Combinatorics of feedback in cellular uptake and metabolism of small molecules

Footnotes

• ^‡To whom correspondence should be addressed. E-mail: sandeep{at}nbi.dk

• 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.

• © 2007 by The National Academy of Sciences of the USA