Numerical analysis of a comprehensive model of M-phase control in <emphasis>Xenopus oocyte</emphasis> extracts and intact embryos
Jeelean
Lim
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML version of the model has been checked in COR and OpenCell. This variant of the model runs to replicate the original published results as depicted in figure 4A of the paper. Please note that actual concentrations are displayed by this model, instead of the percentage concentrations used in the paper. The units have been checked and they are consistent.
Model Structure
ABSTRACT: To contribute to a deeper understanding of M-phase control in eukaryotic cells, we have constructed a model based on the biochemistry of M-phase promoting factor (MPF) in Xenopus oocyte extracts, where there is evidence for two positive feedback loops (MPF stimulates its own production by activating Cdc25 and inhibiting Wee1) and a negative feedback loop (MPF stimulates its own destruction by indirectly activating the ubiquitin pathway that degrades its cyclin subunit). To uncover the full dynamical possibilities of the control system, we translate the regulatory network into a set of differential equations and study these equations by graphical techniques and computer simulation. The positive feedback loops in the model account for thresholds and time lags in cyclin-induced and MPF-induced activation of MPF, and the model can be fitted quantitatively to these experimental observations. The negative feedback loop is consistent with observed time lags in MPF-induced cyclin degradation. Furthermore, our model indicates that there are two possible mechanisms for autonomous oscillations. One is driven by the positive feedback loops, resulting in phosphorylation and abrupt dephosphorylation of the Cdc2 subunit at an inhibitory tyrosine residue. These oscillations are typical of oocyte extracts. The other type is driven by the negative feedback loop, involving rapid cyclin turnover and negligible phosphorylation of the tyrosine residue of Cdc2. The early mitotic cycles of intact embryos exhibit such characteristics. In addition, by assuming that unreplicated DNA interferes with M-phase initiation by activating the phosphatases that oppose MPF in the positive feedback loops, we can simulate the effect of addition of sperm nuclei to oocyte extracts, and the lengthening of cycle times at the mid-blastula transition of intact embryos.
The original paper reference is cited below:
Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos, Bela Novak and John J. Tyson, 1993,
Journal of Cell Science, 106, 1153-1168. PubMed ID: 8126097
Figure 1
The phosphorylation states of MPF.
Figure 2
The positive feedback loops.
Figure 3
The negative feedback loop.
$\mathrm{k25}=\mathrm{V25\_}(\mathrm{Cdc25\_T}-\mathrm{Cdc25\_P})+\mathrm{V25\_\_}\mathrm{Cdc25\_P}\mathrm{kwee}=\mathrm{Vwee\_}\mathrm{Wee1\_P}+\mathrm{Vwee\_\_}(\mathrm{Wee1\_T}-\mathrm{Wee1\_P})\mathrm{k2}=\mathrm{V2\_}(\mathrm{UbE\_T}-\mathrm{UbE})+\mathrm{V2\_\_}\mathrm{UbE}$
$\frac{d \mathrm{cyclin}}{d \mathrm{time}}=\mathrm{k1AA}-\mathrm{k2}\mathrm{cyclin}-\mathrm{k3}\mathrm{cyclin}\mathrm{Cdc2}$
