Controlling Cell Cycle Dynamics Using a Reversibly Binding Inhibitor
Lawson
James
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model runs in both OpenCell and COR to reproduce the published results. The units have been checked and they are consistent.
Model Structure
ABSTRACT: We demonstrate, by using mathematical modeling of cell division cycle (CDC) dynamics, a potential mechanism for precisely controlling the frequency of cell division and regulating the size of a dividing cell. Control of the cell cycle is achieved by artificially expressing a protein that reversibly binds and inactivates any one of the CDC proteins. In the simplest case, such as the checkpoint-free situation encountered in early amphibian embryos, the frequency of CDC oscillations can be increased or decreased by regulating the rate of synthesis, the binding rate, or the equilibrium constant of the binding protein. In a more complex model of cell division, where size-control checkpoints are included, we show that the same reversible binding reaction can alter the mean cell mass in a continuously dividing cell. Because this control scheme is general and requires only the expression of a single protein, it provides a practical means for tuning the characteristics of the cell cycle in vivo.
The original paper reference is cited below:
A theory for controlling cell cycle dynamics using a reversibly binding inhibitor, Timothy S. Gardner, Milos Dolnik and James J. Collins, 1998, Proceedings of the National Academy of Sciences, 95, 14190-14195. PubMed ID: 9826676
cell diagram
Control of the Goldbeter 1991 model with a cyclin inhibitor. M represents cdc2 kinase, X represents the fraction of active (phosphorylated) cyclin protease, and * represents the fraction of inactive enzymes. The Goldbeter model is outlined by the dashed box. Solid arrows indicate protein synthesis, degradation or enzymatic conversion. Dashed arrows represent activation.
$\frac{d C}{d \mathrm{time}}=\mathrm{vi}-\frac{\mathrm{k1}XC}{C+\mathrm{K5}}-\mathrm{kd}C$
$\mathrm{Ctot}=C+Z$
$\mathrm{M\_}=-1$
$\frac{d M}{d \mathrm{time}}=\frac{\mathrm{V1}\mathrm{M\_}}{\mathrm{M\_}+\mathrm{K1}}-\frac{\mathrm{V2}M}{M+\mathrm{K2}}$
$\mathrm{X\_}=1-X$
$\frac{d X}{d \mathrm{time}}=\frac{\mathrm{V3}\mathrm{X\_}}{\mathrm{X\_}+\mathrm{K3}}-\frac{\mathrm{V4}X}{X+\mathrm{K4}}$
$\frac{d Y}{d \mathrm{time}}=\mathrm{vs}-\mathrm{d1}Y-\mathrm{a1}CY+(\mathrm{a2}+\mathrm{alpha}\mathrm{kd})Z$
$\mathrm{Ytot}=Y+Z$
$\frac{d Z}{d \mathrm{time}}=\mathrm{a1}CY-(\mathrm{a2}+\mathrm{alpha}\mathrm{kd}+\mathrm{alpha}\mathrm{d1})Z$
$\mathrm{BP}=1+\frac{\mathrm{Kd}\mathrm{Ytot}}{(C+\mathrm{Kd})^{2}}$
$\mathrm{V1}=\frac{C\mathrm{V1\_dash}}{C+\mathrm{K6}}$
$\mathrm{V3}=M\mathrm{V3\_dash}$
Rebuilt model using fixed Goldbeter 91 model as base. Model now produces correct output.
2007-07-27CollinsJJXfraction of active protease which degrades cyclinc.lloyd@auckland.ac.nz141959514190
A theory for controlling cell cycle dynamics using a reversibly binding inhibitor
LimJeeleancell cyclecell divisionoscillator9826676Auckland Bioengineering InstituteThe University of Auckland2007-12-06
Rewrote model and changed (erroneous) parameters from those given in the Goldbeter 1991 paper to those given in the Gardner paper.
The new version of this model has been re-coded to remove the reaction element and replace it with a simple MathML description of the model reaction kinetics. This is thought to be truer to the original publication, and information regarding the enzyme kinetics etc will later be added to the metadata through use of an ontology. The model runs in the PCEnv simulator to give a nice curved output. However, it does not recreate the spiked output published in the original paper.
keywordLloydMCatherine2007-06-05DolnikM1998-11-24PNASMfraction of active cdc2 kinaseGardnerSTYconcentration of unbound inhibitorLloydMayCatherineCcyclin concentrationLawsonRJames10000200Zconcentration of inhibitor-target complexBPbuffering power