Bayesian model selection applied to the analysis of fluorescence correlation spectroscopy data of fluorescent proteins in vitro and in vivo

Abstract

Fluorescence correlation spectroscopy (FCS) is a powerful technique to investigate molecular dynamics with single molecule sensitivity. In particular, in the life sciences it has found widespread application using fluorescent proteins as molecularly specific labels. However, FCS data analysis and interpretation using fluorescent proteins remains challenging due to typically low signal-to-noise ratio of FCS data and correlated noise in autocorrelated data sets. As a result, naive fitting procedures that ignore these important issues typically provide similarly good fits for multiple competing models without clear distinction of which model is preferred given the signal-to-noise ratio present in the data. Recently, we introduced a Bayesian model selection procedure to overcome this issue with FCS data analysis. The method accounts for the highly correlated noise that is present in FCS data sets and additionally penalizes model complexity to prevent over interpretation of FCS data. Here, we apply this procedure to evaluate FCS data from fluorescent proteins assayed in vitro and in vivo. Consistent with previous work, we demonstrate that model selection is strongly dependent on the signal-to-noise ratio of the measurement, namely, excitation intensity and measurement time, and is sensitive to saturation artifacts. Under fixed, low intensity excitation conditions, physical transport models can unambiguously be identified. However, at excitation intensities that are considered moderate in many studies, unwanted artifacts are introduced that result in nonphysical models to be preferred. We also determined the appropriate fitting models of a GFP tagged secreted signaling protein, Wnt3, in live zebrafish embryos, which is necessary for the investigation of Wnt3 expression and secretion in development. Bayes model selection therefore provides a robust procedure to determine appropriate transport and photophysical models for fluorescent proteins when appropriate models are provided, to help detect and eliminate experimental artifacts in solution, cells, and in living organisms.

Figure 1

Blocking transformation and fitting to tested models. (A) Estimated noise level as a function of block-time for 10 nM EGFP at 10 kW/cm² with acquisition time of 40 s. The fixed point is at approximately 8 ms. Error bars: SD. (B) Fitting of evaluated models to ACF of EGFP calculated from the photon arrival time (PAT) trace. All fits were performed with 3D diffusion models.

Figure 2

ACFs under low and high excitation intensities of (A) Fluorescein and (B) EGFP in 1× PBS.

Figure 3

Model probabilities and model selection of EGFP in 1× PBS at different excitation intensities. The acquisition time of these measurements was 40 s. Model probabilities of (A) EGFP in 1× PBS. All fits were performed with 3D diffusion models. Model selection of (B) fluorescent proteins: EGFP (blue), EYFP (green), and mCherry (red) in 1× PBS. Error bar: SEM.

Figure 4

Model probabilities PMT-EGFP in CHO cells and its ACFs on membrane and in the cytoplasm. (A) Model probabilities for PMT-EGFP on the membrane under different excitation intensities. All fits were performed with 2D diffusion models with the triplet blinking time fixed at 20 µs. Error bars: SEM. (B) Normalized ACFs of measurement in the cytoplasm (red dotted line) and on the membrane (green dotted line) with fits (black line).

Figure 5

Model probabilities of EGFP labeled proteins measured in zebrafish embryos. Error bars: SEM. BV: brain ventricle.