Simplified Equation to Extract Diffusion Coefficients from Confocal FRAP Data

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, straightforward 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 photobleaching is negligible. This is not necessarily the 2I 2 x2 + y2 case for confocal FRAP. Due to the long scanning time of I (x, y) = 0 exp − rn π 2 2 CLSMs (approximate seconds), significant diffusion during rn rn

1590 Trafﬁc 2012; 13: 1589–1600 Simpliﬁed Confocal FRAP Analysis

Table 2: List of parameters and their deﬁnitions

Parameter Meaning Parameter Meaning

D Diffusion coefficient F i Prebleach fluorescence intensity τ1/2 Half time of recovery F 0 Initial postbleach fluorescence intensity rn Nominal radius = bleaching spot radius F ∞ Postbleach steady-state fluorescence intensity = sampling region radius re Effective radius = spreading radius of F 1/2 Fluorescence intensity at the half of recovery = [F 0 + F ∞]/2 postbleach profile q Quantum yield Mf Mobile fraction = [F ∞ − F 0]/[F i − F 0] ∈ τ = 2 Attenuation factor for excitation laser D Diffusion time re / (4D) 2 rn K Bleaching depth parameter Dr D from Soumpasis equation using rn Dr = 0.224 τ n n 1/2 2 re γ The ratio of the nominal and effective Dr D from Soumpasis equation using re Dr = 0.224 τ e e 1/2 radius = rn/re 2+ 2 re rn Ci Prebleach fluorescent protein DConfocal D from = rn/re and τ1/2 DConfocal = τ 8 1/2 concentration n Number of independent experiments N Total number of cells for FRAP data collection

or a uniform laser, where Ci is the prebleach fluorescent protein concentration, and re is the half width at the approximately 14% I0 2 2 2 Ir (x, y) = H r − x − y of bleaching depth from the top. We define r as the n πr2 n e n effective radius of a postbleach profile, in contrast to the where H(·) is the Heaviside function. In both cases, rn is nominal radius (rn) from a user-defined bleaching spot defined as a nominal radius, and the excitation lasers are radius. ε ε represented as Irn (x, y) for attenuation factor ( 1). Following the computation in Axelrod et al. (6,9), for a If we assume the concentration of fluorescent proteins solution of the diffusion equation with unknown diffusion C(x,y,t) satisfies the diffusion equation coefficient D and an initial condition given by eqn (2), a diffusion FRAP equation for confocal FRAP can be found as Ct = DC where D (μm2/s) is a diffusion coefficient and K 2 2 2 2 F (t) = F 1 − M + (1 − M ) F (3) = (∂ /∂x ) + (∂ /∂y ), then the solution can be com- i 2 f f 0 1 + γ + 2t/τD puted from a convolution of the fundamental solution of the diffusion equation and an initial condition as τ = 2 γ = where D re / (4D) and rn/re. Mf is defined as C (x, y, t) = C x − x , y − y ,0 Dt x , y dx dy F∞ − F = 0 where the fundamental solution of the diffusion equation Mf Fi − F0 in the infinite plane is defined as 2 + 2 1 x y for prebleach fluorescence intensity (F i ), postbleach initial Dt (x, y) = exp − . 4πDt 4Dt fluorescence intensity (F 0) and postbleach steady-state fluorescence intensity (F ∞). K can be computed from eqn Therefore, the fluorescence intensity from the bleach ROI (3) at t = 0(i.e.F(0) = F ), can be computed (6,9) from 0

