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

Gene Regulatory Network reconstruction R A TR B TR C p A p A p A BC Input Stimuli C R C B p What is Gene Expression? -> Regulation? -> Gene Regulatory Network? Introduction:

Literature based Gene Regulatory Network Experimental expression data + Missing expression values in grey How to contextualize literature to our experimental conditions Objective

4 Stable state Unstable transient state Biological processes represented as transitions in a landscape “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states” Introduction: Networks of interactions

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

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

7 Why is this an optimization problem? “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states”

8 Why is this an optimization problem? Local consistency “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states”

9 Why is this an optimization problem? Local consistency Edge removal “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states”

10 Why is this an optimization problem? Local consistency Global consistency “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states”

11 Stable state Unstable transient state “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states” Which property are we going to use in the optimization? Network stability

12 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) 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) Iterative network pruning

14 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) Iterative network pruning

15 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) Iterative network pruning

16 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) Iterative network pruning

17 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) Iterative network pruning

18 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) Iterative network pruning

19 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) Iterative network pruning

20 But the contribution of interactions to the network stability it is not linearly independent. The evaluation of one specific link is highly dependent of the links already removed or, in other words, the order of removal. We are going to capture interdependencies between variables considering sequentially both the probability distribution of positive circuits and separated edges. Positive circuit Negative circuit “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states” 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: Positive circuits are necessary condition to have several fixed points

21 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) Iterative network pruning Positive Circuit 1

22 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) Iterative network pruning Positive Circuit 2

23 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) Iterative network pruning Positive Circuit 3

24 Which property are we going to use in the optimization? Network stability “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states”

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

26 Computing attractors in a discrete dynamical system (Boolean) Based on logic functions and the assumption of only 2 possible gene states: active (ON or 1) and inactive (OFF or 0). Logic functions: The state of the node x i at time t+1 depends on the state of its regulators at time t. Updating scheme: Synchronous Types of attractors: fixed points and limit cycles Fixed point Limit cycle “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states”

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

28 Optimization of h(x) (objective function) h(x) = X 1 +X 2 +X 3 +X 4 +X 5 + x 6 X i = 0 or 1 Network topology optimized using an Estimation of Distribution Algorithm (EDA) Toy example: Iterative network pruning “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states”

29 Top 10 solutions Initial population Next population EDA: toy example

30 EDA: toy example Top 10 solutions Initial population Next population

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

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

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

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

35 EDA: toy example Top 10 solutions Initial population Next population

36 EDA: toy example Top 10 solutions Initial population Next population

37 EDA: toy example Top 10 solutions Initial population Next population

38 EDA: toy example Top 10 solutions Initial population Next population

39 EDA: toy example Top 10 solutions Initial population Next population

40 EDA: toy example Top 10 solutions Initial population Next population STOP CRITERIA

41 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) 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) Iterative network pruning

43 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) Iterative network pruning

44 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) Iterative network pruning

45 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) Iterative network pruning

46 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) Iterative network pruning

47 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) Iterative network pruning

48 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) Iterative network pruning

49 But the contribution of interactions to the network stability it is not linearly independent. The evaluation of one specific link is highly dependent of the links already removed or, in other words, the order of removal. We are going to capture interdependencies between variables considering sequentially both the probability distribution of positive circuits and separated edges. Positive circuit Negative circuit “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states” 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: Positive circuits are necessary condition to have several fixed points

50 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) Iterative network pruning Positive Circuit 1

51 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) Iterative network pruning Positive Circuit 2

52 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) Iterative network pruning Positive Circuit 3

53 “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states” Algorithm:

54 Predictions based on the consensus between the familiy of alternative solutions “Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states”

012/08/30/nar.gks785.full Software Paper Availability:

Isaac Crespo Computational Biology Unit (LCSB) Abhimanyu Krishna Bioinformatic core (LCSB) Antony Le Béchec Antonio del Sol Head of Computational Biology Unit (LCSB) Life sciences research unit (LSRU) Vital-IT (SIB) Thank you! Questions?

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