  Biomolecular conformational transitions are usually modeled as barrier
crossings in a free energy landscape. The transition paths connect two local
free energy minima and transition path times (TPT) are the actual durations of
the crossing events. The simplest model employed to analyze TPT and to fit
empirical data is that of a stochastic particle crossing a parabolic barrier.
Motivated by some disagreement between the value of the barrier height obtained
from the TPT distributions as compared to the value obtained from kinetic and
thermodynamic analyses, we investigate here TPT for barriers which deviate from
the symmetric parabolic shape. We introduce a continuous set of potentials,
that starting from a parabolic shape, can be made increasingly asymmetric by
tuning a single parameter. The TPT distributions obtained in the asymmetric
case are very well-fitted by distributions generated by parabolic barriers. The
fits, however, provide values for the barrier heights and diffusion
coefficients which deviate from the original input values. We show how these
findings can be understood from the analysis of the eigenvalues spectrum of the
Fokker-Planck equation and highlight connections with experimental results.