F t = q εI x, y C x, y, t dx dy K ( ) rn ( ) ( ) F = F 1 − 0 i 1 + γ2 where q is the quantum yield of the fluorophores (F − F ) ⇒ K = i 0 (1 + γ2).(4) and C(x,y,t) describes the concentration of fluorescent Fi proteins within the confocal volume at time t. + = F0 F∞ It has been empirically shown that a confocal postbleach If we let F1/2 2 , i.e. the fluorescence intensity at τ = profile can be described as a simple Gaussian function the half time of recovery then, by definition, F( 1/2) F 1/2. (constant minus Gaussian) (21); As F 1/2 can be related to Mf by 2 x2 + y2 C (x, y,0) = C 1 − K exp − ,(2) (Fi − F0) i 2 F = M + F , re 1/2 2 f 0 Traffic 2012; 13: 1589–1600 1591 Kang et al. by setting F(τ1/2) = F 1/2: Table 3: Diffusion coefficients in cells previously reported in the literature for the molecules examined in the current study by K F = F 1 − M + 1 − M F confocal FRAP 1/2 i 2 f ( f ) 0 1 + γ + 2τ1/2/τD μ 2 τ K Marker D ( m /second) Methods References ⇒ 1 + γ2 + 2 1/2 = ; τ F +F D 1 − ( i 0) CTxB 0.15–0.4 FRAP, FCS (5,25,26) 2Fi YFP-GL-GPI 0.2–1.3 FRAP,SPT (5,26,27) − (Fi F0) 2 1 + γ DiIC16 0.9–5 FRAP, FCS, SPT (5,26,28,29) τ1/2 F ⇒ 1 + γ2 + 2 = i , EGFP 20–70 FRAP, FCS (21,30,31) τ F +F D 1 − ( i 0) 2Fi where we applied the definition of K in eqn (4). By multiplying 2F to both the denominator and numerator in i bleach radius (r )of1.1μm by repetitively scanning the right hand side, we obtain n the bleach region. We verified that when diffusion was 2 2τ 2 (Fi − F0) 1 + γ inhibited by fixing the sample prior to bleaching that 1 + γ2 + 1/2 = τ − the radius of the bleach region was similar to the D Fi F0 2τ user-defined nominal bleach radius (Figure 2). Next, we 1 + γ2 + 1/2 = 2 1 + γ2 ; τD calculated the effective bleach radius (re) and bleach depth (K) from the postbleach fluorescence profile 2τ1/2 (Figure 3A,B). For slowly diffusing molecules such as = 1 + γ2 . τD CTxB, the effective bleach radius calculated from the postbleach profile was only slightly larger than the nominal bleach radius (Figure 2). However, for the majority of Finally, by solving for D in τ = r2/ (4D), after applying D e molecules examined exchange of fluorescently tagged γ = r /r ,wehave n e proteins outside of bleach region was evident. This r2 + r2 effect was especially pronounced for the fastest diffusing = e n DConfocal .(5)molecules (Figure 3A,B). Importantly, the postbleach 8τ1/2 profiles were well described by an exponential function When re = rn in eqn (4) (i.e. bleaching is instantaneous), for all of the molecules examined. This indicates that this 2 rn we obtain D = 0.25 τ which is essentially identical to the approximation provides a reasonable description of the 1/2 Soumpasis equation (1). The approximately 3% difference data even for molecules with widely ranging diffusional in the proportionality constants in eqns (1) and (5) is due to mobilities and thus our FRAP equations are valid under the different assumptions on either Gaussian or uniform these conditions. laser profiles. We next interpolated the recovery curves to obtain τ1/2 (Figure 3C, Table 4), and computed D either by fitting the Results and Discussion FRAP data with eqn (3) (Figure 3C) or by plugging these numbers directly into the simplified DConfocal equation To validate our new FRAP equations (eqns (3) and (5)), we (eqn (5)). As illustrated in Figure 4, essentially identical D used them to extract D values from confocal FRAP data values were obtained using eqn (3) (DFitting) and eqn (5) obtained using a CLSM under standard imaging conditions (DConfocal) (Student’s t-test, p > 0.05) showing that the two for a series of proteins and lipid probes localized either to approaches yield similar results as expected. In addition, the plasma membrane, or within the cytosol (Figure 1). the D values obtained in this way were in good agreement The proteins and lipid probes studied included Alexa488- with the range of values previous reported from studies conjugated cholera toxin B-subunit (Alexa-CTxB), a using more elaborate approaches to quantify D (Table 3). glycolipid-binding bacterial toxin commonly studied as Moreover, the estimated Ds obtained using DConfocal and a marker of lipid rafts; a model GPI-anchored protein DFitting are independent of experimental conditions as (YFP-GL-GPI); a fluorescent lipid analog (DiIC16); and assessed by comparing measurements of EGFP diffusion soluble EGFP (Enhanced Green Fluorescent Protein) in in the cytoplasm using different bleaching spot size and the cytosol (EGFP). Additionally, the protein Flotillin-1, photobleaching times (Figure 5 and Table 5 (9), Student’s which is diffusely distributed across the cell surface when t-test, p > 0.05). overexpressed (24) was examined. Previously reported diffusion coefficients for these molecules span over three To illustrate the importance of using the corrected values orders of magnitude (Table 3), covering a range of D values of bleach radius to calculate D values, the same FRAP that are physiologically relevant for most studies of protein data were analyzed by Soumpasis equation (1) using and lipid dynamics in cells. either rn (Drn )orre (Dre ). This approach yielded Dsthat were significantly different from those measured using We performed confocal FRAP analysis of each of these eqn (3) or (5) (Figure 4, Student’s t-test, p < 0.05). The molecules using a circular bleach region with a nominal relation between DConfocal and Drn can be easily seen from

