Stability and instability in complex chemical reaction networks: the big picture

Wednesday, 21 February 2007, 3pm, Alpert 563

Martin Feinberg
Departments of Chemical Engineering and Mathematics
Ohio State University


In nature there are millions of distinct networks of chemical reactions that might present themselves for study at one time or another. Written at the level of elementary reactions taken with classical mass action kinetics, each new network gives rise to its own (usually large) system of polynomial equations for the species concentrations. In this way, chemistry presents a huge and bewildering array of polynomial systems, each determined in a precise way by the underlying network up to parameter values (e.g., rate constants). Polynomial systems in general, even simple ones, are known to be rich sources of interesting and sometimes wild dynamical behavior. It would appear, then, that chemistry too should be a rich source of dynamical exotica.

Yet there is a remarkable amount of stability in chemistry. Indeed, chemical engineers generally expect homogeneous isothermal reactors, even highly complex ones, to behave in quite dull ways. Although this tacit doctrine of stable behavior is supported by a long observational record, there are certainly instances of homogeneous isothermal reactors that give rise, for example, to bistability or even chaotic behavior. The vast landscape of chemical reaction networks, then, appears to have wide regions of intrinsic stability (regardless of parameter values) punctuated by smaller regions in which instability might be extant (for at least certain parameter values).

In this talk, I will present some recent work (with George Craciun and Phillipp Ellison) that goes a long way toward explaining this landscape -- in particular, toward explaining how biological chemistry "escapes" the stability doctrine to (literally) make life interesting. Indeed, theory indicates just why enzyme-driven chemistry is strikingly different from "regular" chemistry. Although it is commonly supposed that biochemical instability results from gross feedback across a pathway, whereby the product of one enzyme-catalyzed reaction promotes or inhibits another such reaction along the pathway, the fact is that sources of instability are already to be found in quite classical and elementary mechanisms for enzyme catalysis of a single reaction. (This seems to be poorly appreciated and might perhaps confound the interpretation of experiments.)

NOTE: This talk is meant for a broad audience and should be suitable for people who are not on the friendliest of terms with advanced mathematics.


G. Craciun, Y. Tang, M. Feinberg, "Understanding bistability in complex enzyme-driven reaction-networks", PNAS 103:8697-02 2006. PubMed

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