707
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Universality of stable multi-cluster periodic solutions in a population model of the cell cycle with negative feedback

& ORCID Icon
Pages 455-522 | Received 23 Feb 2021, Accepted 13 Aug 2021, Published online: 07 Sep 2021

References

  • S. Achuthan and C.C. Canavier, Phase-resetting curves determine synchronization, phase locking, and clustering in networks of neural oscillators, J. Neurosci. 29(16) (2009), pp. 5218–5233.
  • B. Bàràny, G. Moses, and T.R. Young, Instability of the steady state solution in cell cycle population structure models with feedback, J. Math. Biol. 78(5) (2019), pp. 1365–1387.
  • E.M. Boczko, T. Gedeon, C.C. Stowers, and T.R. Young, ODE, RDE and SDE models of cell cycle dynamics and clustering in yeast, J. Biol. Dyn. 4 (2010), pp. 328–345.
  • N. Bose, Tests for Hurwitz and Schur properties of convex combination of complex polynomials, IEEE Trans. Circuits Syst. 36(9) (1989), pp. 1245–1247.
  • N. Breitsch, G. Moses, E. Boczko, and T.R. Young, Cell cycle dynamics: Clustering is universal in negative feedback systems, J. Math. Biol. 70(5) (2014), pp. 1151–1175.
  • R.L. Buckalew, Mathematical models in cell cycle biology and pulmonary immunity, Ph.D. dissertation, Ohio University, 2014. Available at http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1395242276.
  • L. Cai and B.P. Tu, Driving the cell cycle through metabolism, Annu. Rev. Cell Dev. Biol. 28 (2012), pp. 59–87.
  • Z. Chen, E.A. Odstrcil, B.P. Tu, and S.L. McKnight, Restriction of DNA replication to the reductive phase of the metabolic cycle protects genome integrity, Science 316 (2007), pp. 1916–1919.
  • P. Duboc, L. Marison, and U. von Stockar, Physiology of Saccharomyces cerevisiae during cell cycle oscillations, J. Biotechnol. 51 (1996), pp. 57–72.
  • H.J. Fell, On the zeros of convex combinations of polynomials, Pac. J. Math. 89(1) (1980), pp. 43–50.
  • B. Fernandez and L. Tsimring, Typical trajectories of coupled degrade-and-fire oscillators: From dispersed populations to massive clustering, J. Math. Biol. 68(7) (2014), pp. 1627–1652.
  • R.K. Finn and R.E. Wilson, Population dynamic behavior of the chemostat system, J. Agric. Food Chem. 2 (1954), pp. 66–69.
  • B. Futcher, Metabolic cycle, cell cycle and the finishing kick to start, Genome Biol. 7 (2006), pp. 107–111.
  • D. Golomb and J. Rinzel, Clustering in globally coupled inhibitory neurons, Physica D 72(3) (1994), pp. 259–282.
  • Z.P. Kilpatrick and B. Ermentrout, Sparse gamma rhythms arising through clustering in adapting neuronal networks, PLoS Comput. Biol. 7(11) (2011), p. e10022810.
  • I.Z. Kiss, Y. Zhai, and J.L. Hudson, Predicting mutual entrainment of oscillators with experiment-based phase models, Phys. Rev. Lett. 94(24) (2005), p. 248301.
  • I.Z. Kiss, C.G. Rusin, H. Kori, and J.L. Hudson, Engineering complex dynamical structures: Sequential patterns and desynchronization, Science 316(5833) (2007), pp. 1886–1889.
  • R.R. Klevecz, J. Bolen, G. Forrest, and D.B. Murray, A genome-wide oscillation in transcription gates DNA replication and cell cycle, Proc. Natl. Acad. Sci. USA 101(5) (2004), pp. 1200–1205.
  • M.T. Kuenzi and A. Fiechter, Changes in carbohydrate composition and trehalose activity during the budding cycle of Saccharomyces cerevisiae, Arch. Microbiol. 64 (1969), pp. 396–407.
  • A. Mauroy and R. Sepulchre, Clustering behaviors in networks of integrate-and-fire oscillators, Chaos18(3) (2008), p. 037122.
  • H.K. von Meyenburg, Energetics of the budding cycle of Saccharomyces cerevisiae during glucose limited aerobic growth, Arch. Mikrobiol. 66 (1969), pp. 289–303.
  • L. Morgan, G. Moses, and T.R. Young, Coupling of the cell cycle and metabolism in yeast cell-cycle-related oscillations via resource criticality and checkpoint gating, Lett. Biomath. 5 (2018), pp. 113–128. doi:https://doi.org/10.1080/23737867.2018.1456366