1592 Trafﬁc 2012; 13: 1589–1600 Simpliﬁed Confocal FRAP Analysis

AB C

Figure 1: Representative images of the subcellular distribution of the proteins and lipids studied. COS7 cells transfected or exogenously labeled with (A) Alexa-conjugated cholera toxin B-subunit (Alexa-CTxB), (B) a model GPI-anchored protein (YFP-GL-GPI), (C) Flotillin-1-RFP (Flot-1-RFP), (D) a ﬂuorescent lipid analog (DiIC16) or (E) EGFP. Scale bar = 10 μm.

Table 4: FRAP parameters and measured Ds of various markers.

Markers Alexa-CTxB YFP-GL-GPI RFP-Flot DiIC16 EGFP parameter (n = 5, N = 56) (n = 3, N = 36) (n = 3, N = 33) (n = 4, N = 58) (n = 3, N = 37) re (μm) 2.7 ± 0.2 3.2 ± 0.1 2.3 ± 0.1 3.0 ± 0.1 7.1 ± 0.2 τ1/2 (second) 4.1 ± 0.7 1.8 ± 0.1 0.97 ± 0.05 0.43 ± 0.28 0.16 ± 0.03 K 0.95 ± 0.04 0.97 ± 0.02 0.79 ± 0.06 0.64 ± 0.06 0.61 ± 0.09 Mf 0.98 ± 0.04 0.99 ± 0.02 0.95 ± 0.04 0.93 ± 0.02 0.95 ± 0.04 2 DFitting(μm /second) 0.26 ± 0.03 0.73 ± 0.04 0.72 ± 0.08 2.7 ± 0.7 41.3 ± 8.2 re (μm), effective radius measured from the averaged postbleach profiles; τ1/2 (second), halftime-of-recovery of a FRAP curve; K, photobleaching depth parameter; Mf , mobile fraction estimated by data fitting; DFitting, diffusion coefficient determined by data fitting; n, number of independent experiments; N, total number of cells. Mean ± SD over n.

0 < γ ≤ 1and in terms of γ, the ratio rn/re. This relationship also indicates that τ will not scale proportionally with D under 2 1/2 Dr 1.8γ Dr 1.8 n = , e = (6) conditions where re > rn, providing further evidence that + γ2 + γ2 DConfocal 1 DConfocal 1 τ1/2 is not a good approximator of diffusional mobility. For example, depending on the exact imaging conditions which indicates that used, molecules with similar values of D can show different values of τ1/2 (compare results for YFP-GL-GPI Drn < DConfocal < Dre .(7) andRFP-FlotinTable4).

