Composition and Aggregation in Modeling Regulatory Networks Clifford A. Shaffer* Ranjit Randhawa* John J. Tyson + Departments of Computer Science* and Biology + Virginia Tech Blacksburg, VA 24061

Regulatory Network Modeling Wish to deduce physiological properties of a cell from wiring diagrams of control systems

Frogegg Model

Budding Yeast Model Wiring diagrams are converted to reactions for simulation Example: Chen and Tyson’s budding yeast model contains over 30 ODEs, some nonlinear. About 140 rate constant parameters Validate model by comparing simulation results against morphological outcomes from over 100 mutants defective in the regulatory network.

Budding Yeast Model

Problem These models are reaching the limits of human comprehension Making the model suitable for stochastic simulation increases the number of reactions by a factor of 3-5. Models of the Mammalian cell cycle will require (more for stochastic simulation).

Solution Some mechanism must be found to describe models as collections of small building blocks that are combined to form the full model.

Systems Biology Markup Language SBML is the current standard interchange language within the community of systems biology modelers. We implement our proposals within the context of SBML language additions.

Prior Efforts Others (Finney; Ginkel; Schroder&Weimar; Webb) have made proposals for model decomposition within SBML. These various proposals for have never been implemented. A major problem appears to be that they view model decomposition as one monolithic problem to solve. There are actually various distinct mechanisms involved.

Our Approach We recognize four distinct activities related to model decomposition Fusion: Take existing models and merge them Composition: Build up from existing models, no information hiding Aggregation: Build up from building blocks, controlled interfaces Flattening: Merge the building blocks back into a “flat” (non-composed) model (for making simulation runs)

Relationships

Fusion Given two or more existing models, we wish to create a new model that combines the information. Remains standard SBML We provide a tool to support users combining models. Implemented in “wizard” style Status: Prototype

Fusion: Matching Tables Fusion is done primarily by defining matching of SBML components Compartments, reactions, species, etc. A series of matching tables Order is important to deal with dependencies mfmf m1m1 m2m2 1AAA 2BB 3DD mfmf m1m1 m2m2 1A1A 2CBD 3A2A

Fusion Tool Setup Wizard

Species Mapping Table

Reaction Mapping Table

Composition Connects submodels together to form a hierarchy of models Submodels are each valid SBML models Add language features to SBML to support composition Describe hierarchy Describe interactions, links, replacements No information hiding within models Relationship to fusion: the mappings are the glue.

Composition Hierarchy <compartment id="comp2" volume="1"/>

Links <to object="Submodel_Little" Issue: Merge or replace attribute information?

Is Composition the Right Model? Composition allows us to take existing models and use them as components to build larger models No information hiding Submodels might fit together more or less well Links let us replace things in one model with things in another Good for legacy models(?) We might do better to build models from components designed to work as components, with proper information hiding.

Aggregation In aggregation, models are built up from components Each component could be, for example, a collection of reactions This collection exposes certain variables for input/output via “ports” Hopefully this is a natural concept for modelers Not intended as a solution for reusing legacy models.

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Flattening Flattening generates a standard SBML file from our modified file, for the purpose of running simulations, etc. An automated form of fusion. The composition/aggregation language features provide what the user would provide during fusion, so automation is possible.