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Predicting Gene Expression using Logic Modeling and Optimization Abhimanyu Krishna

Predicting Gene Expression using Logic Modeling and Optimization Abhimanyu Krishna. New Challenges in the European Area: Young Scientist’s 1st International Baku Forum. Input Stimuli. Input Stimuli. p. B. p. p. A. A. p. A. B. C. C.

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Predicting Gene Expression using Logic Modeling and Optimization Abhimanyu Krishna

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  1. Predicting Gene Expression using Logic Modeling and Optimization Abhimanyu Krishna New Challenges in the European Area: Young Scientist’s 1st International Baku Forum

  2. Input Stimuli Input Stimuli p B p p A A p A B C C Whatis Gene Expression? -> Regulation? -> Gene Regulatory Network? Introduction: R A R C TRB TRC Gene Regulatory Network reconstruction

  3. Objective How to contextualize literature to our experimental conditions + Experimental expression data Literaturebased Gene Regulatory Network Missing expression values in grey

  4. “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states” Introduction: Biologicalprocessesrepresented as transitions in a landscape Networks of interactions Unstabletransientstate Stablestate Stablestate 4

  5. “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states” Whythesepredictions are not trivial? Noisy network reconstruction process

  6. “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states” Problem: Inconsistencybetween network and experimental expression data Solution: Contextualize the Network usingexperimental expression data 6

  7. “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states” Whyisthis an optimizationproblem?

  8. “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states” Whyisthis an optimizationproblem? Local consistency

  9. “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states” Whyisthis an optimizationproblem? Edgeremoval Local consistency

  10. “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states” Whyisthis an optimizationproblem? Global consistency Local consistency

  11. “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states” Whichproperty are wegoingto use in theoptimization? Network stability Unstabletransientstate Stablestate Stablestate 11

  12. Iterative network pruning Objective function: This score S uses the normalized Hamming distance (h) to compare N Boolean gene expression values (σ) between all calculated steady states (α) of a pruned network and the two known phenotypes (φ1 and φ2) defined by the expression data, in order to identify the two best-matching phenotype/steady state couples (φα1 and φα2) with 12

  13. Iterative network pruning Objective function: This score S uses the normalized Hamming distance (h) to compare N Boolean gene expression values (σ) between all calculated steady states (α) of a pruned network and the two known phenotypes (φ1 and φ2) defined by the expression data, in order to identify the two best-matching phenotype/steady state couples (φα1 and φα2) with

  14. Iterative network pruning Objective function: This score S uses the normalized Hamming distance (h) to compare N Boolean gene expression values (σ) between all calculated steady states (α) of a pruned network and the two known phenotypes (φ1 and φ2) defined by the expression data, in order to identify the two best-matching phenotype/steady state couples (φα1 and φα2) with 14

  15. Iterative network pruning Objective function: This score S uses the normalized Hamming distance (h) to compare N Boolean gene expression values (σ) between all calculated steady states (α) of a pruned network and the two known phenotypes (φ1 and φ2) defined by the expression data, in order to identify the two best-matching phenotype/steady state couples (φα1 and φα2) with 15

  16. Iterative network pruning Objective function: This score S uses the normalized Hamming distance (h) to compare N Boolean gene expression values (σ) between all calculated steady states (α) of a pruned network and the two known phenotypes (φ1 and φ2) defined by the expression data, in order to identify the two best-matching phenotype/steady state couples (φα1 and φα2) with 16

  17. Iterative network pruning Objective function: This score S uses the normalized Hamming distance (h) to compare N Boolean gene expression values (σ) between all calculated steady states (α) of a pruned network and the two known phenotypes (φ1 and φ2) defined by the expression data, in order to identify the two best-matching phenotype/steady state couples (φα1 and φα2) with 17

  18. Iterative network pruning Objective function: This score S uses the normalized Hamming distance (h) to compare N Boolean gene expression values (σ) between all calculated steady states (α) of a pruned network and the two known phenotypes (φ1 and φ2) defined by the expression data, in order to identify the two best-matching phenotype/steady state couples (φα1 and φα2) with 18

