Nonlinear Dynamics

, Volume 79, Issue 1, pp 397–408 | Cite as

Functional characteristics of additional positive feedback in genetic circuits

Original Paper


Multiple-positive feedback circuits are ubiquitous regulatory motifs in complex bio-molecular networks. A popular topic is why multiple-positive feedback mechanisms have been evolved and selected by organisms. To this end, a two-component dual-positive feedback genetic circuit is investigated, which consists of an auto-activation loop and a double negative feedback circuit. The auto-activation loop acts as an additional positive feedback loop (APFL), and our aim is to explore the functional characteristics of the APFL. Investigations reveal that the APFL can regulate the size of bistable region and the robust attractiveness of stable steady states. It is also found that the APFL can regulate global relative input–output sensitivities of the system. Furthermore, the APFL can tune the response speed, noise resistance and stochastic switch behavior of the system, which makes it easy to realize functional tunability and robust decision-making. Therefore, rationalizing why multiple-positive feedback circuits so frequently appear in real-world biological systems. Potential applications of the associated investigations include the design of artificial genetic circuits, the modeling and model reduction for large-scale bio-molecular networks.


Genetic regulatory network Additional positive feedback Bifurcation Signal processing Bistable switch 



The authors would like to thank Profs. Tianshou Zhou and Xiaoqun Wu for their valuable comments. This work is supported by the National Science and Technology Major Project of China under Grant 2014ZX10004-001-014, the 973 Project under Grant 2014CB845302, and the National Natural Science Foundation of China under Grants 61304151, 11105040, 61025017, 11472290, the Australia ARC Discovery Grants DP130104765, the Science Foundation of Henan University under Grants 2012YBZR007.


