Publication Cover
Dynamical Systems
An International Journal
Volume 33, 2018 - Issue 1
136
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Microbial metabolism and growth under conditions of starvation modelled as the sliding mode of a differential inclusion

&
Pages 93-112 | Received 06 Jun 2016, Accepted 13 Feb 2017, Published online: 21 Mar 2017

References

  • V. Acary and B. Brogliato, Numerical Methods for Nonsmooth Dynamical Systems. Applications in Mechanics and Electronics, Lecture Notes in Applied and Computational Mechanics, Springer-Verlag, Berlin, 2008.
  • J.P. Aubin and A. Cellina, Differential Inclusions, Springer-Verlag, Berlin, 1984.
  • S. Bleecken, Model for the feedback control system of bacterial growth I. Growth in discontinuous culture, J. Theor. Biol. 133 (1988), pp. 37–65.
  • C. Broughton, H.A. van den Berg, A.M. Wemyss, D.I. Roper, and A. Rodger, Beyond the discovery void: new targets for antibacterial compounds, Sci. Prog. 99 (2016), pp. 153–182.
  • R. Casey, H. de Jong, and J.L. Gouze, Piecewise-linear models of genetics regulatory networks: equilibria and their stability, J. Math. Biol. 52 (2006), pp. 27–56.
  • E.K.P. Chong, S. Hui, and S.H. Zak, An analysis of a class of neural networks for solving linear programming problems, IEEE Trans. Autom. Control 44 (1999), pp. 1995–2006.
  • E.A. Dawes, Growth and survival of bacteria, in Bacteria in Nature III: Structure, Physiology, and Genetic Adaptability, J.S. Poindexter and E.R. Leadbetter, eds., Plenum, New York, 1989, pp. 67–187.
  • H. de Jong, J.L. Gouze, C. Hernandez, M. Page, T. Sar, and J. Geiselmann, Qualitative simulation of genetic regulatory networks using piecewise-linear models, Bull. Math. Biol. 66 (2004), pp. 301–340.
  • L. Dieci and L. Lopez, Sliding motion in Filippov differential systems: theoretical results and a computational approach, SIAM J. Numer. Anal. 47 (2009), pp. 2023–2051.
  • M.R. Droop, Vitamin B12 and marine ecology. IV. The kinetics of uptake, growth and inhibition in Monochrysis lutheri, J. Mar. Biol. Assoc. 48 (1968), pp. 689–733.
  • M.R. Droop, Vitamin B12 and marine ecology. IV. The kinetics of uptake, growth and inhibition in Monochrysis lutheri, J. Mar. Biol. Assoc. 48 (1968), pp. 689–733.
  • C.P. Fall, E.S. Marland, J.M. Wagner, and J.J. Tyson, Computational Cell Biology, Springer-Verlag, Berlin, 2002.
  • A.F. Filippov, Differential Equations with Discontinuous Right-Hand Side, Kluwer Academic, Dordrecht, 1988.
  • G. Fusco and N. Guglielmi, A regularization for discontinuous differential equations with application to state-dependent delay differential equations of neutral type, J. Diff. Equa. 250 (2011), pp. 3230–3279.
  • L. Glass and S.A. Kauffman, The logical analysis of continuous non-linear biochemical control networks, J. Theor. Biol. 39 (1973), pp. 103–129.
  • J.L. Gouze and T. Sari, A class of piecewise linear differential equations arising in biological models, Dyn. Syst. 17 (2002), pp. 299–316.
  • J.P. Grover, Resource competition in a variable environment: Phytoplankton growing according to the Variable-Internal-Stores model, Am. Nat. 138 (1991), pp. 811–835.
  • D. Herbert, The chemical composition of micro-organisms as a function of their environment, Symp. Soc. Gen. Microbiol. 11 (1961), pp. 391–416.
  • M.R. Jeffrey and S.J. Hogan, The geometry of generic sliding bifurcations, SIAM Rev. 53 (2011), pp. 505–525.
  • K.H. Johansson, A.E. Barabanov, and K.J. Astrom, Limit cycles with chattering in relay feedback systems, IEEE Trans. Autom. Control 247 (2002), pp. 1414–1423.
  • K.H. Johansson, A. Rantzer, and K.J. Astrom, Fast switches in relay feedback systems, Automatica J. IFAC 35 (1999), pp. 539–552.
