Validation of Normalizations, Scaling, and Photofading Corrections for FRAP Data Analysis

Abstract

Fluorescence Recovery After Photobleaching (FRAP) has been a versatile tool to study transport and reaction kinetics in live cells. Since the fluorescence data generated by fluorescence microscopy are in a relative scale, a wide variety of scalings and normalizations are used in quantitative FRAP analysis. Scaling and normalization are often required to account for inherent properties of diffusing biomolecules of interest or photochemical properties of the fluorescent tag such as mobile fraction or photofading during image acquisition. In some cases, scaling and normalization are also used for computational simplicity. However, to our best knowledge, the validity of those various forms of scaling and normalization has not been studied in a rigorous manner. In this study, we investigate the validity of various scalings and normalizations that have appeared in the literature to calculate mobile fractions and correct for photofading and assess their consistency with FRAP equations. As a test case, we consider linear or affine scaling of normal or anomalous diffusion FRAP equations in combination with scaling for immobile fractions. We also consider exponential scaling of either FRAP equations or FRAP data to correct for photofading. Using a combination of theoretical and experimental approaches, we show that compatible scaling schemes should be applied in the correct sequential order; otherwise, erroneous results may be obtained. We propose a hierarchical workflow to carry out FRAP data analysis and discuss the broader implications of our findings for FRAP data analysis using a variety of kinetic models.

Fig 1. Representative images and data from a confocal FRAP experiment, and examples of commonly used normalizations and scalings applied to FRAP data.

(A) Representative images from a FRAP experiment on Alexa488-CTxB. (B) Mean fluorescence intensity (N = 13) from the bleaching ROI (∘, F _Data(t)), whole image (•, F _Whole(t)), and background (▫) from a FRAP experiment of Alexa488-CTxB. The image in the inset shows the locations where F _Data(t) (∘) and background (▫) were measured. (C) In FRAP analysis, prebleach steady state, postbleach initial, and postbleach steady state fluorescence intensities are typically denoted as F _i, F ₀, and F _∞. These parameters can be used to calculate the mobile fraction (M _f) and immobile fraction (1−M _f) from the normalized FRAP data (F _Data(t)/F _i) as indicated in the boxed equation. (D)–(F) The same FRAP curve was subjected to different scaling schemes, including an exponential scaling (D), an affine scaling (E), and a linear scaling (F).

Fig 2. Representative photofading rates obtained from the whole image fluorescence for a variety of different fluorescently tagged molecules.

A photofading model, f(t) = e ^−κt was fitted to normalized whole image fluorescence data F _Data(t)/F _i averaged over multiple data sets (n = 10) for each of the indicated fluorescent proteins or fluorescent lipid probes. (A–B) Best fitting photofading model applied to whole image fluorescence. Solid lines show the best fitting curves. (C) Photofading rate constants obtained from the fits shown in A and B are shown in descending order. Error bar represents the standard deviation (n = 14).

Fig 3. Errors caused by incorrect sequence of scaling or by applying partial scaling corrections.

FRAP analysis was performed on Alexa488-CTxB FRAP data (A–D) or FLOT-RFP FRAP data (E–H) using different scaling scenarios. (A,E) As a positive control, FRAP data corrected for both background fluorescence and photofading were analyzed using f _NDaMf(t) (Eq 37) in the correct order. (B,F) Background-corrected FRAP data were analyzed by f _NDaMf(t) (Eq 37), ignoring the contribution of photofading. (C,G) Photofading-corrected FRAP data, F _Data(t)/F _Whole(t) were analyzed by f _NDaMf(t) (Eq 37), ignoring any background correction. Lower lines show background fluorescence, F _b. (D,H) Background corrected FRAP data were analyzed using a photofading and mobile fraction corrected FRAP equation obtained by using an incorrect scaling order (Eq 44). Dots (•) show the mean FRAP data averaged over one set of experiments (n = 12 and 13 for FLOT-RFP and Alexa488-CTxB, respectively) and solid lines show the best fitting curve.

Fig 4. Best fitting diffusion coefficients (D) and mobile fractions (M _f) of Alexa488-CTxB and FLOT-RFP under different scaling scenarios.

(A) and (B) show the best fitting diffusion coefficients (D), mobile fraction (M _f), and standard errors (N = 4 × 12 or N = 3 × 13). Statistically significant differences are denoted with asterisk (*).

Fig 5. Analysis of the magnitude of errors caused by applying incompatible scaling or by using an incorrect sequence of scaling during FRAP analysis.

FRAP curves were simulated assuming D = 1μm²/s, F ₀ = 0.4, F _i = 1, r _n = 1μm, and r _e = 2μm under different scaling scenarios. Curves were then analyzed as indicated to obtain the best fits for D and M _f. (A) FRAP curves were simulated using (f _dNDaMf(t)+F _b)/(f _dNDaMf(t < 0)+F _b) assuming κ = 0.005 s⁻¹ and 0 ≤ F _b ≤ 0.3 and then analyzed using f _dNDaMf(t) (Eq 42) while ignoring F _b. (B) FRAP curves were simulated using f _dNDaMf(t) assuming M _f = 0.8 and 0 ≤ κ ≤ 0.02 s⁻¹ and then analyzed using f _NDaMf(t) (Eq 37) while ignoring photofading. (C) FRAP curves were simulated using f _dNDaMf(t) (Eq 42) assuming M _f = 0.8 and 0 ≤ κ ≤ 0.02 s⁻¹ and analyzed using an incorrectly scaled FRAP equation (Eq 44). Panels in the 2nd row show best fitting D as a function of variable conditions, F _b and κ. Panels in the 3rd row show best fitting M _f as a function of variable conditions, F _b and κ.

Fig 6. Effect of photofading during image acquisition on fits to FRAP curves for normal diffusion versus anomalous diffusion.

FRAP data with photofading (•) were simulated using f _dADaMf(t) (Eq 42) assuming either a photofading rate of κ = 0.04 s⁻¹ (A,B) or κ = 0.01 s⁻¹ (C,D) under the conditions D = 1μm²/s, F ₀ = 0.2, M _f = 0.8, r _n = 0.2 μm, and r _e = 1 μm. The simulated curve was next fitted by f _NDaMf(t) (Eq 37) (A,C) or f _NDaMf(t) (Eq 37) (B,D). The resulting best fitting parameters were D = 2.1μm²/s and M _f = 0.83 in (A), $\frac{1}{4}\Gamma =9.33$ and M _f = 0.83 in (B), D = 2.7μm²/s and M _f = 0.95 in (C), and $\frac{1}{4}\Gamma =5.32$ and M _f = 0.94 in (D).

Fig 7. Hierarchical workflow of diffusion FRAP analysis to correct for background, photofading and an immobile fraction.