Qualitative causal analyses of biosimulation models Maxwell L. Neal1, John H. Gennari1, Daniel L. Cook1,2 1 Department of Biomedical Informatics and Medical Education 2 Department of Physiology and Biophysics University of Washington Seattle, WA, USA mneal@uw.edu Abstract—We describe an approach for performing qualita- latter, a user can identify which model variables, if perturbed, tive, systems-level causal analyses on biosimulation models that would shift a variable of interest in a given direction. In this leverages semantics-based modeling formats, formal ontology, case a user might ask, “Which perturbations will cause glucose and automated inference. The approach allows users to quickly concentration to increase?” Such thought experiments are a investigate how a qualitative perturbation to an element within a routine and valuable tool researchers use for understanding and model’s network (an increment or decrement) propagates validating hypotheses derived from their empirical studies. We throughout the modeled system. To support such analyses, we anticipate that giving modelers this systems-level perspective must interpret and annotate the semantics of the models, includ- will help guide systems biology experiments and drug target ing both the physical properties modeled and the dependencies identification, as well as model-based clinical decision making. that relate them. We build from prior work understanding the semantics of biological properties, but here, we focus on the se- To perform our qualitative causal analyses, we used auto- mantics for dependencies, which provide the critical knowledge mated inference to programmatically identify the dependencies necessary for causal analysis of biosimulation models. We de- (e.g., chemical reaction rate laws, conservation laws) used in a scribe augmentations to the Ontology of Physics for Biology, via set of test models and the qualitative relations between the OWL axioms and SWRL rules, and demonstrate that a reasoner physical properties (e.g., chemical concentrations, fluid pres- can then infer how an annotated model’s physical properties sures) that participate in those dependencies. Using this infor- influence each other in a qualitative sense. Our goal is to provide mation, we then identify how an increment or decrement in a researchers with a tool that helps bring the systems-level network physical property propagates to other properties in the model. dynamics of biosimulation models into perspective, thus facilitat- ing model development, testing, and application. For example, by semantically identifying the instances of first- order mass-action rate laws used in a chemical network model, Keywords—automated inference; biosimulation; biological a reasoner can infer how the physical properties involved in modeling; network analysis those laws interact, qualitatively. We can then determine how a reaction rate will, say, respond to an increase in the amount of I. INTRODUCTION & BACKGROUND one of its reactants. While running iterative simulations on Biomedical researchers develop computational models to isolated physical dependencies might also be used to accom- understand and predict the dynamics of biological processes. plish this task, it is difficult to determine appropriate parameter With increasing access to computational power and systems- ranges for such simulations so that the approach generalizes level biological data, these models continue to grow in size and across physical scales and modeling domains. We therefore complexity. There is therefore a growing need for informatics developed an ontology-based approach for automatically clas- tools that will help researchers quickly obtain system-level sifying dependencies and for characterizing the roles that the perspectives on these models so they can readily ascertain a properties in those dependencies play. model’s architecture, its underlying assumptions, and how its Here we describe our qualitative reasoning approach and components interact. Additionally, as models become more demonstrate it with a published chemical network model. Our complex, the time required to generate simulation results can approach includes two steps. First, we classify physical de- impede research. Motivated by these needs, we have developed pendencies within the OPB and use reasoning to characterize an approach for performing qualitative causal analyses over the roles played by the properties in such dependencies. Se- biosimulation models that leverages the formal semantic struc- cond, we apply a simple algorithm that propagates perturba- ture of the Ontology of Physics for Biology (OPB [1], [2]), the tions in physical property values (increments or decrements) Semantic Simulation (SemSim) framework [3], [4], and auto- through the dependency network. To implement the first step, mated ontological inference. Our aim is to develop software we augmented the OPB with a set of Web Ontology Language that will allow users to quickly investigate the qualitative ef- (OWL) axioms and Semantic Web Rule Language (SWRL) fects of perturbation experiments on biosimulation models and rules necessary for characterizing how the physical properties to identify perturbations that would influence a model element in a dependency influence each other, qualitatively. Thus, of interest. With the former, users can investigate the impact of when we annotate a biosimulation model against the OPB, we a shift in the value of a model variable and ascertain the sys- can apply a standard OWL reasoner to infer the information tem-wide consequences. For example, a user investigating a needed to trace perturbations throughout a model’s math metabolism dynamics might ask, “What are the consequences dependency network. of increasing glucose concentration in the model?” With the This work was funded by National Institutes of Health (http://www.nih.gov/) grants R01LM011969, P50GM094503, and U01HL122199 Fig. 1. Workflow by which SemGen imports and parses biosimulation model source code (right) and abstracts a SemSim model (in OWL) which is annotated against instances of OPB:Physical property classes. By combining the knowledge in the OPB and the SemSim model we instantiate a “math dependency map” which we traverse to propagate qualitative perturbations of physical property values. A. Model semantics and the Ontology of Physics for Biology putational data structures that represent the quantitative values of model variables. OPB:Physical property is a dual inher- Biosimulation models are becoming more readily available itance hierarchy that distinguishes dynamical property type as public repositories such as BioModels [5] and the Physiome (e.g., forces vs. flow rates vs. amounts) and dynamical domain Model Repository [6] grow in size, and as standardized (e.g., fluid domain vs. chemical domain vs. electrical domain). modeling formats such as the Systems Biology Markup Thus, a variable representing blood flow rate in the aorta, say, Language (SBML) [7] and CellML [8] gain wider adoption. To is semantically distinct and non-conformable with a variable make repositories more useful and amenable to automated for cytosolic glucose concentration. inference, a first step is to annotate model elements to provide explicit semantics for the code-level representations of these The OPB:Physical dependency hierarchy represents math- models. Although standard modeling formats often support ematical dependencies between physical property values. This biological semantic annotation, little research has been carried hierarchy is also dual-inheritance; the OPB dependencies are out to describe the semantics of the physical dependencies (the sub-classed according to dynamical domain and by dynamical mathematical laws used to relate values of physical properties dependency type. For example, an instance of OPB:Resistive to each other) being modeled. We must make these associa- dependency represents an occurrence of a process governed by tions explicit because our qualitative causal analyses require an an analog of Ohm’s Law. Thus, in the electrical domain an explicit representation of how physical dependencies determine electrical current depends on an electrical voltage and the elec- the influence that physical properties have on each other. We trical resistance in the conducting pathway: I=V/R, classically. therefore annotate the semantics of a model’s mathematical Likewise, in the fluid domain, a fluid flow rate depends on a relationships using the OPB, which includes a taxonomy of pressure difference and a fluid flow resistance (an analog of physical dependencies and properties used in biosimulation electrical resistance). In the OPB schema, each OPB:Physical models across biological scales [1], [2]. property instance has two key relations. First, it is linked by a hasPhysicalProperty relation to an instance of the entity or The OPB is a reference ontology that aims to provide a process that bears the property, and by a hasPropertyPlayer to comprehensive, formal representation of the concepts used in the OPB:Physical dependency instance according to the model modeling biophysical processes. It includes, for example, an code. In Section II we describe extensions to the OPB:Physical property taxonomy for annotating model OPB:hasPropertyPlayer relations required for tracking proper- variables (e.g., OPB:Charge amount for electrical charges) and ty value perturbations through a modeled system. an OPB:Physical dependency taxonomy (e.g., OPB:Electrical resistive dependency for Ohm’s Law) for representing the B. The SemSim framework biophysical meaning of a model’s mathematical dependencies. Based on the biophysical semantics of the OPB, we estab- Previously, we have leveraged the OPB for multi-scale model lished the SemSim model framework for annotating and repre- integration tasks [4], [9]. As shown in the middle panel of Fig- senting the mathematics of simulation models (Figure 1). Each ure 1, we use OPB:Physical property classes to annotate com- SemSim model represents the computational structure of a model and provides a logical framework for annotating its var- of capacitance used in electrical dynamics models. Instead of iables and computations in terms of OPB classes. Applications pressure, volume and compliance, the electrical analog relates of the SemSim framework are limited in our work to the do- voltage, charge, and capacitance. As shown in Figure 2, these main of discrete causal models written and archived using two physical dependencies are subclasses of OPB:Capacitive ordinary differential equations. In prior work, we have created force dependency, which subsumes analogous versions of this SemSim models to annotate, decompose, and recompose law for each physical domain represented in the OPB. models in any of several modeling languages: SBML, CellML, and JSim’s Mathematical Modeling Language [10]. To accomplish this we have developed SemGen [4], [9], a Java- based semantic modeling application that automatically creates SemSim models from models coded in these languages. The SemSim framework relies on composite annotations [3] to formally describe the biological meaning of model elements, and SemGen provides tools for creating these annotations de novo and for auto-generating them from annotations present in curated models such as the those in BioModels. Each composite annotation consists of an instance of an OPB:Physical property class that identifies the physical property type of the variable and is classifiable within the OPB:Physical property hierarchy. As we describe below, this critical feature allows us to automatically identify the Fig. 2. Location of Capacitive force dependency in the OPB class hierarchy. mathematical dependencies as