Model Composition and Aggregation in Macromolecular Regulatory Networks
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Mathematical models of regulatory networks become more difficult to construct and understand as they grow in size and complexity. Large regulatory network models can be built up from smaller models, representing subsets of reactions within the larger network. This dissertation focuses on novel model construction techniques that extend the ability of biological modelers to construct larger models by supplying them with tools for decomposing models and using the resulting components to construct larger models. Over the last 20 years, molecular biologists have amassed a great deal of information about the genes and proteins that carry out fundamental biological processes within living cells --- processes such as growth and reproduction, movement, signal reception and response, and programmed cell death. The full complexity of these macromolecular regulatory networks is too great to tackle mathematically at the present time. Nonetheless, modelers have had success building dynamical models of restricted parts of the network. Systems biologists need tools now to support composing "submodels" into more comprehensive models of integrated regulatory networks. We have identified and developed four novel processes (fusion, composition, flattening, and aggregation) whose purpose is to support the construction of larger models. Model Fusion combines two or more models in an irreversible manner. In fusion, the identities of the original (sub)models are lost. Beyond some size, fused models will become too complex to grasp and manage as single entities. In this case, it may be more useful to represent large models as compositions of distinct components. In Model Composition one thinks of models not as monolithic entities but rather as collections of smaller components (submodels) joined together. A composed model is built from two or more submodels by describing their redundancies and interactions. While it is appealing in the short term to build larger models from pre-existing models, each developed independently for their own purposes, we believe that ultimately it will become necessary to build large models from components that have been designed for the purpose of combining them. We define Model Aggregation as a restricted form of composition that represents a collection of model elements as a single entity (a "module"). A module contains a definition of pre-determined input and output ports. The process of aggregation (connecting modules via their interface ports) allows modelers to create larger models in a controlled manner. Model Flattening converts a composed or aggregated model with some hierarchy or connections to one without such connections. The relationships used to describe the interactions among the submodels are lost, as the composed or aggregated model is converted into a single large (flat) model. Flattening allows us to use existing simulation tools, which have no support for composition or aggregation.
- Doctoral Dissertations