Bistability in gene networks

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Bistability in gene networks
UCSD, July 19, 2006
Alexander van Oudenaarden Department of Physics,
MIT http//web.mit.edu/biophysics avano_at_mit.ed
u
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A dramatic example of multistability stem cells
Reya et al. Nature 414, 105 (2001)
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Cellular decision-making taking a step back
1. Transient stimuli produce persistent
responses 2. How is this memory stored? 3.
What limits the stability of a cellular state
(phenotype)?
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Main General Goals
1. Identify the basic gene network motifs that
cells use to define multiple stable
states 2. Experimentally quantify the role of
stochastic fluctuations in gene expression on
the stability of these states 3. Develop general
predicitive mathematical models that provide
quantitative framework
Focus on well characterized gene networks in
simple organisms
Part I Escherichia coli
Part II Saccharomyces cerevisiae
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A simple mechanism for bistability positive
feedback
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Feedbacks are ubiquitous motifs in biological
networks
Eric Davidson et al., Science 295, 1669-1678
(2002)
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g(y)
f(y)
Y
gene Y
PCONST
0
0
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g(y)
Y
f(y)

Y
Y
gene Y
PY
0
y
0
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g(y)
Y
Y
f(y)

Y
Y
Y
gene Y
PY
0
y
0
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The Expression Potential U a Useful Concept from
Classical Mechanics
Classical Mechanics
m
x
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g(y)
f(y)
Y
gene Y
PCONST
0
potential U
y
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g(y)
Y
f(y)

Y
Y
gene Y
PY
0
potential U
y
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g(y)
Y
Y
f(y)

Y
Y
Y
gene Y
PY
0
potential U
y
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Part I Multistability in the lactose utilization
network Ertugrul Ozbudak, Mukund Thattai et al.
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A classic genetic switch the lac operon
transcription is blocked by lac repressor (LacI)
extracellular
intracellular
RNA polymerase
lac repressor (LacI)
Plac
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A classic genetic switch the lac operon
once LacI unbinds, RNA polymerase starts
transcription
extracellular
intracellular
lac repressor (LacI)
RNA polymerase
Plac
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A classic genetic switch the lac operon
RNA polymerase transcribes lac genes
extracellular
intracellular
Permease(LacY)
?-gal (LacZ)
lac repressor (LacI)
RNA polymerase
Plac
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A classic genetic switch the lac operon
intracellular lactose binds LacI resulting in
inactive repressor
extracellular lactose
extracellular
intracellular
intracellular lactose
Plac
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A classic genetic switch the lac operon
increased concentration of LacY results in
synthesis of more LacY
extracellular
intracellular
Plac
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Regulation of lactose uptake a positive feedback
system
extracellular lactose
Permease (LacY)
intracellular lactose
repressor(LacI)
Plac
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Regulation of lactose uptake a positive feedback
system
extracellular lactose
glucose
Permease (LacY)
CRP
repressor(LacI)
Plac
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Positive feedback in a bacterial regulatory
network
lacZ
lacY
lacA
Plac
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The lac system is bistable
n 1
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The lac system is bistable
n 2
Phase diagram
??/?
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Network response can be either discontinuous or
continuous
Continuous
Discontinuous
Decrease repression factor
TMG ?
TMG ?
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Bistability allows memory storage
decrease TMG
Permease concentration (y)
Extracellular TMG
increase TMG
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Experimental protocol
Measure single cell fluorescence histograms (both
GFP and HcRed) in steady-state as afunction
of (i) external TMG concentration (continuous
variable) (ii) external glucose concentration
(continuous variable) (iii) initial condition
(binary variable fully induced versus not
induced) Plac-GFP is integrated in the
chromosome Pgat-HcRed is on a low copy plasmid
TMG
Glu
cAMP
TMG
LacY
lactose metabolism
LacZ
LacI
CRP
lacZ
lacY
lacA
Plac
GFP
gfp
Plac
HcRed
HcRed
Pgat
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Induction protocol, history dependent experiments
gt 24 hours liquid culture ( 24 generations)
gt 12 hours liquid culture 0 mM TMG (all cells OFF)
split singlecolony
gt 12 hours liquid culture 1 mM TMG (all cells ON)
Novick and Weiner, PNAS 43, 553 (1957) Cohn and
Horibata, J. Bacteriol. 78, 601 (1959)
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initial HIGH state
initial LOW state
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Mapping the bistable region as a function of TMG
and glucose concentration
Ozbudak et al. Nature 427, 737 (2004)
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At the phase boundary (switching thresholds)
dy/dt has only two rootstherefore, the
functions ?, ?, and ? can be determined
explicitly as a function of TMG and glucose
concentration
a
b
y
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Functions ?, ?, and ? are calculated from
switching thresholds a and b
- Population averaged red fluorescence is a
sensitve function of external glucose
concentration - Single cell red fluorescence is
independent of history Low glucose ? high cAMP ?
high cAMP-CRP ? high red High glucose ? low cAMP
? low cAMP-CRP ? low red
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Functions ?, ?, and ? are calculated from
switching thresholds a and b
? 1RT/Ro
? maximum lacY synthesis rate obtained if R
? 0 ? / ? minimum lacY synthesis rate
obtained if R ? RT
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Functions ?, ?, and ? are calculated from
switching thresholds a and b
? red fluorescence ? is independent of TMG ?
is independent of red fluorescence ? is
independent of TMG
Interpretation - Plac and Pgat respond
identically to the activator CRP-cAMP - ? is
completely determined by repressor
concentration - results indicate independent
binding of lacI and cAMP-CRP, since lacY
synthesis f(glucose) ? g(TMG)
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Inducer exclusion TMG import rate does not only
depend on extracellular TMG but also depends on
glucose level ?(T,G) ?T(T)?G(G)
(?G)
inducer exclusion glucose binds directly to LacY
inhibiting TMG uptake
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Inducer exclusion TMG import rate does not only
depend on extracellular TMG but also depends on
glucose level ?(T,G) ?T(T)?G(G)
?T(T)
?G(G)
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Network response can be either discontinuous or
continuous
Continuous
Discontinuous
Decrease repression factor
TMG ?
TMG ?
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7 lacO
15 lacO
WT
Turning a binary response into a graded response
1/? 0.005
1/? 0.16
??/?
no hysteresis
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Part II Cellular memory in the galactose
signaling network Murat Acar, Attila Becskei et
al.
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The Galactose Signaling Pathway
Galactose
feedback
Gal2p
feedback
Gal3p
Cytoplasm
Gal3p
-
feedback
Gal80p
PGAL80
PGAL3
Nucleus
Gal80p
PGAL2
PGAL1
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History dependent experiments are useful to
reveal positive feedback loops
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Wild type shows hysteretic behavior
wt
0
0.02
0.06
increasing galactose concentration
normalized cell count
0.1
0.15
0.3
0.5
log10 (PGAL1YFP fluorescence)
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Gal2p knock-out
Galactose
feedback
Gal3p
Cytoplasm
Gal3p
-
feedback
Gal80p
PGAL80
Gal4p
GAL80
PGAL3
Nucleus
Gal4p
GAL3
Gal80p
PGAL1
Gal4p
YFP
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Gal2p is not necessary for bistability
gal2?
wt
0
0
0.02
0.04
0.06
0.06
increasing galactose concentration
normalized cell count
0.1
0.08
0.15
0.1
0.3
0.2
0.5
0.3
log10 (PGAL1YFP fluorescence)
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Gal80p negative loop knock-out (network mutant)
Galactose
feedback
Gal2p
feedback
Gal3p
Cytoplasm
Gal3p
no feedback
Gal80p
PIND
PGAL3
Nucleus
Gal4p
Gal80p
PGAL2
Gal4p
PGAL1
Gal4p
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Gal80p loop knock-out shows enhanced bistability
gal80? PTET GAL80
gal2?
wt
0
0
0
0.02
0.04
0.01
0.06
0.06
0.02
increasing galactose concentration
normalized cell count
0.1
0.05
0.08
0.2
0.15
0.1
0.3
0.3
0.2
0.5
0.5
0.3
log10 (PGAL1YFP fluorescence)
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Gal3p positive loop knock-out
Galactose
feedback
Gal2p
no feedback
Gal3p
Cytoplasm
Gal3p
-
feedback
Gal80p
PGAL80
Gal4p
PIND
Nucleus
Gal80p
PGAL2
Gal4p
PGAL1
Gal4p
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Gal3p is necessary for bistability
0
0
0
0
0.002
0.02
0.04
0.01
0.06
0.006
0.06
0.02
increasing galactose concentration
0.1
0.05
0.012
0.08
0.2
0.15
0.1
0.02
0.3
0.3
0.2
0.03
0.5
0.5
0.3
0.05
Acar, Becskei, AvO. Nature 435, 228 (2005)
log10 (PGAL1YFP fluorescence)
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Full phase space of negative loop knock-out


