Optimality and evolutionary tuning of the expression level of a protein

Article metrics


Different proteins have different expression levels. It is unclear to what extent these expression levels are optimized to their environment. Evolutionary theories suggest that protein expression levels maximize fitness1,2,3,4,5,6,7,8,9,10,11, but the fitness as a function of protein level has seldom been directly measured. To address this, we studied the lac system of Escherichia coli, which allows the cell to use the sugar lactose for growth12. We experimentally measured the growth burden13,14 due to production and maintenance of the Lac proteins (cost), as well as the growth advantage (benefit) conferred by the Lac proteins when lactose is present. The fitness function, given by the difference between the benefit and the cost, predicts that for each lactose environment there exists an optimal Lac expression level that maximizes growth rate. We then performed serial dilution evolution experiments at different lactose concentrations. In a few hundred generations, cells evolved to reach the predicted optimal expression levels. Thus, protein expression from the lac operon seems to be a solution of a cost–benefit optimization problem, and can be rapidly tuned by evolution to function optimally in new environments.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: The lac operon of E. coli and the experimental design in the present study.
Figure 2: Cost and benefit functions of lac expression in wild-type E. coli.
Figure 3: 3 Predicted relative growth rate of cells (the fitness function) as a function of Lac protein expression.
Figure 4: Experimental evolutionary adaptation of E. coli cells to different concentrations of lactose.


  1. 1

    Elena, S. F. & Lenski, R. E. Evolution experiments with microorganisms: the dynamics and genetic bases of adaptation. Nature Rev. Genet. 4, 457–469 (2003)

  2. 2

    Orr, H. A. The genetic theory of adaptation: a brief history. Nature Rev. Genet. 6, 119–127 (2005)

  3. 3

    Ibarra, R. U., Edwards, J. S. & Palsson, B. O. Escherichia coli K-12 undergoes adaptive evolution to achieve in silico predicted optimal growth. Nature 420, 186–189 (2002)

  4. 4

    Hartwell, L. H., Hopfield, J. J., Leibler, S. & Murray, A. W. From molecular to modular cell biology. Nature 402, C47–C52 (1999)

  5. 5

    Rosen, R. Optimality Principles in Biology (Butterworths, London, 1967)

  6. 6

    Savageau, M. A. Biochemical Systems Analysis: a Study of Function and Design in Molecular Biology (Addison-Wesley, Reading, Massachusetts, 1976)

  7. 7

    Hartl, D. L. & Clark, A. G. Principles of Population Genetics (Sinauer, Sunderland, Massachusetts, 1997)

  8. 8

    Heinrich, R. & Schuster, S. The Regulation of Cellular Systems (Chapman and Hall, New York, 1996)

  9. 9

    Maynard Smith, J. & Szathmary, E. The Major Transitions in Evolution (Oxford Univ. Press, Oxford, 1997)

  10. 10

    Hartl, D. L. & Dykhuizen, D. E. The population genetics of Escherichia coli. Annu. Rev. Genet. 18, 31–68 (1984)

  11. 11

    Liebermeister, W., Klipp, E., Schuster, S. & Heinrich, R. A theory of optimal differential gene expression. Biosystems 76, 261–278 (2004)

  12. 12

    Muller-Hill, B. The lac Operon: a Short History of a Genetic Paradigm (Walter de Gruyter, New York, 1996)

  13. 13

    Koch, A. L. The protein burden of lac operon products. J. Mol. Evol. 19, 455–462 (1983)

  14. 14

    Nguyen, T. N., Phan, Q. G., Duong, L. P., Bertrand, K. P. & Lenski, R. E. Effects of carriage and expression of the Tn10 tetracycline-resistance operon on the fitness of Escherichia coli K12. Mol. Biol. Evol. 6, 213–225 (1989)

  15. 15

    Fay, J. C., McCullough, H. L., Sniegowski, P. D. & Eisen, M. B. Population genetic variation in gene expression is associated with phenotypic variation in Saccharomyces cerevisiae. Genome Biol. 5, R26 (2004)

  16. 16

    Conant, G. C. & Wagner, A. Convergent evolution of gene circuits. Nature Genet. 34, 264–266 (2003)

  17. 17

    Stephanopoulos, G. & Kelleher, J. Biochemistry. How to make a superior cell. Science 292, 2024–2025 (2001)

  18. 18

    Segre, D., Vitkup, D. & Church, G. M. Analysis of optimality in natural and perturbed metabolic networks. Proc. Natl Acad. Sci. USA 99, 15112–15117 (2002)

  19. 19

    Cooper, T. F., Rosen, D. E. & Lenski, R. E. Parallel changes in gene expression after 20,000 generations of evolution in Escherichia coli. Proc. Natl Acad. Sci. USA 100, 1072–1077 (2003)

  20. 20

    Dykhuizen, D. E., Dean, A. M. & Hartl, D. L. Metabolic flux and fitness. Genetics 115, 25–31 (1987)

  21. 21

    Honisch, C., Raghunathan, A., Cantor, C. R., Palsson, B. O. & van den Boom, D. High-throughput mutation detection underlying adaptive evolution of Escherichia coli-K12. Genome Res. 14, 2495–2502 (2004)

  22. 22

    Kremling, A. et al. The organization of metabolic reaction networks. III. Application for diauxic growth on glucose and lactose. Metab. Eng. 3, 362–379 (2001)

  23. 23

    Wong, P., Gladney, S. & Keasling, J. D. Mathematical model of the lac operon: inducer exclusion, catabolite repression, and diauxic growth on glucose and lactose. Biotechnol. Prog. 13, 132–143 (1997)

  24. 24

    Yildirim, N., Santillan, M., Horike, D. & Mackey, M. C. Dynamics and bistability in a reduced model of the lac operon. Chaos 14, 279–292 (2004)

  25. 25

    Bremer, H. & Dennis, P. P. in Escherichia coli and Salmonella (ed. Neidhardt, F. C.) 1553 (American Society for Microbiology, Washington DC, 1996)

  26. 26

    Yokobayashi, Y., Weiss, R. & Arnold, F. H. Directed evolution of a genetic circuit. Proc. Natl Acad. Sci. USA 99, 16587–16591 (2002)

  27. 27

    Endy, D., You, L., Yin, J. & Molineux, I. J. Computation, prediction, and experimental tests of fitness for bacteriophage T7 mutants with permuted genomes. Proc. Natl Acad. Sci. USA 97, 5375–5380 (2000)

  28. 28

    Dekel, E., Mangan, S. & Alon, U. Environmental selection of the feed-forward loop circuit in gene-regulation networks. Phys. Biol. 2, 81–88 (2005)

  29. 29

    Milo, R. et al. Network motifs: simple building blocks of complex networks. Science 298, 824–827 (2002)

  30. 30

    Monod, J. The growth of bacterial cultures. Annu. Rev. Microbiol. 3, 371–394 (1949)

Download references


We thank M. Elowitz, R. Kishony, G. Sela, B. Shraiman and all members of our laboratory for discussions. We thank the NIH, ISF and Minerva for support. E.D. thanks the Clore postdoctoral fellowship for support.

Author information

Correspondence to Uri Alon.

Ethics declarations

Competing interests

Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. The authors declare no competing financial interests.

Supplementary information

Supplementary Data

This details additional data on the experiments and calculation presented in the main text. It also contains Supplementary Figure S1-S8 and Supplementary Tables S1 and S2. (PDF 239 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Dekel, E., Alon, U. Optimality and evolutionary tuning of the expression level of a protein. Nature 436, 588–592 (2005) doi:10.1038/nature03842

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.