pathways by which perturbations propagate throughout a set of modeled properties. Leveraging this hierarchical structure, our approach for au- II. METHODS tomatically identifying the physical dependencies used in our test models was to first create logical definitions in the form of To support causal qualitative reasoning, we must augment OWL equivalent class expressions for higher-level OPB physi- the OPB, apply a standard OWL reasoner to produce the math cal dependency classes. These statements define physical de- dependency map, and then apply an algorithm to determine pendencies in terms of the physical properties that participate how qualitative perturbations propagate through a model’s in them. We term these participating physical properties “prop- mathematical network. There are two types of semantic aug- erty players”, language that is reflected in the object property mentations we add to the OPB: axioms that define dependen- names used to construct our logical class definitions. For ex- cies based their property players, and axioms and rules that ample, we used the following equivalent class expression to determine which properties are positive or negative players in a define OPB:Capacitive force dependency, presented here in dependency. Manchester style syntax: A. Classifying physical dependencies in the OPB ((hasPropertyPlayer some Capacitance) or The first steps in performing our qualitative analyses are to (hasPropertyPlayer some Elastance)) convert a model into the SemSim format using SemGen and and (hasPropertyPlayer some 'Amount property') and (hasSolvedPropertyPlayer some 'Force proper- then annotate its physical properties against the OPB. As we ty') will describe below, this step allows us to then classify the physical dependencies in the model and automatically infer the We then applied simple equivalent class axioms to define qualitative influence that physical properties have on each oth- the domain-specific subclasses of OPB:Capacitive force de- er. Many of the models we tested for this study were curated pendency. For example, the equivalency axiom for OPB:Fluid SBML models from BioModels. For these we were able to use capacitive dependency is SemGen to automatically annotate the model’s physical prop- erties against OPB classes, the physical entities they are prop- 'Capacitive force dependency' and (hasPropertyPlayer only (hasPhysicalDomain erties of, and the processes in which the entities participate. We some 'Fluid kinetic domain')) then leveraged this critical information to identify the qualita- tive role that the properties play in the model’s dependencies. This captures the knowledge that OPB:Fluid capacitive de- Since publicly available models do not contain annotations pendency is an OPB:Capacitive force dependency that only against the OPB that indicate which mathematical dependen- relates physical properties from the fluid kinetic domain. cies are used in a model, we developed a method for automati- B. Characterizing the qualitative influence among properties cally classifying a model’s physical dependencies within the OPB hierarchy. To provide an example of a physical depend- To represent how the different physical properties in a de- ency and how we classify it, consider the law of fluid compli- pendency will react to a perturbation in one of those properties, ance, often used in hemodynamic models: P = V/C. Here P is we first identify the physical property that is the “output” of the the transmural fluid pressure in a compartment, V is the com- dependency, as represented in the original SemSim model. partment fluid volume, and C is the compartment compliance. SemSim models currently represent equations as having one (Modelers may choose to use a fluid elastance instead of com- output variable on the left hand side (LHS) and the expression pliance as they are reciprocal.) This law is analogous to the law that solves it on the right hand side (RHS). We use OWL ob- ject property axioms such as Dependency_A Property_B to capture the knowledge that Proper- tions: ty_B is on the LHS of Dependency_A. Physical properties on hasSolvedPropertyPlayer(?dep1, ?prop1), the RHS that produce the same response in the solved property hasPropertyPlayer(?dep1, ?prop2), when increased or decreased are termed “positive property physicalPropertyOf(?prop1, ?ent1), players”. Properties that produce a change in the opposite di- hasSource(?process, ?ent1), physicalPropertyOf(?prop2, ?process) rection are termed “negative property players.” This -> hasNegPropertyPlayer(?dep1, ?prop2) knowledge is captured using object property statements on the physical dependency individuals such as Dependency_A The rule states that if a physical dependency solves for a Property_C. For example, the fluid property of a physical entity, and there is a property of a pro- volume property in the fluid compliance law mentioned above cess that consumes the entity on the RHS, then the latter prop- is a positive property player in the dependency; if increased, erty is a negative player in the dependency. As a specific ex- the solved fluid pressure property on the LHS also increases. ample, this rule indicates that for all reactants in a reaction, the Conversely, the fluid compliance property is a negative proper- reaction rate is a negative player in the conservation equation ty player in the dependency: if it is increased, fluid pressure that determines the amount of the reactant. Thus, if the reaction decreases. Because SemSim models do not include these axi- rate increases, the reactant amount decreases. We created a oms, we use class restriction axioms on OPB dependency clas- similar rule for dependencies that solve for the amount of ses, a set of SWRL rules, and a reasoning engine to generate products involved in reactions. In this case, the reaction rate is them automatically. For example, we added