Sloppy systems biology: tight predictions with loose parameters

Directly measuring the parameters involved in dynamical models of cellular processes is typically very difficult, and collectively fitting such parameters to other data often yields large parameter uncertainties. Nonetheless, a collective fit which only weakly constrains model parameters may strongly constrain model \emph{predictions}, if the model is ill-conditioned: much more sensitive to some directions in parameter space than others. In the quadratic approximation, the model sensitivities are proportional to the inverse square roots of the hessian matrix eigenvalues. Using a collection of 14 models from the systems biology literature, we show that for large systems the eigenvalue spectra are universally \emph{sloppy}; they span huge ranges ($> 10^6$) and have approximately constant logarithmic spacing. Thus the models are ill-conditioned and have no well-defined cutoff between important and unimportant parameter combinations. This universal sloppiness suggests that collective fits will often poorly constrain parameters but usefully constrain many predictions.