Statistical tools and community resources for developing trusted models in biology and chemistry
Keywords: Model identifiability
Bayesian inference
Approximate Bayesian computation
Reproducibility
Cardiac cell modeling

Mathematical modeling has been instrumental to the development of natural sciences over the last half-century. Through iterated interactions between modeling and real-world exper- imentation, these models have furthered our understanding of the processes in biology and chemistry that they seek to represent. In certain application domains, such as the field of car- diac biology, communities of modelers with common interests have emerged, leading to the development of many models that attempt to explain the same or similar phenomena. As these communities have developed, however, reporting standards for modeling studies have been in- consistent, often focusing on the final parameterized result, and obscuring the assumptions and data used during their creation. These practices make it difficult for researchers to adapt exist- ing models to new systems or newly available data, and also to assess the identifiability of said models — the degree to which their optimal parameters are constrained by data — which is a key step in building trust that their formulation captures truth about the system of study.
In this thesis, we develop tools that allow modelers working with biological or chemical time series data to assess identifiability in an automated fashion, and embed these tools within a novel online community resource that enforces reproducible standards of reporting and facilitates exchange of models and data.
We begin by exploring the application of Bayesian and approximate Bayesian inference methods, which parameterize models while simultaneously assessing uncertainty about these estimates, to assess the identifiability of models of the cardiac action potential. We then demon- strate how the side-by-side application of these Bayesian and approximate Bayesian methods can be used to assess the information content of experiments where system observability is limited to "summary statistics" — low-dimensional representations of full time-series data.
We next investigate how a posteriori methods of identifiability assessment, such as the above inference techniques, compare against a priori methods based on model structure. We compare these two approaches over a range of biologically relevant experimental conditions, and high- light the cases under which each strategy is preferable. We also explore the concept of optimal experimental design, in which measurements are chosen in order to maximize model identifia- bility, and compare the feasibility of established a priori approaches against a novel a posteriori approach.
Finally, we propose a framework for representing and executing modeling experiments in a reproducible manner, and use this as the foundation for a prototype "Modeling Web Lab" where researchers may upload specifications for and share the results of the types of inference explored in this thesis. We demonstrate the Modeling Web Lab’s utility across multiple mod- eling domains by re-creating the results of a contemporary modeling study of the hERG ion channel model, as well as the results of an original study of electrochemical redox reactions.
We hope that this works serves to highlight the importance of both reproducible standards of model reporting, as well as identifiability assessment, which are inherently linked by the desire to foster trust in community-developed models in disciplines across the natural sciences.