Cell cycle checkpointskeshet/ShortTyson.pdf · 2008. 5. 19. · Cell cycle checkpoints Tyson,...
Transcript of Cell cycle checkpointskeshet/ShortTyson.pdf · 2008. 5. 19. · Cell cycle checkpoints Tyson,...
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Cell cycle checkpoints
Tyson, Journal of Biotechnology Volume 71, Issues 1-3, 28 May 1999, Pages 239-244
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S
G1
DNAreplication
G2Mmitosis
cell division
The cell cycle is theseries of events where a cell grows,
copies all of its components and divides
them between two daughter cells
...
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Simplified model (Cdk-cyclin vs APCcomplex)
Tyson & Novak JTB (2001)
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‘Toy model’ for cYclin and aPc
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ODE’s
PiP Y=[Cyc] = cyclin cdk dimers
P= APC Cdh1 complex
This is the simplest model for switching between G1 and (S/G2/M)
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ODE’s
PiP
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Assume total aPc constant
P+Pi = 1
Eliminate Pi
This is the system to be studied in the YP plane.
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Phase portraitY=[CycB] = cyclin cdk dimersP=[Cdh1]= APC Cdh1 complex
<- The P nullcline is sigmoidal
<- The Y nullcline is a hyperbola
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Saddle point, invariant manifolds
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Switching behaviour
S-G2-M
G1
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Change in behaviour as the cellgrows (cell mass increases)
Cell mass
m=0.3
m=0.6
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For larger mass:
SS at G1 lost, and cellis forced to the stateS-G2-M, where itdivides
S-G2-M
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BifurcationXPP Auto can be used to produce a bifurcation diagramthat shows the number of steady states and how thisdepends on cell mass.
From XPP
Click:
File
Auto
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Auto Windows
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Choosing some numerics
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Auto bifurcation diagram
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G1
S-G2-M
cyclin
Cell mass m
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The cell cycle
G1
S-G2-M
cyclin
Cell mass m
grow
start todivide
back tostart
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Include A
PiP Y=[Cyc] = cyclin cdk dimers
P= APC Cdh1 complexA= Cdc20, the activator of aPc
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Bifurc diagram for Y vs parameter m in full model
(with no QSS). This diagram is curently incomplete.
Y'=k1-(k2p+k2pp*P)*YP'=Factiv(P)*(1-P)-Fdecay(Y,P)*PA'=k5p+k5pp* ((m*Y/J5)^n)/(1+(y*m/J5)^n)-k6*A
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Fuller model
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Fuller Basic Model
cYclin
aPc (Cdh1)
Cdc20T
Cdc20A
IEP
Mass
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Part of the Bifurcation diagram
Unstable limit cycle
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Full basic model
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Accomplishments:
Understanding the complex regulatory system ina modular fashion, adding complexity graduallyso as to see what each part of the network does.Identifying parameters using random search inparameter space. Accounting for many distinctmutants that are missing specific components, orhave overexpression of other components.Assembling the bifurcation structure of thenetwork as a whole.
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Cell cycle components
Tyson, Journal of Biotechnology Volume 71, Issues 1-3, 28 May 1999, Pages 239-244
In different cells, the chemicals have different names.. Makingthe field challenging.
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References
Tyson, Chen & Novak (2001)Nature Rev Molec Cell Biol 2:908.
Tyson, Csikasz-Nagy & Novak (2002)BioEssays 24:1095.
Csikasz-Nagy et al. (2006)Biophys. J. 90:4361.
You can get other ODE files and references from Tyson’swebsite http://mpf.biol.vt.edu/Research.html