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Wuschel Expression (published model)

Jönsson H, Heisler M, Reddy GV, Agrawal V, Gor V, Shapiro BE, Mjolsness E, Meyerowitz EM (2005) "Modeling the organization of the Wuschel domain in the shoot apical meristem," Bioinformatics 21(S1): i232-i240 View Reference

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Brusselator:

Prigogene L Lefever R (1968) Symmetry breaking instabilities in dissipative systems. II. J. Chem. Phys 48, 1695-1700. View Reference

Oregonator (FIeld-Noyes Model):

Field RJ, Körös E, Noyes RM (1972) Oscillations in Chemical Systems. II. Thorough Analysis of Temporal Oscillations in the Bromate-Cerium-Malonic Acid System. JACS, 94(25):8649-8664. View Reference

Lengyel, Rabai, Epstein. "Experimental and Modeling Study of Oscillations in the Chlorine Dioxide-Iodine-Malonic Acid Reaction." Journal of the Am. Chem. Soc. (1990) 112:9104-9110

XML for Modification of Lengyel reduced model to avoid 5th order reaction (example included in nb file above)

(1) Vilar JMG, Kueh HY, Barkai N, Leibler S, (2002) "Mechanisms of noise resistance in genetic oscillators," PNAS, 99(9):5988-5992. View Reference

(2) Barkai N, Leibler S (2000) "Circadian clocks limited by noise," Nature, 403:267-268. View Reference

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Drosophila Model

Leloup JC, Goldbeter A (1999) Chaos and birhythmicity in a mdoel for circadian oscillations of the PER and TIM proteins in Drosophila. J Theor Biol 198:445-459. View Reference

Gonze D & Goldbeter A (2000) A model for a network of phosphorylation-dephosphorylation cycles displaying the dynamics of dominoes and clocks, J. Theor. Biol; 210:167-186.

Murray AW & Kirschner MW (1989) Dominoes and clocks: the union of two views of the cell cycle, Science: 246:614-621.

Based on figure 11.7 ,page 403 of G.Fain (1999) Molecular and Cellular Physiology of Neurons, Harvard University Press

Chickarmane V, Peterson C (2008) " A Computational Model for Understanding Stem Cell, Trophectoderm and Endoderm Lineage Determination." PLoS ONE 3(10): e3478. Journal web site. [doi/10.1371/journal.pone.0003478]

Kholodenko, Boris N. (2000) "Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades." Eur J Biochem 267:1583-8. View Reference

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Re-interpretation of Kholodenko model using Mass-action rather than Michaelis-Menten Kinetics

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MAPK Cascade in Solution Models

(1) Levchenko, A., Bruck, J., Sternberg, P.W. (2000). Scaffold proteins may biphasically affect the levels of mitogen-activated protein kinase signaling and reduce its threshold properties. PNAS, 97(11):5818–5823. View Reference.

(2) Shapiro, B, Leevchenko A., Mjolsness E. (2001) Automatic Equation Generation for Signal Transduction with Applications to MAP-Kinase, in Foundations of Systems Biology, Edited by H. Kitano, MIT Press.

Illustration of simple mass action arrows in xCellerator.

Alfred Lotka "Undamped Oscillations from the Law of Mass Action" Journal of the American Chemical Society 49:1595-1599 (1920).

Goldbeter, A. A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. (1991) PNAS, 88:9107-1101 (1991).View Reference

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Gardner TS, Dolnik M, Colllins JJ (1998) "A theory for controlling cell cycle dynamics using a reversibly binding inhibitor." PNAS 95:14190-14195. View Reference

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Tyson JJ (1991) "Modeling the cell division cycle: cdc2 and cyclin interactions." View Reference (6 variable model)

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Novak B, Tyson JJ (1997) "Modeling the control of DNA replication in fission yeast," PNAS, 94, pp. 9147–9152. View Reference

Hoffmann A, Levchnko A, Scott M, Baltimore D (2002) Science, 298(5596):1241-1245. View Reference

Elowitz MB, Leibler S (2000) A synthetic oscillatory network of transcriptional regulators. Nature. 403:335-338. View Reference

GRN Model

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Hill Function Model

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Mass-Action Model

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Michaelis-Menten Model (2-Stage)

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Michaelis-Menten Model (1-Stage)

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Michaelis-Menten Model (damped)