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The Erwin Schroedinger Institute for Mathematical Physics

Advances in Chemical Reaction Network Theory

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. Common modeling frameworks include ordinary differential equations and continuous-time Markov chains. Under the classical assumption of mass-action kinetics, the resulting dynamical systems are polynomial, and their equilibria can be studied in the framework of algebraic geometry. Moreover, the plausible assumption that cellular functions are organized according to evolutionary optimality principles adds an extra layer of optimization problems.

All models depend on numerous unknown parameters, the rate constants. Still, there are large classes of networks for which the qualitative dynamics is robust with respect to the model parameters. In particular, for complex-balanced mass-action systems, there exists a unique globally stable positive equilibrium independently of the rate constants. Significant research has been conducted on relating dynamical behaviours to structural properties of the underlying reaction network. For example, network motifs have been identified that contribute to dynamical behaviours such as bistability, periodicity, and persistence.

Research on chemical reaction networks is conducted by researchers in a wide range of mathematical disciplines, including differential equations and control theory, stochastic processes, algebraic geometry, and optimization. Although techniques in these areas can differ considerably, it has been the community's experience that the most successful approaches come from sharing ideas beyond fields of expertise. The workshop aims to bring together researchers from various mathematical areas to discuss recent advances and address open problems in chemical reaction network theory. Topics include long-term dynamical behaviour, continuous-state deterministic versus discrete-state stochastic modeling, and applications to metabolic networks.

At a glance

Type: Workshop
When: Oct 15, 2018 to
Oct 19, 2018
Where: ESI, Boltzmann Lecture Hall
Organizers: Gheorghe Craciun (U Visconsin-Madison), Elisenda Feliu (U Copenhagen), Josef Hofbauer (U Vienna), Stefan Müller (U Vienna)
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