Skip to main content
SpringerLink
Log in

A computational study of the gene expression in the tryptophan operon with two types of cooperativity

  • Published:
Advances in Computational Mathematics Aims and scope Submit manuscript

Abstract

Intrinsic noise is inherent to many biological processes and provokes variation in gene expression in a population of isogenic cells leading to phenotypic diversity. Intrinsic noise is generated by different sources of noise such as the number of molecules, the stochastic binding and unbinding of transcription factor and/or the number and strength of transcription factor binding sites. In this work, we use numerical simulations to study the effects of the number of operators and different types of cooperativity on the Fano factor of three different molecules of the tryptophan (trp) operon of E. Coli. We analyze the Fano factor for the mRNA, anthranilate synthase and tryptophan molecules, because it represents the effects of the noise in the variation or variability of the gene expression, a larger Fano factor implies a larger variation. Our model takes into consideration the presence of intrinsic noise and all the known mechanisms of regulation. In particular, we consider hypothetical promoters in the repression mechanism with different numbers of operators and three cases of cooperativity: positive, negative, and no-cooperativity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Waite, A.J., Frankel, N.W., Emonet, T.: Behavioral variability and phenotypic diversity in bacterial chemotaxis. Annu. Rev. Biophys. 47, 595–616 (2018)

    Article  Google Scholar 

  2. Grillo, A.O., Brown, M.P., Royer Catherine, A.: Probing the physical basis for trp repressor-operator recognition. J Mol Biol 287, 539–554 (1999)

    Article  Google Scholar 

  3. Isakova, A., Hatzimanikatis, V., Berset, Y., Bart, D.: Quantification of cooperativity in heterodimer-dna binding improves the accuracy of binding specificity models. J. Biol. Chem. 291(19), 10293–10306 (2016)

    Article  Google Scholar 

  4. Allewell, N.M.: Transcarbamoylase: structure, energetics, and catalytyc and regulatory mechanism. Annu. Rev. Biophys. Biophys. Chem. 18, 71–92 (1989)

    Article  Google Scholar 

  5. Bialek, W., Setayeshgar, S.: Cooperativity, sensitivity, and noise in biochemical signaling. Phys. Rev. Lett. 100(258101), 1–4 (2008)

    Google Scholar 

  6. Munsky, B., Neuert, G., van Oudenaarden, A.: Using gene expression noise to understand gene regulation. Science 336(6078), 183–187 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. Brown, B.: P22 Arc–energetics and Cooperativity of DNA Binding, Massachusetts Institute of Technology. Department of Biology (1994)

  8. Eaton, B.E., Gold, L., Zichi, D.A.: Let’s get specific: the relationship between specificity and affinity. Chem. Biol. 2, 633–638 (1995)

    Article  Google Scholar 

  9. Bush, E.C., Clark, A.E., DeBoever, C.M., Haynes, L.E., Hussain, S., et al.: Modeling the role of negative cooperativity in metabolic regulation and homeostasis. PLos ONE 7(11), 1–6 (2012)

    Article  Google Scholar 

  10. Cervera, J., Manzanares, J.A., Mafe, S.: The interplay between cooperativity and diversity in model threshold ensembles, J R Soc Interface 11(99), 1–7 (2014)

  11. Cui, Q., Karplus, M.: Allostery and cooperativity revisited. Protein Sci. 17, 1295–1307 (2008)

    Article  Google Scholar 

  12. Murrugarra, D., Veliz-Cuba, A., Aguilar, B., Arat, S., Laubenbacher, R.: Modeling stochasticity and variability in gene regulatory networks. EURASIP J. Bioinforma. Syst. Biol. 5, 1–11 (2012)

    Google Scholar 

  13. Ferrell, J.E.: Q&a: Cooperativity. J. Biol. 8(6), 53 (2009)

    Article  Google Scholar 

  14. Gonze, D., Grard, C., Wacquier, B., Woller, A., Tosenberger, A, Goldbeter, A., Dupont, G.: Modeling-based investigation of the effect of noise in cellular systems, Frontiers in Molecular Biosciences 5(34), 1–12 (2018)

  15. Aramaki, H., Kabata, H., Takeda, S., Itou, H., Nakayama, H., Shimamoto, N.: Formation of repressor-inducer-operator ternary complex: negative cooperativity of d-camphor binding to camr. Genes Cells 16, 1200–1207 (2011)

    Article  Google Scholar 

  16. Golding, I., Paulsson, J., Zawilski, S.M., Cox, E.C.: Real-time kinetics of gene activity in individual bacteria. Cell 123(6), 1025–1026 (2005)

