Inferring phenomenological models of first passage processes

TL;DR

This paper introduces a systematic framework for constructing phenomenological models of first passage times in biochemical networks, using mixtures of Gamma distributions that adapt to data complexity and predict system behavior.

Contribution

The authors develop a data-driven, adaptable modeling approach for first passage times using Gamma mixtures, bridging experimental data and mechanistic understanding.

Findings

Models accurately fit experimental and simulated data.

Framework predicts system behavior under different conditions.

Models provide constraints for more detailed mechanistic models.

Abstract

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.