  Biophysical models describing complex, cellular phenomena typically include
systems of nonlinear differential equations with many free parameters. While
experimental measurements can fix some parameters, those describing internal
cellular processes frequently remain inaccessible. Hence, a proliferation of
free parameters risks overfitting the data, limiting the model's predictive
power. In this study, we develop robust methods, applying statistical analysis
and dynamical-systems theory, to reduce a biophysical model's complexity. We
demonstrate our techniques on an elaborate computational model designed to
describe active, mechanical motility of auditory hair cells. Specifically, we
use two statistical measures, the total-effect and PAWN indices, to rank each
free parameter by its influence on selected, core properties of the model. With
the resulting ranking, we fix most of the less influential parameters, yielding
a low-parameter model with optimal predictive power. We validate the
theoretical model with experimental recordings of active hair-bundle motility,
specifically by using Akaike and Bayesian information criteria after obtaining
maximum-likelihood fits. As a result, we determine the system's most
influential parameters, which illuminate its key biophysical elements of the
cell's overall features. While we demonstrated our techniques on a concrete
example, they provide a general framework, applicable to other biophysical
systems.
