Network Dynamics and Cell Physiology

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Network Dynamics andCell Physiology

• John J. Tyson
• Department of Biological Sciences
• Virginia Bioinformatics Institute

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CollaboratorsBela Novak Kathy Chen
Jill Sible
DARPA, NIH, NSF, McDonnell Foundation
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Signal Transduction Network
Hanahan Weinberg (2000)
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Signal Transduction Network
Hanahan Weinberg (2000)
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Gene Expression
Signal-Response Curve
S
R
Lever
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Protein Phosphorylation
Kinase
ADP
ATP
R
RP
H2O
Pi
Phosphatase
Goldbeter Koshland (1981)
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Protein Synthesis Positive Feedback
S
Open
R
EP
E
Closed
Bistability
Fuse
Griffith (1968)
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dying
Example Fuse
response (R)
living
signal (S)
Apoptosis (Programmed Cell Death)
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MPF activation in frog eggs

• Toggle Switch Oscillations

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Solomons protocol for cyclin-induced
activation of MPF
Solomon et al. (1990) Cell 631013.
Ca2
centrifuge
Wee1
Cyclo- heximide
Cdk1
Cdc25
cytoplasmic extract
no synthesis of cyclin
pellet
no degradation of cyclin
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Threshold
Solomon et al. (1990) Cell 631013.
CDK activity
Novak Tyson (1993) J. Cell Sci. 1061153
Cyclin (nM)
Prediction The threshold concentration of cyclin
B required to activate MPF is higher than the
threshold concentration required to inactivate
MPF.
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MPF activity depends on cyclin concentration and
on the history of the extract
Jill Sible
Jim Ferrell
Sha et al., PNAS 100975-980 (2003)
Pomerening et al., Nature Cell Biology 5346-351
(2003)
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Testing Thresholds in Cycling Extracts
Testing activation threshold for Mitosis I
Mitosis I
MPF activity
D90Cyclin B1 and 100 µg/ml CHX
Interphase
time
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The activation threshold for Mitosis I is between
32 and 40 nM.
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32
0
D90 cyclin B (nM)
40
0 min
90 min
M
D90 cyclin B (nM)
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negative feedback loop
MPF
cyclin
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Pomerening, Kim Ferrell Cell (2005)
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Dynamical Perspective onMolecular Cell Biology
MPF
Cyclin

• Vector Field, Steady State, Bifurcation

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Wee1
Cdc25
d MPF dt
k1 - (kwee k2) MPF k25 (cyclin - MPF)
k1 - k2 cyclin
d cyclin dt
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dx/dtf(x,y)
Phase Plane
dy/dtg(x,y)
(xo,yo)
MPF
Cyclin
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One-parameter bifurcation diagram
(response)
ON
OFF
(signal)
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supercritical
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Second Parameter
subcritical
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SNIC Bifurcation
Invariant Circle
Limit Cycle
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• Saddle-Node
• Supercritical Hopf
• Subcritical Hopf
• Cyclic Fold
• Saddle Loop
• Saddle-Node Invariant Circle

