Noise and Bistability 12/10/07. Noisy gene expression at single cell level Elowitz 2002.

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

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

Measuring intrinsic and extrinsic noise

N

kkk PP

NP

1

)2()1(2 1

Swain 2002


Simultaneously measure the expression levels of two copies of a single gene, controlled by the same promoter.

Elowitz 2002


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


Observation

• No mutation is identified.

• “Resistant” cells can be further killed by antibiotics.

Balaban 2004


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

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


Hysterisis


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

Noise and Bistability 12/10/07. Noisy gene expression at single cell level Elowitz 2002.

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