The document discusses formalizing systems biology models using ontologies. It describes how biological models are specified using the Systems Biology Markup Language (SBML) with semantic annotations from ontologies. These annotated models are then converted into formal ontological representations using the Web Ontology Language (OWL) to enable automated reasoning and knowledge discovery from the models. This allows validating annotations, inferring new knowledge, and querying simulation results in a biologically meaningful way.

1. Formal representation of models in systems biology 1 Michel Dumontier, Ph.D. Associate Professor of Bioinformatics, Department of Biology, School of Computer Science, Institute of Biochemistry, Carleton University Professeur Associé, Département d’informatique et de génielogiciel, Université Laval Ottawa Institute of Systems Biology Ottawa-Carleton Institute of Biomedical Engineering INRIA2011::Dumontier

3. reveal metabolic and signallingcapabilities so as to predict phenotypes

5. efficient software to execute computationally demanding simulationsISMB2011::Dumontier|Hoehndorf::Formalizing Systems Biology with Biomedical Ontologies 2

6. Repressilator: A self-regulating system 3 INRIA2011::Dumontier A synthetic oscillatory network of transcriptional regulators. Elowitz MB, Leibler S. (2000). Nature 403: 335-338.

7. Biomodels are specified using SBML+ semantic annotation 4 INRIA2011::Dumontier

9. 300+ models are annotated with

10. Pubmed- papers

11. ChEBI - chemicals

12. UniProt - proteins

13. KEGG - chemicals, reactions

14. E.C. - reactions

15. Gene Ontology - functions, reactions, compartments

16. Taxonomy - organismhttp://www.ebi.ac.uk/biomodels-main/ ISMB2011::Dumontier|Hoehndorf::Formalizing Systems Biology with Biomedical Ontologies 5

18. Are generally used for semantic annotation of data, which when reused, facilitate integration across domains (granularity, species, experimental methods)

19. Facilitate granular and cross-domain queries

20. Can be used to obtain explanations for inferencesdrawn

21. Can be efficiently processed by algorithms and softwareISMB2011::Dumontier|Hoehndorf::Formalizing Systems Biology with Biomedical Ontologies 6

22. Additional annotations are specified using the Resource Description Framework (RDF) Implicit subject and xml attributes <species metaid="_525530" id="GLCi" compartment="cyto" initialConcentration="0.097652231064563"> <annotation> <rdf:RDFxmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/"> <rdf:Descriptionrdf:about="#_525530"> <bqbiol:is> <rdf:Bag> <rdf:lirdf:resource="urn:miriam:obo.chebi:CHEBI%3A4167"/> <rdf:lirdf:resource="urn:miriam:kegg.compound:C00031"/> </rdf:Bag> </bqbiol:is> </rdf:Description> </rdf:RDF> </annotation> </species> The annotation element stores the RDF subject predicate object The intent is to express that the species represents a substance composed of glucose molecules We also know from the SBML model that this substance is located in the cytosol and with a (initial) concentration of 0.09765M ISMB2011::Dumontier|Hoehndorf::Formalizing Systems Biology with Biomedical Ontologies 7

24. IRIs

25. Statements (aka triples) take the form of

26. <subject> <predicate> <object>

27. Easy to implement

28. stand-alone datasets

29. logical layer over databases

30. Limited reasoning

31. class and property hierarchies

32. domain/range restrictions

33. can’t automatically discover inconsistency

34. Standardized Queries - SPARQL

35. Scalable - to billions of triplesISMB2011::Dumontier|Hoehndorf::Formalizing Systems Biology with Biomedical Ontologies 8

37. Makes it easier to explore or find models

38. By converting models into formal representations of knowledge we get to:

39. validate the accuracy of the annotations

40. infer knowledge explicit in terminological resources

41. discover biological implications inherent in the models and the results of simulations.ISMB2011::Dumontier|Hoehndorf::Formalizing Systems Biology with Biomedical Ontologies 9

42. Approach We formally represent semantically annotated biomodelssuch that it becomes possible to: Capture the semantics of models and the biological systems they represent Check the consistency of biological knowledge represented through automated reasoning query the results of simulations in the context of the biological knowledge 10 INRIA2011::Dumontier

