Stochastic Analysis Stochastic Analysis of of

Bi-stability in Bi-stability in Mixed Feedback Mixed Feedback

LoopsLoopsYishai Shimoni, Hebrew Yishai Shimoni, Hebrew UniversityUniversity

CCS Open DayCCS Open Day

Sep 18Sep 18thth 2008 2008

An Integrated NetworkAn Integrated Network

A feedback loop consists of two genes that A feedback loop consists of two genes that regulate each other’s expressionregulate each other’s expression

In a Mixed Feedback Loop (MFL) each In a Mixed Feedback Loop (MFL) each gene uses a different mechanism for the gene uses a different mechanism for the regulationregulation

Small RNAs (sRNAs)Small RNAs (sRNAs)

Non-coding RNA moleculesNon-coding RNA molecules 50-400 nucleotides long50-400 nucleotides long Base-pairs with mRNAs and Base-pairs with mRNAs and

influences translation (normally influences translation (normally repression)repression)

Approximately 100 sRNAs identified Approximately 100 sRNAs identified in in E. coliE. coli

Participate mostly in stress responses Participate mostly in stress responses due to fast synthesisdue to fast synthesis

Double Negative Double Negative Mixed Feedback Loop Mixed Feedback Loop

(MFL)(MFL)

Time (sec x 105)

Bi-stability

Time (sec x 104)

Meta-stability

A

B

s

A

Double Negative MFLDouble Negative MFL

Double Negative MFLDouble Negative MFL

Double Negative MFLDouble Negative MFL

Questions:Questions: How much of the parameter range How much of the parameter range

displays a meta-stable state?displays a meta-stable state? Does this happen with protein-protein Does this happen with protein-protein

interactions as well?interactions as well? What is the difference?What is the difference?

Run the Monte Carlo simulation with Run the Monte Carlo simulation with different parameters and check if the different parameters and check if the state (A dominated or s/B dominated) state (A dominated or s/B dominated) changes during a given timechanges during a given time

Double Negative MFLDouble Negative MFL

Phase Map of bi-stability in sRNA double negative MFL

Double Negative MFLDouble Negative MFL

Phase Map of bi-stability in protein-protein double negative MFL

Double Negative MFLDouble Negative MFL

Conclusion:Conclusion: Stochastic analysis reveals a new dynamic Stochastic analysis reveals a new dynamic

behaviorbehavior Cannot be seen using deterministic Cannot be seen using deterministic

analysisanalysis Quantitative difference between MFLs Quantitative difference between MFLs

with sRNA regulation and MFLs with with sRNA regulation and MFLs with protein-protein interactionprotein-protein interaction

Both have same qualitative dynamicsBoth have same qualitative dynamics Do simulations fit reality?Do simulations fit reality?

Fur-RyhB MFL in Fur-RyhB MFL in E. ColiE. Coli

In the presence of In the presence of iron Fur represses iron Fur represses RyhB transcriptionRyhB transcription

Iron depletion:Iron depletion: Fur does not repress Fur does not repress

RyhBRyhB RyhB highly expressedRyhB highly expressed RyhB Regulates many RyhB Regulates many

iron uptake genesiron uptake genes

Fur-RyhB MFL in Fur-RyhB MFL in E. ColiE. Coli

Bi-stability is Bi-stability is unsuitableunsuitable

Time (sec x 10-5)

Time (sec x 10-4)

A meta-stable A meta-stable state is perfect!state is perfect!

RyhB

Fur

RyhB

Fur

SummarySummary

Post transcriptional regulation by Post transcriptional regulation by sRNAsRNA Offers different dynamics than other Offers different dynamics than other

kinds of regulationkinds of regulation The dynamics are utilized by the cellThe dynamics are utilized by the cell

Mathematical Models using Mathematical Models using stochastic analysisstochastic analysis can capture can capture important featuresimportant features of the dynamics of the dynamics of biological networksof biological networks

AcknowledgementsAcknowledgements Modeling:Modeling:

Prof. Ofer BihamProf. Ofer Biham Adiel LoingerAdiel Loinger Guy HetzroniGuy Hetzroni

Networks integration, Networks integration, circuit identification:circuit identification: Prof. Hanah MargalitProf. Hanah Margalit Dr. Gilgi FriedlanderDr. Gilgi Friedlander Gali NivGali Niv

Parameters and Parameters and sRNA:sRNA: Prof. Shoshy AltuviaProf. Shoshy Altuvia

Y. Shimoni et. Al, submitted to PLoS Comp Biol