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23. Seno, M.; Iwamoto, K.; Sawada, K. Instability and Oscillatory Behavior of Membrane-Chemical Reaction Systems;
Technical Report; University of Tokyo: Tokyo, Japan, 1978.
24. Tyson, J.J.; Chen, K.C.; Novak, B. Sniffers, buzzers, toggles and blinkers: Dynamics of regulatory and
signaling pathways in the cell. Curr. Opin. Cell Biol. 2003, 15, 221–231. [CrossRef]
25. Edelstein, B.B. Biochemical Model With Multiple Steady States and Hysteresis. J. Theor. Biol. 1970, 29, 57–62.
[CrossRef]
26. Angeli, D.; Ferrell, J.E.; Sontag, E.D. Detection of multistability, bifurcations, and hysteresis in a large class of
biological positive-feedback systems. Proc. Natl. Acad. Sci. USA 2004, 101, 1822–1827. [CrossRef]
27. Nicolis, G.; Prigogine, I. Self-Organization in Nonequilibrium Systems; Wiley-Blackwell: Hoboken, NJ, USA,
1977; Volume 82, p. 672.
28. Heinrich, R.; Rapoport, S.M.; Rapoport, T.A. Metabolic regulation and mathematical models. Proq. Biophys.
Mol. Biol. 1977, 32, 1–82.
29. Kholodenko, B.N. Negative feedback and ultrasensitivity can bring about oscillations in the mitogenactivated protein kinase cascades. Eur. J. Biochem. 2000, 267, 1583–1588. [CrossRef][PubMed]
30. Goldbeter, A. A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. Proc. Natl.
Acad. Sci. USA 1991, 88, 9107–9111. [CrossRef][PubMed]
31. François, P.; Hakim, V. Core genetic module: The mixed feedback loop. Phys. Rev. E 2005, 72, 031908.
[CrossRef][PubMed]
32. Lavrentovich, M.; Hemkin, S. A mathematical model of spontaneous calcium(II) oscillations in astrocytes.
J. Theor. Biol. 2008, 251, 553–560. [CrossRef][PubMed]
c
2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).
20
23. Seno, M.; Iwamoto, K.; Sawada, K. Instability and Oscillatory Behavior of Membrane-Chemical Reaction Systems;
Technical Report; University of Tokyo: Tokyo, Japan, 1978.
24. Tyson, J.J.; Chen, K.C.; Novak, B. Sniffers, buzzers, toggles and blinkers: Dynamics of regulatory and
signaling pathways in the cell. Curr. Opin. Cell Biol. 2003, 15, 221–231. [CrossRef]
25. Edelstein, B.B. Biochemical Model With Multiple Steady States and Hysteresis. J. Theor. Biol. 1970, 29, 57–62.
[CrossRef]
26. Angeli, D.; Ferrell, J.E.; Sontag, E.D. Detection of multistability, bifurcations, and hysteresis in a large class of
biological positive-feedback systems. Proc. Natl. Acad. Sci. USA 2004, 101, 1822–1827. [CrossRef]
27. Nicolis, G.; Prigogine, I. Self-Organization in Nonequilibrium Systems; Wiley-Blackwell: Hoboken, NJ, USA,
1977; Volume 82, p. 672.
28. Heinrich, R.; Rapoport, S.M.; Rapoport, T.A. Metabolic regulation and mathematical models. Proq. Biophys.
Mol. Biol. 1977, 32, 1–82.
29. Kholodenko, B.N. Negative feedback and ultrasensitivity can bring about oscillations in the mitogenactivated protein kinase cascades. Eur. J. Biochem. 2000, 267, 1583–1588. [CrossRef][PubMed]
30. Goldbeter, A. A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. Proc. Natl.
Acad. Sci. USA 1991, 88, 9107–9111. [CrossRef][PubMed]
31. François, P.; Hakim, V. Core genetic module: The mixed feedback loop. Phys. Rev. E 2005, 72, 031908.
[CrossRef][PubMed]
32. Lavrentovich, M.; Hemkin, S. A mathematical model of spontaneous calcium(II) oscillations in astrocytes.
J. Theor. Biol. 2008, 251, 553–560. [CrossRef][PubMed]
c
2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC BY) license (http://creativecommons.org/licenses/by/4.0/).
20