Edited by H. Eugene Stanley, Boston University, Boston, MA, and approved November 5, 2007 (received for review July 3, 2007)
We analyze the connection between structure and function for regulatory motifs associated with cellular uptake and usage of small molecules. Based on the boolean logic of the feedback we suggest four classes: the socialist, consumer, fashion, and collector motifs. We find that the socialist motif is good for homeostasis of a useful but potentially poisonous molecule, whereas the consumer motif is optimal for nutrition molecules. Accordingly, examples of these motifs are found in, respectively, the iron homeostasis system in various organisms and in the uptake of sugar molecules in bacteria. The remaining two motifs have no obvious analogs in small molecule regulation, but we illustrate their behavior using analogies to fashion and obesity. These extreme motifs could inspire construction of synthetic systems that exhibit bistable, history-dependent states, and homeostasis of flux (rather than concentration).
Author contributions: S.K., S.S., and K.S. designed research; S.K., S.S., and K.S. performed research; S.K., S.S., and K.S. contributed new reagents/analytic tools; S.K., S.S., and K.S. analyzed data; and S.K., S.S., and K.S. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
↵ ¶ For iron regulation in E. coli, we estimate a γ of ≈100 (14) (γ is the rate of consumption of the small molecule by one unit of metabolic enzyme). For nutritional molecules like galactose and lactose (15), the estimate is much higher. We use γ = 100, but increasing it does not change any of our conclusions.
↵ ‖ Note that a positive metabolism loop does not mean an increase of the metabolic rate with increase of s. Rather, it means exactly the opposite: an increase of s leads to a decrease of the metabolic rate, hence there is a positive feedback of the s level onto itself.
This article contains supporting information online at www.pnas.org/cgi/content/full/0706231105/DC1.
↵ †† In the Lac system, the association and dissociation of the lactose–LacI complex have been measured to be occurring on a time scale faster than a second (33, 34), which is much faster than transcription, translation and degradation processes. In the iron system, the Fe-Fur complex has a K D ≈ 20 μM (14). Association and dissociation rates have not been separately measured, but assuming that association is diffusion limited, we would get a dissociation time scale of milliseconds, which is also much faster than other processes. Therefore, we believe the assumption of equilibrium is reasonable.
