Cores in parameter-rich Chemical Reaction Networks
Abstract
Parameter-rich CRNs are built upon kinetic laws that have sufficient flexibility to allow the independent choice of fixed-point coordinates and the absolute numerical values of the non-zero entries of the Jacobian. Although this seems to be a tall order, Michaelis-Menten and generalized mass action kinetics are of this type. In this setting, the existence of choices of parameters that make a given inner fixed point Hurwitz unstable is determined entirely by the stoichio-metric matrix. More precisely, the existence of certain quadratic sub-matrices is sufficient. We call these unstable cores. Autocatalytic cores (in the sense of Nghe) turn out to be unstable cores that have the special structure of Metzler matrices. Autocatalysis, therefore can always act as source of instability given suitable choices of parameters, but there are also other causes of dynamic instability, entirely unrelated to autocatalysis. The notion of cores is surprisingly versatile and can be extended to other forms of dynamical behavior that is determined by spectral properties. In particular, it pertains to the search for oscillatory behavior.
About the speaker
Peter F. Stadler received the PhD degree in chemistry from Univercity of Vienna in 1990 and then worked as an assistant and associate professor for theoretical chemistry at the same school. In 2002 he moved to Leipzig as a full professor for bioinformatics. Since 1994 he has been an external professor at Santa Fe Institute. He has been an external scientific member of the Max Planck Society since 2009 and an corresponding member abroad of the Austrian Academy of Sciences since 2010. His work ranges from the formal structures of evolving systems to the methods development in bioinformatics and cheminformatics as well as applicatioss in molecular medicine, evelutionary, structral, synthetic biology, and cultural evolution.
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