Planning for Gene Regulatory Network Intervention

1
Planning for Gene Regulatory Network Intervention

• Daniel Bryce
• Arizona State University
• Seungchan Kim
• Arizona State University
• Translational Genomics Research Institute

2
Prior Work

• Planning for Finding Pathways
• S. Khan, K. Decker, W. Gillis, and C. Schmidt. A
  multi-agent system-driven AI planning approach to
  biological pathway discovery. In Proceedings of
  ICAPS03, 2003.
• Fifth International Planning Competition, 2006.
• Reasoning about change in cellular processes
• N. Tran and C. Baral. Issues in reasoning about
  interaction networks in cells necessity of event
  ordering knowledge. In Proceedings of AAAI05,
  2005.

• Extracting and Expressing Transition Functions
  from Micro-array experiments, Markov chain
  analysis.
• S. Kim, H. Li, E. Dougherty, N. Cao, Y. Chen, M.
  Bittner, and E. Suh. Can Markov chain models
  mimic biological regulation? Journal of
  Biological Systems, 10(4)337357, 2002.
• I. Shmulevich, E. Dougherty, S. Kim, and W.
  Zhang.Probabilistic boolean networks a
  rule-based uncertainty model for gene regulatory
  networks. Bioinformatics 18(2)261274, 2002.
• Non-AI work on planning interventions.
• A. Datta, A. Choudhary, M. Bittner, and E.
  Dougherty. External control in Markovian genetic
  regulatory networks the imperfect information
  case. Bioinformatics, 20(6)924930, 2004.

3
Gene Regulatory Networks (GRNs)
Cell Type (Phenotype, e.g., liver cell)
Tissue

• Questions of interest
• How does cancer occur?
• How can we prevent cancer?
• How do we kill specific cells?
• Can we control Differentiation?
• e.g., Program stem cell to become Liver Cell
• Can we change Phenotype?
• e.g., Revert liver cell to back to stem cell,
  then differentiate to heart cell

Micro array Data
From Wuensche, PSB-98
4
Gene Regulatory Network Behavior
Extra cellular signals can effect the cell state
transitions (e.g., Chemotherapy, Pharmaceuticals,
and Stress)
Edge Thickness Pr(s s)
Cancer Phenotype
Partial Observations of molecular components or
physiology are available
Steady States (normal)
Transient States (intermediate)
Undesirable State
5
GRN Intervention Planning

• Datta et. al. Assumptions
• Synchronous Events
• Exact Representation
• Optimal Bounded Length Plans
• Datta et. al. Approach
• Enumerate Reachable Belief States
• Dynamic Programming
• Our Approach
• AI Planning
• AO Search

Non-Intervention
Observation
Intervention
Observation
6
Evaluation

• WNT5A GRN
• Highly active WNT5A indicates proliferation of
  cancer
• 2 (non)interventions
• 2 variations direct and indirect control
• 2 observations
• 7 genes (binary valued)
• Randomly Generated GRN
• 4 (non)interventions
• 2 observations
• 7 genes (binary valued)

• Compare AI Planning with Datta et. al.
• Scaling horizon
• Sensitivity to Reward Function
• Metric Total Time

7
WNT5A GRN (from TGEN dataset)

• Indirect Control
• Intevene Pirin gene
• Observe WNT5A gene
• Direct Control
• Intervene WNT5A gene
• Observe Pirin gene

8
Random GRN (4 acts)
Goal Reward (AO)
Enumeration
AO exploits Reward Function for Pruning (Improve
d Scalability In Some Cases)
9
Assumptions Revisited

• Finite Horizon
• Not all treatments require same length
• Synchronous Change
• Actions overloaded to include GRN change
• 7 Genes and 1 intervention
• Within human comprehension

10
Indefinite or Finite Horizon?

• Indefinite Horizon If goal state is a steady
  state, then no need to plan more actions to meet
  a given horizon

11
Asynchronous Change

• Decouple Intervention from Gene Regulatory
  Network Simulation
• Triggers (Tran and Baral, AAAI05)
• Probabilistic Exogenous Events (Blythe, UAI94)

12
Larger GRNs

• 50-5000 genes
• More Interventions and Observations
• Representation
• ADD for transition relation blows up
• DBN is better, but exact inference can be costly
• Extensions of Thruns MC-POMDPs, sample based
  representation, is in the right direction
• Search Heuristics
• McLUG Planning Graphs with Probabilistic Actions

13
Conclusion

• Off-the-shelf AI planning improves upon state of
  the art in Intervention Problems
• Future Research Needed
• Scaling
• Indefinite Horizon
• Extra Actions and Observations
• Sample-based Representation
• Search Heuristics
• Modeling
• Asynchronous Probabilistic Change
• Plan Explanation

14
Extra Slides
15
Empirical Comparison
AO
Datta Enumeration
Total Time and Expanded Nodes Better in all Cases
With no heuristics Search performance Correlates
with Reward Function
16
Empirical Comparison
AO
Datta Enumeration
Total Time and Expanded Nodes Better in all Cases
With no heuristics Search performance Correlates
with Reward Function
17
Challenges for AI

• Planning/Search
• Heterogeneous Horizon
• Heuristics/Pruning
• Knowledge Representation Reasoning
• Computing and Representing
• Transition and Observation Function for 50 genes
• Belief states with 250 states
• Handling Asynchronous Exogenous Events (cell
  behavior)
• Machine Learning
• Learn the Transition and Observation Function
  from
• Measurements of various molecular components such
  as mRNA (gene expression microarray) and proteins
  (protein array)
• Knowledge from literature
• Knowledge from domain experts (biologists)
• Human Computer Interaction
• Plan explanation/visualization
• Knowledge Engineering

