Mathematics of Reaction Networks
Mathematical modeling of chemical reaction networks consists of a variety of methods for approaching questions about the dynamical behaviour of chemical reactions arising in real world applications.
This wiki is intended to serve the dual purpose of being an accessible primer for students and researchers new to the area of mathematical modeling of chemical reactions, and a summary of the current state of the discipline for those who are active in the field.
Contents |
Resources for research
The following resources are intended to assist people who are familiar with, and actively involved in, research in modeling of reaction networks. See the active research topics pages for discussion of current research initiatives.
List of active research topics
- Applications to biochemical settings
- Injectivity and multiple equilibria
- Foundations of Chemical Reaction Network Theory
- Model reduction and the QSSA
- Monotone systems theory applied to reaction networks
- Oscillations in chemical reaction networks
- Persistence and the Global Attractor Conjecture
- Stochastic modelling of biochemical reaction networks
List of upcoming events
2012
- November 12-16, Symbolic Methods for Chemical Reaction Networks (Castle Dagstuhl, Germany)
- November 26-27, Workshop November 2012 (Imperial College, London, UK)
2013
- March 25-29, Mathematical problems arising from biochemical reaction networks (American Institute of Mathematics, Palo Alto, California)
- August 1-4, SIAM Conference on Applied Algebraic Geometry (Colorado State University, Fort Collins, Colorado)
List of people
- David Anderson
- David Angeli
- Murad Banaji
- Gheorghe Craciun
- Carsten Conradi
- Alicia Dickenstein
- Mirela Domijan
- Pete Donnell
- Martin Feinberg
- Elisenda Feliu
- Gilles Gnacadja
- Manoj Gopalkrishnan
- Alexander Gorban
- Jeremy Gunawardena
- Matthew Johnston
- Badal Joshi
- Ezra Miller
- Maya Mincheva
- Stefan Müller
- Casian Pantea
- Mercedes Perez Millan
- Anne Shiu
- David Siegel
- Guy Shinar
- Eduardo Sontag
- Gabor Szederkenyi
- Janos Toth
- Carsten Wiuf
List of literature resources
List of software packages
Resources for education
This section is intended as a primer for those who are curious about the mathematics underlying the study of reaction networks.
Chemical reaction network theory
Chemical reaction network theory is a framework for modeling the evolution of chemical concentrations resulting from simultaneously occurring chemical reactions. A key feature of the theory is the relationship between the graphical structure of the reaction network and the resulting dynamics. A strong emphasis, consequently, is placed on results which hold regardless of the parameter values of the network, i.e. results which depend on the network structure alone.
The foundations of chemical reaction network theory were laid down in a series of seminal papers by Fritz Horn, Roy Jackson and Martin Feinberg in the early 1970's [1][2][3]. In these papers, the authors were primarily focused on developing conditions sufficient for uniqueness and stability of equilibrium concentrations, but their foundation has since between adapted to questions of multistability, injectivity, monotonicity, persistence, equivalence of mass-action systems, model reduction, oscillations, and applications. The models have also been adapted to the stochastic framework, reaction-diffusion equations, and kinetic schemes other than mass-action (e.g. Michaelis-Menten, Hill kinetics, etc.).
See also:
- Boundedness
- Biochemistry
- Chemical reaction networks
- Chemical reaction network theory
- Complex balanced systems
- Deficiency theory
- Detailed balanced systems
- Dynamical equivalence
- Global attractor conjecture
- Hill kinetics
- Injectivity
- Linear conjugacy
- Linkage class
- Lumping
- Mass action systems
- Michaelis-Menten kinetics
- Model reduction
- Monotonicity
- Multistability
- Persistence
- Reaction graph
- Reversibility
- Reaction-diffusion models
- Stochastic models
- Toric dynamical systems
- Toric steady states
- Weak reversibility
References
- ↑ R. Horn, R. Jackson, General mass action kinetics, Arch. Ration. Mech. Anal. 47 (1972) 81-116
- ↑ F. Horn, Necessary and sufficient conditions for complex balancing in chemical kinetics, Arch. Ration. Mech. Anal., 49 (1972) 172-186
- ↑ M. Feinberg, Complex balancing in general kinetic systems, Arch. Ration. Mech. Anal., 49 (1972) 187-194
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