  19. Iterative network pruning Objective function: This score S uses the normalized Hamming distance (h) to compare N Boolean gene expression values (σ) between all calculated steady states (α) of a pruned network and the two known phenotypes (φ1 and φ2) defined by the expression data, in order to identify the two best-matching phenotype/steady state couples (φα1 and φα2) with 19

  20. “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states” But the contribution of interactions to the network stabilityitis not linearlyindependent. The evaluation of one specificlinkishighlydependent of the links alreadyremoved or, in otherwords, the order of removal. We are going to capture interdependenciesbetween variables consideringsequentiallyboth the probability distribution of positive circuits and separatededges. Positive circuits are necessary condition to have severalfixed points Thomas R, Thieffry D, Kaufman M: DYNAMICAL BEHAVIOR OF BIOLOGICAL REGULATORY NETWORKS .1. BIOLOGICAL ROLE OF FEEDBACK LOOPS AND PRACTICAL USE OF THE CONCEPT OF THE LOOP-CHARACTERISTIC STATE.Bulletin of Mathematical Biology 1995, 57:247-276. Positive circuit Negative circuit Positive circuit 20

  21. Iterative network pruning Positive Circuit 1 Objective function: This score S uses the normalized Hamming distance (h) to compare N Boolean gene expression values (σ) between all calculated steady states (α) of a pruned network and the two known phenotypes (φ1 and φ2) defined by the expression data, in order to identify the two best-matching phenotype/steady state couples (φα1 and φα2) with 21

  22. Iterative network pruning Positive Circuit 2 Objective function: This score S uses the normalized Hamming distance (h) to compare N Boolean gene expression values (σ) between all calculated steady states (α) of a pruned network and the two known phenotypes (φ1 and φ2) defined by the expression data, in order to identify the two best-matching phenotype/steady state couples (φα1 and φα2) with 22

  23. Iterative network pruning Positive Circuit 3 Objective function: This score S uses the normalized Hamming distance (h) to compare N Boolean gene expression values (σ) between all calculated steady states (α) of a pruned network and the two known phenotypes (φ1 and φ2) defined by the expression data, in order to identify the two best-matching phenotype/steady state couples (φα1 and φα2) with 23

  24. “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states” Whichproperty are wegoingto use in theoptimization? Network stability

  25. “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states” Biological scope targeted by thisapproach: transitions between long term expression patterns or stable states Epithelial Mesenchymal Example: Epithelial-mesenchymaltransition

  26. “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states” Computingattractors in a discretedynamical system (Boolean) Based on logicfunctions and the assumption of only 2 possible gene states: active (ON or 1) and inactive (OFF or 0). Logicfunctions: Types of attractors: fixed points and limit cycles Fixed point The state of the node xiat time t+1 depends on the state of itsregulatorsat time t. Updatingscheme: Synchronous Limit cycle 26

  27. “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states” Consistencybetweenexpression data and networkstablestates 27

  28. “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states” Iterative network pruning Optimization of h(x) (objective function) h(x) = X1+X2+X3+X4+X5+x6 Xi = 0 or 1 Network topologyoptimizedusing an Estimation of Distribution Algorithm (EDA) Toyexample:

  29. EDA: toyexample Initial population Next population Top 10 solutions

  30. EDA: toyexample Initial population Next population Top 10 solutions

  31. EDA: toy example Initial population Next population Top 10 solutions

  32. EDA: toy example Initial population Next population Top 10 solutions

  33. EDA: toy example Initial population Next population Top 10 solutions 0.7

  34. EDA: toy example Initial population Next population Top 10 solutions 0.7 0.7

  35. EDA: toy example Initial population Next population Top 10 solutions 0.7 0.7 0.6

  36. EDA: toy example Initial population Next population Top 10 solutions 0.7 0.7 0.6 0.6

  37. EDA: toy example Initial population Next population Top 10 solutions 0.7 0.7 0.6 0.6 0.8

  38. EDA: toy example Initial population Next population Top 10 solutions 0.7 0.7 0.6 0.6 0.8 0.7

  39. EDA: toy example Initial population Next population Top 10 solutions 0.7 0.7 0.6 0.6 0.8 0.7

  40. EDA: toy example Initial population Next population Top 10 solutions 0.7 0.7 0.6 0.6 0.8 0.7 STOP CRITERIA

  41. Iterative network pruning Objective function: This score S uses the normalized Hamming distance (h) to compare N Boolean gene expression values (σ) between all calculated steady states (α) of a pruned network and the two known phenotypes (φ1 and φ2) defined by the expression data, in order to identify the two best-matching phenotype/steady state couples (φα1 and φα2) with 41