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The Dynamical Perspective
Molec Genetics Biochemistry
Cell Biology
Molecular Mechanism
Kinetic Equations
State Space, Vector Field
Attractors, Transients, Repellors
Bifurcation Diagrams
Signal-Response Curves
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Review
Molec Genetics Biochemistry
Cell Biology
Molecular Mechanism
Kinetic Equations
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The Cell Cycle of Fission Yeast
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G1
cell division
The cell cycle is the sequence of events
whereby a growing cell replicates all its
components and divides them more-or-less
evenly between two daughter cells ...
S
DNA replication
M mitosis
G2
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G1
cell division
1) Alternation of S phase and M phase. 2)
Balanced growth and division. 3) Checkpoints
S
DNA replication
M mitosis
G2
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Wee1
P
Cdc20
Cdc14
TFBA
Wee1
TFBI
CycB
P
APC-P
APC
Cdc14
Cdc25
P
Cdc20
CycB
Cdc14
Cdh1
Cdc25
CycD
CKI
CycB
CycE
TFII
Cdh1
CycD
CycA
TFIA
CKI
CKI
CKI
CycA
CycE
Cyc E,A,B
Cdc20
CycA
CycE
TFEA
CycD
CycB
CycA
TFEI
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Wee1
P
mass/nucleus
Cdc20
Cdc14
TFBA
Wee1
TFBI
CycB
P
APC-P
APC
Cdc14
Cdc25
P
Cdc20
CycB
Cdc14
Cdh1
Cdc25
CycD
CKI
CycB
CycE
TFII
Cdh1
CycD
CycA
TFIA
CKI
CKI
CKI
CycA
CycE
Cyc E,A,B
Cdc20
Fission Yeast
CycA
CycE
TFEA
CycD
CycB
CycA
TFEI
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The mathematical model
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S
G2
M
G1
S
G2
M
G1
S
5
mass/nucleus
4
3
2
1
0
CKI
Cdh1
Cdc20
Wee1
Cdc25
Time (min)
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Mutants in Fission Yeast
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Wee1
P
mass/nucleus
Cdc20
Cdc14
TFBA
neg fdbk osc
Wee1
TFBI
CycB
P
APC-P
APC
Cdc14
Cdc25
P
Cdc20
CycB
Cdc14
Cdh1
Cdc25
CycD
CKI
bistable switch
CycB
CycE
TFII
Cdh1
CycD
CycA
TFIA
CKI
CKI
CKI
bistable switch
CycA
CycE
Cyc E,A,B
Cdc20
CycA
CycE
TFEA
CycD
CycB
CycA
TFEI
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Wee1
P
mass/nucleus
Cdc20
Cdc14
TFBA
Wee1
TFBI
CycB
P
APC-P
APC
Cdc14
Cdc25
P
Cdc20
CycB
Cdc14
Cdh1
Cdc25
CycD
CKI
CycB
CycE
TFII
Cdh1
CycD
CycA
TFIA
CKI
CKI
CKI
CycA
CycE
Cyc E,A,B
Cdc20
CycA
CycE
TFEA
CycD
CycB
CycA
TFEI
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S
G2
M
G1
S
G2
M
G1
S
5
mass/nucleus
4
3
2
1
0
CKI
Cdh1
Cdc20
Wee1
Cdc25
Time (min)
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3.0
Wild type
M
Balanced Growth and Division
0.8
Cdk1CycB
0.4
S/G2
G1
0
0
1
2
3
4
5
mass/nucleus
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3.0
Wild type
M
Alternation of S phase and M phase
0.8
Cdk1CycB
0.4
S/G2
G1
0
0
1
2
3
4
5
mass/nucleus
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Nature, Vol, 256, No. 5518, pp. 547-551, August
14, 1975
Genetic control of cell size at cell division in
yeast Paul Nurse Department of Zoology, West
Mains Road, Edinburgh EH9 3JT, UK
wild-type wee1D
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Wee1
P
mass/nucleus
Cdc20
Cdc14
TFBA
Wee1
TFBI
CycB
P
APC-P
APC
Cdc14
Cdc25
P
Cdc20
CycB
Cdc14
Cdh1
Cdc25
CycD
CKI
CycB
CycE
TFII
Cdh1
CycD
CycA
TFIA
CKI
CKI
CKI
CycA
CycE
Cyc E,A,B
Cdc20
CycA
CycE
TFEA
CycD
CycB
CycA
TFEI
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wee1D cells are about one-half the size of wild
type
wee1?
M
Cdk1CycB
S/G2
G1
mass/nucleus
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Wee1
P
mass/nucleus
Cdc20
Cdc14
TFBA
Wee1
TFBI
CycB
P
APC-P
APC
Cdc14
Cdc25
P
Cdc20
CycB
Cdc14
Cdh1
Cdc25
CycD
CKI
CycB
CycE
TFII
Cdh1
CycD
CycA
TFIA
CKI
CKI
CKI
CycA
CycE
Cyc E,A,B
Cdc20
CycA
CycE
TFEA
CycD
CycB
CycA
TFEI
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The Start module is not required during mitotic
cycles
cki?
M
Cdk1CycB
S/G2
G1
mass/nucleus
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Wee1
P
Cdc20
Cdc14
TFBA
Wee1
TFBI
CycB
P
APC-P
APC
Cdc14
Cdc25
P
Cdc20
CycB
Cdc14
Cdh1
Cdc25
CycD
CKI
CycB
CycE
TFII
Cdh1
CycD
CycA
TFIA
CKI
CKI
CKI
CycA
CycE
Cyc E,A,B
Cdc20
CycA
CycE
TFEA
CycD
CycB
CycA
TFEI
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Cells become progressively smaller without size
control
cki? wee1ts
2.0
Unbalanced Growth and Division is Lethal !
0.8
M
Cdk1CycB
0.4
S/G2
G1
0
0 1 2 3 4 5
mass/nucleus
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The Cell Cycle of Budding Yeast
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Wee1
P
Cdc20
Cdc14
TFBA
Wee1
TFBI
CycB
P
APC-P
APC
Cdc14
Cdc25
P
Cdc20
CycB
variable
Cdc14
Cdh1
Cdc25
CycD
CKI
CycB
CycE
TFII
Cdh1
CycD
CycA
TFIA
CKI
CKI
CKI
parameter
CycA
CycE
Cyc E,A,B
Cdc20
mass/nucleus
CycA
CycE
TFEA
Growth
CycD
CycB
CycA
TFEI
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Wild type cells
M
MDT 90 min 120 min 150 min
S/G2
CycB-dependent kinase activity
G1
mass
SNIC
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CycB
G1
Period
180
150
time (min)
120
90
60
0
1
2
3
4
cell mass (au.)
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• Mutant phenotypes are direct consequences of
  altered bifurcation diagrams.

