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Simplified Equation to Extract Diffusion Coefficients from Confocal FRAP Data

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Simplified Equation to Extract Diffusion Coefficients from Confocal FRAP Data Traffic 2012; 13: 1589–1600 © 2012 John Wiley & Sons A/S doi:10.1111/tra.12008 Toolbox Simplified Equation to Extract Diffusion Coefficients from Confocal FRAP Data Minchul Kang1,2, Charles A. Day1, Anne K. provides a measure of the mean squared displacement Kenworthy1,3,4,∗ and Emmanuele per unit time of the diffusing species. At the cellular level, measurements of D can provide important insights into DiBenedetto1,5,∗ how proteins and lipids interact with their environment, 1Department of Molecular Physiology and Biophysics, such as the binding of transcription factors with DNA and Vanderbilt University School of Medicine, Nashville, of proteins and lipids with membrane domains (1,2). In TN 37232, USA addition, especially for the case of soluble proteins, an 2Current address: School of Science, Technology, and accurate measure of D can provide important information Engineering Management, St. Thomas University, 16401 about the effective size of the diffusing species (3). NW 37th Avenue, Miami Gardens, FL 33054, USA 3Department of Cell and Developmental Biology, Currently, biologists have at their disposal a wide Vanderbilt University School of Medicine, Nashville, range of fluorescence-based techniques to monitor the TN 37232, USA diffusion of biomolecules in cells, including single-particle 4Chemical and Physical Biology Program, Vanderbilt tracking (SPT), fluorescence correlation spectroscopy University School of Medicine, Nashville, TN 37232, USA 5 Department of Mathematics, Vanderbilt University, (FCS), photoactivation and fluorescence recovery after Nashville, TN 37240, USA photobleaching (FRAP) (4). Of these approaches, many require specialized equipment, analytical tools or probes. *Corresponding authors: Anne K. Kenworthy, [email protected] and Emmanuele In contrast, confocal FRAP is one of the most accessible DiBenedetto, [email protected] methods to measure apparent diffusion (or effective diffusion). In FRAP, the diffusion of a population of Quantitative measurements of diffusion can provide fluorescently labeled molecules can be studied by important information about how proteins and lipids photobleaching the molecules contained within a user- interact with their environment within the cell and the defined region of interest (ROI), and then monitoring effective size of the diffusing species. Confocal fluores- fluorescence recovery due to the exchange of bleached cence recovery after photobleaching (FRAP) is one of the molecules within the bleach ROI with the surrounding most widely accessible approaches to measure protein reservoir of unbleached molecules. Most modern confocal and lipid diffusion in living cells. However, straightfor- ward approaches to quantify confocal FRAP measure- laser scanning microscopes (CLSMs) are equipped to ments in terms of absolute diffusion coefficients are cur- perform FRAP measurements, and FRAP measurements rently lacking. Here, we report a simplified equation that are straightforward to carry out. In addition, FRAP can be can be used to extract diffusion coefficients from confocal performed using many fluorescently tagged proteins or on FRAP data using the half time of recovery and effective directly fluorescently labeled molecules (4,5). bleach radius for a circular bleach region, and validate this equation for a series of fluorescently labeled soluble Despite the relative ease of performing confocal FRAP and membrane-bound proteins and lipids. We show that measurements, straightforward methods to quantitatively using this approach, diffusion coefficients ranging over analyze the resulting data are currently lacking. Most three orders of magnitude can be obtained from confocal Ds from confocal FRAP FRAP measurements performed under standard imaging current approaches to calculate conditions, highlighting its broad applicability. data require fitting of recovery curves with analytical diffusion models using customized programs, a process Key words: confocal laser scanning microscope, diffusion which often demands a significant level of knowledge of coefficient, fluorescence microscopy, FRAP, half time of FRAP theory (Table 1). Alternatively, FRAP measurements recovery can be quantified simply in terms of the half time of recovery (τ1/2), defined as the time required for Received 31 May 2012, revised and accepted for a bleach spot to recover half way between initial publication 9 September 2012, uncorrected manuscript and steady-state fluorescence intensities (16–19). An published online 17 September 2012, published online advantage of this approach is that τ can be readily 10 October 2012 1/2 extracted from FRAP recovery curves (16–19). However, τ1/2 is strongly dependent on