  • S.A.L.M. Kooijman, Dynamic Energy Budget Theory for Metabolic Organisation, Cambridge University Press, Cambridge, 2009.
  • P. Kowalczyk and P.T. Piiroinen, Two-parameter sliding bifurcations of periodic solutions in a dry-friction oscillator, Phys. D 237 (2008), pp. 1053–1073.
  • G. Kramer, R.R. Sprenger, M.A. Nessen, W. Roseboom, D. Speijer, L. de Jong, M.J. Texeira de Mattos, J. Back, and C.G. de Koster, Proteome-wide alterations in Escherichia coli translation rates upon anaerobiosis, Mol. Cell. Proteomics 9.11 (2010), pp. 2508–2516.
  • J. Malmborg and B. Bernhardsson, Control and simulation of hybrid systems, Commun. Nonlinear Sci. 30 (1997), pp. 337–347.
  • A.G. Marr, E.H. Nilson, and D.J. Clark, The maintenance requirement of Escherichia coli, Ann. N. Y. Acad. Sci. 102 (1962), pp. 536–548.
  • J. Monod, The growth of bacterial cultures, Annu. Rev. Microbiol. 3 (1949), pp. 371–394.
  • F.C. Neidhardt, J.L. Ingraham, and M. Schaechter, Physiology of the Bacterial Cell: A Molecular Approach, Sinauer Associates, Sunderland, 1990.
  • O.A. Nev and H.A. van den Berg, Variable-Internal-Stores models of microbial growth and metabolism with dynamic allocation of cellular resources, J. Math. Biol. (2016). doi:10.1007/s00285-016-1030-4.
  • S.J. Pirt, The maintenance energy of bacteria in growing cultures, Proc. R. Soc. Lond. 133 (1965), pp. 300–302.
  • E. Plahte and S. Kjoglum, Analysis and genetic properties of gene regulatory networks with graded response functions, Phys.a D 201 (2005), pp. 150–176.
  • H. Schiller and M. Arnold, Convergence of continuous approximation for discontinuous ODEs, Appl. Numer. Math. 62 (2012).
  • J.M. Schumacher, S. Weiland, and W.P.M.H. Heemels, Linear complementarity systems, SIAM J. Appl. Math. 60 (2000), pp. 1234–1269.
  • M. Scott and T. Hwa, Bacterial growth laws and their applications, Curr. Opinion Biotechnol. 22 (2011), pp. 599–565.
  • M. Scott, C.W. Gunderson, E.M. Mateescu, Z. Zhang, and T. Hwa, Interdependence of cell growth and gene expression: origins and consequences, Science 330 (2010), pp. 1099–1102.
  • M. Scott, S. Klumpp, E.M. Mateescu, and T. Hwa, Emergence of robust growth laws from optimal regulation of ribosome synthesis, Mol. Syst. Biol. 10 (2014), p. 747.
  • J. Sotomayor and A.L.F. Machado, Structurally stable discontinuous vector fields in the plane, Qual. Theory Dyn. Syst. 3 (2002), pp. 227–250.
  • J. Sotomayor and M.A. Teixeira, Regularization of discontinuous vector fields, in International Conference on Differential Equations, L. Magalhães, C. Rocha, and L. Sanchez, eds., World Scientific, Singapore, 1995, pp. 207–223.
  • R. Thomas, D. Thieffry, and M. Kaufman, Dynamical behaviour of biological regulatory networks. I. Biological role of feedback loops and practical use of the concept of the loop-characteristic state, Bull. Math. Biol. 57 (1995), pp. 247–276.
  • V.I. Utkin, Variable structure systems with sliding modes, IEEE Trans. Autom. Control 22 (1977), pp. 212–222.
  • V.I. Utkin, Sliding Modes in Control and Optimization, Springer-Verlag, Berlin, 1992.
  • H.A. van den Berg, A generic view of classic microbial growth models, Acta Biotheor. 46 (1998), pp. 117–130.
  • H.A. van den Berg, How microbes can achieve balanced growth in a fluctuating environment, Acta Biotheor. 49 (2001), pp. 1–21.
  • H.A. van den Berg, Y.N. Kiselev, and M.V. Orlov, Homeostatic regulation in physiological systems: A versatile Ansatz, Math. Biosci. 268 (2015), pp. 92–101.
  • F.M. Williams, A model of cell growth dynamics, J. Theor. Biol. 15 (1967), pp. 190–207.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.