Therefore, Drn and Dre can be understood as the upper and lower bounds for D. Importantly, eqns (6) and (7) The non-ﬁtting method using eqn (5) heavily hinges on provide the analytic relations between the equations that obtaining accurate measurements of re and τ1/2, which relate D and τ1/2 for conventional and confocal FRAP can be achieved by analysis of large amount of FRAP

Trafﬁc 2012; 13: 1589–1600 1593 Kang et al.

Figure 2: Diffusion of Alexa-CTxB on live versus fixed cells. A) Representative images of Alexa-CTxB on the plasma membrane during a FRAP experiment on either live or fixed cells for rn = 1.1 μm. Scale bar = 1 μm. B) Postbleach profiles of Alexa-CTxB on the plasma membranes of live (, n = 12) and fixed (, n = 5) cells. (C) FRAP data of Alexa-CTxB on the plasma membranes of live (, n = 12) and fixed (, n = 5) cells. As the bleach ROI is slightly off center in our system as seen in the images of (A) at t = 0, a correction was made to align the center of the postbleach profile to determine re.

Table 5: Comparison of FRAP parameters for EGFP in the cytosol obtained by confocal FRAP under different experimental conditions

1.1 μm diameter ROI 2.2 μmdiameterROI Experimental setup parameters 20 iterations (N = 8) 40 iterations (N = 10) 20 iterations (N = 10) 40 iterations (N = 8) rn (μm) 0.55 0.55 1.1 1.1 re(μm) 7.2 7.3 8.6 9.3 τ1/2 (second) 0.28 ± 0.10 0.30 ± 0.12 0.22 ± 0.02 0.28 ± 0.02 K 0.29 ± 0.01 0.32 ± 0.02 0.38 ± 0.01 0.41 ± 0.01 Mf 0.89 ± 0.04 0.89 ± 0.03 0.84 ± 0.01 0.87 ± 0.02 rn (μm) user defined nominal radius; re (μm), effective radius measured from the averaged postbleach profiles; τ1/2 (second), halftime- of-recovery of an individual FRAP curve; K, photobleaching depth parameter; Mf , mobile fraction calculated by eqn (3); iterations, the number of cycles in photobleaching laser scans. FRAP curves (n = 1) taken from (9) were re-analyzed without correction for background and photofading. Mf s found in Table 4 were estimated from data fitting and are therefore larger than Mf sinTable5.N, total number of cells. Mean ± SE over N. data (n > 3, and N > 10). Here, the statistics of individual size is large (Figure 6, Student’s t-test, p > 0.05). Working re, τ1/2, D and Mf were carefully compared with the with averaged FRAP data is more advantageous than using values from the averaged FRAP curve for a set of the mean value arising from individual measurements experiments. We found that there was no significant from a computational cost perspective, especially for noisy difference between the values found from averaged FRAP data from a small ROI size (rn) or fast diffusion. We also data and mean values of the parameters obtained over carefully compared D and Mf obtained from individual multiple individual FRAP data as long as the FRAP dataset FRAP data with the values from the averaged FRAP curve

1594 Trafﬁc 2012; 13: 1589–1600 Simpliﬁed Confocal FRAP Analysis

ABC

Figure 3: Confocal FRAP data of Alexa-CTxB, YFP-GL-GPI, Flot-1-RFP, DiIC16 and EGFP. A) Representative pre- and postbleach images. Dashed circles represent user-defined bleaching spots with diameter 2.2 μm(i.e.rn = 1.1 μm). To speed data acquisition for the FRAP analysis, we cropped the imaging window to make it slightly larger than the bleaching spot size. Scale bar = 1 μm. B) Averaged postbleach profiles for N = 12∼14 cells along the diagonals of postbleach images () and the best fitting Gaussian (eqn (2), – ). Dotted vertical lines show x =±rn (user-defined bleach ROI). Dash-dot horizontal lines are 14% of bleaching depth from the top. C) Representative FRAP recovery curves () and the best fit to eqn (3) ( – ). Insets show full FRAP curves for Alexa-CTxB and YFP-GL-GPI. In (B) and (C), y-axes are normalized fluorescence intensities, i.e. F i = 1. Since the bleach ROI is slightly off center in our system, a correction was made to determine re as described in the Materials and Methods.

