the eukaryotic cell cycle: molecules, mechanisms and mathematical models
DESCRIPTION
The Eukaryotic Cell Cycle: Molecules, Mechanisms and Mathematical Models. John J. Tyson Biological Sciences, Virginia Tech & Virginia Bioinformatics Institute. Funding: NIH-GMS. The cell cycle is the sequence of events whereby a growing cell replicates all its components and divides - PowerPoint PPT PresentationTRANSCRIPT
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The Eukaryotic Cell Cycle: Molecules, Mechanisms and Mathematical Models
John J. TysonBiological Sciences, Virginia Tech& Virginia Bioinformatics InstituteFunding: NIH-GMS
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S
DNA synthesis
G2
G1
cell division+
Metaphase
Anaphase
Telophase
Prophase
The cell cycle is thesequence of events wherebya growing cell replicates allits components and dividesthem more-or-less evenly
between two daughter cells...
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Why study the cell cycle?
All living organisms are made of cells.All cells come from previously existing cells by the process of cell growth and division.
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S
DNA synthesis
G2
G1
cell division+
Metaphase
Anaphase
Telophase
Prophase
Alternation of DNA synthesis and mitosisCheckpoints
Balanced growth and division
Robust yet noisy
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S
DNA synthesis
G2
G1
cell division+
Metaphase
Anaphase
Telophase
Prophase
Cdk
Cln2
Clb5Clb2
APC
Cdh1Sic1 APCCdc20
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Cdc20
Cdc20
Cdh1
Sic1
Clb2
Clb2Sic1
Cln2
APC-PAPCMcm1
Mcm1A
Clb5 SBFA
SBF
Swi5A
Swi5
Sic1
Clb5
Cdc14
Cdc14
Cln2
Clb2
Cdh1
Cdc20Cdh1
Budding YeastChen et al. (2004)
Whi5SBFA
Whi5
Whi5 P
Net1
Cdc14Net1Net1
P
Cln3 Cell Size Sensor
Clb2
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Tyson & Novak, “Irreversible transitions, bistability and checkpoint controls in the eukaryotic cell cycle: a systems-level understanding,” in Handbook of Systems Biology (2012)
Tyson & Novak, “Temporal Organization of the Cell Cycle,” Current Biology (2008)
Kathy Chen
Bela Novak
Deterministic Modeling
Attila Csikasz-NagyAndrea Ciliberto
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Cdc20
Cdc20
Cdh1
Sic1
Clb2
Clb2Sic1
Cln2
APC-PAPCMcm1
Mcm1A
Clb5 SBFA
SBF
Swi5A
Swi5
Sic1
Clb5
Cdc14
Cdc14
Cln2
Clb2
Cdh1
Cdc20Cdh1
Budding YeastChen et al.
Whi5SBFA
Whi5
Whi5 P
Net1
Cdc14Net1Net1
P
Cln3 Cell Size Sensor
Clb2Deterministic Model
-
-
' "1 2 2
3 4
3 4
d ( )dd (1 )d 1
X k S k k Y XtY k Y k XYt J Y J Y
differential equations
X
YP
Y
mechanism
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' "1 1 2
3 4
3 4
d ( )d
(1 )dd 1
X k S k k Y Xt
k A YY k XYt J Y J Y
differential equations
Clb
2-de
p ki
nase
S/A, parameter
ON
OFF
What mechanisms flipthe switch on and off?
2
steady statebifurcation diagram
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Cdc20
Cdc20
Cdh1
Sic1
Clb2
Clb2Sic1
Cln2
APC-PAPCMcm1
Mcm1A
Clb5 SBFA
SBF
Swi5A
Swi5
Sic1
Clb5
Cdc14
Cdc14
Cln2 Cdh1
Cdc20Cdh1
Budding YeastChen et al.
Whi5SBFA
Whi5
Whi5 P
Net1
Cdc14Net1Net1
P
Cln3
Clb2
-
Clb2
-
-Clb2
Cdh1
Cln2
-
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Clb2
Cln2
Entry
DN
A Synthesis
G1
G2/M
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Cdc20
Cdc20
Cdh1
Sic1
Clb2
Clb2Sic1
Cln2
APC-PAPCMcm1
Mcm1A
Clb5 SBFA
SBF
Swi5A
Swi5
Sic1
Clb5
Cdc14
Cdc14
Cln2
Clb2
Cdh1
Cdc20Cdh1
Budding YeastChen et al.
