Using Formal Models For Analysis Of Biological Pathways
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The document discusses the application of formal models in analyzing biological pathways, specifically focusing on the EGF-NGF and Akt signaling pathways. It outlines methods such as ODEs, stochastic approaches, and Petri nets for modeling complex interactions and emphasizes the importance of model fitting and parameter estimation for accurate biological predictions. Additionally, it highlights future directions for integrating molecular information with experimental data to enhance understanding of biological systems.
![Mass action law
V1
S1 + S2 2P
V2
dP = k1. [S1] [S2] – k2 [P]2
Unknown!
(can be known in vitro with these molecules only,
but in the cell/in a cell population different)
+ no close form solutions: Simulate ODE by taking small time step
9](https://image.slidesharecdn.com/20120521-usingformalmodelsforanalysisofbiologicalpathways-120524205415-phpapp02/85/Using-Formal-Models-For-Analysis-Of-Biological-Pathways-9-320.jpg)
![Dynamic Bayesian Network (DBN)
ODE DBN
……. Et Et+1 Et+2
dS
= −k1.S .E + k 2 .ES …….
dt St+2
St St+1
dE
= −k1.S .E + (k 2 + k3 ).ES
dt
ESt ESt+1 ESt+2
dES
= k1.S .E − (k 2 + k3 ).ES
dt
dP ……. Pt Pt+1 Pt+2
…….
= k3 .ES
dt t t+1 t+2
Liu.et.al [ TCS 2011]
• Discretize time domain into finite time points
• Discretize the value domain of each species
=> Probability distribution
13](https://image.slidesharecdn.com/20120521-usingformalmodelsforanalysisofbiologicalpathways-120524205415-phpapp02/85/Using-Formal-Models-For-Analysis-Of-Biological-Pathways-13-320.jpg)
Using Formal Models For Analysis Of Biological Pathways
- 1. Using formal models in analysis of Biological Pathways Prof. P.S. Thiagarajan NUS Liu Bing and S. Akshay Postdocs NUS Sucheendra Palaniappan PhD student NUS Subra Biswas and Alexandre Gouaillard BMRC Blaise Genest CNRS Bruno Karelovic CNRS Master student
- 2. Studying Pathway dynamics Methods: ODEs , Stochastic approaches, Petri Net… 2
- 4. EGF-NGF Pathway as ODEs ODE (differential equations) for « Smooth » behaviors (enough reactants or enough cells) 4
- 5. Akt Signaling Pathway Growth Factors Bcl-2 will factors then Phosphorylated will bind Akt and PDK will AKT will Activated PI3K will PI3K will then get then Growth then dimerize with besurface receptors then Bax at to into cellto translocate Mitochondrial phosphorylate membrane recruited to the to cell freedthePIP2 cytoplasm where it is membrane,where Akt membrane activated PIP3 it is preventing where P phosphorylate Bad apoptosis phosphorylated PI3K P PIP2 P P P GTP P Ras Akt P21 P Activated - Kinase Interaction of Phosphatase PI3K Raf1 Raf1 and Inhibitors such as LYAkt P P MEK MEK PDK1 P P ERK Bax ERK P Bax Bad Na+/H+ Exchangers Bad Bad P Bad Bcl-2 Bcl-2 Mitochondria Growth Factors can also activate the MAPK pathway at the same time 5
- 6. What we want to obtain: 6
- 7. What Biologists have and want Have: Hypothesised diagram of interactions (see previous slide) Want: Is it correct (enough)? Have: Some (few, noisy) data for concentration of some species at some (few,noisy) time point + some (few, noisy) rates of reactions. 0.6 0.4 Concentration of 1 molecule over time, with 3 data points 0.2 0.0 1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 Want: model fitting experiments
- 8. What Biologists want Want: if model correct, in silico predictions Reaction 2 and 5 blocked In silico model computations 0.6 0.4 0.2 Interesting? Do wet lab experiments, with drugs 0.0 blocking reaction 2 and 5 to confirm 1 8 15 22 29 36 43 50 57 64 71 78 85 92 99
- 9. Mass action law V1 S1 + S2 2P V2 dP = k1. [S1] [S2] – k2 [P]2 Unknown! (can be known in vitro with these molecules only, but in the cell/in a cell population different) + no close form solutions: Simulate ODE by taking small time step 9
- 10. Determining Parameter Values Experimental measurements Expensive Not possible to measure all the parameters In vitro measurements may not reflect the actual physiological conditions in the cell (Minton, 2001) Cell population-based measurements are not very accurate +Noisy (Kim & Price, 2010) Akt* 10