for a set of experiments to check if the normalization of variations of re and τ1/2 are constrained by the relation the FRAP curves incidently masks biological variability, given by eqn (5) for large range of K as long as the post such as expression level-dependent diffusion coefficients bleach profiles can be described by a Gaussian (eqn (2)). (32). However, for the proteins and lipids examined here, D and Mf obtained from individual FRAP data did not In summary, we derived and tested a new, simplified show any significant differences from those obtained from equation for the quantitative analysis of confocal FRAP the averaged FRAP curves (Figure 6, Student’s t-test, data based on the pure isotropic diffusion model. An p > 0.05). overall workflow to determine the apparent diffusion coefficient, D from τ1/2, rn and re is summarized in In a previous study, we found that re varies with both rn Figure 7. Taking advantage of widely available technology, and bleaching time, and is more sensitive to rn than the this new approach should be accessible to many bleaching time. For larger rn and longer bleaching time, a biologists, since most researchers already have access larger re is obtained (9,21). In addition, the sensitivity of to CLSMs. Importantly, this method does not require re to experimental definition of rn and bleaching time is generation of new constructs or the use of specialized higher for rapidly diffusing proteins (9,21). Nevertheless, fluorescent dyes or labels, and can be applied to both

Trafﬁc 2012; 13: 1589–1600 1595 Kang et al.

Figure 4: Comparison of diffusion coefficients determined by various schemes. Comparison of diffusion coefficients Figure 5: Comparison of diffusion coefficients for EGFP in the cytosol obtained by confocal FRAP under different determined by FRAP data fitting (DFitting, eqn (3)), versus the experimental conditions as calculated using the Soumpasis DConfocal equation (eqn (5)), or the Soumpasis equation using equation or DConfocal equation. Diffusion coefficients were either rn (Drn )orre (Dre ) in log scale. Ds were found from averaged FRAP curves (N ≥ 12 cells per experiment) for three or determined by FRAP data fitting (DFitting, eqn (3)), by the DConfocal more separate experiments (n≥3). Error bars represent standard equation (eqn (5)), by the Soumpasis equation using rn (Drn ), and errors. Dashed boxes show D’s reported in the literature (Table 3). by the Soumpasis equation using re (Dre ) for individual confocal FRAP curves (N ≥ 6). Dashed box indicates the range of EGFP’s *p < 0.05 compared to DFitting, Student’s t-test. diffusion coefficients in the cytosol reported in the literature. re was measured from an averaged postbleach profile (n = 1, soluble and plasma membrane-associated molecules as N = 10 cells) and Ds were obtained from individual FRAP data illustrated here. Finally, it should be possible to readily (n = 1, N = 8, 10, 10 and 8 cells). *p < 0.05 compared to DFitting, incorporate this method into automated approaches Student’s t-test. to perform and analyze FRAP (33), and thus provide quantitative values for use in systems biology.

