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Extracting Essential Features of Biological Networks

Extracting Essential Features of Biological Networks. Natalie Arkus, Michael P. Brenner. School of Engineering and Applied Sciences Harvard University. Model. Empirical System. Biological System. Explanations. Predictions. Biological System. Model. B. A. B. A.

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Extracting Essential Features of Biological Networks

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  1. Extracting Essential Features of Biological Networks Natalie Arkus, Michael P. Brenner School of Engineering and Applied Sciences Harvard University

  2. Model Empirical System Biological System Explanations Predictions

  3. Biological System Model B A B A

  4. Nerve growth factor signaling Importin nuclear protein import Map Kinase Pathway p53 Pathway Courtesy of http://www.london-nano.com, Guillaume Charras

  5. Biological System Model B A B A

  6. Biological System Complicated Model X Explanations Predictions ? Analysis? B A • Many nonlinear coupled equations → can’t solve analytically • Many unknown parameters → many possible solutions B = f(A) Current Methods • Numerical simulation not falsifiable!

  7. X Current Methods: Another Option Biological System Complicated Model Simple Model Explanations! Predictions! Input Output

  8. A C B Knowingly ignores biology Can be fully analyzed Captures everything Too complicated to fully analyze

  9. Courtesy of BB310 Molecular Genetics Webpage from strath.ac.uk ? Simple Model Biological System Complicated Model math Explanations Predictions e. Coli heat shock response system El Samad et al., PNAS, 102, 2736 (2005) What is the role of feedback loops in heat shock response?

  10. Courtesy of BB310 Molecular Genetics Webpage from strath.ac.uk Heat Shock Response (HSR): Proteins unfold/misfold and malfunction σ32 is upregulated Heat shock gene (hsg) transcription ↑ Heat shock proteins (hsp’s) Ex. DnaK, FtsH Refold and degrade unfolded proteins

  11. Feedback Loop: DnaK (chaperone) sequestersσ32 (transcription factor) → decreases rate of hsg transcription

  12. Another Feedback Loop: Proteases (FtsH, HslVU) degradeσ32 (transcription factor) → decreases rate of hsg transcription

  13. 1st Feedback Loop 2nd Feedback Loop El Samad et al., PNAS, 102, 2736 (2005) Differential Equations = ODEs Algebraic Equations = AEs They reduced these systems a priori by assuming that all binding reactions were fast • 2 feedback loop model • 23 ODEs, 8 AEs, 60 parameters • 2) 1 feedback loop model • 14 ODEs, 5 AEs, 39 parameters • 3) 0 feedback loop model • 13 ODEs, 5 AEs, 37 parameters → 11 ODEs, 20 AEs, 48 parameters → 5 ODEs, 14 AEs, 33 parameters → 5 ODEs, 13 AEs, 32 parameters

  14. What is the response time? • How do feedback loops ([σ32:DnaK], [FtsHt],…) effect the response time? Can ask such questions… but are not equipped to answer such questions…

  15. Differential Equations (ODEs) Reduction Method: Algebraic Equations (AEs) 1) Separation of scales → Reduction in the # of differential equations ≈ 0 2)Dominant Balance Let us focus on 1 feedback loop model as an example… 3)

  16. 1Feedback Loop Model Transcription & Translation Equations Mass Balance (Conservation) Equations Algebraic Binding Equations

  17. Reduction Method 1) Separation of scales → Reduction in the # of differential equations ≈ 0 2)Dominant Balance 3)

  18. Look for a separation of time scales: Transcription & Translation Equations 0.5 Only 1 slow variable! 0.03 0.5 1.4 ~100

  19. Temperature upshift Temperature upshift → 1 ODE, 18 AEs, 29 parameters

  20. 1) Separation of scales → Reduction in the # of differential equations Reduction Method ≈ 0 2)Dominant Balance 3)

  21. Solving Algebraic Components Algebraic System:

  22. One Example → σ32 sequestration hardly effects DnaKf levels!

  23. X X

  24. 1) Separation of scales → Reduction in the # of differential equations Reduction Method ≈ 0 2)Dominant Balance 3)

  25. . . (after many dominant balances) .

  26. ✓ With reduced system, are equipped to answer questions of interest… • How do feedback loops ([σ32:DnaK], [FtsHt],…) effect the response time?

  27. Reduced Model for all Feedback Loops: Effect of 1st feedback loop Effect of 2 feedback loops

  28. Simple Model Biological System Complicated Model math Explanations Predictions

  29. What Sets the Time of Heat Shock Response? Temperature upshift El Samad et al.'s conclusion: Response time decreases as number of feedback loops increase. Is response time feedback- or parameter-dependent?

  30. Response time set by when [DnaKt] = 1.9*10^4 High [DnaKt] Limit: Low [DnaKt] Limit: (using linear [DnaKf] approximation) Response of folded proteins is a feedback-loop independent property

  31. Reduced Model for all Feedback Loops: Degradation Term Production Term A = effect of 0F loop B = effect of 1F loop C = combined effect of 1F and 2F loops B > 0 → smaller production term → slower response time C > 0 → smaller production term → slower response time Feedback loops → slower response time How can the response time decrease with additional feedback loops?

  32. Changes in Network Topology and Parameter Values Cause Models with More Feedback Loops to Respond Faster For the same value of A, feedback loops  slower response time However, the topology of the σ32t equation changes in the 2 feedback loop model  a different expression for the effective parameter A (the 0F term) in the 2 feedback loop model Will be encompassed within C

  33. Parameter changes across the feedback loop models Translation of [mRNA(DnaK)] Degradation of [σ32] Effect of parameter changes is unclear in full model

  34. Effect of Parameter Changes Is Apparent in Reduced Model Reduced Model for all Feedback Loops: 0 feedback loop: 1 feedback loop: 2 feedback loop:

  35. * *

  36. If is the same over the 3 feedback loop models and in a certain parameter regime  1 and 0 feedback loop models respond quicker.

  37. Constructing Reduced Models Allows One to Extract Essential Biological Components Here, the effect of topology and parameters were decoupled And it was shown, for example, that response time is a parameter dependent and not a feedback loop dependent property Is this system special, were we just lucky?

  38. System Is Not Special… Wnt signaling pathway (Protein network involved in embryogenesis and cancer) Lee et al, PLoS Biology, 1, 116 (2003)

  39. Curves a-d: Curve d:

  40. Conclusions Courtesy of BB310 Molecular Genetics Webpage from strath.ac.uk • simple models with all relevant biological components • Back and forth with experiments testable, falsifiable! 31 equations  1 equation 14 equations  3 equations Yeast Cell Cycle (Tyson et al, 2004) 62 equations  17 equations

  41. Future Directions f(dimenionless parameters) ? { Reduced Model 1, …} Reduced Model 2, Reduced Model 3,

  42. Courtesy of cancerworld.org Can we explain a biological system in a way that experiments alone can not?

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