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Noise and Bistability
12/10/07
Noisy gene expression at single cell level
Elowitz 2002
Noise distribution of protein concentration
Bar-Even 2006
Dependence of noise level on protein concentration
Bar-Even 2006
Proteins are produced in bursts
Cai 2006
Proteins are produced in bursts
Cai 2006
Intrinsic and extrinsic noise
extrinsic noise:
fluctuations in the amounts or states of other cellular components lead indirectly to variation in the expression of a particular gene
intrinsic noise:
The inherent stochasticity of biochemical processes such as transcription and translation
Elowitz 2002
Intrinsic and extrinsic noise
extrinsic noise:
fluctuations in the amounts or states of other cellular components lead indirectly to variation in the expression of a particular gene
intrinsic noise:
The inherent stochasticity of biochemical processes such as transcription and translation
Elowitz 2002
Distinguishing intrinsic from extrinsic noise
Average over cell population
For a fixed time t,
Total noise level, Average over time
Swain 2002
Distinguishing intrinsic from extrinsic noise
Average over cell population
For a fixed time t,
Total noise level, Average over time
Swain 2002
Measuring intrinsic and extrinsic noise
N
kkk PP
NP
1
)2()1(2 1
Swain 2002
Measuring intrinsic and extrinsic noise
Simultaneously measure the expression levels of two copies of a single gene, controlled by the same promoter.
Elowitz 2002
Measuring intrinsic and extrinsic noise
Elowitz 2002
Controlling noise
• Noise can hamper the precision of decision making by a cell.
• Noise can be controlled by using negative feedback loops.
• Essential genes are less noisy than other genes, suggestive of selection pressure.
A B
A
B t
t
Benefit of noise
• Noise can diversify phenotypic responses.
• Different pheontypes may be adapted for different environmental conditions.
• Population diversity can help the population to survive as a whole.
Alternative ways to adapt to environmental changes
Leibler 2005
Noise-induced drug resistance
Balaban 2004
Noise-induced drug resistance
Observation
• No mutation is identified.
• “Resistant” cells can be further killed by antibiotics.
Balaban 2004
Noise-induced drug resistance
Observation
• No mutation is identified.
• “Resistant” cells can be further killed by antibiotics.
Explanation
• Genetically identical cells have different responses to environment due to noise.
• A subpopulation of cells “persisters” escape the antibiotics by initiating the “right” response.
Balaban 2004
Bistability
Veening 2006
• Gene activities can be regulated by on-off switches.
• Large-scale continuous response can be due to change of proportions of responsive cells.
Bistability
• Bistability is characterized by bimodal distribution.
• Single stable state corresponds to a unimodal distribution.
Veening 2006
Positive feedback loops and bistability
A B
A
B
t
t
Positive feedback loops and bistability
A B
A
B
t
t
Ordinary differential equations
pyyfdt
d,, ),( 1 yy
y
y
t
)(tyy
Ordinary differential equations
),(
),(
212
211
yygdt
dy
yyfdt
dy
y1
t
y2
y1
phase diagram
Steady states
y2
y1
0),(
0),(
212
211
yygdt
dy
yyfdt
dy*22
*11 , yyyy
Steady states
y2
y1
0),(
0),(
212
211
yygdt
dy
yyfdt
dy*22
*11 , yyyy
unstable y2
y1
stable
Bistability
0),(
0),(
212
211
yygdt
dy
yyfdt
dyy2
y1
Modeling positive feedback loops
dBcAdt
dB
bBaAdt
dA
A B
The positive feedback loops can be modeled by ODEs
dBcAdt
dB
bBaAdt
dA
A B
)exp()exp()(
)exp()exp()(
2211
2211
tttB
tttA
The solution is
The only possible stable states are 0 and infinity. Therefore, nonlinear models are required to model bistability.
Modeling positive feedback loops
Ferrell & Xiong 2001
Single stable steady states in simple Michaelis-Menen systems
Ferrell & Xiong 2001
Ferrell & Xiong 2001
Hysterisis
Ferrell & Xiong 2001
Readling List
• Elowitz et al. 2002– Defined intrinsic and extrinsic noise
• Balaban et al. 2004– Noise-induced drug resistance
• Ferrell and Xiong 2001– Introduction to bistability
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