Stochastic gene expression

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Stochastic gene expression from prokaryotes to
eukaryotes and from steady-state to
out-of-equilibrium
Alexander van Oudenaarden Department of Physics,
MIT http//web.mit.edu/biophysics avano_at_mit.edu
2
Noise in gene expression can randomly flip a
genetic switch the lambda lysis-lysogeny
decision
Arkin, Ross and McAdams. Genetics 149, 1633 (1998)
3
Biochemical reactions are intrinsically noisy
The randomness is a natural consequence of the
discreteness of molecules
Describing the dynamics of a constitutively
transcribed gene ?
y mRNA concentration ? transcription rate t time
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Noise can be observed in the expression of a
single gene
?
IPTG
IPTG
y
LacI
GFP
gfp
Pspac
?y
?y?
Ozbudak et al., Nature Genetics 31, 69
(2002)Elowitz et al., Science 297, 1183 (2002)
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Biological Relevance of Noisy Gene Expression ?
NOISE is BENEFICIAL Stochastic gene expression
introduces a significant variability in mRNA and
protein concentrations from cell-to-cell in an
isogenic population. This might be beneficial for
survival in fluctuating environments. NOISE is
DETRIMENTAL Fluctuations in gene expression
might impair faithful signal propagation in gene
cascades and signal transduction pathways
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Part I Noise propagation in gene
networks (Escherichia coli) Juan Pedraza, AvO
Science 307, 1965 (2005)
7
Stochastic gene expression from prokaryotes to
eukaryotes and from steady-state to
out-of-equilibrium
8
Main topics of part I - Experimentally measure
how noise propagates in a gene cascade -
Develop mathematical models that quantitatively
describe and predict the noise properties A
synthetic cascade in E. coli to probe noise
propagation
Gene 1
Gene 2
Gene 0
Gene 3
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A synthetic cascade in E. coli to probe noise
propagation
Gene 1
Gene 2
Related studies Rosenfeld et al. Science 307,
1962 (2005) Hooshangi et al. PNAS 102, 3581
(2005)
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The average signal does not reflect single cell
behavior
Gene 2
Gene 1
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A typical data set ( 5000 single cells 3
colors/cell)

F2
F1
F3
286 998 2217 1010 424 716 1519 1062 966 286 40 377
968 1293 1616 172 910 87 655 1512 115 1146 383 87
0 73 990 1097 1393 192 369 1722 19 476 1294 179 19
50 951 690 127 301 817 1252 408 637 1069 2758 249
105 95 2630 468 352 1037 452 225 781 1362 75 339 4
5 184 463 1136 1229 96 1311 371 407 863 825 1150 2
019 383 1064 709 559 1001 1651 865 790 755 1228 90
2 1833 2141 1320 239 179 418 1481
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
15000 data points for one concentration of IPTG
and ATC
image analysis
3 color fluorescence microscopy
...
...
...
...
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Correlations capture rich structure of 3D
distributions

F2
F1
F3
286 998 2217 1010 424 716 1519 1062 966 286 40 377
968 1293 1616 172 910 87 655 1512 115 1146 383 87
0 73 990 1097 1393 192 369 1722 19 476 1294 179 19
50 951 690 127 301 817 1252 408 637 1069 2758 249
105 95 2630 468 352 1037 452 225 781 1362 75 339 4
5 184 463 1136 1229 96 1311 371 407 863 825 1150 2
019 383 1064 709 559 1001 1651 865 790 755 1228 90
2 1833 2141 1320 239 179 418 1481
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
15000 data points for one concentration of IPTG
and ATC
1 correlation for one concentration of IPTG and
ATC
image analysis
calculate correlations
3 color fluorescence microscopy
Cij
i 1, 2, 3 j 1, 2, 3
...
...
...
...
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Auto correlations capture the cell-to-cell
variability in the expression of a single gene
averaged over single cells in population
For example, i j 1 (gene 1 is reported by CFP)
(?CFP)2
2
(auto-correlation, coeficient of variation)
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(?CFP)2
F1