  • G. Moses, Dynamical systems in biological modeling: Clustering in the cell division cycle of yeast, Ph.D. dissertation, Ohio University, 2015. Available at http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1438170442.
  • D. Muller, S. Exler, L. Aguilera-Vazquez, E. Guerrero-Martin, and M. Reuss, Cyclic AMP mediates the cell cycle dynamics of energy metabolism in Saccharomyces cervisiae, Yeast 20 (2003), pp. 351–367.
  • T. Munch, B. Sonnleitner, and A. Fiechter, The decisive role of the Saccharomyces cervisiae cell cycle behavior for dynamic growth characterization, J. Biotechnol. 22 (1992), pp. 329–352.
  • L.L. Newcomb, J.A. Diderich, M.G. Slattery, and W. Heideman, Glucose regulation of Saccharomyces cerevisiae cell cycle genes, Eukaryot. Cell 2 (2003), pp. 143–149.
  • P.R. Patnaik, Oscillatory metabolism of Saccharomyces cerevisiae: An overview of mechanisms and models, Biotech. Adv. 21 (2003), pp. 183–192.
  • K. Prathom, Stability regions of cyclic solutions under negative feedback and uniqueness of periodic solutions for uneven cluster systems, Ph.D. dissertation, Ohio University, 2019. Available at https://etd.ohiolink.edu/etdc/view?acc_num=ohiou1562778288743268.
  • K.C. Rabi, Study of some biologically relevant dynamical system models: (In)stability regions of cyclic solutions in cell cycle population structure model under negative feedback and random connectivities in multi-type neuronal network models, Ph.D. dissertation, Ohio University, 2020. Available at http://rave.ohiolink.edu/etdc/view?acc_num=ohiou16049254273607.
  • K.C. Rabi, A. Algoud, and T.R. Young, Instability of k-cluster solutions in a cell cycle population model when k is prime, J. Appl. Nonlinear Dyn. 11(1) (2022), pp. 87–138.
  • J.B. Robertson, C.C. Stowers, E.M. Boczko, and C.H. Johnson, Real-time luminescence monitoring of cell-cycle and respiratory oscillations in yeast, Proc. Natl. Acad. Sci. USA 105 (2008), pp. 17988–17993.
  • J. Rombouts, K. Prathom, and T. Young, Clusters tend to be of equal size in a negative feedback population model of cell cycle dynamics, SIAM J. Appl. Dyn. Syst. 19(2) (2020), pp. 1540–1573. doi:https://doi.org/10.1137/19M129070X
  • C. Stowers, T.R. Young, and E. Boczko, The structure of populations of budding yeast in response to feedback, Hypoth. Life Sci. 1(3) (2011), pp. 71–84.
  • A.F. Taylor, P. Kapetanopoulos, B.J. Whitaker, R. Toth, L. Bull, and M.R. Tinsley, Clusters and switchers in globally coupled photochemical oscillators, Phys. Rev. Lett. 100(21) (2008), p. 214101.
  • A. Taylor, M. Tinsley, and K. Showalter, Insights into collective cell behaviour from populations of coupled chemical oscillators, Phys. Chem. Chem. Phys. 17(31) (2015), pp. 20047–20055.
  • K. Uchiyama, M. Morimoto, Y. Yokoyama, and S. Shioya, Cell cycle dependency of rice α-amylase production in a recombinant yeast, Biotechnol. Bioeng. 54 (1996), pp. 262–271.
  • M. Wickramasinghe and I.Z. Kiss, Spatially organized dynamical states in chemical oscillator networks: Synchronization, dynamical differentiation, and chimera patterns, PLoS ONE 8(11) (2013), p. e80586.
  • D. Wilson and J. Moehlis, Clustered desynchronization, from high-frequency deep brain stimulation, PLoS Comput. Biol. 11 (2015), p. e1004673.
  • T.R. Young, B. Fernandez, R. Buckalew, G. Moses, and E.M. Boczko, Clustering in cell cycle dynamics with general response/signaling feedback, J. Theor. Biol. 292 (2012), pp. 103–115.
  • J. Zhang, Z. Yuan, and T. Zhou, Synchronization and clustering of synthetic genetic networks: A role for CIS-regulatory modules, Phys. Rev. E 79 (2009), p. e041903.
  • G. Zhao, Y. Chen, L. Carey, and B. Futcher, Cyclin-dependent kinase co-ordinates carbohydrate metabolism and cell cycle in S. cerevisiae, Mol. Cell 62 (2016), pp. 546–557.