18
The Network
19
The Parameters and Functions
20
Computational Biology

• Bioinformatics
• Knowledge Discovery Data-mining
• Manage and Analyze Biological Data
• Systems Biology
• Simulation
• Model Dynamic Systems

21
Representing State Distributions
Algebraic Decision Diagram
Explicit Vector
g1
g2
g2
.2
.25
.35
22
Representing State Distributions
Algebraic Decision Diagram
Explicit Vector
g1
g2
.2
.25
.35
23
Representing Probabilistic Actions
Explicit Transition Matrix
Algebraic Decision Diagram
g1
g1
g1
g2
g2
g2
g2
g2
g2
g2
g2
g2
g2
g2
g2
0
.1
.2
.3
.5
.6
.8
1
24
Representing Probabilistic Actions
Explicit Transition Matrix
Algebraic Decision Diagram
g1
g1
g1
g2
g2
g2
g2
g2
g2
g2
g2
g2
g2
g2
0
.1
.2
.3
.5
.6
.8
1
25
Modeling Network Dynamics
(- (influence2 ?g3 ?g4 ?g) (noise))
(noise)
(noise)
(- (influence1 ?g1 ?g2 ?g) (noise))
(predicts ?g3 ?g4 ?g)
(predicts ?g1 ?g2 ?g)
?g1
?g2
?g3
?g4
0
1
?g
26
Network Dynamics Encoding ltdynamicsgt
Bind all genes to variables
(forall (?g ?g1 ?g2 ?g3 ?g4 - gene)
constraint for grounding that binds only those
genes ?g1 - ?g4 that predict ?g. External
control actions add predicates to the
antecedent below so that ?g does not bind to
controlled genes. (when (and (predicts1 ?g1 ?g2
?g) (predicts2 ?g3 ?g4 ?g))
(probabilistic (- (influence1 ?g1 ?g2
?g) (noise)) predictor 1 probability
(and (when (or conditions
to set ?g up (and
(not (up-regulated ?g1)) (not (up-regulated
?g2))
(pred-fn ?g1 ?g2 ?g zz))
(and (not (up-regulated ?g1))
(up-regulated ?g2)
(pred-fn ?g1 ?g2 ?g zo))
(and (up-regulated ?g1) (not
(up-regulated ?g2))
(pred-fn ?g1 ?g2 ?g oz))
(and (up-regulated ?g1)
(up-regulated ?g2)
(pred-fn ?g1 ?g2 ?g oo))
)
(up-regulated ?g)) set ?g up
(when (or conditions to
set ?g down (and (not
(up-regulated ?g1)) (not (up-regulated ?g2))
(not (pred-fn ?g1
?g2 ?g zz))) (and
(not (up-regulated ?g1)) (up-regulated ?g2)
(not (pred-fn
?g1 ?g2 ?g zo))) (and
(up-regulated ?g1) (not (up-regulated
?g2))
(not (pred-fn ?g1 ?g2 ?g oz)))
(and (up-regulated ?g1)
(up-regulated ?g2)
(not (pred-fn ?g1 ?g2 ?g oo)))
) (not
(up-regulated ?g))) set ?g down )
(- (influence2 ?g3 ?g4 ?g) (noise))
predictor 2 probability (and ...)
predictor 2, similar to
predictor 1 (noise) (up-regulated ?g)
noise to set ?g up (noise)
(not (up-regulated ?g)) noise to set ?g
down ) ) )
Binding constraints
probability Of using predictor1
conditions to up-regulate with predictor1
up-regulate with predictor1
Conditions to down-regulate
down-regulate with predictor1
Rules for predictor2 and noise
27
Network Parameters
.68
.30
.01
.01
(predicts stc2 ret2 s100p)
(predicts wnt5a ret2 s100p)
wnt5a
ret2
stc2
ret2
0
1
s100p
28
Predictor Encoding

• ( (noise) .01)
• s100p predictor1
• (predicts1 wnt5a ret2 s100p)
• (pred-fn wnt5a ret2 s100p zo) 1
• (pred-fn wnt5a ret2 s100p oz) 1
• (pred-fn wnt5a ret2 s100p oo) 1
• ( (influence1 wnt5a ret2 s100p) .69)
• s100p predictor2
• (predicts2 stc2 ret2 s100p)
• (pred-fn stc2 ret2 s100p oz) 1
• (pred-fn stc2 ret2 s100p oo) 1
• ( (influence2 stc2 ret2 s100p) .31)

29
Control Encoding ltcontrolgt, perfect/partial
obeservation

• (action down-regulate
• parameters (?gr ?go - gene)
• precondition (and (observed ?go)
• (controlled ?gr)
• (started))
• effect
• (and (decrease (reward) 1)
• (when (up-regulated ?gr) (not
  (up-regulated ?gr)))
• ltdynamics (not ( ?g ?gr))gt
• )
• observation (
• ((up-regulated ?go) (up-regulated
  ?go) 1)
• ((not (up-regulated ?go)) (not
  (up-regulated ?go)) 1)
• )
• )

Could be better model!?
(when (up-regulated ?gr) (probabilistic .75
(not (up-regulated ?gr))))