Symbolic Methods for Chemical Reaction Networks

Summary

Systems of differential equations and hybrid systems more generally are prevalent in chemical engineering and systems biology. The analysis of such systems focuses on resolving their dynamical properties, for instance, determining their equilibria and capacity for multistationarity or Hopf bifurcations. The additional tasks of parameter estimation, model reduction, and model inference are also relevant for these systems. These goals are difficult in general, especially due to the large size of these systems, especially those arising in systems biology. Non-numeric methods are essential in this context, because reaction parameters can vary over a wide range, parameter uncertainty is predominant in systems biology, and even the qualitative behavior of a system typically varies among different regions of the parameter space. Two major lines of research in this area are represented by chemical reaction network theory and stoichiometric network analysis. Our Dagstuhl seminar brought together researchers from both of these research areas, as well as researchers in symbolic computation and those on the application side (chemical engineering and systems biology). The aim of our seminar was twofold: to introduce practitioners to existing relevant theory and software from symbolic computation, and to allow participants to pose current computational challenges in this area, in order to spur development of symbolic computation methods to resolve these problems. To this end, collaborative working groups on various related topics were held throughout the week.