  1. 1.
    Alon, U.: An Introduction to Systems Biology: Design Principles of Biological Circuits. Chapman & Hall/CRC, Boca Raton (2007)Google Scholar
  2. 2.
    Gardner, T., Cantor, C., Cantor, J.: Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000)CrossRefGoogle Scholar
  3. 3.
    Dubnau, D., Losick, R.: Bistability in bacteria. Mol. Microbiol. 61, 564–572 (2006)CrossRefGoogle Scholar
  4. 4.
    Tyson, J., Novák, B.: Functional motif in biochemical reaction networks. Annu. Rev. Phys. Chem. 61, 219–240 (2010)CrossRefGoogle Scholar
  5. 5.
    Wang, J., Zhang, J., Yuan, Z., Zhou, T.: Noise-induced switches in network systems of the genetic toggle switch. BMC Syst. Biol. 1, 50 (2007)CrossRefGoogle Scholar
  6. 6.
    Shah, N., Sarkar, C.: Robust network topologies for generating switch-like cellular responses. PLoS Comput. Biol. 7, e1002085 (2011)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Strelkowa, N., Barahona, M.: Switchable genetic oscillator operating in quasi-stable mode. J. R. Soc. Interface 7, 1071–1082 (2010)CrossRefGoogle Scholar
  8. 8.
    Tsai, T., Choi, Y., Ma, W., Pomerening, J., Tang, C., Ferrell Jr, J.E.: Robust, tunable biological oscillations from interlinked positive and negative feedback loops. Science 321, 126–129 (2008)CrossRefGoogle Scholar
  9. 9.
    Kim, J., Yoon, Y., Cho, K.: Coupled feedback loops from dynamic motifs of cellular networks. Biophys. J. 94, 359–365 (2008)CrossRefGoogle Scholar
  10. 10.
    Stricker, J., Cookson, S., bennett, M., Mather, W., Tsimring, L., Hasty, J.: A fast, robust and tunable synthetic gene oscillator. Nature 456, 516–519 (2008)CrossRefGoogle Scholar
  11. 11.
    Brandman, O., Ferrell Jr, J.E., Li, R., Meyer, T.: Interlinked fast and slow positive feedback loops drive reliable cell decisions. Science 310, 496–498 (2005)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Tian, X., Zhang, X., Liu, F., Wang, W.: Interlinking positive and negative feedback loops creates a tunable motif in gene regulatory networks. Phys. Rev. E 80, 011926 (2009)CrossRefGoogle Scholar
  13. 13.
    Song, H., Smolen, P., Av-Ron, E., Baxter, D., Byrne, J.: Dynamics of a minial model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins. Biophys. J. 92, 3407–3424 (2007)CrossRefGoogle Scholar
  14. 14.
    Süel, G., Garcia-Ojalvo, J., Liberman, L., Elowitz, M.: An excitable gene regulatory circuit induces transient cellular differentiation. Nature 440, 545–550 (2006)CrossRefGoogle Scholar
  15. 15.
    Lindner, B., Garcia-Ojalvo, J., Neiman, A., Schimansky-Geier, L.: Effects of noise in excitable systems. Phys. Rep. 392, 321–424 (2004)CrossRefGoogle Scholar
  16. 16.
    Rue, P., Garcia-Ojalvo, J.: Gene circuit designs for noisy excitable dynamics. Math. Biosci. 231, 90–97 (2011)CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Novák, B., Tyson, J.: Design principles of biochemical oscillators. Nat. Rev. Mol. Cell Biol. 9, 981–991 (2008)CrossRefGoogle Scholar
  18. 18.
    Chen, A.: Modeling a synthetic biological chaotic system: relaxation oscillators coupled by quorum sensing. Nonlinear Dyn. 63, 711–718 (2011)CrossRefGoogle Scholar
  19. 19.
    Zhang, Z., Ye, W., Qian, Y., Zheng, Z., Huang, X., Hu, G.: Chaotic motifs in gene regulatory networks. PLoS One 7(7), e39355 (2012)CrossRefGoogle Scholar
  20. 20.
    Wang, P., Zhang, Y., Tan, S., Wan, L.: Explicit ultimate bound sets of a new hyperchaotic system and its application in estimating the Hausdorff dimension. Nonlinear Dyn. 74, 133–142 (2013)CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    Wang, P., Li, D., Wu, X., Lü, J., Yu, X.: Ultimate bound estimation of a class of high dimensional quadratic autonomous dynamical systems. Int. J. Bifurc. Chaos 21, 2679–2694 (2011)CrossRefMATHGoogle Scholar
  22. 22.
    Xiong, W., Ferrell Jr, J.E.: A positive-feedback-based bistable ‘memory module’ that governs a cell fate decision. Nature 426, 460–465 (2003)CrossRefGoogle Scholar
  23. 23.
    Snoussi, E.: Necessary conditions for multistationary and stable periodicity. J. Biol. Syst. 6, 3–9 (1998)CrossRefMATHGoogle Scholar
  24. 24.
    Ozbudak, E., Thattai, M., Lim, H., Shraiman, B., Van Oudenaarden, A.: Multistability in the lactose utilization network of Escherichia coli. Nature 427, 737–740 (2004)CrossRefGoogle Scholar
  25. 25.
    Shibata, T., Fujimoto, K.: Noisy signal amplification in ultrasensitive signal transduction. Proc. Natl. Acad. Sci. USA 102, 331–336 (2005)CrossRefGoogle Scholar
  26. 26.
    Hornung, G., Barkai, N.: Noise propagation and signaling sensitivity in biological networks: a role for positive feedback. PLoS Comput. Biol. 4, e8 (2008)CrossRefMathSciNetGoogle Scholar
  27. 27.
    Sriram, K., Soliman, S., Fages, F.: Dynamics of the interlocked positive feedback loops explaining the robust epigenetic switching in Candida albicans. J. Theor. Biol. 258, 71–88 (2009)CrossRefGoogle Scholar
  28. 28.
