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Design principles for robust oscillatory behavior

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Systems and Synthetic Biology

Abstract

Oscillatory responses are ubiquitous in regulatory networks of living organisms, a fact that has led to extensive efforts to study and replicate the circuits involved. However, to date, design principles that underlie the robustness of natural oscillators are not completely known. Here we study a three-component enzymatic network model in order to determine the topological requirements for robust oscillation. First, by simulating every possible topological arrangement and varying their parameter values, we demonstrate that robust oscillators can be obtained by augmenting the number of both negative feedback loops and positive autoregulations while maintaining an appropriate balance of positive and negative interactions. We then identify network motifs, whose presence in more complex topologies is a necessary condition for obtaining oscillatory responses. Finally, we pinpoint a series of simple architectural patterns that progressively render more robust oscillators. Together, these findings can help in the design of more reliable synthetic biomolecular networks and may also have implications in the understanding of other oscillatory systems.

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References

  • Alon U (2007) Network motifs: theory and experimental approaches. Nat Rev Gen 8:450–461

    Article  CAS  Google Scholar 

  • Ananthasubramaniam B, Herzel H (2014) Positive feedback promotes oscillations in negative feedback loops. PLoS One 9(8):e104761

    Article  PubMed Central  PubMed  Google Scholar 

  • Barabasi A, Oltvai Z (2004) Network biology: understanding the cell’s functional organization. Nat Rev Genet 5:101–113

    Article  CAS  PubMed  Google Scholar 

  • Bashor C, Horwitz A, Peisajovich S, Lim W (2010) Rewiring cells: synthetic biology as a tool to interrogate the organizational principles of living systems. Annu Rev Biophys 39:515–537

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Batchelor E, Mock C, Bhan I, Loewer A, Lahav G (2008) Recurrent initiation: a mechanism for triggering p53 pulses in response to dna damage. Mol Cell 30:277–289

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Burda Z, Krzywicki A, Martin O, Zagorski M (2011) Motifs emerge from function in model gene regulatory networks. Proc Natl Acad Sci USA 108:17263–17268

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Chandra F, Buzi G, Doyle J (2011) Glycolytic oscillations and limits on robust efficiency. Science 333:187–192

    Article  CAS  PubMed  Google Scholar 

  • Clewley R, Sherwood W, LaMar M, Guckenheimer J (2007) Pydstool, a software environment for dynamical systems modeling. http://pydstool.sourceforge.net

  • Cotterell J, Sharpe J (2010) An atlas of gene regulatory networks reveals multiple three-gene mechanisms for interpreting morphogen gradients. Mol Syst Biol 6:425

    Article  PubMed Central  PubMed  Google Scholar 

  • Danino T, Mondragon-Palomino O, Tsimring L, Hasty J (2010) A synchronized quorum of genetic clocks. Nature 463:326–330

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Elowitz M, Leibler S (2000) A synthetic oscillatory network of transcriptional regulators. Nature 403:335–338

    Article  CAS  PubMed  Google Scholar 

  • Ferrell JJ, Tsai T, Yang Q (2011) Modeling the cell cycle: why do certain circuits oscillate? Cell 144:874–885

    Article  CAS  PubMed  Google Scholar 

  • Franco E, Friedrichs E, Kim J, Jungmannb R, Murray R, Winfree E, Simmel F (2011) Timing molecular motion and production with a synthetic transcriptional clock. Proc Natl Acad Sci USA 108:E784–E793

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Frank K, Petrie B, Fisher J, Leggett W (2011) Transient dynamics of an altered large marine ecosystem. Nature 477:86–89

    Article  CAS  PubMed  Google Scholar 

  • Khalil A, Collins J (2014) Synthetic biology: applications come of age. Nat Rev Genet 11:367–379

    Article  Google Scholar 

  • Kim J, Winfree E (2011) Synthetic in vitro transcriptional oscillators. Mol Syst Biol 7:465

    Article  PubMed Central  PubMed  Google Scholar 

  • Kim T, Kim J, Heslop-Harrison P, Cho K (2010) Evolutionary design principles and functional characteristics based on kingdom-specific network motifs. Bioinformatics 27:245–251

    Article  PubMed  Google Scholar 

  • Krzywinski M, Birol I, Jones S, Marra M (2012) Hive plots—rational approach to visualizing networks. Brief Bioinform 5:627–644

    Article  Google Scholar 

  • Lomnitz J, Savageau M (2014) Strategy revealing phenotypic differences among synthetic oscillator designs. ACS Synth Biol 3(9):686–701

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Ma W, Trusina A, El-Samad H, Lim W, Tan C (2009) Defining network topologies that can achieve biochemical adaptation. Cell 138:760–773

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Matplotlib (2013) Python 2d plotting library. http://matplotlib.sourceforge.net/

  • Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U (2002) Network motifs: simple building blocks of complex networks. Science 298:824–827

    Article  CAS  PubMed  Google Scholar 

  • Mondragon-Palomino O, Danino T, Selimkhanov J, Tsimring L, Hasty J (2011) Entrainment of a population of synthetic genetic oscillators. Science 333:1315–1319

    Article  CAS  PubMed  Google Scholar 

  • Nielsen A, Voigt C (2014) Multi-input crispr/cas genetic circuits that interface host regulatory networks. Mol Syst Biol 10:763

