  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 \emph{in vivo} biochemical parameters is difficult, and
collectively fitting them to other 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 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.
