  Biochemical processes in cells are governed by complex networks of many
chemical species interacting stochastically in diverse ways and on different
time scales. Constructing microscopically accurate models of such networks is
often infeasible. Instead, here we propose a systematic framework for building
phenomenological models of such networks from experimental data, focusing on
accurately approximating the time it takes to complete the process, the First
Passage (FP) time. Our phenomenological models are mixtures of Gamma
distributions, which have a natural biophysical interpretation. The complexity
of the models is adapted automatically to account for the amount of available
data and its temporal resolution. The framework can be used for predicting the
behavior of various FP systems under varying external conditions. To
demonstrate the utility of the approach, we build models for the distribution
of inter-spike intervals of a morphologically complex neuron, a Purkinje cell,
from experimental and simulated data. We demonstrate that the developed models
can not only fit the data but also make nontrivial predictions. We demonstrate
that our coarse-grained models provide constraints on more mechanistically
accurate models of the involved phenomena.
