The Eukaryotic Cell Cycle: Molecules, Mechanisms and Mathematical Models

The Eukaryotic Cell Cycle: Molecules, Mechanisms and Mathematical Models

John J. TysonBiological Sciences, Virginia Tech& Virginia Bioinformatics InstituteFunding: NIH-GMS

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...

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.

Why study budding yeast?

http://www.olympusconfocal.com/gallery/cells/muntjac/muntjaccells.html

S

DNA synthesis

G2

G1

cell division+

Metaphase

Anaphase

Telophase

Prophase

Alternation of DNA synthesis and mitosisCheckpoints

Balanced growth and division

Robust yet noisy

S

DNA synthesis

G2

G1

cell division+

Metaphase

Anaphase

Telophase

Prophase

Cdk

Cln2

Clb5Clb2

APC

Cdh1Sic1 APCCdc20

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

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

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


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

' "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

Cdc20

Cdc20

Cdh1

Sic1

Clb2

Clb2Sic1

Cln2

APC-PAPCMcm1

Mcm1A

Clb5 SBFA

SBF

Swi5A

Swi5

Sic1

Clb5

Cdc14

Cdc14

Cln2 Cdh1

Cdc20Cdh1


Whi5SBFA

Whi5

Whi5 P

Net1

Cdc14Net1Net1

P

Cln3

Clb2

-

Clb2

-

-Clb2

Cdh1

Cln2

-

Clb2

Cln2

Entry

DN

A Synthesis

G1

G2/M

Cdc20

Cdc20

Cdh1

Sic1

Clb2

Clb2Sic1

Cln2

APC-PAPCMcm1

Mcm1A

Clb5 SBFA

SBF

Swi5A

Swi5

Sic1

Clb5

Cdc14

Cdc14

Cln2

Clb2

Cdh1

Cdc20Cdh1


Whi5SBFA

Whi5

Whi5 P

Net1

Cdc14Net1Net1

P


Clb2

-

-

+

+

Clb2

Cdh1

Cdc14

Clb2

Cdc14

Exit

Cell D

ivision

G1

G2/M

Clb2

Cln2 Cdc14

G1 G1

S

G2 M A

T

Clb2

Cdh1

Cln2 Cdc14

Clb2

Cln2 Cdc14

G1 G1

S

G2 M A

T

Clb2

Cdh1

Cln2 Cdc14

Clb2

Cln3 Cdc14

G1 G1

S

G2 M A

T

Clb2

Cdh1

Cln2 Cdc14

Cln3

Clb2

Cln3 Cdc14

G1 G1

G2 M A

T

Clb2

Cdh1

Cln2 Cdc14

Cln3

S

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

R = raffinoseG = galactose

Standard for protein loading

G1 cells

S/G2/M cells

Start with allcells in G1

Make some Cln3

Shift toneutral

Clb2

Cln2 Cdc14

G1 G1

S

G2 M A

T

Clb2

Cdh1

Cln2 Cdc14

Clb2

Cln2 Cdc14

G1 G1

S

G2 M A

T

Clb2

Cdh1

Cln2 Cdc14

Cdh1CA

Clb2

Cln2 Cdc14

G1

S

G2 M A

T

Clb2

Cdh1

Cln2 Cdc14

Cdh1CA

G1

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

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

S

DNA synthesis

G2

G1

cell division+

Metaphase

Anaphase

Telophase

Prophase

Alternation of DNA synthesis and mitosisCheckpoints

Balanced growth and division

Robust yet noisy

Clb2

Cln2 Cdc14

G1 G1

S

G2 M A

T

DNA Damage

Clb2

Cdh1

Cln2 Cdc14

ChromosomeAlignmentProblems

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)

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


Cell cycleGene



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



Cell cycleGene



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



Cell cycleGene



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



Cell cycleGene



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


PP

P P

1

1 3%1000

CVN N

pP

p

2P P

kN

N

Birth-Death Process

Transcription-TranslationCoupling

MP

P M P M

1 1

1 1 1 70%1000 2 1

CVN N

Swain, Paulsson, etc.

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%

Budding: Myo1-GFPCell size: ACT1pr-DsRed


Whi5 exit: Whi5-GFPCell size: ACT1pr-DsRed

Daughter Cells

Debashis Barik & Sandip Kar

Jean Peccoud Yang Cao

Mark PaulBill Baumann

Stochastic Modeling

Multisite Phosphorylation Model (Barik, et al.)

Clb2

Cdh1 bistableswitch


Cell size control

Clb2

Cdh1

Cln2


Clb2

Cdh1

Cln2 Cdc14

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%

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

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%

Daughter cellsModel Di Talia et al.

Mother cellsModel Di Talia et al.

Daughter cells

Expt.: Di Talia et al, Nature (2007)

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.

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)

Budding: Myo1-GFPCell size: ACT1pr-DsRed

Whi5 exit: Whi5-GFPCell size: ACT1pr-DsRed


Whi5

Cyclin

Whi5PStart

Exit

BE

DNAsynth

Daughter cell


T2 = TG1 – T1 = constant

Mother cells

Expt.: Di Talia et al, Nature (2007)

TG1

T1

Daughter cells

T2

T1 = Time when Whi5exits from nucleus

Documents

The Eukaryotic Cell Cycle: Molecules, Mechanisms and Mathematical Models