RULE-BASED REASONING FOR SYSTEM DYNAMICS IN CELL SYSTEMS

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1 25 RULE-BASED REASONING FOR SYSTEM DYNAMICS IN CELL SYSTEMS EUNA JEONG MASAO NAGASAKI SATORU MIYANO Human Genome Center, Institute of Medical Science, University of Tokyo, Tokyo , Japan A system-dynamics-centered ontology, called the Cell System Ontology (CSO), has been developed for representation of diverse biological pathways. Many of the pathway data based on the ontology have been created from databases via data conversion or curated by expert biologists. It is essential to validate the pathway data which may cause unexpected issues such as semantic inconsistency and incompleteness. This paper discusses three criteria for validating the pathway data based on CSO as follows: (1) structurally correct models in terms of Petri nets, (2) biologically correct models to capture biological meaning, and (3) systematically correct models to reflect biological behaviors. Simultaneously, we have investigated how logic-based rules can be used for the ontology to extend its expressiveness and to complement the ontology by reasoning, which aims at qualifying pathway knowledge. Finally, we show how the proposed approach helps exploring dynamic modeling and simulation tasks without prior knowledge. Keywords: Cell System Ontology; CSO; rule-based inference; pathway knowledge base; ontology validation 1. Introduction The Cell System Ontology (CSO) [5] has been developed as a unified framework for the representation of biological pathways, based on the notion of hybrid functional Petri net with extension [8]. CSO defines classes for modeling, visualizing, and simulating biological pathways and relationships between classes in the Web Ontology Language (OWL) [12]. Furthermore, the selected controlled vocabularies are defined in CSO to easily represent biological pathways. The pathway data based on the CSO classes are created by data integration and exchange efforts such as BioPAX2CSO [4] and Transpath2CSML [9], modeling and simulating tools such as Cell Illustrator [14, 15], or ontology editors such as Protégé [13] and SWOOP [18]. The Cell System Markup Langauge (CSML) [16] is fully compatible with CSO. The static pathway models in other biological knowledge resources are reconstructed into mathematical models with improved visualization in CSO via data conversion. The CSO tools [6, 7, 14, 15] allow to explore the possible dynamic behavior of pathway components. Unfortunately, there is ambiguous and missing information in those resources [4, 9] which makes any semantic inconsistency

2 26 E. Jeong, M. Nagasaki & S. Miyano and incompleteness in the pathway data in CSO. As a huge volume of the CSO data is generated, it is crucial to provide a knowledge base which enables dynamic simulation and hypothesis testing of biological models. In this paper, we first propose three criteria for validating the pathway data in CSO in terms of both Petri nets and biological meaning. Modeling and validating biological pathways with Petri nets are shown in many studies [2, 3, 10, 11] because Petri nets allow graphical representation and simulation for biological pathways. However, the related studies are focused on representing dynamics of the system such as how to set relevant logical parameters for Petri net components. In fact, the Petri net components rarely embed semantics in biology in the sense that whether a place represents a gene or a protein, or whether a transition is gene expression or protein modification is not important. Secondly, we propose a rule-based approach to extend the expressiveness of the ontology and to complement the ontology by reasoning, which aims at qualifying pathway knowledge. In the next section, we briefly introduce how CSO describes biological pathways. In Sec. 3, we define three criteria for validating the pathway data and present how rules are used in conjunction with CSO. Finally, a small example shows how the proposed rule-based approach helps exploring dynamic modeling and simulation tasks without prior knowledge. 2. Cell System Ontology CSO defines a model as a set of processes. The processes have entities as participants. The processes and entities are related via directed connectors. The main classes to represent biological interactions are Process, Entity, and Connector. Each process represents a biological event such as binding, translation, and activation. CSO currently supports biological entities such as genes, proteins, RNA, small molecules, and complexes. RNA is further classified into its subclasses. A connector defines a role of the entity which is involved into a process. Depending on its role, the connector class is further classified into InputAssociationBiological, InputInhibitorBiological, InputProcessBiological, and OutputProcessBiological which mean an activator, an inhibitor, an input, and an output, respectively. These basic elements are defined as BiologicalElement in CSO as shown in Figure 1A. Furthermore, with the CSO schema, one can specify simulation-related parameters for mathematical models, graphical visualization of biological elements, and available literature data. CSO also provides comprehensive controlled vocabularies for such as biological events, cellular compartments, organism type, and cell type, to model biological pathways with different scales and modalities in cell systems. The formal schema of the complete ontology is available at [16]. Figure 1B describes asserted facts for a simple model, where simulation- and visualization-related properties are abbreviated for convenience. In the figure, the property values for a biological event, a cellular compartment, and a fea-

