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

May Validation of Normalizations, Scaling, and Photofading Corrections for FRAP Data Analysis Data Availability Statement: All relevant data are within the paper. 0 1 Minchul Kang 0 1 Manuel Andreani 0 1 Anne K. Kenworthy 0 1 0 1 School of Science, Technology & Engineering Management, St. Thomas University , Miami Gardens, Florida , USA , 2 Department of Molecular Physiology and Biophysics, Vanderbilt University School of Medicine , Nashville, Tennessee , USA 1 Academic Editor: Jorg Langowski, German Cancer Research Center , GERMANY 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. - Funding: This work was funded in part by grant NSF/ DMS 0970008 (http://www.nsf.gov/funding/pgm_ summ.jsp?pims_id=5300&org=DMS) from the National Science Foundation (to AKK). This work was also funded in part by St Thomas University undergraduate research program (http://www.stu.edu/ ResearchOpportunities/tabid/4860/Default.aspx) from St Thomas University (to MK and MA). The funding sources had no role in the study design, collection, analysis or interpretation of data, writing the report, or the decision to submit the paper for publication Over the past few decades, Fluorescence Recovery After Photobleaching (FRAP) has become an indispensable biophysical tool for tracking cellular organelles, proteins, and lipids in cells in a spatio-temporal manner [17]. Over the course of those years, there have been considerable advances in microscope technology. However, the basic principle of FRAP remains the same. Competing Interests: The authors have declared that no competing interests exist. In diffusion FRAP, fluorescently tagged molecules in a small region of interest (ROI) are irreversibly photobleached using a high intensity laser source for a short period of time, and then the exchange of fluorescent and photobleached molecules in and out of the bleached region is monitored using low intensity laser excitation to follow fluorescence recovery. In this process, the microscope system records the fluorescence intensity in a relative scale (for example 8 bit images: 0 * 256 scale) and generates a series of fluorescence images (Fig 1A). The fluorescence intensity in the bleached ROI is then collected and plotted as a function of time to produce a FRAP recovery curve (Fig 1B). In this curve, Fi, F0, and F1 are used to denote the prebleach intensity, the fluorescence intensity immediately after the photobleaching, and the fluorescence intensity obtained after the recovery has plateaued, respectively (Fig 1C). When a partportion of fluorescently tagged molecules exists as an immobile pool in the ROI, only the mobile fraction (Mf) of fluorescentce molecules will contribute to the fluorescence recovery (Fig 1C). The immobile fraction is formally defined as 1Mf, where Mf is given by By fitting a FRAP curve with appropriate mathematical models to describe the FRAP, the dynamics of fluorescently labeled molecules can be quantitatively analyzed in terms of kinetic parameters such as the half time of recovery (1/2), diffusion coefficient (D(t) or D), binding rate constants (kon or koff), and mobile fractions (Mf) [1, 8, 9]. These and other nomenclature and symbols used throughout the manuscript were are summarized in Table 1. How to quantitatively analyze FRAP data is still an active area of research, as several different factors affect the accuracy of FRAP measurements. For example, those factors that can occur during FRAP experiments include but are not limited to diffusion of molecules during photobleaching as the result of the finite time it takes to bleach an ROI [2, 1012], photoswitching of fluorescent proteins [13, 14], and photofading that can occur when the sample is repetitively imaged during the recovery phase [15]. To correct for these processes, various FRAP models have been developed and successfully applied in FRAP analysis. Additionally, several corrections, scalings and normalizations are typically made to FRAP data in order to apply FRAP models for quantitative FRAP analysis. First, to adjust the basal fluorescence intensity to true zero, a constant background fluorescence is subtracted from the FRAP data. Next, an additional correction has to be made to account for the loss of fluorescence due to photofading, a process that occurs as the result of repetitively imaging the specimen during the recovery phase of the experiment. FRAP data are also typically normalized to set the prebleach intensity to one in order to be able to compare data across experiments [3, 16, 17]. Last, but not least, another critical factor that must be taken into account in FRAP analysis is the possible presence of an immobile fraction (Fig 1C). These corrections are important for a number of reasons. For example, since photofading during the recovery phase can be easily confused with an immobile fraction (Fig 1B), it is critical to distinguish photofading from an immobile fraction [3, 6, 13, 15, 1820]. However, when corrections for both mobile fraction and photofading are made by introducing additional scalings and normalizations, FRAP models may become complicated, and even worse some FRAP models may not be compatible with a certain type of scaling. Therefore, caution must be used in FRAP analysis; otherwise errors introduced by incorrect scaling may lead to unreliable results. Moreover, since different commonly used scaling schemes generate FRAP curves with (...truncated)