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1.B. Chemical Reaction Network Theory: Less Mathematical Articles

Although the following articles have mathematical content, they were not written with an audience of mathematicians in mind. Some are biological in flavor, while others (the ones with “CFSTR” in the title) were meant more for chemical engineers. In each case, though, the writing is directed only a little toward the nominal target audience.

It will help non-chemical engineers to know that “CFSTR” means con­tinuous flow stirred tank reactor. In effect, this is just a stirred cell with a feed stream of fixed composition continuously entering it and a exit stream continuously leaving it. In the exit stream every species is withdrawn at a rate proportional to its concentration within the cell. The mathematics is roughly the same as that for a biochemical system in which every species is synthesized at a fixed rate (perhaps zero) and every species degrades at a rate proportional to its current concentration.

I’ll begin with a “CFSTR” article, based on remarkable PhD work by Paul Schlosser, that moved chemical reaction network theory results in a direction substantially different from the deficiency-oriented ones. The newer results, organized around the Species-Complex-Linkage Graph, were a precursor of later results centered on the Species-Reaction Graph, which in turn came from Gheorghe Craciun’s (also remarkable) PhD thesis.

[1.B1] P. M. Schlosser and M. Feinberg. A theory of multiple steady states in isothermal homogeneous CFSTRs with many reactions. Chemical Engineer­ing Science, 49(11):1749–1767, 1994.

The following article gives a description of results in Gheorghe’s thesis, centered around the Species-Reaction Graph, this time with an explicitly biological flavor:

[1.B2] Gheorghe Craciun, Yangzhong Tang, and Martin Feinberg. Understanding bistability in complex enzyme-driven reaction networks. Proceedings of the National Academy of Sciences, 103:8697–8702, 2006.

The next review article is much more recent than the preceding ones and chronologically out of sequence. It is in the same vein as [1.B1] and [1.B2], but there is no reliance on the presumption of mass action kinetics. Although the underlying mathematical machinery is not made explicit, the results derive from the theory of concordant chemical reaction networks described elsewhere in this bibliography and developed in collaboration with Guy Shinar. Much like prior work by Banaji and Craciun, the theory of concordant reaction networks extends earlier Species-Reaction Graph results to broad categories of kinetics.

[1.B3] Guy Shinar, Daniel Knight, Haixia Ji, and Martin Feinberg. Stability and instability in isothermal CFSTRs with complex chemistry: Some recent results. AIChE Journal, 59(9):3403-3411, September, 2013.

The next articles are different from the preceding ones because they deal with a very different issue: concentration robustness. It seems that certain reaction networks have the capacity to maintain the steady-state concentra­tion of a certain critical species within very narrow bounds even against very large changes in the total supplies of the various network constituents. The first article [1.B4] connects that capacity to reaction network structure (and draws on deficiency one theory). The second article [1.B5] sets the first article within a broader context.

[1.B4] Guy Shinar and Martin Feinberg. Structural sources of robustness in biochemical reaction networks. Science, 327(5971):1389–1391, March 2010.

[1.B5] Guy Shinar and Martin Feinberg. Design principles for robust biochem­ical reaction networks: What works, what cannot work, and what might almost work. Mathematical Biosciences, 231(1):39–48, May 2011.