43. Have you heard of OWL? COMBINE2011:Dumontier 11

45. existential, universal, cardinality restriction

46. negation

47. disjunction

48. property characteristics

49. transitive, functional, inverse functional, symmetric, antisymmetric, reflexive, irreflexive

50. complex classes in domain and range restrictions

51. property chains12 COMBINE2011:Dumontier 12

53. Satisfiability: determines whether classes can have instances.

54. Subsumption: is class C1 implicitly a subclass of C2?

55. Classification: repetitive application of subsumption to discover implicit subclass links between named classes

56. Realization: find the most specific class that an individual belongs to. 13 COMBINE2011:Dumontier 13

58. intended meaning:

59. C1 SubClassOf: C2

60. C1 SubClassOf: R some C2

61. C1 SubClassOf: R only C2

62. C2 SubClassOf: R some C1

63. C1 SubClassOf: S some C2

64. C1 DisjointFrom: C2

65. C1 and C2 SubClassOf: owl:Nothing

66. R some C1 DisjointFrom: R some C2

67. C1 EquivalentClasses C2

68. ...

69. in general: P(C1, C2), where P is an OWL axiom (template)ISMB2011::Dumontier|Hoehndorf::Formalizing Systems Biology with Biomedical Ontologies 14

70. INRIA2011::Dumontier 15 Conceptualization:Models and their components represent physical entities (material entities, processes) Formalization: every element E of the SBML language represents a class Rep(E) and we assert that E subClassOf: represents some Rep(E)

71. Top-level ontologies can make additional commitment by enforcing disjointnessamong basic types Material object, Process, Function and Quality are mutually disjoint. ISMB2011::Dumontier|Hoehndorf::Formalizing Systems Biology with Biomedical Ontologies 16

72. Relations impose additional constraints, such that inconsistencies arise when incorrectly used ISMB2011::Dumontier|Hoehndorf::Formalizing Systems Biology with Biomedical Ontologies 17

73. For each model annotation, we make a commitment to what it represents OWL Axiom: Model SubClassOf: represents some MaterialEntity Conversion rule: a Model annotated with class C represents: If C is a SubClassOfMaterialEntity then M SubClassOf: represents some C If C is a SubClassOfFunction then M SubClassOf: represents some (has-function some C) If C is a SubClassOfProcess then M SubClassOf: represents some (has-function some (realized-by only C))

75. O1 has a function F1

76. F1 is realized by processes of the type heterotrimeric G-protein complex cycleM SubClassOf: represents some O1 O1 SubClassOf: (has-function some (realized-by only GO:0031684)

78. part of the object represented by the model

79. compartment’s species represent objects that are located in O2

80. C SubClassOf: represents some A2

82. ISMB2011::Dumontier|Hoehndorf::Formalizing Systems Biology with Biomedical Ontologies 22

84. Jena RDF API to parse RDF annotations

86. includes all referenced ontologies

87. GO (functions, compartments, processes)

88. ChEBI (molecules)

89. Celltype (cell types)

90. FMA (anatomy)

92. Model verification After reasoning, we found 27 models to be inconsistent reasons our representation - functions sometimes found in the place of physical entities (e.g. entities that secrete insulin). better to constrain with appropriate relations SBML abused – e.g. species used as a measure of time constraints in the ontologies themselves mean that the annotation is simply not possible ISMB2011::Dumontier|Hoehndorf::Formalizing Systems Biology with Biomedical Ontologies 25

95. represents some (has-function some C) and represents some (has-function some (realized-by only C)) are unsatisfiableISMB2011::Dumontier|Hoehndorf::Formalizing Systems Biology with Biomedical Ontologies 27

96. Species are further described with ‘modifiers’ in the context of a reaction 28 INRIA2011::Dumontier essential activator <listOfModifiers> <modifierSpeciesReferencesboTerm="SBO:0000461" species="X"/> </listOfModifiers> partial inhibitor <listOfModifiers> <modifierSpeciesReferencesboTerm="SBO:0000536" species="PX"/> </listOfModifiers>

97. Roles are realized in the context of processes by material entities INRIA2011::Dumontier model sio: has proper part sio: represents sio: has direct part species ChEBI:molecule ChEBI:substance sio: role of SBO: participant role sio: has participant SBMLHarvester+ sio: realizes sio: represents GO:Process reaction Class role chain: realizes o role of -> has participant Individual Datatype 29

