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

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik
VOR-ORT

An/Abmeldung

Hinweis: Ihr Anmeldezeitpunkt innerhalb der Frist hat keine Auswirkungen auf die Platzvergabe (kein "first come, first served").

Details

max. 25 Teilnehmer*innen
Sprache: Englisch

Lehrende

Termine (iCal) - nächster Termin ist mit N markiert

Mittwoch 06.10. 13:15 - 14:45 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Mittwoch 13.10. 13:15 - 14:45 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Mittwoch 20.10. 13:15 - 14:45 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Mittwoch 27.10. 13:15 - 14:45 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Mittwoch 03.11. 13:15 - 14:45 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Mittwoch 10.11. 13:15 - 14:45 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Mittwoch 17.11. 13:15 - 14:45 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Mittwoch 24.11. 13:15 - 14:45 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Mittwoch 01.12. 13:15 - 14:45 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Mittwoch 15.12. 13:15 - 14:45 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Mittwoch 12.01. 13:15 - 14:45 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Mittwoch 19.01. 13:15 - 14:45 Hörsaal 8 Oskar-Morgenstern-Platz 1 1.Stock
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock

Information

Ziele, Inhalte und Methode der Lehrveranstaltung

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).

Art der Leistungskontrolle und erlaubte Hilfsmittel

Mindestanforderungen und Beurteilungsmaßstab

Prüfungsstoff

Literatur

Chemical reaction networks

Feinberg, Foundations of Chemical Reaction Network Theory, Springer, 2019

Mueller and Regensburger, Generalized Mass-Action Systems ... , 2014.
https://arxiv.org/abs/1406.6587

Metabolic networks

Mueller and Regensburger, Elementary Vectors and Conformal Sums ... , 2016.
http://journal.frontiersin.org/article/10.3389/fgene.2016.00090/full

Mueller, Regensburger, and Steuer, Enzyme allocation problems in kinetic metabolic networks ... , 2014.
https://arxiv.org/abs/1308.0510

Zuordnung im Vorlesungsverzeichnis

MBIV

Letzte Änderung: Mo 11.10.2021 17:29