F2
F3
2
286 998 2217 1010 424 716 1519 1062 966 286 40 377
968 1293 1616 172 910 87 655 1512 115 1146 383 87
0 73 990 1097 1393 192 369 1722 19 476 1294 179 19
50 951 690 127 301 817 1252 408 637 1069 2758 249
105 95 2630 468 352 1037 452 225 781 1362 75 339 4
5 184 463 1136 1229 96 1311 371 407 863 825 1150 2
019 383 1064 709 559 1001 1651 865 790 755 1228 90
2 1833 2141 1320 239 179 418 1481
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
Cell count
sCFP
Single cell CFP fluorescence
repeat for other colors and other IPTG and ATC
concentrations
...
...
...
...
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i j Autocorrelations
Why are noise profiles qualitatively different
for gene 1 and 2 ? What determines the shape of
the profiles ?
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Cross correlations capture how variability in
expression couples between different genes
averaged over single cells in population
For example, i 1 j 2 (gene 1 is reported by
CFP gene 2 is reported by YFP)
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F1

F2
F3
286 998 2217 1010 424 716 1519 1062 966 286 40 377
968 1293 1616 172 910 87 655 1512 115 1146 383 87
0 73 990 1097 1393 192 369 1722 19 476 1294 179 19
50 951 690 127 301 817 1252 408 637 1069 2758 249
105 95 2630 468 352 1037 452 225 781 1362 75 339 4
5 184 463 1136 1229 96 1311 371 407 863 825 1150 2
019 383 1064 709 559 1001 1651 865 790 755 1228 90
2 1833 2141 1320 239 179 418 1481
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
...
...
...
...
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F1