    Article  Google Scholar 

  • Noman N, Monjo T, Moscato P, Iba H (2015) Evolving robust gene regulatory networks. PLoS One 10(1):e0116258

    Article  PubMed Central  PubMed  Google Scholar 

  • Novak B, Tyson J (2008) Design principles of biochemical oscillators. Nat Rev Mol Cell Biol 9:981–991

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Okamoto H, Gourgout A, Chang CY, Onomitsu K, Mahboob I, Chang E, Yamaguchi H (2013) Coherent phonon manipulation in coupled mechanical resonators. Nat Phys 9:480–484

    Article  CAS  Google Scholar 

  • Pershin Y, Ventra MD (2010) Practical approach to programmable analog circuits with memristors. IEEE Trans Circuits Syst 57(8):1857–1864

    Article  Google Scholar 

  • Pokhilko A, Fernandez A, Edwards K, Southern M, Halliday K, Millar A (2012) The clock gene circuit in arabidopsis includes a repressilator with additional feedback loops. Mol Syst Biol 8:574

    Article  PubMed Central  PubMed  Google Scholar 

  • Purcell O, Savery N, Grierson C, di Bernardo M (2010) A comparative analysis of synthetic genetic oscillators. J R Soc Interface 7:1503–1524

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Rhodius V, Segall-Shapiro T, Sharon B, Ghodasara A, Orlova E, Tabakh H, Burkhardt D, Clancy K, Peterson T, Gross C, Voigt C (2013) Design of orthogonal genetic switches based on a crosstalk map of \(\sigma\)s, and promoters. Mol Syst Biol 9:702

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Rocks (2013) Open-source toolkit for real and virtual clusters. http://www.rocksclusters.org/

  • Scipy (2013) http://www.scipy.org/

  • Semenov S, Wong A, van der Made R, Postma S, Groen J, van Roekel H, de Greef T, Huck H (2015) Rational design of functional and tunable oscillating enzymatic networks. Nat Chem 7:160–165

    Article  CAS  Google Scholar 

  • Shah N, Sarkar C (2011) Robust network topologies for generating switch-like cellular responses. PLoS Comp Biol 7(e1002):085

    Google Scholar 

  • Shin Y, Hencey B, Lipkin S, Shen X (2011) Frequency domain analysis reveals external periodic fluctuations can generate sustained p53 oscillation. PLoS One 6(e22):852

    Google Scholar 

  • Stanton B, Nielsen A, Tamsir A, Clancy K, Peterson T, Voigt C (2014) Genomic mining of prokaryotic repressors for orthogonal logic gates. Nat Chem Biol 10(2):99–105

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Stricker J, Cookson S, Bennett M, Mather W, Tsimring L, Hasty J (2008) A fast, robust and tunable synthetic gene oscillator. Nature 456:516–519

    Article  CAS  PubMed  Google Scholar 

  • Tiana G, Krishna S, Pigolotti S, Jensen M, Sneppen K (2007) Oscillations and temporal signalling in cells. Phys Biol 4:R1–R17

    Article  CAS  PubMed  Google Scholar 

  • Tigges M, Marquez-Lago T, Stelling J, Fussenegger M (2009) A tunable synthetic mammalian oscillator. Nature 457:309–312

    Article  CAS  PubMed  Google Scholar 

  • Toettcher J, Mock C, Batchelor E, Loewer A, Lahav G (2010) A syntheticnatural hybrid oscillator in human cells. Proc Natl Acad Sci USA 107:17047–17052

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Tsai T, Choi Y, Ma W, Pomerening J, Tang C, Ferrell JJ (2008) Robust, tunable biological oscillations from interlinked positive and negative feedback loops. Science 321:126–129

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Tyson J, Albert R, Golbeter A, Ruoff P, Sible J (2008) Biological switches and clocks. J R Soc Interface 5:S1–S8

    Article  PubMed Central  PubMed  Google Scholar 

  • Velar J, Kueh H, Barkai N, Leibler S (2002) Mechanisms of noise-resistance in genetic oscillators. Proc Natl Acad Sci USA 99:5988–5992

    Article  Google Scholar 

  • Wagner A (2005) Circuit topology and the evolution of robustness in two-gene circadian oscillators. Proc Natl Acad Sci USA 102:11775–11780

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Yeger-Lotem E, Sattath S, Kashtan N, Itzkovitz S, Milo R, Pinter R, Alon U, Margalit H (2004) Network motifs in integrated cellular networks of transcription–regulation and proteinprotein interaction. Proc Natl Acad Sci USA 101:5934–5939

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Zhang E, Kay S (2010) Clocks not winding down: unravelling circadian networks. Nat Rev Mol Cell Biol 11:764–776

    Article  CAS  PubMed  Google Scholar 

Download references

Acknowledgments

The authors gratefully acknowledge the generous funding and support of Instituto de Investigación de Facultad de Ingeniería Mecánica (INIFIM), Instituto General de Investigación (IGI), Centro de Tecnologías de Información y Comunicaciones (CTIC), all part of Universidad Nacional de Ingeniería (UNI), Lima, Perú.

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Correspondence to Elizabeth R. Villota.

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Castillo-Hair, S.M., Villota, E.R. & Coronado, A.M. Design principles for robust oscillatory behavior. Syst Synth Biol 9, 125–133 (2015). https://doi.org/10.1007/s11693-015-9178-6

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  • DOI: https://doi.org/10.1007/s11693-015-9178-6

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