  Physical models of biological systems can become difficult to interpret when
they have a large number of parameters. But the models themselves actually
depend on (i.e. are sensitive to) only a subset of those parameters. Rigorously
identifying this subset of "stiff" parameters has been made possible by the
development of parameter space compression (PSC). However, PSC has only been
applied to analytically-solvable physical models. We have generalized this
powerful method by developing a numerical approach to PSC that can be applied
to any computational model. We validated our method against
analytically-solvable models of random walk with drift and protein production
and degradation. We then applied our method to an active area of biophysics
research, namely to a simple computational model of microtubule dynamic
instability. Such models have become increasingly complex, perhaps
unnecessarily. By adding two new parameters that account for prominent
structural features of microtubules, we identify one that can be "compressed
away" (the "seam" in the microtubule) and another that is essential to model
performance (the "tapering" of microtubule ends). Furthermore, we show that the
microtubule model has an underlying, low-dimensional structure that explains
the vast majority of our experimental data. We argue that numerical PSC can
identify the low-dimensional structure of any computational model in
biophysics. The low-dimensional structure of a model is easier to interpret and
identifies the mechanisms and experiments that best characterize the system.
