Quantitative model refinement in four different frameworks, with applications to the heat shock response

Quantitative model refinement is an essential step in the model development cycle. Starting with a high level, abstract representation of a biological system, one often needs to add details to this representation to reflect changes in its constituent elements. Any such refinement step has two aspects: one structural and one quantitative. The structural aspect of the refinement defines an increase in the resolution of its representation, while the quantitative one specifies a numerical setup for the model that ensures its fit preservation at every refinement step. We discuss in this paper the implementation of quantitative model refinement in four extensively used bio-modelling frameworks: ODE-based models, rule-based models, Petri net models, and guarded command language models, emphasizing the specificity for every model implementation. We argue that quantitative model refinement is framework-independent, being implementable in all chosen frameworks despite their different underlying modelling paradigms. Quantitative model refinement is an essential step in the model development cycle. Starting with a high level, abstract representation of a biological system, one often needs to add details to this representation to reflect changes in its constituent elements. Any such refinement step has two aspects: one structural and one quantitative. The structural aspect of the refinement defines an increase in the resolution of its representation, while the quantitative one specifies a numerical setup for the model that ensures its fit preservation at every refinement step. We discuss in this paper the implementation of quantitative model refinement in four extensively used bio-modelling frameworks: ODE-based models, rule-based models, Petri net models, and guarded command language models, emphasizing the specificity for every model implementation. We argue that quantitative model refinement is framework-independent, being implementable in all chosen frameworks despite their different underlying modelling paradigms.