3 Rule-Based Reasoning for System Dynamics in Cell Systems 27 BiologicalElement Connector Input InputAssociation InputAssociationBiological InputAssociationNonBiol. InputInhibitor InputInhibitorBiological InputInhibitorNonBiol. InputProcess InputProcessBiological InputProcessNonBiol. Output OutputProcess OutputProcessBiological OutputProcessNonBiol. Entity EntityBiological EntityBiologicalCell EntityBiologicalCompartment EntityBiologicalEnvironment EntityBiologicalMolecule Complex Dna ObjectOther ObjectUnknown Protein Rna SmallMolecule EntityBiologicalOther EntityBiologicalUnknown EntityNonBiological Fact Process ProcessBiological ProcessNonBiol. A. Biological elements defined in CSO. ProcessBiological(p1) hasbiologicalevent(p3, ME phosphorylation) hasconnector(p1, c6) hasconnector(p1, c7) ProcessBiological(p2) hasbiologicalevent(p2, ME binding) hasconnector(p2, c1) hasconnector(p2, c3) hasconnector(p2, c2) ProcessBiological(p3) hasbiologicalevent(p1, ME translocation) hasconnector(p3, c4) hasconnector(p3, c5) InputProcessBiological(c1) hasentity(c1, e1) InputProcessBiological(c2) hasentity(c2, e2) OutputProcessBiological(c3) hasentity(c3, c3) InputProcessBiological(c4) hasentity(c4, e2) OutputProcessBiological(c5) hasentity(c5, e4) InputProcessBiological(c6) hasentity(c6, e1) OutputProcessBiological(c7) hasentity(c7,e5) Protein(e1) Protein(e2) locatedin(e2, CC cytoplasm) Complex(e3) Protein(e4) locatedin(e4, CC nucleus) Protein(e5) hasfeature(e5, FT phosphorylated) B. Asserted facts in CSO for a simple model. C. A simple model visualized in Cell Illustrator. Fig. 1. The biological elements defined in CSO (A), asserted facts for a simple model (B), and its visualization in Cell Illustrator (C). ture type refer to the controlled vocabulary terms defined in CSO, prefixed with ME, CC, and FT, respectively. For example, p3 represents a biological event as translocation and has two connectors, c4 and c5, each of which is an instance of InputProcessBiological and OutputProcessBiological, respectively. The connector c4 (c5) is related to the entity e2 (e4), respectively. The two entities, e2 and e4, have location properties. The related facts are underlined in the figure.

4 28 E. Jeong, M. Nagasaki & S. Miyano Figure 1C shows a graphical illustration of the simple model imported into Cell Illustrator. The graphical images and positions for biological elements are also stored in CSO as a machine-readable format. Because of this, visualization tools can facilitate these data for automatic drawing of biological networks considering cellular compartments [6] and the hierarchy of the CSO classes [7]. 3. Rule-Based Reasoning for Ontology Validation We define three criteria for qualifying pathway knowledge as follows: Structurally correct models in terms of Petri nets. Biologically correct models to capture biological meaning. Systematically correct models to reflect biological behaviors. Although CSO defines sophisticated classes and relationships to describe the details of any given interaction unambiguously, sometimes only an OWL ontology is not enough for providing a qualified knowledge base of biological pathways. In OWL, there is no proper way to constrain what kind of entities can participate in which types of biological processes, or what data values are valid for a particular process. For ontology validation based on the three criteria, we use a rule-based approach represented in OWL constructors and axioms [12]. The available constructors and their correspondence in the Description Logic (DL) with the First Order Logic (FOL) are shown in Table 1. Table 1. OWL constructors and DL FOL equivalence. Constructor DL syntax FOL syntax intersectionof C 1 C n C 1 (x) C n (x) unionof C 1 C n C 1 (x) C n (x) complementof C C(x) oneof {a 1 a n } x = a 1 x = a n allvaluesfrom P.C y.(p (x, y) C(y)) somevaluesfrom P.C y.(p (x, y) C(y)) mincardinality np.c n y.(p (x, y) C(y)) maxcardinality np.c n y.(p (x, y) C(y)) In Tab. 1, C (i) is a class, P is a property, a (i) is an individual, n is a non-negative integer, and x and y are variables. In FOL, classes correspond to unary predicates, properties correspond to binary predicates, and individuals are equivalent to constants. In the following description, rules are described in FOL. A rule has the form: H B 1 B n, where H, B i are OWL constructors and axioms. H is called the head of the rule and B i is called the body of the rule. The rule is read as if [body], then [head].

