The Limitations of Model-Based Experimental Design and Parameter Estimation in Sloppy Systems.

We explore the relationship among experimental design, parameter estimation, and systematic error in sloppy models. We show that the approximate nature of mathematical models poses 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 be included 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 become relevant. When this occurs, the model will have a large systematic error and fail to give a good 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 and DNA repair) with optimally selected experiments. We find that although parameters may be accurately estimated, the discrepancy in the model renders it less predictive than it was in the sloppy regime where systematic error is small. We introduce the concept of a sloppy system-a sequence of models of increasing complexity that become sloppy in the limit of microscopic accuracy. We explore the limits of accurate parameter estimation in sloppy systems and argue that identifying underlying mechanisms controlling system behavior is better approached by considering a hierarchy of models of varying detail rather than focusing on parameter estimation in a single model.

Use of the LQ model with large fraction sizes results in underestimation of isoeffect doses.

PURPOSE: To test the appropriateness of the linear-quadratic (LQ) model to describe survival of jejunal crypt clonogens after split doses with variable (small 1-6 Gy, large 8-13 Gy) first dose, as a model of its appropriateness for both small and large fraction sizes. METHODS: C3Hf/KamLaw mice were exposed to whole body irradiation using 300 kVp X-rays at a dose rate of 1.84 Gy/min, and the number of viable jejunal crypts was determined using the microcolony assay. 14 Gy total dose was split into unequal first and second fractions separated by 4 h. Data were analyzed using the LQ model, the lethal potentially lethal (LPL) model, and a repair-saturation (RS) model. RESULTS: Cell kill was greater in the group receiving the larger fraction first, creating an asymmetry in the plot of survival vs size of first dose, as opposed to the prediction of the LQ model of a symmetric response. There was a significant difference in the estimated ßs (higher ß after larger first doses), but no significant difference in the αs, when large doses were given first vs small doses first. This difference results in underestimation (based on present data by approximately 8%) of isoeffect doses using LQ model parameters based on small fraction sizes. While the LPL model also predicted a symmetric response inconsistent with the data, the RS model results were consistent with the observed asymmetry. CONCLUSION: The LQ model underestimates doses for isoeffective crypt-cell survival with large fraction sizes (in the present setting, >9 Gy).