association in the course directory

MBIV

Last modified: Mo 13.09.2021 14:09