98. Semanticscience Integrated Ontology (SIO) OWL2 ontology 1000+ classes covering basic types (physical, processual, abstract, informational) with an emphasis on biological entities 183 basic relations (mereological, participatory, attribute/quality, spatial, temporal and representational) axioms can be used by reasoners to compute inferences for consistency checking, classification and answering questions about life science knowledge embodies emerging ontology design patterns specifies a data model dereferenceable URIs searchable in the NCBO bioportal Available at http://semanticscience.org/ontology/sio.owl 30 INRIA2011::Dumontier

99. Examining Mathematical Expressions 31 INRIA2011::Dumontier <assignmentRulemetaid="metaid_0400235" variable="k_tl"> <math> <apply> <divide/> <ci> eff </ci> <ci> t_ave </ci> </apply> </math> </assignmentRule> <kineticLawsboTerm="SBO:0000049"> <math> <apply> <times/> <ci> k_tl </ci> <ci> X </ci> </apply> </math> </kineticLaw> <parameter metaid="metaid_0000233" id="k_tl" name="k_tl" constant="false" sboTerm="SBO:0000016"> (unimolecularrate constant) <notes> <p xmlns="http://www.w3.org/1999/xhtml">Translation rate constant</p> </notes> </parameter> <parameter metaid="metaid_0000025" id="eff" name="translation efficiency" value="20"> <notes> <p xmlns="http://www.w3.org/1999/xhtml">Average number of proteins per transcript</p> </notes> </parameter>

100. SBML Reactions may be specified by mathematical expressions, which contain quantitative variables that denote quantities SBO:Reaction Quantity sio: is specified by sio:denotes sio: has proper part SBO: systems description parameter SBO:mathematical expression sio: has value Literal Class sio:derives from SBMLFarmer Individual Datatype INRIA2011::Dumontier 32

101. When running a simulation, some attributes change with time 33 INRIA2011::Dumontier species double sio:has attribute sio: has value sio: has unit uo:unit attribute sio: measured at sio: has value datetime time sio: result of sio: has agent simulation software sio: conforms to sio: has participant KISAO: algorithm parameter model expression Class Individual Datatype

102. 34 INRIA2011::Dumontier

103. Copasi output:not machine understandable 35 INRIA2011::Dumontier

104. Query Answering over RDF/OWL Find those concentration measurements for species that represent molecular entities that contain ribonucleotide residues ‘concentration’ and (‘measured at’ some double[>20.0, <40.0]) and ‘is attribute of’ some ( ‘species’ and ‘represents’ some (‘has part’ some ‘ribonucleotide residue’) ) 36 INRIA2011::Dumontier ChEBI ontology

106. Line Segments

111. Can be local minima/maxima

112. Can be inflection pointsTEDDY_0000144 Point: Stationary Point (Maximum) B A C Curve Segment Overall Change (Slope) Constituent Points Concentration strictly increasing TEDDY_0000008 strictly decreasing Curve: Overall Change D TEDDY_0000009 Time INRIA2011::Dumontier

113. Queries ‘local maximum’ and ‘is attribute of’ some ( species and represents some ( ‘has function’ some ‘dna binding’ )) 38 INRIA2011::Dumontier Biomodel + UniProt + GO

114. Get the non-monotonic curves for protein species ‘non-monotonic curve’ and ‘has part’ some ( ‘concentration’ and ‘is attribute of’ some ( ‘species’ and ‘represents’ some ‘protein’)) ) 39 INRIA2011::Dumontier

115. Conclusion The SBML-derived ontologies can be i) checked for their consistency, thereby uncovering erroneous curations ii) infer attributes and relations of the substances, compartments and reactions beyond what was originally described in the models iii) answer sophisticated questions across a model knowledge base iv) extended with modifiers, mathematical expressions and parameters, simulation Results (from tab files) to answer questions about simulation results with reference to the semantic annotations (GO) in biomodels, UniProt 40 INRIA2011::Dumontier

116. 41 Acknowledgements Leonid Chepelev Robert Hoehndorf INRIA2011::Dumontier

117. Michel Dumontier michel_dumontier@carleton.ca 42 INRIA2011::Dumontier Publications: http://dumontierlab.com Presentations: http://slideshare.com/micheldumontier