5 3.1. Structurally correct models Rule-Based Reasoning for System Dynamics in Cell Systems 29 We define a structurally correct model as a bipartite graph with two disjoint sets of entities and processes. This means that if one entity is involved in a process, it has to play only one role in the process. The relationship between a process and its participants in CSO is described in Fig. 1B. Process p2 and entity e1 are related to each other via connector c1. For this relationship, four facts are used: ProcessBiological(p2), hasconnector(p2,c1), InputProcessBiological(c1), and hasentity(c1,e1). CSO defines that one process can have multiple hasconnector properties and one connector has only one hasentity property. In OWL, however, a ternary relationship among classes cannot be represented. A rule is required to constrain their relationships among three classes as follows: R1: VALIDCONNECTION(x 1, x 2 ) Process(x 1 ) x 2, 1 x 3.(hasConnector(x 1, x 3 ) Connector(x 3 ) hasentity(x 3, x 2 ) Entity(x 2 )) Given any pair of one entity and one process, if there exists zero or one connector between them, this relationship is correct. Some biological knowledge resources allow physical entities to have multiple roles in a process. The results of data conversion from those resources into CSO may violate this rule. There also exist gaps between different levels of abstraction, different structured manners used in biological knowledge resources. For example, in BioPAX [1], a catalyzed inactivation process is represented as two different processes: a catalysis and an inactivation. A catalysis describes that an enzyme catalyses the inactivation process. In this case, the enzyme may participate as an activator of the catalysis process as well as an input of the inactivation process. In CSO, a catalyzed inactivation is described as one process. After conversion from BioPAX to CSO, one input entity is connected to the process with two roles: a catalyzer and a substrate. It is not allowed in CSO based on Petri nets because a catalyzer does not change its concentration during interaction, but a substrate does it. A query to evaluate the relationship between process x 1 and entity x 2 can be written as follows: Q1: If not VALIDCONNECTION(x 1, x 2 ) then alert In Q1, it requires user intervention (alert) to select a correct relationship if there exist multiple connections between x 1 and x 2, because it is difficult to decide which one is correct without understanding the details of interaction Biologically correct models In many cases, controlled vocabularies are used to control and limit terms to describe biological processes, whose definitions are usually given as comments for human users. In CSO, the type of a process is identified with the property of a biological

6 30 E. Jeong, M. Nagasaki & S. Miyano event which has cardinality 1. On the other hand, it is optional in BioPAX and has different meaning [9] in TRANSPATH [21]. It is useful to formalize the definitions based on shared knowledge underlying biological processes. We define a biologically correct model as a model to correctly represent biological meaning of processes as a machine-readable format. In this paper, the three processes depicted in Fig. 1C are considered to represent rules. Translocation is a process which has a biological event as ME Translocation. Similarly, binding and phosphorylation are processes annotated as ME Binding and ME Phosphorylation, respectively. The following rules define the three processes. R2: TRANSLOCATION(x 1 ) Process(x 1 ) hasbiologicalevent(x 1, ME Translocation) R3: BINDING(x 1 ) Process(x 1 ) hasbiologicalevent(x 1, ME Binding) R4: PHOSPHORYLATION(x 1 ) Process(x 1 ) hasbiologicalevent(x 1, ME Phosphorylation) The following queries, Q2, Q3, and Q4, are evaluating whether the given process satisfies some conditions. In the queries, HASINPUT and HASOUTPUT are defined as follows: HASINPUT(x 1, x 3 ) x 2, x 3.(hasConnector(x 1, x 2 ) Input(x 2 ) hasentity(x 2, x 3 )) HASOUTPUT(x 1, x 3 ) x 2, x 3.(hasConnector(x 1, x 2 ) Output(x 2 ) hasentity(x 2, x 3 )) If an entity is connected to a process via the Input connectors, then we say that the process has an input entity. On the other hand, the process has an output entity if the entity is connected to the process via Output. In the queries, DifferentFrom and SameAs, are OWL axioms for identification of individuals. Each has the form {x 1 } {x 2 } and {x 1 } {x 2 } in DL, respectively. Q2: If TRANSLOCATION(x 1 ) then If ( x i,2 i 7.HASINPUT(x 1, x 2 ) Entity(x 2 ) locatedin(x 2, x 4 ) hasxref(x 2, x 6 ) HASOUTPUT(x 1, x 3 ) Entity(x 3 ) locatedin(x 3, x 5 ) hasxref(x 3, x 7 ) DifferentFrom(x 4, x 5 ) SameAs(x 6, x 7 )) then alert Q3: If BINDING(x 1 ) then If ( 2 x 2, 1 x 3.HASINPUT(x 1, x 2 ) Entity(x 2 )) alert HASOUTPUT(x 1, x 3 ) Complex(x 3 )) then

