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Winter 2014/15
Seminar: Chemical Reaction Networks
Prof. Dr. Bernold Fiedler,
Isabelle Schneider
Schedule, Winter 2014/15
- Seminar:
- Wednesday 14.00-16.00, Seminarraum 140, Arnimallee 7
Description
Based on the course Dynamical Systems I, we will explore the dynamics of chemical reaction networks using ordinary differential equations. Starting with Feinberg's notation,
we want to draw a line from general results such as the existence of positive steady states
to real-life applications such as the Citric acid cycle, cell-differentiation and control of
mammalian circadian rhythms.
Aufbauend auf der Vorlesung Dynamische Systeme I wollen wir mit Hilfe von Differentialgleichungen die Dynamik chemischer Netzwerke untersuchen. Wir beginnen mit
Feinbergs Notation und wollen einen Bogen schlagen von allgemeinen Resultaten wie der
Existenz von positiven Gleichgewichten bis hin zu Anwendungen wie dem Zitratzyklus,
der Zell-Differentiation und dem zirkadianen Rhythmus von Säugetieren.
Topics
Chemical reaction networks - existence and uniqueness
of steady states, Oct 15+22, 2014
(Chemische Netzwerke - Existenz und Eindeutigkeit von Gleichgewichten)
- Examples of chemical reaction networks and the corresponding ODEs
- Definitions: weakly reversible, deficiency
- Statement of the Deficiency-Zero and Deficiency-One Theorems
- Proof of (part of) the Deficiency Zero Theorem
- References: [F95], [Lecture 5]
Dynamics of concordant chemical reaction networks, Oct 29, 2014
(Dynamik von konkordanten chemischen Netzwerken)
- Properties of concordant networks
- Injective kinetic systems, weakly monotonic kinetics
- The existence of positive equilibria
- References: [SF12]
Concordant chemical reaction networks and the Species-
Reaction Graph, Nov 5, 2014
(Konkordante chemische Netzwerke und der Spezies-Reaktions-Graph)
- The Species-Reaction Graph
- When is a network concordant? Find out by the SR-Graph.
- Proof of (part of) Theorem 2.1
- References: [SF13]
Sensitivity of chemical reaction networks: a structural
approach (Part 1), Nov 12+19+26, 2014
(Sensibilität von chemischen Netzwerken: ein struktureller Ansatz
(Teil 1))
- Sensitivity matrix
- Network motifs
- Flux Response Theorem and proof
- If time allows: Concentration Response Theorem and proof
- References: [MF14], [FM14]
Sensitivity of chemical reaction networks: a structural
approach (Part 2), Dec 3, 2014
(Sensibilität von chemischen Netzwerken: ein struktureller Ansatz
(Teil 2))
- Transitivity Theorem + proof
- Examples: flux influence graph
- References: [MF14], [FM14]
Dynamics and control at feedback vertex sets (Part 1), Dec 10+17, 2014
(Dynamik und Kontrolle auf dem Feedback Vertex Set (Teil 1))
- Definitions feedback vertex set, determining nodes
- From feedback vertex sets to determining nodes: proof
- Examples: acyclic regulatory networks, single self-loop, single loop of length two,
the Lorenz attractor
- References: [MFKS13] , [FMKS13]
Dynamics and control at feedback vertex sets (Part 2), Jan 14+21, 2015
(Dynamik und Kontrolle auf dem Feedback Vertex Set (Teil 2))
- From determining nodes to feedback vertex sets: proof
- Examples: Cell differentiation, signal transduction, control of circadian rhythm
- References: [MFKS13] , [FMKS13]
References
- [F95] M. Feinberg, The Existence and Uniqueness of Steady States for a
Class of Chemical Reaction Networks, Arch. Rational Mech. Anal. 132 (1995)
311-170
- [Lecture 5] http://www.crnt.osu.edu/LecturesOnReactionNetworks
- [SAF09] G. Shinar, U. Alon and M. Feinberg, Sensitivity and robustness
in chemical reaction networks, SIAM J. Appl. Math. 69 4 (2009) 977-998
- [SF12] G. Shinar and M. Feinberg, Concordant chemical reaction
networks, Mathematical Biosciences 240 (2012) 92-113
- [SF13] G. Shinar and M. Feinberg, Concordant chemical reaction networks
and the Species-Reaction Graph, Mathematical Biosciences 241 (2013) 1-23
- [MF14] A. Mochizuki and B. Fiedler, Sensitivity of chemical reaction
networks: a structural approach. 1. Examples and the carbon metabolic
network, submitted 2014
- [FM14] B. Fiedler and A. Mochizuki, Sensitivity of chemical reaction
networks: a structural approach. 2. Regular monomolecular systems, submitted
2014
- [MFKS13] A. Mochizuki, B. Fiedler, G. Kurosawa, D. Saito, Dynamics and
control at feedback vertex sets. II: A faithful monitor to determine the
diversity of molecular activities in regulatory networks, J. Theor. Biology
335 (2013) 130-146
- [FMKS13] B. Fiedler, A. Mochizuki, G. Kurosawa, D. Saito, Dynamics and
control at feedback vertex sets. I: Informative and determining nodes in
regulatory networks, J. Dynamics Di . Equations (2013), DOI
10.1007/s10884-013-9311-8
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Last change: Jan. 14, 2015
