We explore the relationship among experimental design, parameter estimation, and systematic error in sloppy models. We show that the approximate nature of mathematical modelsposes challenges for experimental design in sloppy models. In many models of complex biological processes it is unknown what are the relevant physical mechanisms that must beincluded to explain system behaviors. As a consequence, models are often overly complex,with many practically unidentifiable parameters. Furthermore, which mechanisms are relevant/irrelevant vary among experiments. By selecting complementary experiments, experimental design may inadvertently make details that were ommitted from the model becomerelevant. When this occurs, the model will have a large systematic error and fail to give agood fit to the data. We use a simple hyper-model of model error to quantify a model’s discrepancy and apply it to two models of complex biological processes (EGFR signaling andDNA repair) with optimally selected experiments. We find that although parameters may beaccurately estimated, the discrepancy in the model renders it less predictive than it was inthe sloppy regime where systematic error is small. We introduce the concept of a sloppysystem–a sequence of models of increasing complexity that become sloppy in the limit ofmicroscopic accuracy. We explore the limits of accurate parameter estimation in sloppy systems and argue that identifying underlying mechanisms controlling system behavior is betterapproached by considering a hierarchy of models of varying detail rather than focusing onparameter estimation in a single model.
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