Functional & Integrative Genomics

, Volume 4, Issue 3, pp 188–195 | Cite as

Calculating biological behaviors of epigenetic states in the phage λ life cycle

  • X.-M. Zhu
  • L. Yin
  • L. Hood
  • P. AoEmail author
Original Paper


The biology and behavior of bacteriophage λ regulation have been the focus of classical investigations of molecular control of gene expression. Both qualitative and quantitative aspects of this behavior have been systematically characterized experimentally. Complete understanding of the robustness and stability of the genetic circuitry for the lysis-lysogeny switch remains an unsolved puzzle. It is an excellent test case for our understanding of biological behavior of an integrated network based on its physical, chemical, DNA, protein, and functional properties. We have used a new approach to non-linear dynamics to formulate a new mathematical model, performed a theoretical study on the phage λ life cycle, and solved the crucial part of this puzzle. We find a good quantitative agreement between the theoretical calculation and published experimental observations in the protein number levels, the lysis frequency in the lysogen culture, and the lysogenization frequency for mutants of OR. We also predict the desired robustness for the λ genetic switch. We believe that this is the first successful example in the quantitative calculation of robustness and stability of the phage λ regulatory network, one of the simplest and most well-studied regulatory systems.


Phage lambda Gene regulatory network Robustness and stability Mathematical modeling 



We thank G.K. Ackers, D. Galas, and J.W. Little for valuable comments and critical discussions. This work was supported in part by the Institute for Systems Biology (P.A. and L.H.) by USA NIH grant under HG002894-01 (P.A.) and by a USA NSF grant under DMR 0201948 (L.Y.).


  1. Ackers GK, Johnson AD, Shea MA (1982) Quantitative model for gene regulation by λ phage repressor. Proc Natl Acad Sci USA 79:1129–1133PubMedGoogle Scholar
  2. Ao P (2002) Stochastic force defined evolution in dynamical systems. Submitted to Phys Rev Lett (physics/0302081)Google Scholar
  3. Arkin A, Ross J, McAdams HH (1998) Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells. Genetics 149:1633–1648PubMedGoogle Scholar
  4. Aurell E, Sneppen K (2002) Epigenetics as a first exit problem. Phys Rev Lett 88:048101–1-4CrossRefPubMedGoogle Scholar
  5. Aurell E, Brown S, Johanson J, Sneppen K (2002) Stability puzzle in phage, λ. Phys Rev E 65:051914–1-9CrossRefGoogle Scholar
  6. Calef E, Avitabile LdG, Marchelli C, Menna T, Neubauer Z, Soller A (1971) The genetics of the anti-immune phenotype of defective lambda glycogens. In: Hershey AD (ed) The bacteriophage lambda. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, N.Y., pp 609–620Google Scholar
  7. Darling PJ, Holt JM, Ackers GK (2000) Coupled energetics of λ cro repressor self-assembly and site-specific DNA operator binding. II. Cooperative interactions of Cro dimers. J Mol Biol 302:625–638CrossRefPubMedGoogle Scholar
  8. Dodd IB, Perkins AJ, Tsemitsidis DT, Egan JB (2001). Octamerization of λ CI repressor is needed for effective repression of PRM and efficient switching from lysogeny. Genes Dev 15:3013–3022CrossRefPubMedGoogle Scholar
  9. Eisen H, Brachet P, Pereira da Silva L, Jacob F (1970) Regulation of repressor expression in λ. Proc Natl Acad Sci USA 66:855–862PubMedGoogle Scholar
  10. Hochschild A, Douhan J III, Ptashne M (1986) How λ repressor and λ Cro distinguish between OR1 and OR3. Cell 47:807–816PubMedGoogle Scholar
  11. Jana R, Hazbun TR, Mollah AKMM, Mossing MC (1997) A folded monomeric intermediate in the formation of lambda Cro dimer-DNA complexes. J Mol Biol 273:402–416CrossRefPubMedGoogle Scholar
  12. Kim JG, Takeda Y, Matthews BW, Anderson WF (1987) Kinetic studies on Cro repressor-operator DNA interaction. J Mol Biol 196:149–158PubMedGoogle Scholar
  13. Koblan KS, Ackers GK (1991) Energetics of subunit dimerization in bacteriophage lambda cI repressor: linkage to protons, temperature and KCl. Biochemistry 30:7817–7821PubMedGoogle Scholar
  14. Koblan KS, Ackers GK (1992) Site-specific enthalpic regulation of DNA transcription at bacteriophage λ OR. Biochemistry 31:57–65PubMedGoogle Scholar
  15. Kramers HA (1940) Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7:284Google Scholar
  16. Kwon C, Ao P, Thouless DJ (2003) Structure of stochastic dynamics near fixed points. Proc Natl Acad Sci USA (in press)Google Scholar
  17. Little JW, Shepley DP, Wert DW (1999) Robustness of a gene regulatory circuit. EMBO J 18:4299–4307CrossRefPubMedGoogle Scholar
  18. Pakula AA, Young VB, Sauer RT (1986) Bacteriophage λ cro mutations: effects on activity and intracellular degradation. Proc Natl Acad Sci USA 83:8829–8833Google Scholar
  19. Ptashne M (1992) A genetic switch: phage λ and higher organisms, 2nd edition, Cell Press & Blackwell Scientific, OxfordGoogle Scholar
  20. Ptashne M, Gann A (2002) Genes and signals. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, N.Y.Google Scholar
  21. Reik W, Dean W (2002) Back to the beginning: epigenetic reprogramming. Nature 420:127CrossRefPubMedGoogle Scholar
  22. Reinitz J, Vaisnys JR (1990) Theoretical and experimental analysis of the phage lambda genetic switch implies missing levels of cooperativity. J Theor Biol 145:295–318PubMedGoogle Scholar
  23. Rozanov DV, D’Ari R, Sineoky SP (1998) RecA-independent pathways of lambdoid prophage induction in Escherichia coli. J Bacteriol 180:6306–6315PubMedGoogle Scholar
  24. Sagai M, Wolynes PG (2003) Stochastic gene expression as a many-body problem. Proc Natl Acad Sci USA 100:2374–2379CrossRefPubMedGoogle Scholar
  25. Shea MA, Ackers GK (1985) The OR control system of bacteriophage lambda, a physical-chemical model for gene regulation. J Mol Biol 181:211–230PubMedGoogle Scholar
  26. Takeda Y, Sarai A, Rivera VM (1989) Analysis of the sequence-specific interactions between Cro repressor and operator DNA by systematic base substitution experiment. Proc Natl Acad Sci USA 86:439–443PubMedGoogle Scholar
  27. Takeda Y, Ross PD, Mudd CP (1992) Thermodynamics of Cro protein-DNA interactions. Proc Natl Acad Sci USA 89:8180–8184PubMedGoogle Scholar

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.GENMATHSeattleUSA
  2. 2.School of PhysicsPeking UniversityBeijingChina
  3. 3.Institute for Systems BiologySeattleUSA
  4. 4.Departments of Mechanical Engineering and PhysicsUniversity of WashingtonSeattleUSA

Personalised recommendations