- 11. Parameter Estimation Goal: Find values of parameter so that model prediction generated by simulations using these values can match experimental data krbNGF = 0.33, KmAkt = 0.16, kpRaf1 = 0.42 … … target krbNGF = 0.49, KmAkt = 0.08, kpRaf1 = 0.97 … … krbNGF = 0.88, KmAkt = 0.21, kpRaf1 = 0.05 … … Time 11
- 12. Global Methods Evolutionary strategy Genetic algorithm Simulated annealing Particle swarm optimization 12
- 13. Dynamic Bayesian Network (DBN) ODE DBN ……. Et Et+1 Et+2 dS = −k1.S .E + k 2 .ES ……. dt St+2 St St+1 dE = −k1.S .E + (k 2 + k3 ).ES dt ESt ESt+1 ESt+2 dES = k1.S .E − (k 2 + k3 ).ES dt dP ……. Pt Pt+1 Pt+2 ……. = k3 .ES dt t t+1 t+2 Liu.et.al [ TCS 2011] • Discretize time domain into finite time points • Discretize the value domain of each species => Probability distribution 13
- 14. Validation of the DBN wrt. ODE (Contd) 2.7 1.5 pJAK2 pEpoR 1.8 1 0.9 0.5 0 0 1 21 41 61 81 1 21 41 61 81 actSHP1 mSHP1 12 3.6 8 2.4 4 1.2 0 1 21 41 61 81 0 1 21 41 61 81 14
- 15. Semantics of DBN E0 E1 E2 ……… Et-1 Et S0 S1 S2 ……… St-1 St Exponential Complexity ……… ES0 ES1 ES2 Est-1 ESt ……… P0 P1 P2 Pt-1 Pt 15 Joint at time t-1
- 16. Pathway Decomposition Decomposition: Akt/MAPK Pathway Decompositional approach Treat components one by one in order to feed the computation to next steps. But: seldom all theoretically valid fragments are small enough => resort to approximation to find not so bad experimental decomposition (Bruno’s work) HFPN model of the Akt / MAPK pathway (Koh et al 2006) 16
- 17. Pathway Decomposition Decomposition Approximate probability distributions in 2 different ways. Best: 2sd way is “more exact” (that we have). Assume the similar approx distributions to be the exact ones If none, 2 “better” approximations. Delete the similar approx and decompose again (less constraints)… 17
- 18. Conclusion • Formal models can be helpful in bioinformatics: Compact representation Structurally decompose pathway in pieces. Error Analysis … High dimension: we need approximations, be pragmatic => be optimistic! Believe the fastest will work. (ODE vs Gillpesie, FF vs HFF vs exact etc) => then validation to be sure we don’t do nonsense. => if we do nonsense, then work more.
- 19. Problem: Size = 5^32 states ⇒ Resort to approximated computation and representation. Ususally: Factored Frontier (FF): all species independant. New: Hybrid FF, between FF and exact
- 20. Biological Applications TLR4 signalling pathway with new components. Important pathway for the Human immune system Involved in Sepsis (complex disease, characterized by whole-body inflammatory response) Collaboration with A*STAR/SiGN (Biopolis) (Groups of Subra Biswas and of Alexandre Gouaillard)
- 21. Future? Medical image not always sufficient to detect accurately pathology Multimode analysis (tissular, molecular) Image not always conclusive Molecular information not always sufficient ⇒ Add molecular information => may need number of cells with some form, multi modal analysis
- 22. Near Future? In between: population of cells Experimental data = image analysis Modeling: local forces (cellular automata) + biochemical reactions (apopthosis = death of cells) + cell division With P.S. Thiagarajan (NUS) and Gregory Batt (INRIA Rocquencourt)
- 23. Akt-MAPK Pathway as a Petri Net Serum R 1 Ract For discrete behaviors DPI 46 NOX5 Rint (few molecules in a cell, ROS 3 LY294002 2 need to count them 1 by 1) 47 Ras 15 Rasa Pak 48 Pakp PI3K 4 PI3Ka 16 49 5 Leads to stochastic behaviors 17 18 PIP2 6 PIP3 AKTcyto PTEN 7 (each cell can evolve in 2 Raf Rafp 19 20 PDK1cyto 50 8 9 different ways at random) 21 22 24 25 51 PDK1 PDK2 PIP3.AKT 10 MEK MEKp MEKpp PIP3.AKTp 23 26 12 11 13 27 29 PIP3.AKTpp 14 ERK ERKp ERKpp PP2A Ex: pathogene 28 30 34 35 37 38 evading host response) Badp112 Badp136 Bax 40 Baxcyto MKP3 Bad 31 32 36 39 41 Bcl2.Bax 42 44 P90RSK 33 P90RSKp Bcl2.Bad 43 45 Bcl2 23