between 1.78 and 1.81 Airy units. The imaging window was further Materials and Methods narrowed to a square observation ROI of 70 × 70 pixel (7.7 × 7.7 μm). The 70 × 70 window contained a circular bleach ROI 20 pixels (2.2 μm) in diameter. FRAP conditions were optimized for each molecule under Cell labeling and reagents study. Samples were imaged and bleached using a 30 mW Argon laser COS-7 cells were acquired from ATCC (Manassas). Cells were maintained (488 and 514 laser lines) or 1.0 mW HeNe laser (543 nm laser line). Laser ◦ in DMEM containing 10% fetal bovine serum at 37 C and 5% powers for prebleach and postbleach imaging were maintained between CO2. Cells were plated on coverslips 2 days prior to experiments. 6.8 and 17.1 nW (488 or 514 nm) or between 13.8 and 21.0 nW (543 nm). Cells were transfected 1 day prior to imaging with the model GPI- Bleaching of Alexa 488-CTxB was performed using the 488 nm line at 0.99 anchored protein (YFP-GL-GPI) (5), Flotillin-1-RFP (Flot-1-RFP, the gift μW. EGFP and Flot-1-RFP were bleached using the 488 nm line at 2.28 of Dr Ai Yamamoto, Columbia University) (34) or EGFP (Clontech) μW, and YFP-GL-GPI was bleached using the 514 nm line at 1.38 μW. To using FuGENE 6 transfection reagent (Roche Diagnostics). DiIC16 bleach DiIC16 we combined the 488 nm line (40 nW), 514 (360 nW) and (1,1 -dihexadecyl-3,3,3 ,3 -tetramethylindocarbocyanine perchlorate) and 543 (540 nW). Bleaching regions were scanned 10 (Alexa-CTxB, YFP-GL- Alexa488 fluorophore-conjugated cholera toxin B-subunit from Vibrio GPI) or 20 times (EGFP, Flot-1-RFP or DiIC16). Prebleach and postbleach cholerae were obtained from Invitrogen. For exogenous labeling the cells images were collected with either no line averaging or with line averaging were rinsed twice with media and then incubated for 5 min at room of 2. Time series images were collect using 2 seconds delay (Alexa- μ temperature with 100 nM Alexa488-CTxB or 5 g/mL DiIC16. Cells were CTxB), 0.25 seconds delay (YFP-GL-GPI) or no delay (Flot-1-RFP, DiIC16, then rinsed twice with media and imaged. Cells were maintained in DMEM EGFP). This resulted in bleach times of 1.12 seconds (Alexa-CTxB), 0.69 supplemented with 1 mg/mL Bovine Serum Albumin and 25 mM HEPES seconds (YFP-GL-GPI), 0.56 seconds (Flot-1-RFP), 0.49 seconds (DiIC16) buffer during imaging. For FRAP on fixed samples, cell were labeled live and 0.27 seconds (EGFP). During recovery, images were collected every with Alexa488-CTxB (as above). Immediately after labeling, cells were fixed 2.27 seconds (Alexa-CTxB), 0.52 seconds (YFP-GL-GPI), 0.14 seconds with 3.4% paraformaldehyde for 15 min at room temperature. Cells were (Flot-1-RFP), 0.068 seconds (DiIC16) or 0.035 seconds (EGFP). All FRAP ◦ then rinsed with 1× PBS and mounted in Fluoromount G supplemented was performed at 37 C using a stage heater. with 25 mg/mL DABCO (1,4 diazabicyclo[2.2.2]octane) (Sigma-Aldrich) and allowed to solidify overnight prior to imaging. Correction for background and photofading FRAP methods To correct for background (Fbk), fluorescence from a cell-free area of FRAP experiments were carried out on a Zeiss LSM510 confocal the coverslip was measured under the same conditions as FRAP was microscope (Carl Zeiss MicroImaging) using filter sets provided by the performed. To correct for observational photofading (FFading(t)), a time manufacturer. Imaging was performed using a 40 × 1.3 NA Zeiss Plan- series was collected as for the FRAP studies, except no photobleaching × Neofluar objective at 4 digital zoom. The confocal pinhole was set step was performed. The raw FRAP data, FRaw(t), were corrected for