    Bosl, W., Li, R.: The role of noise and positive feedback in the onset of autosomal dominant diseases. BMC Syst. Biol. 4, 93 (2010)CrossRefGoogle Scholar
  29. 29.
    Marucci, L., Barton, D., Cantone, I., Ricci, M., Cosma, M., Santini, S., di Bernardo, D., di Bernardo, M.: How to turn a genetic circuit into a synthetic tunable oscillator, or a bistable switch. PLoS One 4, e8083 (2009)CrossRefGoogle Scholar
  30. 30.
    Ferrell Jr, J.E.: Self-perpetuating states in signal transduction: positive feedback, double-negative feedback and bistability. Curr. Opin. Chem. Biol. 6, 140–148 (2002)CrossRefGoogle Scholar
  31. 31.
    Smolen, P., Baxter, D., Byrne, J.: Interlinked dual-time feedback loops can enhance robustness to stochasticity and persistence of memory. Phys. Rev. E 79, 031902 (2009)CrossRefMathSciNetGoogle Scholar
  32. 32.
    Mitrophanov, A., Groisman, E.: Positive feedback in cellular control systems. BioEssays 30, 542–555 (2008)CrossRefGoogle Scholar
  33. 33.
    Banerjee, S., Bose, I.: Functional characteristics of a double positive feedback loop coupled with autorepression. Phys. Biol. 5, 046008 (2008)CrossRefGoogle Scholar
  34. 34.
    Shi, C., Zhou, T., Yuan, Z.: Functional tunability of biological circuits from additional toggle switches. IET Syst. Biol. 7(5), 126–134 (2013)CrossRefGoogle Scholar
  35. 35.
    Shi, C., Li, H., Zhou, T.: Architecture-dependent robustness in a class of multiple positive feedback loops. IET Syst. Biol. 7(1), 1–10 (2013)CrossRefGoogle Scholar
  36. 36.
    Zhang, X., Cheng, Z., Liu, F., Wang, W.: Linking fast and slow positive feedback loops creates an optimal bistable switch in cell signaling. Phys. Rev. E 76, 031924 (2007)CrossRefGoogle Scholar
  37. 37.
    Li, F., Long, T., Liu, Y., Ouyang, Q., Tang, C.: The yeast cell-cycle is robustly designed. Proc. Natl. Acad. Sci. USA 101, 4781–4786 (2004)CrossRefGoogle Scholar
  38. 38.
    Wang, G., Du, C., Chen, H., Simha, R., Rong, Y., Xiao, Y., Zeng, C.: Process-based network decomposition reveals backbone motif structure. Proc. Natl. Acad. Sci. USA 107, 10478–10483 (2010)CrossRefGoogle Scholar
  39. 39.
    Wang, P., Lü, J., Ogorzalek, M.J.: Global relative parameter sensitivities of the feed-forward loops in genetic networks. Neurocomputing 78, 155–165 (2012)CrossRefGoogle Scholar
  40. 40.
    Wang, P., Lü, J., Zhang, Y., Ogorzalek, M. J.: Global relative input–output sensitivities of the feed-forward loops in genetic networks. In: Proceedings of the 31th Chinese Control Conference, July 25–27, 7376–7381 (2012)Google Scholar
  41. 41.
    Pigliucci, M., Murren, C.J.: Genetic assimilation and a possible evolutionary paradox: can macroevolution sometimes be so fast as to pass us by? Evol. Int. J. Org. Evol. 57, 1455–1464 (2003)CrossRefGoogle Scholar
  42. 42.
    Raser, J.M., O’Shea, E.K.: Noise in gene expression: origins, consequences, and control. Science 309, 2010–2013 (2005)CrossRefGoogle Scholar
  43. 43.
    Gonze, D., Halloy, J., Goldbeter, A.: Deterministic versus stochastic models for circadian rhythms. J. Biol. Phys. 28, 637–653 (2002)Google Scholar
  44. 44.
    Gonze, D., Goldbeter, A.: Circadian rhythms and molecular noise. Chaos 16, 026110 (2006)CrossRefGoogle Scholar
  45. 45.
    Wang, P., Lü, J., Wan, L., Chen, Y.: A stochastic simulation algorithm for biochemical reactions with delays. IEEE Int. Conf. Syst. Biol. Aug. 23–25, 109–114 (2013)Google Scholar
  46. 46.
    Gillespie, D.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81, 2340–2361 (1977)CrossRefGoogle Scholar
  47. 47.
    Zheng X, Yang X, Tao Y.: Bistability, probability transition rate and first-passage time in an autoactivating positive-feedback loop. PLoS One 6, e1704 (2011)Google Scholar
  48. 48.
    Masoliver, J., West, B.J., Lindenberg, K.: Bistability driven by Gaussian colored noise: first passage times. Phys. Rev. A. 35, 3086–3094 (1987)CrossRefMathSciNetGoogle Scholar
  49. 49.
    Wang, P., Lü, J.: Control of genetic regulatory networks: opportunities and challenges. Acta Autom. Sin. 39(12), 1969–1979 (2013)CrossRefGoogle Scholar
  50. 50.
    Wang, P., Lü, J., Zhang, Y., Ogorzalek, M.J.: Intrinsic noise induced state transition in coupled positive and negative feedback genetic circuit. IEEE Int. Conf. Syst. Biol. Sep. 2–4, 356–361 (2011)Google Scholar
  51. 51.
    Liu, H., Yan, F., Liu, Z.: Oscillatory dynamics in a gene regulatory network mediated by small RNA with time delay. Nonlinear Dyn. 76, 147–159 (2014)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Pei Wang
    • 1
    • 2
  • Yuhuan Zhang
    • 1
  • Jinhu Lü
    • 3
    • 4
  • Xinghuo Yu
    • 2
  1. 1.School of Mathematics and Information SciencesHenan UniversityKaifengPeople’s Republic of China
  2. 2.School of Electrical and Computer EngineeringRMIT UniversityMelbourneAustralia
  3. 3.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingPeople’s Republic of China
  4. 4.Faculty of EngineeringKing Abdulaziz UniversityJeddahSaudi Arabia

Personalised recommendations