the following class a positive player in the dependency. We also created three ad- restriction to OPB:Capacitive force dependency: ditional SWRL rules to identify the polarity of property players (hasPosPropertyPlayer exactly 1 'Amount property') in dependencies that solve for reaction rates: and (((hasPropertyPlayer exactly 1 Capacitance) and (hasNegPropertyPlayer exactly 1 Capacitance)) 1. If a process rate is solved using the property of a thermo- or ((hasPropertyPlayer exactly 1 Elastance) dynamic source of that process, then the source property and (hasPosPropertyPlayer exactly 1 Elastance))) is a positive player This axiom indicates that if a physical dependency individ- 2. If a process rate is solved using the property of ual is classified as an OPB:Capacitive force dependency, it a thermodynamic sink of that process, then the sink prop- must have exactly one positive property player that is an erty is a negative player OPB:Amount property (e.g., fluid volume or electrical charge), 3. If a process rate is solved using the property of a mediator along with one negative player that is an OPB:Capacitance of that process, then the mediator property is a positive (e.g., fluid compliance or electrical capacitance) or one positive player player that is an OPB:Elastance (e.g., fluid elastance or electri- Rule 1, for example, identifies reactant concentrations on the cal elastance). In combination with the equivalent class axioms RHS of first-order reaction rate equations as positive players in mentioned above, an automated reasoner can infer from these those equations; as reactant concentration increases, so does axioms that if a physical dependency is an OPB:Capacitive the reaction rate. We achieved our inference goals applying force dependency and it has one fluid compliance property only a very few SWRL rules because the basic dependency player, then the compliance is a negative property player. As relations are declared at a superclass level in the OPB:Physical described in Section III, we can then use this knowledge to dependency hierarchy. Thus, a single SWRL rule suffices for determine how a perturbation in the compliance will affect the both fluid and electrical analogs of Ohm’s Law (i.e., fluid pressure property in the dependency. OPB:Resistive flow dependency) or for Hooke’s Law (i.e., These class restriction axioms are effective for characteriz- OPB:Capacitice force dependency; see Figure 2) as examples. ing properties as positive or negative players when the proper- C. Automatically inferring math dependency maps ties differ in type, as in our fluid compliance law example. However, they are less effective when multiple instances of the To automatically classify the dependencies in a model and same property type are on the RHS of a dependency. For ex- identify their positive and negative players, we first automati- ample, the mass conservations equations used to compute fluid cally instantiated the SemSim model’s physical dependencies, volume changes in hemodynamic models or the species properties, entities and processes as OWL individuals in our amounts in chemical network models often have multiple flow augmented OPB. Properties were asserted as individuals in rates on the RHS. These rates may be positive or negative whichever OPB:Physical property class was used in their com- players, depending on the model’s formulation. For example, posite annotation. Dependencies, entities and processes were the conservation equations that determine chemical species asserted as individuals in the top-level OPB classes represent- amounts are often formulated by summing the rates of the reac- ing these concepts. Using the SemSim object model underly- tions that produce a species and subtracting those that consume ing SemGen, we automatically identified which dependencies it. The rate of a reaction that consumes a chemical would be a involved which property players. As mentioned above, we as- negative player in the dependency, while the rate of a reaction serted this knowledge by applying hasSolvedPropertyPlayer that produces it would be a positive player. To determine the and hasPropertyPlayer object property axioms on the depend- polarity of the property players in these dependencies, we cre- ency individuals. We then used HermiT [11] version 1.3.8 to ated five SWRL rules that leverage the model’s underlying programmatically classify the resulting ontology and infer biological semantics. As an example, the following rule identi- which properties were positive players in the model’s depend- encies and which were negative. This single classification step simultaneously reasons over the new OPB OWL class re- partial differentials between dependent variables. Even with strictions and the SWRL rules described above to generate a this assumption, however, ambiguities can arise when an in- math dependency map for that model. In the next section, we crement converges with a decrement to produce an ambiguous describe how we used the inferred information from the rea- result resolvable only by quantitative analysis. That being said, soner to traverse this map and determine the outcomes of per- an ambiguity resulting from feedback may be interpretable: a turbation experiments. positive feedback loop will only reinforce the originating per- turbation while one might be able to assume that a negative III. QUALITATIVE PERTURBATION EXPERIMENTS feedback signal is quantitatively less than the originating signal The inferences produced by the HermiT reasoner include and, hence, can be ignored by the propagation algorithm. How- the knowledge necessary to determine how an increment or ever, we would caution that the longer the pathway, the less decrement in a given physical property within a dependency confidence one might have in the result, especially in highly will affect the property that is solved by the dependency. To