F2
F3
286 998 2217 1010 424 716 1519 1062 966 286 40 377
968 1293 1616 172 910 87 655 1512 115 1146 383 87
0 73 990 1097 1393 192 369 1722 19 476 1294 179 19
50 951 690 127 301 817 1252 408 637 1069 2758 249
105 95 2630 468 352 1037 452 225 781 1362 75 339 4
5 184 463 1136 1229 96 1311 371 407 863 825 1150 2
019 383 1064 709 559 1001 1651 865 790 755 1228 90
2 1833 2141 1320 239 179 418 1481
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
repeat for other colors combinations and other
IPTG and ATC concentrations
...
...
...
...
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i ? j Cross-correlations
Why determines the cross-correlation between gene
1 and 2 ? Why are C13 and C23 dependent on IPTG
?
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Modeling signal noise transmission
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Transmitted noise depends on the logaritmic gain
Two types of transmitted noise 1. Transmitted
intrinsic noise
(gene 2)
2. Transmitted global noise
(gene 1)
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Building up the noise
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Interpretation of the noise profiles
Noise profile of gene 1 is mixture of intrinsic
and transmitted noise Noise profile of gene 2 is
dominated by the transmitted noise (profile
resembles shape of H21)
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Interpretation of the noise profiles
Crosscorrelations C13 and C23 are due to
transmission of correlated global noise
(independent of intrinsic noise)
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Why does C13 depend on H10 and therefore on
IPTG ?
global noise is correlated between gene 1 and
3 a global fluctuation resulting in increased
expression of all genes (including gene 0) will
lead to an increased repression of gene 1
depending on the coupling between gene 0 and 1
(H10)
global noise couples genes even in the absence of
a direct genetic interaction
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Global fit to means, autocorrelations and
cross-correlations
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Predictive power of model (no fit parameters)
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Conclusions, Part I
Noise in a gene is determined by its intrinsic
fluctuations, transmitted noise from upstream
genes and global noise affecting all genes. A
model was developed that explains the complex
behavior exhibited by the correlations, and
reveals the dominant noise sources.
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Part II Noise amplification and
correlation (Saccharomyces cerevisiae) Attila
Becskei, Ben Kaufmann, AvO
Nature Genetics 37, 937 (2005)
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Stochastic gene expression from prokaryotes to
eukaryotes and from steady-state to
out-of-equilibrium
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The majority of yeast transcription factorshave
less than one mRNA/cell small number of mRNA
molecules ? huge fluctuations
?
Holand et al. JBC 277, 14363 (2002)
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First problem Most promoters are too weak for
direct read-out
direct read-out
Elowitz et al. Science 297, 1183 (2002) Raser and
OShea. Science 304, 1811 (2004)
Solution a synthetic signal and noise amplifier
doxycycline
Becskei, Boselli and AvO. Nature Cell Biology 6,
451 (2004) Becskei, Kaufmann and AvO. Nature
Genetics 37, 937 (2005)
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Goal determine input noise ?1 of several weak
promoters
standard deviation mean
? CV
dox
rtTA
YFP
...
input module
response module
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What would you expect theoretically ?
averaging constant
independent of input promoter !
logarithmic gain
Paulsson. Nature 427, 415 (2004) Pedraza and AvO.
Science 307, 1965 (2005)
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Input noise is found by globally fitting to the
model
Becskei, Kaufmann and AvO. Nature Genetics 37,
937 (2005)
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Contribution of intrinsic input noiseshould
depend on input signal
N
experimental knob N multiple Pinput-rtTA
integrations
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N
fully uncorrelated
fully correlated
Related study Volfson et al., Nature,
doi10.1038 (2005)
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Output noise is independent of N noise from
multiple promoter copies is strongly correlated
N 1
N 2
N ? 5
PSWI6
Output noise ?2
Output signal x2 (fluorescence)
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Correlated noise depends on chromosomal position
5xade2
ade2
ade2/ade2
Normalized noise ?1
Output noise ?2
2xhis3
his3
his3/his3
Output signal x2 (fluorescence)
dox25 (mg/ml)
Becskei, Kaufmann and AvO. Nature Genetics 37,
937 (2005)
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Conclusions, Part II Although SWI6 promoter is
one of weakest yeast promoters, noise is fully
correlated between tandem copies Noise
originates from rare events of promoter
activation (not randombirth and deaths of mRNA
molecules) and depends on chromosomal position
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Part III Noise in a circadian oscillator
(Synechococcus elongatus) Jeff Chabot, Juan
Pedraza, AvO
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Stochastic gene expression from prokaryotes to
eukaryotes and from steady-state to
out-of-equilibrium
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Cyanobacteria as a model system for circadian
rhythms
Kondo et al. (1993)
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Cyanobacteria as a model system for circadian
rhythms
Kondo et al. (1993)
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The circadian clock consists of only 3 proteins
and can be reconstituted in vitro
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Monitoring circadian oscillations in single
cells using fluorescent proteins
Circadian oscillations in Synechococcus elongatus
PCC7942
Related study Mihalcescu et al., Nature 430, 81
(2004).
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Establishing fluorescence as a useful tool for
exploring circadian rhytms in Synechococcus
YFP
Fluorescence (a.u.)
Fluorescence (a.u.)
Fluorescence (a.u.)
YFPLVA
Time in LL (hours)
Time after IPTG removal (hours)
Time after IPTG induction (hours)
protein half-life YFP 12.8 hrs protein
half-life YFPLVA 5.6 hrs
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deterministic model
Experimentally known
?R 2.8 hr-1 ?P 0.12 hr-1
Since y(t) is known, kR(t) can be determined (in
a.u.)
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Lets use the same gene-doubling technique to
determine correlation between expression
fluctuations
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NS I II fully correlated (CV2)one copy
(CV2)two copies (s2)one copy 4(s2)two
copies NS I II fully uncorrelated (CV2)one
copy 0.5(CV2)two copies (s2)one copy
2(s2)two copies
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(No Transcript)
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Using this formalism q(t) can be extracted from
the experiments
Rosenfeld et al. Science 307, 1962 (2005)
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Global noise is consistent with global
fluctuations in creation rate kR(t)
?N ? ?P ?G ? 0.4
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Local noise is not consistent with intrinsic
fluctuations
For intrinsic noise
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Conclusions, Part III Cell-to-cell variability
was measured in cyanobacteria during a circadian
period An out-of-equilibrium method
was developed to extract the fluctuations introduc
ed at the transcription level Data are
consistent with a constant global noise and a
time-varying local noise introduced at the
transcription level
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Thanks !
Juan Pedraza
Attila Becskei
Jeff Chabot
Ben Kaufmann
NIH NSF