Abstract
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.
Highlights
Biological systems are often characterized using qualitative data, such as stained images, immunoblots, microarrays, or observations of cell morphology, rather than absolute values
We address these limitations in model-data integration in the context of a stem cell niche in the Drosophila germarium, as the available data are largely qualitative and it has become a model system from which we hope to gain insight into stem cell regulation
The regulation of stem cell self-renewal vs. differentiation depends on signaling by Decapentaplegic (Dpp), a bone morphogenic protein (BMP) ligand homologue, which is expressed by the cap cells
Summary
Biological systems are often characterized using qualitative data, such as stained images, immunoblots, microarrays, or observations of cell morphology, rather than absolute values (e.g. molecular concentration). We estimate Representative parameter sets (Pareto points, in this study) for each model and discriminate among models based on their simultaneous fitness to published qualitative protein and mRNA distribution data from wild type and mutant organisms. Representative parameter estimation procedure We developed a new approach to search for Representatives that best satisfy qualitative data, which incorporates three elements: (1) the novel application of Optimal Scaling to quantitatively estimate model fitness, (2) global optimization to select a single best solution for each objective, and (3) multiobjective optimization to find a set of Representatives irrespective of weighting among objectives Predictions for the 2nd experiment, Nos in Nos +/2 Dpp +/2, show wide variance among Representatives, with little difference among models in either mean values or distributions (Figure 8B) Based on these predicted simulations, we expect that a combination of experiments designed to reduce parameter uncertainty and to subsequently discriminate will be most effective. It is important to properly represent the conditions of the experiment, so models may need to be adapted
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