Whi5SBFA
Whi5
Whi5 P
Net1
Cdc14Net1Net1
P
Cln3 Cell Size Sensor
Clb2
-
-
+
+
Clb2
Cdh1
Cdc14
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Clb2
Cdc14
Exit
Cell D
ivision
G1
G2/M
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Clb2
Cln2 Cdc14
G1 G1
S
G2 M A
T
Clb2
Cdh1
Cln2 Cdc14
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Clb2
Cln2 Cdc14
G1 G1
S
G2 M A
T
Clb2
Cdh1
Cln2 Cdc14
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Clb2
Cln3 Cdc14
G1 G1
S
G2 M A
T
Clb2
Cdh1
Cln2 Cdc14
Cln3
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Clb2
Cln3 Cdc14
G1 G1
G2 M A
T
Clb2
Cdh1
Cln2 Cdc14
Cln3
S
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Protocol to demonstrate hysteresis at Start
Cross et al., Mol. Biol. Cell 13:52 (2002)
Genotype: cln1D cln2D cln3D GAL-CLN3 cdc14ts
Knockout all the G1cyclins
Turn on CLN3 with galactose; turn off with
glucose
Temperature-sensitive allele of
CDC14: on at 23oC, off at 37oC.
“Neutral” conditions: glucose at 37oC (no Cln’s, no Cdc14)
Fred Cross
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R = raffinoseG = galactose
Standard for protein loading
G1 cells
S/G2/M cells
Start with allcells in G1
Make some Cln3
Shift toneutral
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Clb2
Cln2 Cdc14
G1 G1
S
G2 M A
T
Clb2
Cdh1
Cln2 Cdc14
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Clb2
Cln2 Cdc14
G1 G1
S
G2 M A
T
Clb2
Cdh1
Cln2 Cdc14
Cdh1CA
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Clb2
Cln2 Cdc14
G1
S
G2 M A
T
Clb2
Cdh1
Cln2 Cdc14
Cdh1CA
G1
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Protocol to demonstratehysteresis at Exit
Lopez-Aviles et al., Nature 459:592 (2009)
Genotype: MET-CDC20 GAL-CDH1CA cdc16ts
Turn off Cdc20;block in metaphase
Turn on Cdh1; degrade Clb2 and exit from mitosis
Inactivate APC at 37oC; block any
further activity of Cdh1
Add galactose at 23oC to turn on Cdh1, then raise temperature to 37oC to turn off Cdh1
Frank Uhlmann
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0 min 50 min 140 min
0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 min
Tubulin
370C
MET-CDC20 GAL-CDH1CA APCcdc16(ts)
Cdh1CA
CKI
CycB
Gal
metaphasemetaphase interphase
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S
DNA synthesis
G2
G1
cell division+
Metaphase
Anaphase
Telophase
Prophase
Alternation of DNA synthesis and mitosisCheckpoints
Balanced growth and division
Robust yet noisy
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Clb2
Cln2 Cdc14
G1 G1
S
G2 M A
T
DNA Damage
Clb2
Cdh1
Cln2 Cdc14
ChromosomeAlignmentProblems
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Clb2
Cln2 Cdc14
G1 G1
S
G2 M A
T
Clb2
Cdh1
Cln2 Cdc14
Growth
Is this deterministic model robust in the face of the inevitable molecular noise in a tiny yeast cell
(volume = 40 fL = 40 x 10-15 L)
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Table 1. Numbers of molecules (per haploid yeast cell) and half-lives for several cell cycle components.
Cell cycleGene
# molecules per cell Half-life (min)
Protein mRNA Protein mRNA
CDC28 6700 2.2 300 23
CLN2 1300 1.2 5 10
CLB2 340 1.1 22 13
CLB5 520 0.9 44 9
SWI5 690 0.8
MCM1 9000 1.6 300 14
SIC1 770 1.9
CDC14 8500 1.0 20 11
Molecular Noise
Budding Yeast CellsVol = 40 fL
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Table 1. Numbers of molecules (per haploid yeast cell) and half-lives for several cell cycle components.
Cell cycleGene
# molecules per cell Half-life (min)
Protein mRNA Protein mRNA
CDC28 6700 2.2 300 23
CLN2 1300 1.2 5 10
CLB2 340 1.1 22 13
CLB5 520 0.9 44 9
SWI5 690 0.8
MCM1 9000 1.6 300 14
SIC1 770 1.9
CDC14 8500 1.0 20 11
Molecular Noise
Budding Yeast CellsVol = 40 fL
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Table 1. Numbers of molecules (per haploid yeast cell) and half-lives for several cell cycle components.
Cell cycleGene
# molecules per cell Half-life (min)
Protein mRNA Protein mRNA
CDC28 6700 2.2 300 23
CLN2 1300 1.2 5 10
CLB2 340 1.1 22 13
CLB5 520 0.9 44 9
SWI5 690 0.8
MCM1 9000 1.6 300 14
SIC1 770 1.9
CDC14 8500 1.0 20 11
Molecular Noise
Budding Yeast CellsVol = 40 fL
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Table 1. Numbers of molecules (per haploid yeast cell) and half-lives for several cell cycle components.
