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![Page 1: Stochasticity in Signaling Pathways and Gene Regulation: The NFκB Example and the Principle of Stochastic Robustness Marek Kimmel Rice University, Houston,](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f1b5503460f94c30191/html5/thumbnails/1.jpg)
Stochasticity in Signaling Pathways and Gene Regulation:
The NFκB Example and the Principle of Stochastic Robustness
Marek Kimmel
Rice University, Houston, TX, USA
![Page 2: Stochasticity in Signaling Pathways and Gene Regulation: The NFκB Example and the Principle of Stochastic Robustness Marek Kimmel Rice University, Houston,](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f1b5503460f94c30191/html5/thumbnails/2.jpg)
Credits
• Rice University– Pawel Paszek– Roberto Bertolusso
• UTMB – Galveston– Allan Brasier– Bing Tian
• Politechnika Slaska– Jaroslaw Smieja– Krzysztof Fujarewicz
• Baylor College of Medicine– Michael Mancini– Adam Szafran– Elizabeth Jones
• IPPT – Warsaw– Tomasz Lipniacki– Beata Hat
![Page 3: Stochasticity in Signaling Pathways and Gene Regulation: The NFκB Example and the Principle of Stochastic Robustness Marek Kimmel Rice University, Houston,](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f1b5503460f94c30191/html5/thumbnails/3.jpg)
Gene regulation
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TNF
TNF Signaling PathwayTNF Signaling Pathway
Apoptosis Signal
NF-B AP-1
Inflammation Proliferation
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Nuclear Factor-B (NF-B)
• Inducible (cytoplasmic) transcription factor• Mediator of acute phase phase reactant
transcription (angiotensinogen, SAA)• Mediator of cytokine and chemokine
expression in pulmonary cytokine cascade• Plays role in anti-apoptosis and confering
chemotherapy resistance in drug resistant cancers
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IB
Rel A:NF-B1
nucleus
TNF
TRAF2/TRADD/RIP
TAK/TAB1
IKK
Nuclear factor-Nuclear factor-B (NF-B (NF-B) PathwayB) Pathway
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Rel A:NF-B1
nucleus
2
Activated IKK
NF-B “Activation”
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IKK
nucleus
TNFR1
Rel A:NF-B1
A20
Negative autoregulation of the NF-B pathway
Rel A
IB
IBC-Rel
NF-B1
NF-B2
RelB
Rel ATRAF1
TNF mRNA
TTP/Zf36
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Intrinsic sources of stochasticity
• In bacteria, single-cell level stochasticity is quite well-recognized, since the number of mRNA or even protein of given type, per cell, might be small (1 gene, several mRNA, protein ~10)
• Eukaryotic cells are much larger (1-2 genes, mRNA ~100, protein ~100,000), so the source of stochasticity is mainly the regulation of gene activity.
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Simplified schematic of gene expression
• Regulatory proteins change gene status.
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1)(,0)(
,,
AI
IAAI
GG
genectivegenenactive dc
rK
HG
proteinmRNA
mRNA 1
Discrete Stochastic Model
Time-continuous Markov chain with state space
and transition intensities
ProteinRNAGene}1,0{ ZZ
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)()()(
)()(
trytKxdt
tdy
txHGdt
tdx
Continuous Approximationonly gene on/off discrete stochastic
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0 2 4 60
2
4
6x 10
4 Free nuclear NF-kB
0 2 4 60
0.5
1
1.5Activity of IkBa gene
0 2 4 60
100
200
300IkBa mRNA transcript
0 2 4 60
5
10x 10
4 Total IkBa
0 2 4 60
2
4
6x 10
4
0 2 4 60
0.5
1
1.5
0 2 4 60
100
200
300
0 2 4 60
5
10x 10
4
0 2 4 60
2
4
6x 10
4
0 2 4 60
0.5
1
1.5
0 2 4 60
100
200
300
0 2 4 60
5
10
15x 10
4
0 2 4 60
2
4
6x 10
4
0 2 4 60
0.5
1
1.5
0 2 4 60
100
200
300
0 2 4 60
5
10x 10
4
Four single cell simulations
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Trajectories projected on (IB,NF-Bn,,time) space, red: 3 single cells, blue: cell population
Any single cell trajectory differs from the “averaged” trajectory
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White et al. experiments
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What happens if the number of active receptors is small?