coupled networks. investigate the system-wide effects of such perturbations, we B. Example perturbation experiment developed a Java-based algorithm that takes as input a property perturbation (an increment or decrement), and determines how Figure 3 illustrates the results of our approach. It shows the that perturbation propagates throughout the math dependency outcome of a qualitative perturbation experiment on BioModel network of the model. This algorithm, similar to those used in #313, an SBML-encoded model that simulates the Janus kinase colored petri net analyses, is based on the “PathTracing” func- signaling pathway in a primary mediastinal B-cell lymphoma tion of the Chalkboard software for composing and investigat- cell line. In the model’s source publication [13], the authors ing the dynamics of network models [12]. Our algorithm be- used numerical sensitivity analysis to identify the STAT5 pro- gins by identifying the dependencies in which the perturbed tein as a potential drug target that could reduce the amount of property participates, determines how the perturbation affects CD274, an mRNA associated with cell proliferation. Guided the dependency’s solved property based on the perturbed prop- by this result, we tested whether our qualitative approach erty’s positive/negative player status, records how the solved would generate similar results. We converted the SBML model property is perturbed, then continues iteratively by identifying into the SemSim format, used automatic classification to iden- the dependencies in which the solved property participates. tify the positive and negative players in the model’s dependen- Iteration continues until the algorithm returns to the original cies, and performed a perturbation experiment where we de- perturbed property or, in the case of negative feedback loops, if creased STAT5. Automatic classification of the model via it finds that a physical property is both increased and decreased HermiT finished in four seconds on a MacBook Pro 2.8 GHz by a perturbation. The algorithm then lists the physical proper- Intel Core 2 Duo laptop. Performing the perturbation on the ties that are increased by the perturbation, those that are de- classified ontology’s math dependency network is much faster, creased, and those that are influenced in both directions (an finishing in 33 milliseconds. As shown in Figure 3, the net- ambiguous effect). work-wide results of the perturbation experiment include a decrease in CD274 mRNA. By simply reversing this algorithm and traversing the math dependency map in the opposite direction, we are also able to IV. DISCUSSION investigate which perturbations will cause a property of interest This study demonstrates how the comprehensive, hierar- to increase or decrease. In this case, the inputs to the algorithm chical knowledge contained in the OPB can be leveraged to are a property of interest, and whether it is increased or de- automatically identify physical dependencies in models and creased. The algorithm then lists how to perturb the other prop- then characterize how the physical properties in these models erties in the model to shift the property of interest in the speci- influence each other. This inferred knowledge can form the fied direction. basis of qualitative perturbation experiments, as reported here, A. Scope and caveats but it could also potentially be used to help guide and/or auto- mate the model annotation process. For example, once a mod- Before describing the performance of our qualitative infer- el’s physical dependencies are classified within the OPB, this ence methods, we want to properly position our work and tools knowledge could be applied to flag inconsistent model annota- in the context of biological research and modeling. Our aim is tions and also suggest which OPB terms to use for un- to offer a “thinking tool” of practical use to those who struggle annotated physical properties. to understand the behavior of complex causal networks. From our own experience, both investigators and students routinely Our intent with this work is not to supplant the more pre- explore the behavior of these systems by tracing event paths cise, quantitative analyses that numerical simulations of bi- through both informal and consensus network representations. osimulation models provide, but rather develop an additional Thus, our methods are intended to formalize, illustrate and tool that researchers can use to quickly check model assump- explore biological hypotheses. tions and explore how qualitative perturbations propagate through networks. The perturbation experiment shown in Fig- We are well aware of important assumptions and limita- ure 3 demonstrates that we can quickly generate systems-level tions to the qualitative pathway analysis that we have imple- information that could potentially help researchers identify mented. First, we assume that the system is at a stable operat- drug targets without the costs associated with iterative numeri- ing point far away from dynamical instabilities and that pertur- cal simulation. While a concern for the use of rich ontological bations are infinitesimal. Thus, we assume that perturbations representations and inference can be the computation cost of propagate through the system without changing the signs of the general-purpose reasoning engines, our experience shows that Fig. 3. BioModel #313 reaction network. Overlaid are the results of a qualitative perturbation experiment where species STAT5 is decreased. Qualitative shifts for species and reactions are indicated in rectangles below nodes. Yellow rectangles indicate an ambiguous shift. Rectangles are absent for nodes unaffected by the perturbation. for models similar in size to that of Figure 3, generating the [3] J. H. Gennari, M. L. Neal, M. Galdzicki, and D. L. 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