    Article  Google Scholar 

  17. Barnes, I.W., Turner, D.H.: Long-range cooperativity in molecular recognition of rna by oligodeoxynucleotides with multiple c5-(1-propynyl) pyrimidines. J. Am. Chem. Soc. 123(18), 4107–4118 (2001)

    Article  Google Scholar 

  18. Peacock, J., Jaynes, J.B.: Using competition assays to quantitatively model cooperative binding by transcription factors and other ligands. Biochim. Biophys. Acta 1861(11), 2789–2801 (2017)

    Article  Google Scholar 

  19. Yang, J., Gunasekera, A., Lavoie, T.A., Lewis, L.J.D.E.A., Carey, J.: In vivo and in vitro studies of trpr-dna interactions. J. Mol. Biol. 258, 37–52 (1996)

    Article  Google Scholar 

  20. Shenker, J.Q., Lin, M.M.: Cooperativity leads to temporally-correlated fluctuations in the bacteriophage lambda genetic switch. Front. Plant Sci. 6, 1–10 (2015)

    Article  Google Scholar 

  21. Koshland, D.E. Jr, Hamadani, K.: Proteomics and models for enzyme cooperativity. J. Biol. Chem. 277(49), 46841–46844 (2002)

    Article  Google Scholar 

  22. Norregaard, K., Andersson, M., Sneppen, K., Nielsen, P.E., Brown, S., Oddershedea, L.B.: Dna supercoiling enhances cooperativity and efficiency of an epigenetic switch. PNAS 110(43), 17386–17391 (2013)

    Article  Google Scholar 

  23. Koh, R.S., Dunlop, M.J.: Modeling suggests that gene circuit architecture controls phenotypic variability in a bacterial persistence network. BMC Syst. Biol. 6 (47), 1–9 (2012)

    Google Scholar 

  24. Krejci, A., Tucek, S.: Changes of cooperativity between n-methylscopolamine and allosteric modulators alcuronium and gallamine induced by mutations of external loops of muscarinic m3 receptors. Mol. Pharmacol. 60(4), 761–767 (2001)

    Google Scholar 

  25. Lei, Q.-L., Ren, C.-L., Su, X.-H., Ma, Y.-Q.: Crowding-induced cooperativity in dna surface hybridization. Sci. Rep. 5, 1–7 (2015)

    Google Scholar 

  26. Levitzki, A., Koskland, D.E. Jr: Negative cooperativity in regulatory enzymes. PNAS 62(4), 1121–1128 (1969)

    Article  Google Scholar 

  27. Liu, J.Y.: Modeling the Effect of Cooperativity on Ligand-Driven Fluctuations of Metabotropic Glutamate Receptors, Master’s thesis. College of William and Mary (2015)

  28. Agnati, L.F., Tarakanov, A.O., Guidolin, D.: A simple mathematical model of cooperativity in receptor mosaics based on the ”symmetry rule”. BioSystem 80, 165–173 (2005)

    Article  Google Scholar 

  29. Tabaka, M., Cybulski, O., Holyst, R.: Accurate genetic switch in escherichia coli Novel mechanism of regulation by co-repressor. J. Mol. Biol. 377, 1002–1014 (2008)

    Article  Google Scholar 

  30. Merino, F., Bouvier, B., Cojocaru, V.: Cooperative dna recognition modulated by an interplay between protein-protein interactions and dna-mediated allostery. PLoS Comput. Biol. 11(6), 1–23 (2015)

    Article  Google Scholar 

  31. Jørgensen, G.M., Raaphorst, R., Veening, J.-W.: Noise and Stochasticity in Gene Expression: A Pathogenic Fate Determinant, vol. 40 Elsevier, chap 6 (2013)

  32. Mora, T., Walczak, A.M.: Effect of phenotypic selection on stochastic gene expression. J. Phys. Chem. B 117(42), 13194–13205 (2013)

    Article  Google Scholar 

  33. Pan, Y., Nussinov, R.: Cooperativity dominates the genomic organization of p53-response elements: A mechanistic view. PLoS Comput. Biol. 5(7), 1–11 (2009)

    Article  Google Scholar 

  34. Choi, P.J., Cai, L., Frieda, K., Sunney Xie, X.: A stochastic single-molecule event triggers phenotype switching of a bacterial cell. Science 322(5900), 442–446 (2008)

    Article  Google Scholar 

  35. Liu, P., Song, R., Elison, G.L., Peng, W., Acar, M.: Noise reduction as an emergent property of single-cell aging. Nat. Commun. 8(1), 1–13. Article ID 680 (2017)