7 Rule-Based Reasoning for System Dynamics in Cell Systems 31 Q4: If PHOSPHORYLATION(x 1 ) then If ( x i,2 i 5.HASINPUT(x 1, x 2 ) Entity(x 2 ) hasxref(x 2, x 4 ) HASOUTPUT(x 1, x 3 ) Entity(x 3 ) hasxref(x 3, x 5 ) hasfeature(x 3, FE phosphorylated) SameAs(x 4, x 5 )) then alert The definition of translocation in CSO is the process that an entity located in one cellular compartment is moved to another cellular compartment. In CSO, the same molecule in different locations is recognized as two different entities. Q2 describes that a translocation process has to satisfy the constrains that the input and output entities have the same external reference and different cellular locations. A binding process is an interaction of a molecule with specific sites on another molecule. In Q3, a binding process needs at least two input entities and generates one output entity as Complex. Formally, phosphorylation is the process of introducing a phosphate group into a molecule, usually with the formation of a phosphoric ester. In Q4, the constraints describe that the input and output entities have the same external reference and the sequence of the output entity has phosphorylated features. If the constraints are not satisfied, then prompt users for intervention (alert). Users may be guided to add missing constraints into the knowledge base Systematically correct models CSO is an ontology to represent dynamics of biological pathways and is supposed to simulate complex molecular mechanisms at different level of details. Once a mathematical model of biological pathways has been generated, it is necessary to estimate any free parameters and unknown rate constants based upon experimental data. We limit our consideration to generating a simulatable model ready for evaluation. We define a systematically correct model as a model to capture generic behaviors that govern the system dynamics. In the current state of this paper, we focused on protein turnover. Normally, proteins are synthesized within the cell and over time are gradually broken down into individual amino acids, and this cycle is repeated. To capture this behavior, we define three rules to recognize which entities are synthesized and degraded. R5 defines a starting entity as an entity except for a complex, which is connected to processes via only Input connectors. This indicates that a starting entity is not a product of any process. A predicate with a superscript of minus sign means the inverse of the predicate, e.g. hasentity. R6 identifies a starting entity whose type is complex. In addition, R7 is defined for biological entities except for genes to be degraded. R5: STARTINGENTITY(x 1 ) Entity(x 1 ) Complex(x 1 ) x 2.(hasEntity (x 1, x 2 ) Input(x 2 ))

8 32 E. Jeong, M. Nagasaki & S. Miyano R6: STARTINGCOMPLEX(x 1 ) Complex(x 1 ) x 2.((hasEntity (x 1, x 2 ) Input(x 2 )) R7: DEGRADINGENTITY(x 1 ) Protein(x 1 ) Complex(x 1 ) mrna(x 1 ) The next three queries are generated from rules R5, R6, and R7, which will complement the given models by adding new instances (add-instance) and properties (add-property). The variable in braces, e.g. {x 2 }, denotes a new instance ID. In Q5, if a given entity is STARTINGENTITY whose type is not complex, then a production process ({x 2 }) as a pre-process of the entity, a connector ({x 3 }) to relate x1 and {x 2 }, and any necessary properties are added. This will make the starting entity be a product of the production process. In Q6, if a given entity is STARTINGCOMPLEX, then we assume that the complex is generated via a binding process whose participants are the components of the complex. Depending on the number of components of the complex, multiple connectors will be added. For degrading entities including protein, complex, and mrna, a degradation process is added with a connector between the entity and the degradation process in Q7. In the Petri net formalism, adding pre-processes for starting entities (complexes) makes those processes to be fired without any constraints when the simulation is started. All entities consume their initial concentrations at the starting point of simulation. This complementation of the pathway data in CSO will help users to intuitively understand the given model and how it works. Q5: If STARTINGENTITY(x 1 ) then add-instance Process({x 2 }), OutputProcessBiological({x 3 }) add-property hasbiologicalevent({x 2 }, ME UnknownProduction), hasconnector({x 2 }, {x 3 }), hasentity({x 3 }, x 1 ) Q6: If STARTINGCOMPLEX(x 1 ) then add-instance Process({x 2 }), OutputProcessBiological({x 4 }) add-property hasbiologicalevent({x 2 }, ME Binding), hasconnector ({x 4 }, {x 2 }) for all hascomponents(x 1, x 3 ) do add-instance InputProcessBiological({x i }) add-property hasconnector (x 3, {x i }) Q7: If DEGRADEDENTITY(x 1 ) then add-instance Process({x 2 }), InputProcessBiological({x 3 }) add-property hasbiologicalevent({x 2 }, ME Degradation), hasconnector({x 2 }, {x 3 }), hasentity({x 3 }, x 1 )