  42. Iterative network pruning Objective function: This score S uses the normalized Hamming distance (h) to compare N Boolean gene expression values (σ) between all calculated steady states (α) of a pruned network and the two known phenotypes (φ1 and φ2) defined by the expression data, in order to identify the two best-matching phenotype/steady state couples (φα1 and φα2) with

  43. Iterative network pruning Objective function: This score S uses the normalized Hamming distance (h) to compare N Boolean gene expression values (σ) between all calculated steady states (α) of a pruned network and the two known phenotypes (φ1 and φ2) defined by the expression data, in order to identify the two best-matching phenotype/steady state couples (φα1 and φα2) with 43

  44. Iterative network pruning Objective function: This score S uses the normalized Hamming distance (h) to compare N Boolean gene expression values (σ) between all calculated steady states (α) of a pruned network and the two known phenotypes (φ1 and φ2) defined by the expression data, in order to identify the two best-matching phenotype/steady state couples (φα1 and φα2) with 44

  45. Iterative network pruning Objective function: This score S uses the normalized Hamming distance (h) to compare N Boolean gene expression values (σ) between all calculated steady states (α) of a pruned network and the two known phenotypes (φ1 and φ2) defined by the expression data, in order to identify the two best-matching phenotype/steady state couples (φα1 and φα2) with 45

  46. Iterative network pruning Objective function: This score S uses the normalized Hamming distance (h) to compare N Boolean gene expression values (σ) between all calculated steady states (α) of a pruned network and the two known phenotypes (φ1 and φ2) defined by the expression data, in order to identify the two best-matching phenotype/steady state couples (φα1 and φα2) with 46

  47. Iterative network pruning Objective function: This score S uses the normalized Hamming distance (h) to compare N Boolean gene expression values (σ) between all calculated steady states (α) of a pruned network and the two known phenotypes (φ1 and φ2) defined by the expression data, in order to identify the two best-matching phenotype/steady state couples (φα1 and φα2) with 47

  48. Iterative network pruning Objective function: This score S uses the normalized Hamming distance (h) to compare N Boolean gene expression values (σ) between all calculated steady states (α) of a pruned network and the two known phenotypes (φ1 and φ2) defined by the expression data, in order to identify the two best-matching phenotype/steady state couples (φα1 and φα2) with 48

  49. “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states” But the contribution of interactions to the network stabilityitis not linearlyindependent. The evaluation of one specificlinkishighlydependent of the links alreadyremoved or, in otherwords, the order of removal. We are going to capture interdependenciesbetween variables consideringsequentiallyboth the probability distribution of positive circuits and separatededges. Positive circuits are necessary condition to have severalfixed points Thomas R, Thieffry D, Kaufman M: DYNAMICAL BEHAVIOR OF BIOLOGICAL REGULATORY NETWORKS .1. BIOLOGICAL ROLE OF FEEDBACK LOOPS AND PRACTICAL USE OF THE CONCEPT OF THE LOOP-CHARACTERISTIC STATE.Bulletin of Mathematical Biology 1995, 57:247-276. Positive circuit Negative circuit Positive circuit 49

  50. Iterative network pruning Positive Circuit 1 Objective function: This score S uses the normalized Hamming distance (h) to compare N Boolean gene expression values (σ) between all calculated steady states (α) of a pruned network and the two known phenotypes (φ1 and φ2) defined by the expression data, in order to identify the two best-matching phenotype/steady state couples (φα1 and φα2) with 50

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