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Yildirim (2003), lac Operon

December 2006, model of the month by Melanie Stefan
Original model: BIOMD0000000065

The preferred carbon source of E. coli is glucose. However, if glucose is unavailable, E. coli has an alternative option: It can break down lactose to produce glucose and galactose [1]. The switch between these two alternative pathways relies on the regulation of three structural genes by a control element. This functional unit, called "operon", was first described by Jacob et al. [2].

The lac operon contains three genes: lacZ codes for β-galactosidase, which is needed for breaking down lactose. lacA codes for galactoside permease, which is needed for lactose transport into the cell. lacA codes for thiogalactoside transacetylase, which does, however, not seem to play a role in this context [1].

Regulatory mechanisms within the lac operon are illustrated in figure 1: If glucose is present and lactose is absent, the lac repressor binds to the operator region. This prevents lac gene transcription. If both glucose and lactose are both present, lactose binds to the repressor and prevents it from binding to the operator region. The block of lac gene transcription is thus lifted, and a small amount of mRNA is produced. But since glucose is still available, the need for β-galactosidase and galactoside permease is limited. If, however, glucose is absent and lactose becomes the only available carbon source, the picture changes. Lactose still prevents the repressor from binding to the operator region. But in addition, the lack of glucose leads to a rise in cyclic AMP (cAMP) concentration. cAMP forms a complex with the catabolite activator protein (CAP). This complex binds to the promoter region and stimulates the transcription of the three lac genes. Large amounts of lac mRNA are produced.

Shortly after the operon concept was first described, people started developing mathematical models for lac operon function (reviewed in [4]). More recent models (e.g. [5]) include more biological detail.

Schematic representation of the lac operon.

Figure 1: Schematic representation of the lac operon (from [3]) (a) In the presence of glucose and the absence of lactose, the repressor binds to the operator and the transcription of lac genes is suppressed. (b) If both glucose and lactose are present, lactose binds to the repressor, and thus prevents it from binding to the operator. (c) If glucose is absent, then the cAMP concentration is high. cAMP forms a complex with CAP, which binds to the promoter and stimulates lac gene transcription.

The model presented here was proposed by Yildirim and Meckey in 2003 [6] (BIOMD0000000065). It includes mRNA synthesis under different conditions, mRNA degradation, β-galactosidase turnover, accolactose production and degradation, lactose transport and degradation, as well as permease turnover. It also accounts for transcriptional and translational delays. The authors were both careful and transparent about parameter choice: Details about estimation and experimental evidence for each of the parameters is given in the appendix.

One of the results is shown in figure 2: The simulated response of β-galactosidase activity to periodic phosphate feeding is compared to experimental results (from [7]).

β-galactosidase activity in response to periodic phosphate feeding.

Figure 2: β-galactosidase activity in response to periodic phosphate feeding (from [6]). Experimental values are taken from the first figure in [7].

Bibliographic References

  1. J. M. Berg, J. L. Tymoczko, L. Stryer, and N. D. Clarke. Biochemistry. W. H. Freeman, 2002.
  2. F. Jacob, D. Perrin, C. Sánchez, J. Monod, and S. Edelstein. [The operon: a group of genes with expression coordinated by an operator. C. R. Acad. Sci. Paris 250 (1960) 1727-1729]. C R Biol, 328(6):514-520, Jun 2005. [PubMed]
  3. H. Lodish, A. Berk, L. S. Zipursky, P. Matsudaira, D. Baltimore, and J. Darnell. Molecular Cell Biology. W. H. Freeman, 4th edition, 2000.
  4. J. J. Tyson and H. G. Othmer. The dynamics of feedback control circuits in biochemical pathways. Procgress in Theoretical Biology, 5:1-62, 1978.
  5. P. Wong, S. Gladney, and. J. D. Keasling. Mathematical model of the lac operon: inducer exclusion, catabolite repression, and diauxic growth on glucose and lactose. Biotechnol Prog, 13(2):132-143, 1997. [PubMed]
  6. N. Yildirim and M. C. Mackey. Feedback regulation in the lactose operon: A mathematical modeling study and comparison with experimental data. Biophys J, 84(5):2841-2851, May 2003. [PubMed]
  7. B. C. Goodwin. Control dynamics of beta-galactosidase in relation to the bacterial cell cycle. Eur J Biochem, 10(3):515-522, Oct 1969. [PubMed]