John J. Tyson - King's College London - Home · S DNA synthesis G2 G1 cell division + Metaphase Anaphase Telophase Prophase Cdk Cln2 Clb5 Clb2 APC Cdh1 Cdc14 APC Cdc20

John J. TysonBiological Sciences & the Biocomplexity Institute

Virginia Tech

Getting Things Right in a Noisy Milieu:

Stochastic Models of Cell Cycle Dynamics

in Budding Yeast

S

DNA synthesis

G2

G1

cell division+

Metaphase

Anaphase

Telophase

Prophase

Balanced growth and division

Alternation of DNA synthesis and mitosis

Checkpoints

Robust yet noisy

S

DNA synthesis

G2

G1

cell division+

Metaphase

Anaphase

Telophase

Prophase

Cdk

Cln2

Clb5

Clb2

APC

Cdh1Cdc14

APC

Cdc20

Deterministic Models

Chen et al (2000) Mol Biol Cell


Csikasz-Nagy et al (2006) Biophys J

Tyson & Novak (2008) Curr Biol

Kraikivsky et al (2015) npj Syst Biol Appl

Deterministic Models



Csikasz-Nagy et al (2006) Biophys J

Tyson & Novak (2008) Curr Biol

Kraikivsky et al (2015) npj Syst Biol Appl

Clb2

Cdh1

Cln2 Cdc14

Clb2

Cln2 Cdc14

G1 G1

S

G2 M A

T

Clb2

Cdh1

Cln2 Cdc14

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 cycle

Gene

# 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 Cells

Vol = 40 fL

PP

P P

1

1 3%

1000

CVN N

p

P

p

2

P P

kN

N

Birth-Death Process

Transcription-Translation

Coupling

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 Duration

Mean = 16 min

CV = 48%

Cycle Time

Mother

Daughter

87 min ± 14%

112 min ± 22%

Size @ Div 68 fL ± 19%

Budding: Myo1-GFP

Cell size: ACT1pr-DsRed


Whi5 exit: Whi5-GFP


Daughter Cells

Constant?

Budding: Myo1-GFP


Whi5 exit: Whi5-GFP



Whi5

Cyclin

Whi5PStart

Exit

BE

DNA

synth

Daughter cell


T2 = TG1 – T1 = constant

Debashis Barik & Sandip Kar

Andrea Ciliberto &

Mohsen Sabouri

Jean Peccoud Yang Cao

Mark PaulBill Baumann

Stochastic Modeling

Multisite Phosphorylation Model (Barik, et al.)

Clb2

Cdh1bistable

switch


Cell size control

Clb2

Cdh1

Cln2


Clb2

Cdh1

Cln2 Cdc14


SBF

Transcription-translation coupling?Use simple birth-death processes.

Assume short mRNA half-life.

Assume rapid, reversible binding of SBF to promoter.

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:


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 cellsSize control: Daughter cells

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

Mother cellsSize control of mother cells?

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

TG1

T1

Daughter cells

T2

T1 = Time when Whi5

exits from nucleus

CLN3 WHI5

CLN2 CDH1 CLB2

CDC14NET1

Histograms of mRNAs of different genes

SBF

CLN3 WHI5

CLN2 CDH1 CLB2

CDC14NET1


SBF

NET1

David Ball Jean Peccoud

Poisson

FISH = Fluorescence In Situ Hybridization

CLN3 WHI5

CDH1 CLB2

CDC14NET1


SBF

CLN2

David Ball, Jean Peccoud, et al.

CLN2

Debashis Barik, revised model

model

Data from:

David A. Ball; Tae-Hyuk Ahn; Pengyuan

Wang; Katherine C. Chen; Yang Cao; John J.

Tyson; Jean Peccoud; William T. Baumann;

Cell Cycle 2011, 10, 999-1009.

DOI: 10.4161/cc.10.6.14966

Copyright © 2011 Landes Bioscience

Some mutant strains exhibit “partial viability”…a

phenotype inconsistent with deterministic models

Smulations from:

Debashis Barik; David Ball; Jean Peccoud;

John J. Tyson; manuscript in preparation

Mutant strain:

CLB2-dbΔ clb5 Δ

MDT = ln2 / 0.00467 min−1 = 148 min

0 500 1000 1500 200010

0

101

102

103

104

Time (min)

No

. o

f C

ell

140

150

160

Do

ub

lin

g t

ime

0 500 1000 1500 2000 250010

0

101

102

103

104

Time (min)

170

180

190

Do

ublin

g tim

e

WT(Galactose)

WT(Glycerol−Ethanol)

0 500 1000 1500 200010

0

101

102

103

Time (min)

No

. o

f C

ell

180

200

220

Do

ublin

g t

ime (

min

)

CLB2−dbD clb5D (Galactose)

50 150 250 3500

400

800

1200

Tdiv

(min)

Ce

ll C

ou

nt

50 150 250 3500

400

800

1200

1600

2000

Tsg2m

(min)

Ce

ll C

ou

nt

Mother

Daughter

WT:

MDT = ln2 / 0.00467 min−1 = 148 min

NDT = 151 min

Mutant:

MDT = 148 min

NDT = 190 min

WT

mutant

45%

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.

• Tyson & Novak (2008) Curr Biol 18:R759

• Kar et al. (2009) PNAS 106:6471

• Barik et al. (2010) Mol Syst Biol 6:405

• Tyson & Novak (2012) Handb Syst Biol

• Kraikivsky et al. (2015) npj Syst Biol Appl

• Barik et al. (in ppn)

References

Documents

John J. Tyson - King's College London - Home · S DNA synthesis G2 G1 cell division + Metaphase Anaphase Telophase Prophase Cdk Cln2 Clb5 Clb2 APC Cdh1 Cdc14 APC Cdc20