experimental parameters such as the nominal radius of the user-defined bleach Diffusion is a fundamental process that is relevant over all spot (rn) and the exact bleaching protocol, as well scales of biology. How rapidly diffusion occurs is charac- as the characteristic dynamics of the molecule under terized by the diffusion coefficient D, a parameter that investigation. Therefore, τ1/2 is an empirical parameter that www.traffic.dk 1589 Kang et al. Table 1: Analytic 2D FRAP models Bleaching Laser Postbleach Diffusion during Data Target References geometry profiles profile photobleach types Microscopy proteins 2 Kang et al. (9) Circle in Gaussian (rn) Gaussian (re) Corrected f(t) CLSM/wide-field Slow/fast static Smisdom et al. (13) Circle in 2 Gaussian (ρ) Uniform with Not corrected f(t)CLSM Slow Gaussian edge 2 Axelrod et al. (6) Circle in Gaussian Gaussian Not corrected f(t)/τ1/2 Wide-field static Slow (rn)/uniform (rn) (rn)/uniform (rn) 2 Braga et al. (8) Circle in Uniform (rn) Gaussian (re) Corrected f(t) CLSM Slow/fast 2 Soumpasis (7) Circle in Uniform (rn) Uniform (rn) Not corrected f(t)/τ1/2 Wide-field static Slow 2 Sprague et al. (14) Circle in Uniform (rn) Uniform (rn) Not corrected f(t) Wide-field static Slow/fast 2 Waharte et al. (15) Circle in not available Gaussian (re) Corrected f(x,t) CLSM Slow/fast 2 Current study Circle in Gaussian (rn) Gaussian (re) Corrected f(t)/τ1/2 CLSM/wide-field Slow/fast static Angelides et al. (10) Circle in a Gaussian (rn) Gaussian (rn) Not corrected f(t) Wide-field static Slow box Deschount et al. Box in 2 Gaussian (ρ) Uniform with Not corrected f(t)CLSM Slow (11) Gaussian edge Seiffert & Circle/line not available Gaussian (re) Corrected f(x,t)/re(t)CLSM Slow Oppermann (12) in 2 2 , infinite 2 dimensional plane; rn, bleaching spot radius = static laser radius; ρ, scanning laser radius; re, effective radius measured from a fluorescent intensity profile; f(t), fluorescence intensity from an ROI; f(x,t), time course of spreading radius of postbleach profiles. cannot be readily compared across studies. In contrast, the photobleaching may occur in confocal FRAP. rn thus D provides a quantitative measure of diffusion (6,7). may not provide an accurate description of the initial Knowledge of the absolute magnitude of D has many conditions required for this equation to be valid. Failure advantages over measurements of τ1/2. For example, to take this into account can lead to underestimation D is uniquely determined by the size of the diffusing of D when the Soumpasis or Axelrod equations are molecule as well as its local environment (20). Therefore, used to analyze confocal FRAP data, especially for fast- discrepancies between the theoretically expected D and diffusing soluble proteins (8,9,22,23). This discrepancy measured apparent (or effective) diffusion coefficients can be resolved using a modified form of the conventional may indicate possible molecular interactions or more FRAP equations by using the postbleach fluorescence complex situations. For example, in cell membranes intensity profile to correct for any diffusion that occurs the presence of microdomains prevents proteins from during the photobleaching by incorporating an empirically undergoing free diffusion (2). Accurate estimates of D determined measure, the effective bleach radius re from are also a necessary starting point for reaction–diffusion the postbleach profile (9). However, this approach also analysis (1,21). requires full fitting of the FRAP recovery curves to calculate D. In this study, we sought to further simplify One potential solution to the problem of extracting this approach by deriving an equation to calculate D from quantitative D values from confocal FRAP data is to utilize confocal FRAP data obtained using circular bleach regions. the explicit forms of the classical two-dimensional (2D) FRAP equations for small circular bleaching spots derived by Axelrod for a Gaussian laser (6) and by Soumpasis for a uniform laser (7). Both Axelrod and Soumpasis (6,7) Theory reported equations that relate D, τ1/2 and rn for a pure isotropic diffusion model. For example, the Soumpasis All the parameters and their meanings are summarized equation is given by in Table 2. For simplicity, we assume that cells are flat enough (as in the case of COS7 cells) so that both the r2 = n plasma membrane as well as the cytosol can be treated Drn 0.224 (1) τ1/2 as 2D objects. We also assume that bleaching spot size is small compared with the cell size, so that we can treat where rn is the radius of the uniform bleach laser the cell as an infinite plane. Having these, laser intensity and the coefficient 0.224 was numerically determined profiles for photobleaching lasers in the infinite plane are (7). However, the derivation of both the Axelrod and described as either a Gaussian laser: Soumpasis FRAP equations assumed that diffusion during
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