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
Ananthasubramaniam B, Herzel H (2014) Positive feedback promotes oscillations in negative feedback loops. PLoS One 9(8):e104761
Barabasi A, Oltvai Z (2004) Network biology: understanding the cell’s functional organization. Nat Rev Genet 5:101–113
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
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
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
Chandra F, Buzi G, Doyle J (2011) Glycolytic oscillations and limits on robust efficiency. Science 333:187–192
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
Danino T, Mondragon-Palomino O, Tsimring L, Hasty J (2010) A synchronized quorum of genetic clocks. Nature 463:326–330
Elowitz M, Leibler S (2000) A synthetic oscillatory network of transcriptional regulators. Nature 403:335–338
Ferrell JJ, Tsai T, Yang Q (2011) Modeling the cell cycle: why do certain circuits oscillate? Cell 144:874–885
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
Frank K, Petrie B, Fisher J, Leggett W (2011) Transient dynamics of an altered large marine ecosystem. Nature 477:86–89
Khalil A, Collins J (2014) Synthetic biology: applications come of age. Nat Rev Genet 11:367–379
Kim J, Winfree E (2011) Synthetic in vitro transcriptional oscillators. Mol Syst Biol 7:465
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
Krzywinski M, Birol I, Jones S, Marra M (2012) Hive plots—rational approach to visualizing networks. Brief Bioinform 5:627–644
Lomnitz J, Savageau M (2014) Strategy revealing phenotypic differences among synthetic oscillator designs. ACS Synth Biol 3(9):686–701
Ma W, Trusina A, El-Samad H, Lim W, Tan C (2009) Defining network topologies that can achieve biochemical adaptation. Cell 138:760–773
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
Mondragon-Palomino O, Danino T, Selimkhanov J, Tsimring L, Hasty J (2011) Entrainment of a population of synthetic genetic oscillators. Science 333:1315–1319
Nielsen A, Voigt C (2014) Multi-input crispr/cas genetic circuits that interface host regulatory networks. Mol Syst Biol 10:763
Noman N, Monjo T, Moscato P, Iba H (2015) Evolving robust gene regulatory networks. PLoS One 10(1):e0116258
Novak B, Tyson J (2008) Design principles of biochemical oscillators. Nat Rev Mol Cell Biol 9:981–991
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
Pershin Y, Ventra MD (2010) Practical approach to programmable analog circuits with memristors. IEEE Trans Circuits Syst 57(8):1857–1864
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
Purcell O, Savery N, Grierson C, di Bernardo M (2010) A comparative analysis of synthetic genetic oscillators. J R Soc Interface 7:1503–1524
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
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
Shah N, Sarkar C (2011) Robust network topologies for generating switch-like cellular responses. PLoS Comp Biol 7(e1002):085
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
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
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
Tiana G, Krishna S, Pigolotti S, Jensen M, Sneppen K (2007) Oscillations and temporal signalling in cells. Phys Biol 4:R1–R17
Tigges M, Marquez-Lago T, Stelling J, Fussenegger M (2009) A tunable synthetic mammalian oscillator. Nature 457:309–312
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
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
Tyson J, Albert R, Golbeter A, Ruoff P, Sible J (2008) Biological switches and clocks. J R Soc Interface 5:S1–S8
Velar J, Kueh H, Barkai N, Leibler S (2002) Mechanisms of noise-resistance in genetic oscillators. Proc Natl Acad Sci USA 99:5988–5992
Wagner A (2005) Circuit topology and the evolution of robustness in two-gene circadian oscillators. Proc Natl Acad Sci USA 102:11775–11780
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
Zhang E, Kay S (2010) Clocks not winding down: unravelling circadian networks. Nat Rev Mol Cell Biol 11:764–776
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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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