Toward Bayesian inference of the spatial distribution of proteins from three-cube Förster resonance energy transfer data

: Forster resonance energy transfer (FRET) is a quantum-physical phenomenon where energy may be transferred from one molecule to a neighbor molecule if the molecules are close enough. Using fluorophore molecule marking of proteins in a cell, it is possible to measure in microscopic images to what extent FRET takes place between the fluorophores. This provides indirect information of the spatial distribution of the proteins. Questions of particular interest are whether (and if so to which extent) proteins of possibly different types interact or whether they appear independently of each other. In this paper we propose a new likelihood-based approach to statistical inference for FRET microscopic data. The likelihood function is obtained from a detailed modeling of the FRET data-generating mechanism conditional on a protein configuration. We next follow a Bayesian approach and introduce a spatial point process prior model for the protein configurations depending on hyperparameters quantifying the intensity of the point process. Posterior distributions are evaluated using Markov chain Monte Carlo. We propose to infer microscope-related parameters in an initial step from reference data without interaction between the proteins. The new methodology is applied to simulated and real datasets.