Cep-construction and Design of Multistorey Building by Abhimanyu Parida
Predicting Gene Expression using Logic Modeling and Optimization Abhimanyu Krishna
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Predicting Gene Expression using Logic Modeling and Optimization Abhimanyu Krishna New Challenges in the European Area: Young Scientist’s 1st International Baku Forum
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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. - PowerPoint PPT Presentation
Transcript of 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
Gene Regulatory Network reconstruction
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Input Stimuli
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Input Stimuli
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What is Gene Expression? -> Regulation? -> Gene Regulatory Network?
Introduction:
Literature based Gene Regulatory Network
Experimental expression data
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Missing expression values in grey
How to contextualize literature to our experimental conditions
Objective
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Stable state 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
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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”
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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”
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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”
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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”
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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”
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Why is this an optimization problem?
Local consistencyGlobal consistency
“Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states”
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Stable state 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
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with
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
with
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
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with
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
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with
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
with
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
with
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
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with
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
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with
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
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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 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, 57:247-276.
Positive circuits are necessary condition to have several fixed points
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with
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 pruningPositive Circuit 1
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with
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 pruningPositive Circuit 2
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with
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 pruningPositive Circuit 3
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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”
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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:
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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 xi 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”
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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”
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Optimization of h(x) (objective function)
h(x) = X1+X2+X3+X4+X5+x6
Xi = 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”
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Top 10 solutions
Initial population Next population
EDA: toy example
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EDA: toy example
Top 10 solutions
Initial population Next population
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EDA: toy example
Top 10 solutions
Initial population Next population
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EDA: toy example
Top 10 solutions
Initial population Next population
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EDA: toy example
Top 10 solutions
Initial population Next population
0.7
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EDA: toy example
Top 10 solutions
Initial population Next population
0.7 0.7
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EDA: toy example
Top 10 solutions
Initial population Next population
0.7 0.7 0.6
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EDA: toy example
Top 10 solutions
Initial population Next population
0.7 0.7 0.6 0.6
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EDA: toy example
Top 10 solutions
Initial population Next population
0.7 0.7 0.6 0.6 0.8
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EDA: toy example
Top 10 solutions
Initial population Next population
0.7 0.7 0.6 0.6 0.8 0.7
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EDA: toy example
Top 10 solutions
Initial population Next population
0.7 0.7 0.6 0.6 0.8 0.7
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EDA: toy example
Top 10 solutions
Initial population Next population
0.7 0.7 0.6 0.6 0.8 0.7
STOP CRITERIA
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with
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
with
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
with
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
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with
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
with
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
with
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
with
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
with
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 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, 57:247-276.
Positive circuits are necessary condition to have several fixed points
50
with
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 pruningPositive Circuit 1
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with
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 pruningPositive Circuit 2
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with
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 pruningPositive Circuit 3
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“Predicting missing expression values in gene regulatory networks using a discrete logic modeling optimization guided by network stable states”
Algorithm:
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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”
http://nar.oxfordjournals.org/content/early/2012/08/30/nar.gks785.full
Software http://maia.uni.lu/demo/
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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