9 4. Experimental Results Rule-Based Reasoning for System Dynamics in Cell Systems 33 In order to perform the rule-based system, we used AllegroGraph [17] for the CSO data storage and query engine, SPQRQL query language [20] for querying, Java applications and Perl scripts for query manipulation and knowledge base manipulation, respectively. AllegroGraph is a RDF graph database with support for SPARQL. Signaling by FGFR pathway from Reactome (ID=190236) [19] is selected as an example. The 22 members of the fibroblast growth factor (FGF) family of growth factors mediate their cellular responses by binding to and activating the different isoforms encoded by the four receptor tyrosine kinases (RTKs) designated FGFR1, FGFR2, FGFR3, and FGFR4. These receptors are key regulators of several developmental processes in which cell fate and differentiation to various tissue lineages are determined. This leads to stimulation of intracellular signaling pathways that control cell proliferation, cell differentiation, cell migration, cell survival and cell shape, depending on the cell type or stage of maturation [19]. The Reactome data exported into the BioPAX format is converted into the CSO format by BioPAX2CSO [4]. Figure 2 shows the result of BioPAX2CSO. In the figure, the squared boxes point places to be evaluated by queries described in Sec. 3. Figure 3 shows the result of ontology validation for the same model in Fig. 2. Via ontology validation, seven not-valid connections are corrected and six starting complexes have pre-binding processes. In addition, 15 unknown production and 43 degradation processes are added for starting entities and degrading entities, respectively. This validation makes the given model to be simulatable when loaded in Cell Illustrator without any changes. The results of simulation are shown as charts in the below of Fig Conclusions We have presented a rule-based approach to provide qualified knowledge bases for biological pathways. Three criteria had been proposed for ontology validation in terms of both Petri nets and biological meaning. The experimental result shows how ontology validation can be done by using rules in conjunction with CSO. The main contributions of this work are summarized as follows: (1) to give a formal representation for biological events and biological behaviors and (2) to provide new criteria for qualifying biological pathway knowledge. Our proposed method can be used for biological pathway models generated via data conversion and manual curation. In addition, it can be used as a plugin of modeling and simulating tools such as Cell Illustrator. When users create models, users are guided to generate models which are simulatable as well as biologically correct. As a result, the proposed method helps to generate qualified pathway models, which allow to easily explore the possible dynamic behavior of pathway components. In future work, we plan to define rules for the biological events defined in CSO as much as possible. Furthermore, we will define more rules to capture generic

10 34 E. Jeong, M. Nagasaki & S. Miyano Fig. 2. CSO. The signaling by FGFR pathway from Reactome (ID=190236) [19] after conversion into biological behaviors learned from modeling experts and literature. For example, the speed of processes are different depending on biological events: binding and dimerization may have different speed; the speed of natural degradation is slower than other processes; and the transcription speed of mrna is quicker than that of mirna. Moreover, time to translate a protein and time to transcribe a gene are different depending on species.

11 August 4, :42 WSPC - Proceedings Trim Size: 9.75in x 6.5in ws-gi-975x65 2e master Rule-Based Reasoning for System Dynamics in Cell Systems 35 Fig. 3. The results of ontology validation of the pathway described in Fig. 2 and the simulation results with default values of parameters. References [1] Bader, G. and Cary, M., BioPAX biological pathways exchange language level 2, version 1.0 documentation, 2005.

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