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Ronald L. Westra Systems Theory Group Department Mathematics Maastricht University

Systems Theoretical Modelling of Genetic Pathways. Ronald L. Westra Systems Theory Group Department Mathematics Maastricht University. Dynamic Genetic Pathways. What is a Genetic Pathway Static versus dynamic view on Genetic Pathway Modelling Genetic Pathway

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Ronald L. Westra Systems Theory Group Department Mathematics Maastricht University

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  1. Systems Theoretical Modelling of Genetic Pathways Ronald L. Westra Systems Theory Group Department Mathematics Maastricht University

  2. Dynamic Genetic Pathways What is a Genetic Pathway Static versus dynamic view on Genetic Pathway Modelling Genetic Pathway  Some approaches to modelling dynamic pathways Framework for System Theoretic Approach

  3. Genetic Pathway Network of those genes that are connected by causal relations in their expressions Input: few microarray data of gene expression as function of some experiments Implicit assumption of convergent behaviour

  4. Static Genetic Pathways Start with isolated microarray data Reconstruct causal relations with conditional probability models, e.g.: Bayesian belief networks Bootstrap methods

  5. Reconstruction of Genetic Pathway Microarray experiments Gene expression data Exp1 Exp2 Exp3 Exp4 Gen1 1.8 -0.2 1.7 -0.4 Gen2 -1.1 -1.9 1.0 1.6 Gen3 0.4 1.3 -1.3 -1.8 Gen4 -0.1 -0.2 -0.4 -0.6 Gen5 1.6 0.5 1.7 1.3 Gen6 1.0 1.2 1.7 -2.0

  6. G1 G2 G6 G3 G4 G5 Reconstructed Genetic Pathway

  7. Problems with Genetic Pathways Equilibrium: * oscillation (N-cycle) * punctuated (intermitted stasis) Non-equilibrium: * pulse reaction * growth Chaotic: * carcinogenesis

  8. Problems with Genetic Pathways Emergent and complex behaviour Cooperative behaviour due to multigene interaction upward complexity

  9. Problems with Genetic Pathways In vivo the expression of a specific gene varies over time Moreover a gene can be expressed because: being expressed is its default value it is part of another active pathway

  10. What exactly represents the measured value of gene expression Gene expression measured at: * certain moment: sampling * during some time: averaging

  11. Conclusion: Genetic Pathways are Dynamic Systems

  12. What happens in a Genetic pathway ? cause at t = 0: x1: degree of expression ofG1 G1 j1: strength of proteine current Pr1 Pr1 Biochemical Environment Pr2 G2 j2: strength of proteine current Pr2 result at t = T: x2: degree of expression ofG2

  13. Dynamic Genetic Pathways Example of dynamic GP in non-equilibrium is during growth Model is the regulation of the Endo16 gene in sea urchin (Strongylocentrotis purpuratus) Eric H. Davidson, C-H Yu, Caltech (http://www.its.caltech.edu)

  14. Dynamic Genetic Pathways Place of Endo16 in Sea urchin genome map

  15. Dynamic Genetic Pathways Sea urchin -Endo16 related gene and gene products expressions

  16. Dynamic Genetic Pathways Circuit diagram for Endo16 transcription

  17. Dynamic Genetic Pathways Decision rules for Endo16 Dynamics

  18. Modelling Dynamic Genetic Pathways The if-then modelling by Davidson and Yuh is efficient but phenomenological Can we provide deep models for dynamic gene networks?

  19. Modelling Dynamic Genetic Pathways Upinder Bhalla (National Center Biological Sciences, India) and Ravi Iyengar (Mount Sinai school of Medicine, New York) : neural networks Kurt Kohn (National Cancer Institute, Bethesda, USA): electrical circuits

  20. Modelling Dynamic Genetic Pathways Upinder Bhalla (National Center Biological Sciences, India) and Ravi Iyengar (Mount Sinai school of Medicine, New York) : neural networks

  21. Modelling Dynamic Genetic Pathways

  22. Bahalla and Iyengar used 15 genetic circuits in their model

  23. Bahalla and Iyengar used GENESIS neural network simulator to model 15 genetic circuits • Validation of model on a testset: • open: neural network simulation • filled: real data

  24. Bhalla, Iyengar Approach conclusion: Modelling DGP as neural network provides good fit, but : * model can be sub-optimal * each new case must be trained separately * black-box, no deep model

  25. Modelling Dynamic Genetic Pathways Kurt Kohn (National Cancer Institute, Bethesda, USA): electrical circuits

  26. Gene networks as electric logic circuits

  27. Gene networks as electric logic circuits

  28. Gene control clock

  29. Gene control clock

  30. Modelling Dynamic Genetic Pathways Systems Theory:compartimental time- delayed dynamical system

  31. cause at t = 0: x1: degree of expression ofG1 G1 j1: strength of proteine current Pr1 Pr1 Biochemical Environment Pr2 G2 j2: strength of proteine current Pr2 result at t = T: x2: degree of expression ofG2 Modelling Dynamic Genetic Pathways

  32. Modelling Dynamic Genetic Pathways xk = Present expression of gene k . It results from past expressions of – potentially all – other geneswith certain transfer function Gand parameters q (time delay, coupling strength, threshold)

  33. Modelling Dynamic Genetic Pathways Several problems e.g. : how to model the environment? Transfer-function – parameter set Input (in case of external agent, eg toxic)

  34. Modelling Dynamic Genetic Pathways Basic model: xk = expression of gene k uk = external inputs (eg toxic agents) yk = observable output (eg proteine) nk = noise q = parameter set(time delay, coupling strength, threshold)

  35. -0.71 G1 G2 +0.36 +0.48 +0.27 +1.03 -0.18 +0.19 G6 G3 G4 +0.75 -0.84 +0.23 G5 Modelling Dynamic Genetic Pathways GP as directed and weighted graph

  36. Use of System Model Validate “known” Genetic pathway Calculate relevant constants as gene-gene-coupling parameters, relative thresholds, effective time-delays Qualitatively “explain” observed complex behaviour from the model Reconstruct genetic pathways from individual dynamic gene-expressions

  37. Bilinear Systems Approach approach 1 : Linear autoregression ARX approach 2 : subspace identification N4SID

  38. Experimental Data model for a dynamic genetic pathway : induction of multiple gene expression changes in the human hepatoma HepG2 cell line by the established human carcinogen benzo(a)pyrene. 2 series measurement each 5 minutes during 120 minutes Ma costs ~50*600 euro : 30.000 euro

  39. Preliminary Results Cross validation of specific gene expression

  40. Conclusions Genetic Pathways are dynamic systems In vivo micro array measurement can be obscured by dynamic behaviour of gene expression Modelling of DGP with NN results in black box Modelling of DGP with electrical circuits is successful but only in forward direction Modelling with Systems Identification approach allows for forward and backward modelling Modelling with Systems Identification approach allows for reconstruction of GP from dynamical data Disadvantage: many measurements necessary, sensitive to hidden parameters and missing values

  41. Ronald L. Westra Systems Theory Group Department Mathematics Maastricht University Westra@math.unimaas.nl

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