1,577
Views
9
CrossRef citations to date
0
Altmetric
Original Articles

Stability analysis of an artificial biomolecular oscillator with non-cooperative regulatory interactions

, , &
Pages 102-120 | Received 22 Apr 2016, Accepted 26 Sep 2016, Published online: 10 Nov 2016

References

  • D. Angeli and E. Sontag, Monotone control systems, IEEE Trans. Automat. Control 48 (2003), pp. 1684–1698. doi: 10.1109/TAC.2003.817920
  • F. Blanchini, C. Cuba Samaniego, E. Franco, and G. Giordano, Design of a molecular clock with RNA-mediated regulation, Proceedings of the IEEE Conference on Decision and Control, 2014, pp. 4611–4616.
  • F. Blanchini and E. Franco, Structurally robust biological networks, BMC Syst. Biol. 5 (2011), p. 74. doi: 10.1186/1752-0509-5-74
  • F. Blanchini, E. Franco, and G. Giordano, A structural classification of candidate oscillatory and multistationary biochemical systems, Bull. Math. Biol. 76 (2014), pp. 2542–2569. doi: 10.1007/s11538-014-0023-y
  • F. Blanchini, E. Franco, and G. Giordano, Structural conditions for oscillations and multistationarity in aggregate monotone systems, Proceedings of the IEEE Conference on Decision and Control, Osaka, Japan, 2015, pp. 609–614.
  • F. Blanchini and S. Miani, Set-Theoretic Methods in Control, Systems & Control: Foundations & Applications, Birkhäuser, Basel, 2015.
  • N.E. Buchler and M. Louis, Molecular titration and ultrasensitivity in regulatory networks, J. Mol. Biol. 384 (2008), pp. 1106–1119. doi: 10.1016/j.jmb.2008.09.079
  • H. Chen, K. Shiroguchi, H. Ge, and X.S. Xie, Genome-wide study of mRNA degradation and transcript elongation in Escherichia coli, Mol. Syst. Biol. 11 (2015), p. 781. doi: 10.15252/msb.20145794
  • C. Cuba Samaniego, G. Giordano, J. Kim, F. Blanchini, and E. Franco, Molecular titration promotes oscillations and bistability in minimal network models with monomeric regulators, ACS Synth. Biol. 5 (2016), pp. 321–333. doi: 10.1021/acssynbio.5b00176
  • C. Cuba Samaniego, S. Kitada, and E. Franco, Design and analysis of a synthetic aptamer-based oscillator, in American Control Conference (ACC), 2015, 2015, pp. 2655–2660.
  • T. Danino, O. Mondragon-Palomino, L. Tsimring, and J. Hasty, A synchronized quorum of genetic clocks, Nature 463 (2010), pp. 326–330. doi: 10.1038/nature08753
  • A.D. Ellington and J.W. Szostak, In vitro selection of RNA molecules that bind specific ligands, Nature 346 (1990), pp. 818–822. doi: 10.1038/346818a0
  • M.B. Elowitz and S. Leibler, A synthetic oscillatory network of transcriptional regulators, Nature 403 (2000), pp. 335–338. doi: 10.1038/35002125
  • G.A. Enciso, Monotone input/output systems, and applications to biological systems, Ph.D. thesis, Graduate School – New Brunswick, Rutgers, The State University of New Jersey, 2005.
  • E. Franco, E. Friedrichs, J. Kim, R. Jungmann, R. Murray, E. Winfree, and F.C. Simmel, Timing molecular motion and production with a synthetic transcriptional clock, Proc. Natl. Acad. Sci. 108 (2011), pp. E784–E793. doi: 10.1073/pnas.1100060108
  • T. Fujii and Y. Rondelez, Predator–prey molecular ecosystems, ACS nano 7 (2012), pp. 27–34. doi: 10.1021/nn3043572
  • J. Kim and R.M. Murray, Analysis and design of a synthetic transcriptional network for exact adaptation, in Biomedical Circuits and Systems Conference (BioCAS), 2011, pp. 345–348.