Cell cycleGene
# molecules per cell Half-life (min)
Protein mRNA Protein mRNA
CDC28 6700 2.2 300 23
CLN2 1300 1.2 5 10
CLB2 340 1.1 22 13
CLB5 520 0.9 44 9
SWI5 690 0.8
MCM1 9000 1.6 300 14
SIC1 770 1.9
CDC14 8500 1.0 20 11
Molecular Noise
Budding Yeast CellsVol = 40 fL
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Table 1. Numbers of molecules (per haploid yeast cell) and half-lives for several cell cycle components.
Cell cycleGene
# molecules per cell Half-life (min)
Protein mRNA Protein mRNA
CDC28 6700 2.2 300 23
CLN2 1300 1.2 5 10
CLB2 340 1.1 22 13
CLB5 520 0.9 44 9
SWI5 690 0.8
MCM1 9000 1.6 300 14
SIC1 770 1.9
CDC14 8500 1.0 20 11
Molecular Noise
Budding Yeast CellsVol = 40 fL
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PP
P P
1
1 3%1000
CVN N
pP
p
2P P
kN
N
Birth-Death Process
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Transcription-TranslationCoupling
MP
P M P M
1 1
1 1 1 70%1000 2 1
CVN N
Swain, Paulsson, etc.
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How variable is the yeast cell cycle?
Di Talia et al., Nature (2007)
G1 DurationMean = 16 min
CV = 48%
S/G2/M DurationMean = 74 min
CV = 19%Cycle Time Mother Daughter
87 min ± 14% 112 min ± 22%
Size @ Div 68 fL ± 19%
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Budding: Myo1-GFPCell size: ACT1pr-DsRed
Di Talia et al., Nature (2007)
Whi5 exit: Whi5-GFPCell size: ACT1pr-DsRed
Daughter Cells
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Debashis Barik & Sandip Kar
Jean Peccoud Yang Cao
Mark PaulBill Baumann
Stochastic Modeling
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Multisite Phosphorylation Model (Barik, et al.)
Clb2
Cdh1 bistableswitch
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Multisite Phosphorylation Model (Barik, et al.)
Cell size control
Clb2
Cdh1
Cln2
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Multisite Phosphorylation Model (Barik, et al.)
Clb2
Cdh1
Cln2 Cdc14
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Deterministic calculations
The model consists of 58 species, 176 reactions and 68 parameters Mass-action kinetics for all reactions At division daughter cells get 40% of total volume and mothers get 60%
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Stochastic calculations
The model consists of 58 species, 176 reactions and 68 parameters Mass-action kinetics for all reactions Protein populations: ~1000’s of molecules per gene product mRNA populations: ~10 molecules per gene transcript mRNA half-lives: ~ 2 min Reactions are simulated using Gillespie’s SSA
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Experimental data from:Di Talia et al., Nature (2007)
Mother Daughter
Cycle Time (min) Expt 87 ± 14% 112 ± 22%
Model 89 ± 20% 114 ± 22%
G1 duration (min) Expt 16 ± 50% 37 ± 50%
Model 21 ± 48% 41 ± 48%
Size@birth (fL) Expt 40 ± 18% 28 ± 20%
Model 41 ± 23% 28 ± 23%
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Daughter cellsModel Di Talia et al.
Mother cellsModel Di Talia et al.
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Daughter cells
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Expt.: Di Talia et al, Nature (2007)
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Summary• Cell cycle control in eukaryotes can be
framed as a dynamical system that gives a coherent and accurate account of the basic physiological properties of proliferating cells.
• The control system seems to be operating at the very limits permitted by molecular fluctuations in yeast-sized cells.
• A realistic stochastic model is perfectly consistent with detailed quantitative measurements of cell cycle variability.
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ComputationTheory
Experiment
Current Biology 18:R759 (2008)Proc Natl Acad Sci 106:6471 (2009)
Mol Syst Biol 6:405 (2010)Handbk of Syst Biol (to appear)
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Budding: Myo1-GFPCell size: ACT1pr-DsRed
Whi5 exit: Whi5-GFPCell size: ACT1pr-DsRed
Di Talia et al., Nature (2007)
Whi5
Cyclin
Whi5PStart
Exit
BE
DNAsynth
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Daughter cell
Di Talia et al., Nature (2007)
T2 = TG1 – T1 = constant
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Mother cells
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Expt.: Di Talia et al, Nature (2007)
TG1
T1
Daughter cells
T2
T1 = Time when Whi5exits from nucleus