experimental data
model
Galactose
Relative Gal80p concentration
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gal80? PTET GAL80
Definition of persistent memory


0

0.01
0.02
increasing galactose concentration
0.05
Galactose
0.2

0.3
0.5
Relative Gal80p concentration
log10 (PGAL1YFP fluorescence)
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Definition of destabilized memory


time (hrs)
Galactose
?
Relative Gal80p concentration
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Experimental measurement of switching rates
persistent memory
Fraction ON cells
destabilized memory
time (hrs)
normalized cell count
Time (hr)
Find escape rates
kON
OFF ON
kOFF
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The Expression Potential U a Useful Concept from
Classical Mechanics
Classical Mechanics
m
x
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Definition of energy in the context of chemical
kinetics
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Analogy with Arhennius equation for chemical
reaction rates
A particle which is caught in a potential hole
and which, through the shuttling action of
Brownian motion, can escape over a potential
barrier yields a suitable model for elucidating
the applicability of the transition state method
for calculating the rate of chemical reactions.
H. A. Kramers. Physica 7 (1940)
Svante Arrhenius (1895)
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The Arhennius equation for phenotype switching
escape rates
ON?OFF
kOFF
Escape rate (1/hr)
kON
OFF?ON
Energy barrier DU (mM2/s)
High noise ON states versus low noise OFF
states
Some numbers 10-4 1/hr 1/year 1 year
6000 yeast generations
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Stability versus noise Evolutionary advantage?
Some numbers 10-4 1/hr 1/year 1 year 6000
yeast generations expression state is inherited
Can stochastic transitions between phenotypes
enhance the population fitness? Yes, if the
environment is fluctuating !
Thattai, AvO. Genetics 167, 1523 (2004)
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Bistability in gene networks
Escherichia coli
Saccharomyces cerevisiae
1. Single cells have the potential to remember
environmental conditions for more than
hundreds/thousands of generations 2. Noise in
gene expression limits the stability of the
cellular memory 3. Phase diagram and energy
landscape analogy provides a quantitative and
concise mathematical description of gene
network stability and noise
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Thanks !
Ertugrul Ozbudak
Murat Acar
Mukund Thattai
Attila Becskei
Han Lim
Boris Shraiman
NIH NSF