Planning for Gene Regulatory Network Intervention

1
Planning for Gene Regulatory Network Intervention

• Daniel Bryce
• Arizona State University
• Seungchan Kim
• Arizona State University
• TGEN

2
Motivation

• Much of Computational Systems Biology research
  involves simulating a biological model
• Many models
• Differential Equations
• Boolean Networks
• Rule Based Systems
• Bayesian Networks
• Common Assumption No external intervention
• Common Goal Control a Biological System

3
Outline

• Related Work
• Gene Regulatory Networks
• Simulation (Markov Process)
• Planning (Markov Decision Process)
• Empirical Comparison
• Conclusions

4
Related Work

• Previous 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.
• 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.
• 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.
• 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.

5
Gene Regulatory Networks

• Regulatory network described by
• Genes G g1, g2, , gn
• Each gene has an activity level v(g1) l
• Regulatory Influences v(g1) Ã f(v(g2), v(g3))
• Describes a Transition Relation
• Time t v(g1) v(g2) v(g3)
• Time t1 v(g1) v(g2) v(g3)

f1
f2
f3
6
Simulating Gene Regulatory Networks
Deterministic Model (Boolean Networks) (Rule-Based
) (Differential Equations)
v(g1) v(g2) v(g3)
v(g1) v(g2) v(g3)
1.0
0.7
0.7
Non-Deterministic/Probabilistic Model (Bayesian
Networks) (Probabilistic Boolean Networks)
v(g1) v(g2) v(g3)
0.3
0.3
Assimilate Observation
Assumption Full Observability Know which
transition is made
v(g1) v(g2) v(g3)
0.1
Removing Assumption means Partial Observability
Hidden State Observations improve information
about Hidden State
v(g1) v(g2) v(g3)
0.9
7
Simulating Gene Regulatory Networks
v(g1) v(g2) v(g3)
v(g1) v(g2) v(g3)
1.0
v(g1) v(g2) v(g3)
0.7
0.3
v(g1) v(g2) v(g3)
0.3
v(g1) v(g2) v(g3)
0.2
v(g1) v(g2) v(g3)
0.1
v(g1) v(g2) v(g3)
0.4
v(g1) v(g2) v(g3)
0.9
8
Planning

• Adding Choice to the model
• Interventions Inhibit a gene, change
  environment, etc.

0.1
Observation 1
No Inhibit
0.9
0.7
0.4
0.3
0.6
0.6
1.0
Observation 2
0.4
0.2
Inhibit g1
0.8
9
Planning Objectives

• So many possible plans, which are the best?
• Assign reward to every action
• Assign reward to terminal states
• Find maximal reward plan

5
0.1
0.5
0
0.9
0.5
0.5
0.1
0.8
1.0
5
0.9
0.2
5
-1
0.4
1.75
2.75
0.7
1.0
1
5
0.2
0.3
-1
0
0.6
0.8
1.08
0.35
2.08
0.6
0.1
0.65
0.4
0.9
0
0.6
5
3
0.4
0
2.3
2.3
10
Finding Plans, 2 Algorithms

• Enumeration DP

• Search

Prune least rewarding sub-plan at each decision
point
Generate only promising sub-plans
UB 5
UB 4
UB 3
UB 5
UB 4.5
UB 4
UB 4
11
Empirical Comparison
12
Conclusions

• Complex therapies require planning technology
• Tweak and simulate only works with a one step
  intervention
• Simple AI search algorithm outperforms exhaustive
  dynamic programming
• AI planning has much more to offer
• Modeling languages flexible, logic-based
• Efficient data-structures ADDs
• Heuristics better upper bounds for pruning
• Additional Improvements
• Decompose transition functions
• Enhance model to include proteins and other
  molecules