Cell cycle checkpoints
Tyson, Journal of Biotechnology Volume 71, Issues 1-3, 28 May 1999, Pages 239-244
G1
cell division
The cell cycle is the
series of events where a cell grows,
copies all of its
components and divides
them between two
daughter cells
...
M
mitosis
S
DNA
replication
G2
Simplified model (Cdk-cyclin vs APC
complex)
Tyson & Novak JTB (2001)
‘Toy model’ for cYclin and aPc
ODE’s
Pi
P
Y=[Cyc] = cyclin cdk dimers
P= APC Cdh1 complex
This is the simplest model for switching between G1 and (S/G2/M)
ODE’s
Pi
P
Assume total aPc constant
P+Pi = 1
Eliminate Pi
This is the system to be studied in the YP plane.
Phase portrait
Y=[CycB] = cyclin cdk dimers
P=[Cdh1]= APC Cdh1 complex
<- The P nullcline is sigmoidal
<- The Y nullcline is a hyperbola
Saddle point, invariant manifolds
Switching behaviour
G1
S-G2-M
Change in behaviour as the cell
grows (cell mass increases)
Cell mass
m=0.3
m=0.6
For larger mass:
SS at G1 lost, and cell
is forced to the state
S-G2-M, where it
divides
S-G2-M
Bifurcation
XPP Auto can be used to produce a bifurcation diagram
that shows the number of steady states and how this
depends on cell mass.
From XPP
Click:
File
Auto
Auto Windows
Choosing some numerics
Auto bifurcation diagram
cyclin
S-G2-M
G1
Cell mass m
The cell cycle
cyclin
S-G2-M
back to
start
G1
start to
divide
grow
Cell mass m
Include A
Pi
P
Y=[Cyc] = cyclin cdk dimers
P= APC Cdh1 complex
A= Cdc20, the activator of aPc
Y'=k1-(k2p+k2pp*P)*Y
P'=Factiv(P)*(1-P)-Fdecay(Y,P)*P
A'=k5p+k5pp* ((m*Y/J5)^n)/(1+(y*m/J5)^n)-k6*A
Bifurc diagram for Y vs parameter m in full model
(with no QSS). This diagram is curently incomplete.
Fuller model
Fuller Basic Model
cYclin
aPc (Cdh1)
Cdc20T
Cdc20A
IEP
Mass
Part of the Bifurcation diagram
Unstable limit cycle
Full basic model
Accomplishments:
Understanding the complex regulatory system in
a modular fashion, adding complexity gradually
so as to see what each part of the network does.
Identifying parameters using random search in
parameter space. Accounting for many distinct
mutants that are missing specific components, or
have overexpression of other components.
Assembling the bifurcation structure of the
network as a whole.
Cell cycle components
In different cells, the chemicals have different names.. Making
the field challenging.
Tyson, Journal of Biotechnology Volume 71, Issues 1-3, 28 May 1999, Pages 239-244
References
You can get other ODE files and references from Tyson’s
website http://mpf.biol.vt.edu/Research.html
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.