1. Inference of Gene Relations from Microarray Data by Abduction Irene Papatheodorou & Marek Sergot Imperial College, London UK

2. Outline Gene Regulation & Microarrays Abductive Logic Programming Proof Procedure Model of Gene Interactions Applications & Tests Evaluation & Further Work

3. Gene Regulation External Stimulus Cell Response Gene Regulation: ABC Microarrays measure gene expression Gene Expression: DNA/gene mRNA Protein

4. Microarray Experiment AA BB Experiment: gene mutation/environmental stress Measures levels of gene expression

6. Expression Data to Gene Relations Mycobacterium tuberculosis experiments from CMMI Genomic Information-Background Knowledge Gene Relations- inhibits/induces Inference Method: Abduction

7. Deduction model of how genes work (in general) Organism A gene X regulates gene Y gene U inhibits gene V : observed gene expression + Infer the effect from rules

8. Abduction model of how genes work (in general) Organism A gene X regulates gene Y gene U inhibits gene V : observed gene expression + Inference from effect to cause

9. Abductive Inference Theory represented by (P, A, I) –P is a logic program –A is a set of abducible predicates-Do not occur in head of any clause in P –I Integrity Constraints, logic rules

10. Abductive Explanation Given an abductive logic theory (P, A, I), an abductive explanation for a query Q is a set Δ of ground abducible atoms on the predicates A such that: P ∪ Δ |= LP Q P ∪ Δ is consistent P ∪ Δ |= LP I. |= LP denotes some standard logical entailment relation of logic programming

11. Kakas-Mancarella Procedure Extension of basic resolution used in SLD SLDNF for ordinary logic programs Assumptions: Negative Literals, Abducibles Abductive Derivation: Adds abducible atoms encountered to assumptions in hypothesis Consistency Derivation: Checks consistency of hypothesis. Implementation: Alpha (R. Craven)

12. Gene Interaction Model Rules & Integrity Constraints of Gene Interactions Observables: increases_expression(Expt, Gene) reduces_expression(Expt, Gene) Abducibles: induces(GeneA, GeneB) inhibits(GeneA, GeneB)

13. The Rules (Summary) GENE 1GENE 2 Knocked out in expt E Increased expression in expt E INHIBITS* *Unless GENE 2 affected by another gene or GENE 2 affected by environmental stress Recursive rules 2 Parameters

14. The Model Concept of gene interaction increases_expression(Expt, X) ← knocks_out(Expt, G), inhibits(G,X).

15. The Model: Exceptions Top-level: Base case rule increases_expression(Expt, X) ← knocks_out(Expt, G), inhibits(G,X), not affected_by_other_gene(Expt, G, X), not affected_by_EnvFactor(Expt, X).

16. Rules of Gene Interaction Top-level recursive rule: increases_expression(Expt, X) ← knocks_out(Expt, G), candidate_gene(Expt,G1,G), reduces_expression(Expt,G1), inhibits(G,X), not affected_by_EnvFactor(Expt, X). Parameter: candidate_gene/3

17. Rules of Gene Interaction affected_by_other_gene(Expt,G,X) ← increases_expression(Expt,Gx), Gx  X, Gx  G, related_genes(Gx, G), induces(Gx, X). Parameter: related_genes/2

18. The Parameters “Related Genes” & “Intermediate Genes” Focus search on different sets of genes Transcription factors Similar Function

19. Integrity Constraints Self-consistency: False: induces(G1,G2), inhibits(G1,G2). Consistency with prior knowledge: False: induces(a,G). False: induces(G1,X), induces(G2,X), same_operon(G1,G2). Experimental Consistency: False: candidate_gene(E,G1,G2), mutates(E,G2), not affects(E,G1).

20. M.tuberculosis: 1 Observation Observation: increases_expression(hspR, ‘Rv0350’) Hypothesis: Hyp = [inhibits(‘Rv0353’, ‘Rv0350’)] –‘Rv0353’ is mutated in hspR –‘Rv0350’ is not affected by Environmental Factor –‘Rv0350’ is not affected by other gene

21. M.tuberculosis: 2 Hypotheses Observation: reduces_expression(sigH, ‘Rv2710’) Hypotheses: Hyp = [induces(‘Rv3223c’, ‘Rv2710’)] Hyp = [induces(‘Rv3223c’, ‘Rv1221’), induces(‘Rv1221’, ‘Rv2710’)]

22. M.tuberculosis: Regulators

23. Evaluation General Method for Microarray Analysis Simple and Flexible Model Enables comparison of experiments Reduces Time of Analysis

24. Future Work Directions Integrate output with pathway information Investigate different methods of formulating the problem Improve Performance of Abductive Interpreters

25. Summary Gene Regulation & Microarrays Visualising Experiments Abductive Model for Gene Interactions Applications Future Work

26. Questions? Irene Papatheodorou ivp@doc.ic.ac.uk