Quantitative Model Refinement in Four Different Frameworks, with Applications to the Heat Shock Response

When compiling a biological model, one often starts with an abstract representation,
that is subsequently refined through several consecutive steps to incorporate
more details regarding various reactants and/or reactions. To avoid the computationally
expensive refitting of the model after each refinement step, the new
parameters should be set so that the numerical behavior of the initial model is
preserved. The iterative process of adding details to a model while preserving its
numerical behavior is called quantitative model refinement, and it has been previously
discussed for ODE-based models and for kappa-based models. In this
paper, we investigate and compare this approach in four modeling frameworks:
ordinary differential equations, rule-based modeling, Petri nets and guarded command
languages. As case study we use a model for the eukaryotic heat shock
response that we refine to include the acetylation of one molecule. We discuss
how to perform the refinement in each of these frameworks in order to avoid the
combinatorial state explosion of the refined model. We conclude that Bionetgen
(and rule-based modeling in general) is well-suited for a compact representation
of the refined model, Petri nets offer a good solution through the use of colors,
while the PRISM refined model may be much larger than the basic model.