Discovery in developmental biology is often driven by intuition that relies on the integration of multiple types of data such as fluorescent images, phenotypes, and the outcomes of biochemical assays. Mathematical modeling helps elucidate the biological mechanisms at play as the networks become increasingly large and complex. However, the available data is frequently under-utilized due to incompatibility with quantitative model tuning techniques. This is the case for stem cell regulation mechanisms explored in the Drosophila germarium through fluorescent immunohistochemistry. To enable better integration of biological data with modeling in this and similar situations, we have developed a general parameter estimation process to quantitatively optimize models with qualitative data. The process employs a modified version of the Optimal Scaling method from social and behavioral sciences, and multi-objective optimization to evaluate the trade-off between fitting different datasets (e.g. wild type vs. mutant). Using only published imaging data in the germarium, we first evaluated support for a published intracellular regulatory network by considering alternative connections of the same regulatory players. Simply screening networks against wild type data identified hundreds of feasible alternatives. Of these, five parsimonious variants were found and compared by multi-objective analysis including mutant data and dynamic constraints. With these data, the current model is supported over the alternatives, but support for a biochemically observed feedback element is weak (i.e. these data do not measure the feedback effect well). When also comparing new hypothetical models, the available data do not discriminate. To begin addressing the limitations in data, we performed a model-based experiment design and provide recommendations for experiments to refine model parameters and discriminate increasingly complex hypotheses.
Author Summary
We developed a process to quantitatively fit mathematical models using qualitative data, and applied it in the study of how stem cells are regulated in the fruit fly ovary. The available published data we collected are fluorescent images of protein and mRNA expression from genetic experiments. Despite lacking quantitative data, the new process makes available quantitative model analysis techniques to reliably compare different models and guide future experiments. We found that the current consensus regulatory model is supported, but that the data are indeed insufficient to address more complex hypotheses. With the quantitatively fit models, we evaluated hypothetical experiments and estimated which future measurements should best refine or test models. The model fitting process we have developed is applicable to many biological studies where qualitative data are common, and can accelerate progress through more efficient experimentation.