1596 Trafﬁc 2012; 13: 1589–1600 Simpliﬁed Confocal FRAP Analysis

Figure 6: Comparison of values obtained from averaged FRAP data versus mean of values from individual FRAP data. Comparison of mean ± SE of (A) re,(B)τ1/2,(C)D and (D) Mf determined using averaged FRAP data from more than three independent experiments with 10 cells (n ≥ 3, N = 10) or means from 10 individual FRAP data in a single experiment (N = 10). Error bars represent standard errors. p > 0.05 cross comparison, Student’s t-test. background and photofading by ROIs of 70 × 70 pixel (7.7 × 7.7 μm) from the prebleach image obtained immediately prior to and after photobleaching. Between the profiles F (t) − F F t = Raw bk . Corrected ( ) − obtained from two diagonals, the dataset with better symmetry was FFading (t) Fbk chosen for analysis. The profiles were then normalized by dividing the Finally, the corrected data were normalized by the prebleach intensity, postbleach profile by the prebleach profile. The normalized postbleach Fi = ∼ Corrected as profiles were averaged over datasets (N 12 14). Since the bleach ROI F (t) F (t) = Corrected . was slightly off center in some cases, if necessary, the symmetry axis was Fi = Corrected found and set to be x 0 from the normalized mean postbleach profile. The mean profiles were then fitted to τ measurements 1/2 x2 τ f (x) = 1 − K exp − To measure 1/2 from the FRAP data a linear interpolation method was Postbleach 2 re used. For the FRAP data {F(0), F(t1), F(t2), ···, F(tn)} such that F(0) = F0 and F(tn) = F∞, the fluorescence intensity at half of recovery is defined as for K and re using a nonlinear least-squares fitting routine (nlinfit.m) F = (F + F∞)/2. If F(t ) = F for some t then we chose τ = t .If ® 1/2 0 k 1/2 k 1/2 k available in MATLAB (version 7.10, R2010a, The Mathworks Inc.). F(tk ) < F1/2 < F(tk + 1) then we chose − Alternatively, re can be determined by direct measurement following F1/2 F tk τ = t + t + − t . three steps. First, K can be determined from the bleaching depth in 1/2 k F t − F t k 1 k k+1 k the normalized postbleach profile as referred as in Figure 8. Then, the half width of cross-sections between the horizontal line at the re measurements height of 0.86 K from the bottom of the postbleach profile (Figure 8) In order to obtain normalized initial postbleach profiles, fluorescence and the postbleach profiles yields re without involving any fitting intensities were measured along a diagonal of the square observation (Figure 8).

Trafﬁc 2012; 13: 1589–1600 1597 Kang et al.

Figure 7: Workﬂow of applying the DConfocal equation.

