Inferring phenomenological models of first passage processes

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 behavior of 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.Author summary: Building microscopically accurate models of biological processes that offer meaningful information about the behavior of these systems is a hard task that requires a lot of prior knowledge and experimental data that are not available most of the time. Here instead we propose a mathematical framework to infer phenomenological models of biochemical systems, focusing on approximating the probability distribution of time it takes to complete the process. We apply the method to study statistical properties of spiking in morphologically complex neurons, Purkinje cells, and make nontrivial predictions about this system.