  • J. Kim, K.S. White, and E. Winfree, Construction of an in vitro bistable circuit from synthetic transcriptional switches, Mol. Syst. Biol. 2 (2006), p. 68. doi: 10.1038/msb4100099
  • J. Kim and E. Winfree, Synthetic in vitro transcriptional oscillators, Mol. Syst. Biol. 7 (2011), p. 465. doi: 10.1038/msb.2010.119
  • P.A. Krieg and D. Melton, In vitro RNA synthesis with SP6 RNA polymerase, Methods Enzymol. 155 (1987), pp. 397–415. doi: 10.1016/0076-6879(87)55027-3
  • W.T. McAllister, H. Küpper, and E.K. Bautz, Kinetics of transcription by the bacteriophage-T3 RNA polymerase in vitro, Eur. J. Biochem. 34 (1973), pp. 489–501. doi: 10.1111/j.1432-1033.1973.tb02785.x
  • K. Montagne, R. Plasson, Y. Sakai, T. Fujii, and Y. Rondelez, Programming an in vitro DNA oscillator using a molecular networking strategy, Mol. Syst. Biol. 7 (2011), p. 466. doi: 10.1038/msb.2010.120
  • Y. Mori, Y. Nakamura, and S. Ohuchi, Inhibitory RNA aptamer against SP6 RNA polymerase, Biochem. Biophys. Res. Commun. 420 (2012), pp. 440–443. doi: 10.1016/j.bbrc.2012.03.014
  • S. Ohuchi, Y. Mori, and Y. Nakamura, Evolution of an inhibitory RNA aptamer against T7 RNA polymerase, FEBS Open Bio. 2 (2012), pp. 203–207.
  • D. Richeson and J. Wiseman, A fixed point theorem for bounded dynamical systems, Illinois J. Math. 46 (2002), pp. 491–495.
  • D. Richeson and J. Wiseman, Addendum to: ‘A fixed point theorem for bounded dynamical systems’ [Illinois J. Math. 46(2):491–495, 2002], Illinois J. Math. 48 (2004), pp. 1079–1080.
  • E. Snoussi, Necessary conditions for multistationarity and stable periodicity, J. Biol. Syst. 6 (1998), pp. 3–9. doi: 10.1142/S0218339098000042
  • E. Sontag, Molecolar systems biology and control, Eur. J. Control 11 (2005), pp. 396–435. doi: 10.3166/ejc.11.396-435
  • R. Srzednicki, On rest points of dynamical systems, Fund. Math. 126 (1985), pp. 69–81.
  • J. Stricker, S. Cookson, M.R. Bennett, W.H. Mather, L.S. Tsimring, and J. Hasty, A fast, robust and tunable synthetic gene oscillator, Nature 456 (2008), pp. 516–519. doi: 10.1038/nature07389
  • S. Tabor and C.C. Richardson, A bacteriophage T7 RNA polymerase/promoter system for controlled exclusive expression of specific genes, Proc. Natl. Acad. Sci. 82 (1985), pp. 1074–1078. doi: 10.1073/pnas.82.4.1074
  • R. Thomas, On the Relation Between the Logical Structure of Systems and their Ability to Generate Multiple Steady States or Sustained Oscillations, Vol. 9, Springer-Verlag, Berlin, Heidelberg, 1981.
  • M. Tigges, T.T. Marquez-Lago, J. Stelling and M. Fussenegger, A tunable synthetic mammalian oscillator, Nature 457 (2009), pp. 309–312. doi: 10.1038/nature07616
  • U. Vogel and K.F. Jensen, The RNA chain elongation rate in Escherichia coli depends on the growth rate, J. Bacteriol. 176 (1994), pp. 2807–2813. doi: 10.1128/jb.176.10.2807-2813.1994
  • M. Weitz, J. Kim, K. Kapsner, E. Winfree, E. Franco, and F.C. Simmel, Diversity in the dynamical behaviour of a compartmentalized programmable biochemical oscillator, Nat. Chem. 6 (2014), pp. 295–302. doi: 10.1038/nchem.1869
  • A.T. Winfree, The Geometry of Biological Time, Springer-Verlag, New York, NY, 1980.
  • B. Yurke and A.P. Mills, Using DNA to power nanostructures, Genet. Program. Evol. Mach. 4 (2003), pp. 111–122. doi: 10.1023/A:1023928811651
  • D.Y. Zhang, A.J. Turberfield, B. Yurke, and E. Winfree, Engineering entropy-driven reactions and networks catalyzed by DNA, Science 318 (2007), pp. 1121–1125. doi: 10.1126/science.1148532