$\frac{d \mathrm{cyclin\_Cdc2}}{d \mathrm{time}}=\mathrm{kinh}\mathrm{MPF\_active}-(\mathrm{kwee}+\mathrm{kcak}+\mathrm{k2})\mathrm{cyclin\_Cdc2}+\mathrm{k25}\mathrm{Tyr15P\_dimer}+\mathrm{k3}\mathrm{cyclin}\mathrm{Cdc2}$
$\frac{d \mathrm{Tyr15P\_dimer}}{d \mathrm{time}}=\mathrm{kwee}\mathrm{cyclin\_Cdc2}-(\mathrm{k25}+\mathrm{kcak}+\mathrm{k2})\mathrm{Tyr15P\_dimer}+\mathrm{kinh}\mathrm{MPF\_pre}$
$\frac{d \mathrm{MPF\_pre}}{d \mathrm{time}}=\mathrm{kwee}\mathrm{MPF\_active}-(\mathrm{kinh}+\mathrm{k25}+\mathrm{k2})\mathrm{MPF\_pre}+\mathrm{kcak}\mathrm{Tyr15P\_dimer}$
$\frac{d \mathrm{MPF\_active}}{d \mathrm{time}}=\mathrm{kcak}\mathrm{cyclin\_Cdc2}-(\mathrm{kinh}+\mathrm{kwee}+\mathrm{k2})\mathrm{MPF\_active}+\mathrm{k25}\mathrm{MPF\_pre}$
$\mathrm{Cdc2}=\mathrm{Cdc2\_T}-\mathrm{cyclin\_Cdc2}+\mathrm{MPF\_active}+\mathrm{MPF\_pre}+\mathrm{Tyr15P\_dimer}$
$\mathrm{cyclin\_T}=\mathrm{cyclin}+\mathrm{cyclin\_Cdc2}+\mathrm{MPF\_active}+\mathrm{MPF\_pre}+\mathrm{Tyr15P\_dimer}$
$\frac{d \mathrm{Cdc25\_P}}{d \mathrm{time}}=\frac{\mathrm{ka}\mathrm{MPF\_active}(\mathrm{Cdc25\_T}-\mathrm{Cdc25\_P})}{\mathrm{K\_a}+\mathrm{Cdc25\_T}-\mathrm{Cdc25\_P}}-\frac{\mathrm{kbPPase}\mathrm{Cdc25\_P}}{\mathrm{K\_b}+\mathrm{Cdc25\_P}}$
$\frac{d \mathrm{Wee1\_P}}{d \mathrm{time}}=\frac{\mathrm{ke}\mathrm{MPF\_active}(\mathrm{Wee1\_T}-\mathrm{Wee1\_P})}{\mathrm{K\_e}+\mathrm{Wee1\_T}-\mathrm{Wee1\_P}}-\frac{\mathrm{kfPPase}\mathrm{Wee1\_P}}{\mathrm{K\_f}+\mathrm{Wee1\_P}}$
$\frac{d \mathrm{IE\_P}}{d \mathrm{time}}=\frac{\mathrm{kg}\mathrm{MPF\_active}(\mathrm{IE\_T}-\mathrm{IE\_P})}{\mathrm{K\_g}+\mathrm{IE\_T}-\mathrm{IE\_P}}-\frac{\mathrm{khPPase}\mathrm{IE\_P}}{\mathrm{K\_h}+\mathrm{IE\_P}}$
$\frac{d \mathrm{UbE}}{d \mathrm{time}}=\frac{\mathrm{kc}\mathrm{IE\_P}(\mathrm{UbE\_T}-\mathrm{UbE})}{\mathrm{K\_c}+\mathrm{UbE\_T}-\mathrm{UbE}}-\frac{\mathrm{kd\_antiIE}\mathrm{UbE}}{\mathrm{K\_d}+\mathrm{UbE}}$
30
8126097
Bela
Novak
Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos.
106
1153
1168
The University of Auckland
Auckland Bioengineering Institute
Journal of Cell Science
Jeelean
Lim
Jeelean Lim
1993-12-00 00:00
Jeelean Lim
Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos: parameter values have been taken from the original published paper to reproduce figure 4A.
The University of Auckland, Auckland Bioengineering Institute
John
Tyson
keyword
cell cycle
oocyte
metabolism
jlim063@aucklanduni.ac.nz
Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos.
106
1153
1168
2009-02-18T12:32:42+13:00
Journal of Cell Science
This CellML version of the model has been checked in COR and PCEnv. This variant of the model runs to reproduce the original published results as depicted in figure 4A of the paper. Please note that actual concentrations are displayed by this model, instead of the percentage concentrations used in the paper. The units have been checked and are consistent.
1993-12-00 00:00
Jeelean
Lim
2009-01-14T00:00:00+00:00
Bela
Novak
This is the CellML description of Novak and Tyson's 1993 numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos.
This is the CellML description of Novak and Tyson's 1993 numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos.
John
Tyson
Jeelean Lim
8126097
added cmeta id's to several variables