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Wee1
P
Cdc20
Cdc14
TFBA
Wee1
TFBI
CycB
P
APC-P
APC
Cdc14
Cdc25
P
Cdc20
CycB
Cdc14
Cdh1
Cdc25
CycD
CKI
CycB
CycE
TFII
Cdh1
CycD
CycA
TFIA
CKI
CKI
CKI
CycA
CycE
Cyc E,A,B
Cdc20
CycA
CycE
TFEA
Growth
CycD
CycB
CycA
TFEI
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ckiD
cdh1D
CycB-dependent kinase activity
lack of one of the G1 enemies viable
mass
mass
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Wee1
P
Cdc20
Cdc14
TFBA
Wee1
TFBI
CycB
P
APC-P
APC
Cdc14
Cdc25
P
Cdc20
CycB
Cdc14
Cdh1
Cdc25
CycD
CKI
CycB
CycE
TFII
Cdh1
CycD
CycA
TFIA
CKI
CKI
CKI
CycA
CycE
Cyc E,A,B
Cdc20
CycA
CycE
TFEA
Growth
CycD
CycB
CycA
TFEI
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sic1D
cdh1D
Clb2-dependent kinase activity
lack of one of the G1 enemies viable
mass
mass
cdc20D
cdc14D
CycB-dependent kinase activity
Incomplete CycB destruction
No CycB destruction
mass
mass
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Defects in Exit from Mitosis
APC-A cdh1D
wild-type
A
D
MDT 300 min 200 min 150 min 120 min 90 min
D
CycB-dependent kinase activity
CLB2Ddb
cdc20ts pds1D
E
F
cell mass (au.)
Viability depends on growth rate!
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• Two-parameter bifurcation diagrams connect
  genetics to physiology.

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Two-parameter bifurcation diagram
SN
SL
CF
BISTABILITY
SN
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Two-parameter bifurcation diagram
OSCILLATIONS
SN
SL
CF
BISTABILITY
SN
Hopf (super)
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GENETICS
activation
Cdh1
synthesis
Cki
cell mass (au.)
cell mass (au.)
PHYSIOLOGY
activation
Cdc14
Cdc20
synthesis
cell mass (au.)
cell mass (au.)
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The Dynamical Perspective
Molec Genetics Biochemistry
Cell Biology
Molecular Mechanism
Kinetic Equations
State Space, Vector Field
Attractors, Transients, Repellors
Two-parameter Bifurcation Diagrams
Bifurcation Diagrams
Signal-Response Curves
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• In metazoans, a signaling network controls the
  accelerators and brakes of cell growth, division
  and death.

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Wee1
P
Cdc20
Unreplicated DNA
Cdc14
TFBA
Wee1
TFBI
CycB
P
APC-P
APC
Cdc14
Cdc25
P
Cdc20
CycB
Cdc14
Cdh1
Cdc25
CycD
CKI
CycB
CycE
TFII
Cdh1
CycD
CycA
TFIA
CKI
CKI
CKI
CycA
CycE
Cyc E,A,B
Cdc20
CycA
CycE
TFEA
Growth
CycD
CycB
CycA
TFEI
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dx/dtf(x,y)
Phase Plane
dy/dtg(x,y)
MPF
Cyclin
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dx/dtf(x,y)
Phase Plane
dy/dtg(x,y)
MPF
Cyclin
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dx/dtf(x,y)
Phase Plane
dy/dtg(x,y)
MPF
Cyclin
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Hopf Bifurcation