Objective, Bayesian Analysis of Fluorescence Correlation Spectroscopy Data

Abstract

Fluctuations in fluorescence intensity provide quantitative insight into a range of molecular processes including diffusion, active transport, and binding kinetics in living cells and tissues. Classical fluorescence correlation spectroscopy (FCS) measures fluctuations in fluorescence intensity in a small detection volume to infer molecular transport properties from governing continuum diffusion-convection equations. Essential to the interpretation of FCS data is the use of an underlying mathematical model that governs the molecular process under study. Autocorrelations in fluctuations in fluorescence intensity may then be fit to the analytical solution of the model, and corresponding molecular properties may be inferred. While the choice of physical process may be unambiguous for special cases of free molecular diffusion or convective transport in solution, the correct choice of model becomes considerably less unambiguous in the application of FCS to complex biological processes in living cells or extracellular matrices. For this reason, an objective and unbiased approach to model selection and parameter estimation is of interest. The method of Bayesian inference provides such a framework. At the level of parameter estimation, Bayesian inference is similar to Maximum Likelihood Estimation when flat priors are chosen for initial parameter estimates. At the level of model selection, however, Bayesian inference assigns explicit model probabilities that are proportional to their marginal likelihoods by considering the full range of parameter values and their posterior probability distributions rather than only using point-wise, Maximum Likelihood estimates, thereby appropriately penalizing model complexity and preventing over-fitting of experimental data. Here we illustrate application of Bayesian inference to the problem of model selection and parameter estimation of molecular transport properties from FCS data, comparing it to traditional model selection approaches.