Composition and Aggregation in Modeling Regulatory Networks

Clifford A. Shaffer*Ranjit Randhawa*

John J. Tyson+

Departments of Computer Science* and Biology+

Virginia TechBlacksburg, 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 100-1000 (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 SBMLWe 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

mf m1 m2

1 A A A

2 B B

3 D D

mf m1 m2

1 A1 A

2 C B D

3 A2 A

Fusion Tool Setup Wizard

Species Mapping Table

Reaction Mapping Table

Composition

Connects submodels together to form a hierarchy of modelsSubmodels are each valid SBML modelsAdd language features to SBML to support composition Describe hierarchy Describe interactions, links, replacements

No information hiding within modelsRelationship to fusion: the mappings are the glue.

Composition Hierarchy

<model id="Big"> <listOfCompartments> <compartment id="comp1" volume="1"/> </listOfCompartments> <listOfSubmodels> <model id="Little"> <listOfCompartments> <compartment id="comp2" volume="1"/> </listOfCompartments> </model> </listOfSubmodels></model>

Links

<link>

<from object="comp1"/>

<to object="Submodel_Little"

<subobject object="comp2"/>

</to>

</link>

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 modelsNo information hidingSubmodels might fit together more or less well Links let us replace things in one model with things in

anotherGood 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 componentsEach component could be, for example, a collection of reactionsThis collection exposes certain variables for input/output via “ports”Hopefully this is a natural concept for modelersNot intended as a solution for reusing legacy models.

Toggle Switch

Iconified Toggle Switch

Toggle Switch Component

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.