Multistability in the lactose utilization network of Escherichia coli
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Transcript of Multistability in the lactose utilization network of Escherichia coli
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Multistability in the lactose utilization network of Escherichia coli
Advisors: Tang Leihan & Namiko Mitarai
Group two members:
He Xiaojuan Bi Hongjie Wang Peng
Wang Jinshui Li Xiang Li Mengyao
Zheng Muhua Jiang Chongming
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our photo & introduction
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Outline
Backgrounds The lactose utilization network Deterministic model Deterministic model & Noise Stochastic model The lactose utilization network + lactose metabolism
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Backgrounds:
Regulatory network: regulatory system that consists of a collection of nodes, pairs of which are connected by links.
Feedback loops: a cyclic chain of links in a regulatory network. Positive feedback loops: self-activation or double negative
feedback. Multistability: the capacity to achieve multiple internal states
in response to a single set of external inputs. Biological switch: cell fate, cell-cycle oscillations.
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The lactose utilization networkTwo external inputs: Glucose & TMG(thio-methylgalactoside)TMG: a non-metabolizable lactose analogue.
Red lines: regulatory interactions.Black arrows: protein creation through transcription and translation.Dotted arrows: uptake process
Operon: promoter + expressible genes
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The lactose utilization network and reportor system
GFP: green fluorescent protein, expressed at the lac promoter. HcRed: red fluorescent protein,expressed at the gat promoter.
LacY catalyses the uptake of TMG, which induces further expression of LacY, resulting in a positive feedback.
Bi-stability !!!Two transcriptional regulators:LacI: a repressor.CRP: an activator.
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Experimental results:
b. Behavior of a large cell population c. The phase diagram describing the state of the lactose utilization network in wild-type cells
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Deterministic model
ρ: dissociation constant of LacI from its main DNA-binding site.
ρ=1+RT/R0 : describes how tightly LacI is able to regulate the expression of the lac operon.
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Our results
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Theoretical phase diagram
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Model analysis
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Model analysis & Add noise
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Stochastic model & Gillespie algorithm
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Stochastic model & Gillespie algorithm
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The lactose utilization network + lactose metabolism
2
0
)(1
1
wwR
R
T
(S2)
(S3)
(S4)
(S5)
Lactose
Lactose (x)
Allolactose (w)
LacI
Plac
LacZ (z)
LacY (y)
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The lactose utilization network + lactose metabolism
τ ydydt
= αw2 +1w2 + ρ
− y
simplified model: Lactose
Lactose (x)
Allolactose (w)
LacI
Plac
LacZ (z)
LacY (y)
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The lactose utilization network + lactose metabolism
steady state:
)1()(1
2
2
wwwx
2
2 1wwy
]1)11)[(()1( 2222
wwww
Analyze the third equation, and let: 22 )1()( wwf ]1)11)[(()( 22
wwwwg
;0)(,)1(4)( '2' wfwwwf
;0)(),()11(2]1)11)[((3)( '2222' wgwwwwwg
We find:
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The lactose utilization network + lactose metabolism
phase diagram
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Conclusion
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References:
Ertugrul M. Ozbudak, Mukund Thattai, Han N. Lim,Boris I. Shraiman & Alexander van Oudenaarden. 2004. Multistability in the lactose utilization network of Escherichia coli.
Kim Sneppen, Sandeep Krishna, and Szabolcs Semsey. 2010. Simplified models of biological networks.
Danlel T. Gillespie. 1977. Exact stochastic simulation of coupled chemical reactions.
Michael B. Elowitz et al. 2002. Stochastic gene expression in a single cell. Jerome T. Mettetal, Dale Muzzey, Juan M. Pedraza, Ertugrul M. Ozbudak, and
Alexander van Oudenaarden. Predicting stochastic gene expression dynamics in single cells.
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Thanks for your listening!