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

our photo & introduction

Outline

Backgrounds The lactose utilization network Deterministic model Deterministic model & Noise Stochastic model The lactose utilization network + lactose metabolism

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.

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

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.

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

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.

Our results

Theoretical phase diagram

Model analysis

Model analysis & Add noise

Stochastic model & Gillespie algorithm

Stochastic model & Gillespie algorithm

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)

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)

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:

The lactose utilization network + lactose metabolism

phase diagram

Conclusion

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.

Thanks for your listening!