Universally Sloppy Parameter Sensitivities in Systems Biology Models

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Abstract
Quantitative computational models play an increasingly important role in modern biology. Such models typically involve many free parameters, and assigning their values is often a substantial obstacle to model development. Directly measuring in vivo biochemical parameters is difficult, and collectively fitting them to other experimental data often yields large parameter uncertainties. Nevertheless, in earlier work we showed in a growth-factor-signaling model that collective fitting could yield well-constrained predictions, even when it left individual parameters very poorly constrained. We also showed that the model had a “sloppy” spectrum of parameter sensitivities, with eigenvalues roughly evenly distributed over many decades. Here we use a collection of models from the literature to test whether such sloppy spectra are common in systems biology. Strikingly, we find that every model we examine has a sloppy spectrum of sensitivities. We also test several consequences of this sloppiness for building predictive models. In particular, sloppiness suggests that collective fits to even large amounts of ideal time-series data will often leave many parameters poorly constrained. Tests over our model collection are consistent with this suggestion. This difficulty with collective fits may seem to argue for direct parameter measurements, but sloppiness also implies that such measurements must be formidably precise and complete to usefully constrain many model predictions. We confirm this implication in our growth-factor-signaling model. Our results suggest that sloppy sensitivity spectra are universal in systems biology models. The prevalence of sloppiness highlights the power of collective fits and suggests that modelers should focus on predictions rather than on parameters. Dynamic systems biology models typically involve many kinetic parameters, the quantitative determination of which has been a serious obstacle to using these models. Previous work showed for a particular model that useful predictions could be extracted from a fit long before the experimental data constrained the parameters, even to within orders of magnitude. This was attributed to a “sloppy” pattern in the model's parameter sensitivities; the sensitivity eigenvalues were roughly evenly spaced over many decades. Consequently, the model behavior depended effectively on only a few “stiff” parameter combinations. Here we study the converse problem, showing that direct parameter measurements are very inefficient at constraining the model's behavior. To yield effective predictions, such measurements must be very precise and complete; even a single imprecise parameter often destroys predictivity. We also show here that the characteristic sloppy eigenvalue pattern is reproduced in 16 other diverse models from the systems biology literature. The apparent universality of sloppiness suggests that predictions from most models will be very fragile to single uncertain parameters and that collective parameters fits can often yield tight predictions with loose parameters. Together these results argue that focusing on parameter values may be a very inefficient route to useful models.

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