Stochastic Analysis of Bi-stability in Mixed Feedback Loops Yishai Shimoni, Hebrew University CCS Open Day Sep 18 th 2008

An Integrated Network A feedback loop consists of two genes that regulate each other’s expression In a Mixed Feedback Loop (MFL) each gene uses a different mechanism for the regulation

Small RNAs (sRNAs) ‏ Non-coding RNA molecules Non-coding RNA molecules nucleotides long nucleotides long Base-pairs with mRNAs and influences translation (normally repression) Base-pairs with mRNAs and influences translation (normally repression) Approximately 100 sRNAs identified in E. coli Approximately 100 sRNAs identified in E. coli Participate mostly in stress responses due to fast synthesis Participate mostly in stress responses due to fast synthesis

Double Negative Mixed Feedback Loop (MFL) Time (sec x 10 5 )‏ Bi-stability Time (sec x 10 4 )‏ Meta-stability A B s A

Double Negative MFL

Questions: Questions: How much of the parameter range displays a meta- stable state? How much of the parameter range displays a meta- stable state? Does this happen with protein-protein interactions as well? Does this happen with protein-protein interactions as well? What is the difference? What is the difference? Run the Monte Carlo simulation with different parameters and check if the state (A dominated or s/B dominated) changes during a given time Run the Monte Carlo simulation with different parameters and check if the state (A dominated or s/B dominated) changes during a given time

Double Negative MFL Phase Map of bi-stability in sRNA double negative MFL

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

Double Negative MFL Conclusion: Conclusion: Stochastic analysis reveals a new dynamic behavior Stochastic analysis reveals a new dynamic behavior Cannot be seen using deterministic analysis Cannot be seen using deterministic analysis Quantitative difference between MFLs with sRNA regulation and MFLs with protein-protein interaction Quantitative difference between MFLs with sRNA regulation and MFLs with protein-protein interaction Both have same qualitative dynamics Both have same qualitative dynamics Do simulations fit reality? Do simulations fit reality?

Fur-RyhB MFL in E. Coli In the presence of iron Fur represses RyhB transcription Iron depletion: Iron depletion: Fur does not repress RyhB Fur does not repress RyhB RyhB highly expressed RyhB highly expressed RyhB Regulates many iron uptake genes RyhB Regulates many iron uptake genes

Fur-RyhB MFL in E. Coli Bi-stability is unsuitable Bi-stability is unsuitable Time (sec x )‏ Time (sec x )‏ A meta-stable state is perfect! A meta-stable state is perfect! RyhB Fur RyhB Fur

Summary Post transcriptional regulation by sRNA Post transcriptional regulation by sRNA Offers different dynamics than other kinds of regulation Offers different dynamics than other kinds of regulation The dynamics are utilized by the cell The dynamics are utilized by the cell Mathematical Models using stochastic analysis can capture important features of the dynamics of biological networks Mathematical Models using stochastic analysis can capture important features of the dynamics of biological networks

Acknowledgements Modeling: Modeling: Prof. Ofer Biham Prof. Ofer Biham Adiel Loinger Adiel Loinger Guy Hetzroni Guy Hetzroni Networks integration, circuit identification: Networks integration, circuit identification: Prof. Hanah Margalit Prof. Hanah Margalit Dr. Gilgi Friedlander Dr. Gilgi Friedlander Gali Niv Gali Niv Parameters and sRNA: Parameters and sRNA: Prof. Shoshy Altuvia Prof. Shoshy Altuvia Y. Shimoni et. Al, submitted to PLoS Comp Biol

Small RNAs (sRNAs) ‏ Normally act as repressors by blocking the ribosomal binding site Normally act as repressors by blocking the ribosomal binding site S. Altuvia and E.G. Wagner, PNAS (2000); 97(18)

Experiments and Models Experiment Dynamics Interactions Model Dynamics Experiment

The known sRNA network in E. Coli

Ranges of Parameters All rates are 1/sec All rates are 1/sec mRNA transcription initiation 1/100– 1/2 mRNA transcription initiation 1/100– 1/2 sRNA transcription initiation 1/10– 5 sRNA transcription initiation 1/10– 5 Protein translation initiation 1/100– 1/2 Protein translation initiation 1/100– 1/2 Protein complex formation 1/2000– 1/20 Protein complex formation 1/2000– 1/20 sRNA-mRNA complex formation 1/2000– 1/40 sRNA-mRNA complex formation 1/2000– 1/40 Protein binding to DNA 1/200– 1/4 Protein binding to DNA 1/200– 1/4 Protein dissociating from DNA 1/1000– 1/20 Protein dissociating from DNA 1/1000– 1/20 mRNA degradation 1/500– 1/20 mRNA degradation 1/500– 1/20 sRNA degradation 1/3000– 1/200 sRNA degradation 1/3000– 1/200 Protein degradation 1/1000– 1/20 Protein degradation 1/1000– 1/20

Rate Equations Rate (mass action) equations: Rate (mass action) equations: Dynamics of the average concentration Dynamics of the average concentration Assumes large concentrations Assumes large concentrations s m

Master Equations transcription binding degradation (m,s) (m-1,s) (m+1,s) (m,s+1)(m,s-1) (m-1,s-1) (m+1,s+1)

Master and Rate Equations Averaging transcription binding degradation

Mixed Interaction Network