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Low dose responses
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How to find out if on/off transcrition stochasticity plays a role?
• If on/off rapid enough, its influence on the system is damped
• Recent photobleaching experiments →
TF turnover ~10 sec
• However, does this quick turnover reflect duration of transcription “bursts”?
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FRAP (Mancini Lab)Fluorescence recovery after photobleaching
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f
N
B
AR
E
The Model
Nkfkt
N
Bkfkt
B
fkkNkBkfDt
f
dNN
dBB
NBdNdB
)(
zyx
kB
kdB
kdN
kN
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The Model
• Fit the model to photobleaching data
• Obtain estimates of binding constants of the factor
• Invert binding constants to obtain mean residence times
• Effect: ~10 seconds
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Estimation of mean times of transcription active/ inactive
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Estimation of mean times of transcription active/ inactive
Transcription of the gene occurs in bursts, which are asynchronous in different cells.
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Estimation of mean times of transcription active/ inactive
hrTE
hrTE
AI
IA
I
A
2.2)(
8.0)(
,
,
1
1
Parameters estimated by fitting the distribution of the level of nuclear message, apparently contradict photobleaching experiments.
![Page 30: Stochasticity in Signaling Pathways and Gene Regulation: The NFκB Example and the Principle of Stochastic Robustness Marek Kimmel Rice University, Houston,](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f1b5503460f94c30191/html5/thumbnails/30.jpg)
A single gene (one copy) using K-E approximation
)()()(
tGtydt
tdy
Amount of protein:
Where:• and are the constitutive activation and deactivation
rates, respectively,• is an inducible activation rate due to the action of protein dimers.
,1)(,0)(
,, 02
20
AI
IAAI
GG
dycc
oc od
2c
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Deterministic description
The system has one or two stable equilibrium points depending on the parameters.
,][
),()()(
02
20
220
dycc
yccGE
GEtydt
tdy
![Page 32: Stochasticity in Signaling Pathways and Gene Regulation: The NFκB Example and the Principle of Stochastic Robustness Marek Kimmel Rice University, Houston,](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f1b5503460f94c30191/html5/thumbnails/32.jpg)
Transient probability density functions
Stable deterministic solutions are at 0.07 and 0.63
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Transient probability density functions
Stable deterministic solutions are at 0.07 and 0.63
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Transient probability density functions
Stable deterministic solutions are at 0.07 and 0.63
![Page 35: Stochasticity in Signaling Pathways and Gene Regulation: The NFκB Example and the Principle of Stochastic Robustness Marek Kimmel Rice University, Houston,](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f1b5503460f94c30191/html5/thumbnails/35.jpg)
Transient probability density functions
Stable deterministic solutions are at 0.07 and 0.63
![Page 36: Stochasticity in Signaling Pathways and Gene Regulation: The NFκB Example and the Principle of Stochastic Robustness Marek Kimmel Rice University, Houston,](https://reader035.fdocuments.us/reader035/viewer/2022062422/56649f1b5503460f94c30191/html5/thumbnails/36.jpg)
Conclusions from modeling
• Stochastic event of gene activation results in a burst of mRNA molecules, each serving as a template for numerous protein molecules.
• No single cell behaves like an average cell.• Decreasing magnitude of the signal below a threshold
value lowers the probability of response but not its amplitude.
• “Stochastic robustness” allows individual cells to respond differently to the same stimulus, but makes responses well-defined (proliferation vs. apoptopsis).
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References
• Lipniacki T, Paszek P, Brasier AR, Luxon BA, Kimmel M. Stochastic regulation in early immune response. Biophys J. 2006 Feb 1;90(3):725-42.
• Paszek P, Lipniacki T, Brasier AR, Tian B, Nowak DE, Kimmel M. Stochastic effects of multiple regulators on expression profiles in eukaryotes. J Theor Biol. 2005 Apr 7;233(3):423-33.
• Lipniacki T, Paszek P, Brasier AR, Luxon B, Kimmel M. Mathematical model of NF-kappaB regulatory module. J Theor Biol. 2004 May 21;228(2):195-215.