    Article  Google Scholar 

  36. Porter, C.M., Miller, B.G.: Cooperativity in monomeric enzymes with single ligand-binding sites. Bioorg. Chem. 43, 44–50 (2012)

    Article  Google Scholar 

  37. Rudnick, J., Bruinsma, R.: Dna-protein cooperative binding through variable-range elastic coupling. Biophys. J. 76, 1725–1733 (1999)

    Article  Google Scholar 

  38. Salazar-Cavazos, E., Santillán, M.: Optimal performance of the tryptophan operon of e. coli: a stochastic, dynamical, mathematical-modeling approach. Bull. Math. Biol. 76(2), 314–334 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  39. Sanchez, A., Garcia, H.G., Jones, D., Phillips, R., Kondev, J.: Effect of promoter architecture on the cell-to-cell variability in gene expression. PLoS Comput. Biol. 7(3), 1–20 (2011)

    Article  Google Scholar 

  40. Santillán, M.: On the use of the hill functions in mathematical models of gene regulatory networks. Math. Model Nat. Phenom. 3(2), 85–97 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  41. Senear, D.F., Brenowitz, M.: Determination of binding constants for cooperative site-specific protein-dna interactions using the gel mobility-shift assay. J. Biol. Chem. 266(21), 13661–13671 (1991)

    Google Scholar 

  42. Singh, A., Soltani, M.: Quantifying intrinsic and extrinsic variability in stochastic gene expression models. PLoS ONE 8(12), 1–12 (2013)

    Article  Google Scholar 

  43. Owen-Hughes, T., Workman, J.L.: Experimental analysis of chromatin function in transcription control. Crit. Rev. Eukaryot. Gene Expr. 4, 403–441 (1994)

    Google Scholar 

  44. Thattai, M., van Oudenaarden, A.: Intrinsic noise in gene regulatory networks. PNAS 98(15), 8614–8619 (2001)

    Article  Google Scholar 

  45. Tkacik, G., Gregor, T., Bialek, W.: The role of input noise in transcriptional regulation. PLoS ONE 3(7), 1–11 (2008)

    Article  Google Scholar 

  46. Tsimring, L.S.: Noise in biology. Rep. Prog. Phys. 77(2), 1–62 (2014)

    Article  Google Scholar 

  47. Teslenko, V.I., Kapitanchuk, O.L., Yang, Z.: Controlling cooperativity of a metastable open system coupled weakly to a noisy environment. Chin. Phys. B 24 (2), 1–12. Article ID 028702 (2015)

    Article  Google Scholar 

  48. Yan, C., Wu, S., Pocetti, C., Bai, L.: Regulation of cell-to-cell variability in divergent gene expression, Nature communications 7(11099 EP -), 1–10 (2016)

  49. Taniguchi, Y., Choi, P.J., Li, G.-W., Chen, H., Babu, M., Hearn, J., Emili, A., Sunney Xie, X.: Quantifying e. coli proteome and transcriptome with single-molecule sensitivity in single cells. Science 329(5991), 533–538 (2010)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universidad Autónoma de Coahuila, Escuela de Sistemas PMRV, Real de Catorce 123 Fracc. Los Reales., Cd., Acuña, Coahuila, Mexico

    José Roberto Cantú-González

  2. Universidad Autónoma de Chiapas, Facultad de Ciencias en Física y Matemáticas, Tuxtla Gutiérrez, Chiapas, Mexico

    O. Díaz-Hernández, Elizeth Ramírez-Álvarez, A. Flores Rosas & Gerardo J. Escalera Santos

  3. Conacyt-Universidad Autónoma de Chiapas, Facultad de Ciencias en Física y Matemáticas, Tuxtla Gutiérrez, Chiapas, Mexico

    C. I. Enríquez Flores

Authors
  1. José Roberto Cantú-González
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. Díaz-Hernández
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Elizeth Ramírez-Álvarez
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. C. I. Enríquez Flores
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. A. Flores Rosas
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Gerardo J. Escalera Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to José Roberto Cantú-González.

Additional information

Communicated by: Pavel Solin

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cantú-González, J.R., Díaz-Hernández, O., Ramírez-Álvarez, E. et al. A computational study of the gene expression in the tryptophan operon with two types of cooperativity. Adv Comput Math 45, 1843–1851 (2019). https://doi.org/10.1007/s10444-018-09661-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10444-018-09661-x

Keywords

Mathematics Subject Classification (2010)

Search

Navigation