1598 Trafﬁc 2012; 13: 1589–1600 Simpliﬁed Confocal FRAP Analysis

8. Braga J, Desterro JM, Carmo-Fonseca M. Intracellular macro- molecular mobility measured by fluorescence recovery after photobleaching with confocal laser scanning microscopes. Mol Biol Cell 2004;15:4749–4760. 9. Kang M, Day CA, Drake K, Kenworthy AK, DiBenedetto E. A gen- eralization of theory for two-dimensional fluorescence recovery after photobleaching applicable to confocal laser scanning microscopes. Biophys J 2009;97:1501–1511. 10. Angelides KJ, Elmer LW, Loftus D, Elson E. Distribution and lateral mobility of voltage-dependent sodium channels in neurons. J Cell Biol 1988;106:1911–1925. 11. Deschout H, Hagman J, Fransson S, Jonasson J, Rudemo M, Loren´ N, Braeckmans K. Straightforward FRAP for quantitative diffusion measurements with a laser scanning microscope. Opt Express 2010;18:22886–22905. 12. Seiffert S, Oppermann W. Systematic evaluation of FRAP experiments performed in a confocal laser scanning microscope. J Microsc 2005;220:20–30. 13. Smisdom N, Braeckmans K, Deschout H, vandeVen M, Rigo JM, De Smedt SC, Ameloot M. Fluorescence recovery after photobleaching on the confocal laser-scanning microscope: generalized model without Figure 8: Determination of re from a postbleach profile. restriction on the size of the photobleached disk. J Biomed Opt 2011;16:046021. FRAP data fitting for D and M and weighted residual 14. Sprague BL, Pego RL, Stavreva DA, McNally JG. Analysis of binding f reactions by fluorescence recovery after photobleaching. Biophys J The FRAP curves were normalized by the mean prebleach fluorescence 2004;86:3473–3495. intensity (i.e. F = 1) and the mean of multiple normalized FRAP datasets i 15. Waharte F, Steenkeste K, Briandet R, Fontaine-Aupart MP. Diffusion was used for data fitting. Data fitting was carried out for D and Mf by measurements inside biofilms by image-based fluorescence recovery ® a nonlinear least-squares fitting routine (nlinfit.m) available in MATLAB after photobleaching (FRAP) analysis with a commercial confocal laser (version 7.10, R2010a, The Mathworks, Inc.) minimizing a weighted scanning microscope. Appl Environ Microbiol 2010;76:5860–5869. residual between averaged FRAP data from 10 experiments (FData(t)) 16. Salmon ED, Leslie RJ, Saxton WM, Karow ML, McIntosh JR. Spin- and a theoretical FRAP curve (F(t), eqn (3)), where the weighted residual dle microtubule dynamics in sea urchin embryos: analysis using a is defined by fluorescein-labeled tubulin and measurements of fluorescence redis- tribution after laser photobleaching. J Cell Biol 1984;99:2165–2174. s F (z) − F (z) 17. Stricker J, Maddox P, Salmon ED, Erickson HP. Rapid assembly ||F (t) − F (t) || = Data dz. Data s dynamics of the Escherichia coli FtsZ-ring demonstrated by 0 + fluorescence recovery after photobleaching. Proc Natl Acad Sci z FData (w) dw U S A 2002;99:3171–3175. 0 18. Cheerambathur DK, Civelekoglu-Scholey G, Brust-Mascher I, Sommi where s is the end time of FRAP data. If F(0) computed using K from P, Mogilner A, Scholey JM. Quantitative analysis of an anaphase B postbleach profile fitting showed any discrepancy from FData(0), K was switch: predicted role for a microtubule catastrophe gradient. J Cell = + γ2 − Biol 2007;177:995–1004. recalibrated using K (1 )(1 FData(0)) before data fitting. 19. Lajoie P, Partridge EA, Guay G, Goetz JG, Pawling J, Lagana A, Joshi B, Dennis JW, Nabi IR. Plasma membrane domain organization regulates EGFR signaling in tumor cells. J Cell Biol 2007;179:341–356. Acknowledgments 20. Saxton MJ. Modeling 2D and 3D diffusion. Methods Mol Biol 2007;400:295–321. This work was supported by R01 GM073846, NSF/DMS 0970008 and a 21. Kang M, Day CA, DiBenedetto E, Kenworthy AK. A quantitative Vanderbilt Discovery grant. The funding sources had no role in the study approach to analyze binding diffusion kinetics by confocal FRAP. design, collection, analysis or interpretation of data, writing the report or Biophys J 2010;99:2737–2747. the decision to submit the article for publication. 22. Weiss M. Challenges and artifacts in quantitative photobleaching experiments. Traffic 2004;5:662–671. 23. Pucadyil TJ, Chattopadhyay A. Confocal fluorescence recovery after References photobleaching of green fluorescent protein in solution. J Fluoresc 2006;16:87–94. 1. Mueller F, Mazza D, Stasevich TJ, McNally JG. FRAP and kinetic 24. Otto GP, Nichols BJ. The roles of flotillin microdomains--endocytosis modeling in the analysis of nuclear protein dynamics: what do we and beyond. J Cell Sci 2011;124:3933–3940. really know? Curr Opin Cell Biol 2010;22:403–411. 25. Bacia K, Scherfeld D, Kahya N, Schwille P. Fluorescence correlation 2. Day CA, Kenworthy AK. Tracking microdomain dynamics in cell spectroscopy relates rafts in model and native membranes. Biophys membranes. Biochim Biophys Acta 2009;1788:245–253. J 2004;87:1034–1043. 3. Drake KR, Kang M, Kenworthy AK. Nucleocytoplasmic distribution 26. Day CA, Kenworthy AK. Mechanisms underlying the confined diffusion and dynamics of the autophagosome marker EGFP-LC3. PLoS One of cholera toxin B-subunit in intact cell membranes. PLoS One 2010;5:e9806. 2012;7:e34923. 4. Miyawaki A. Proteins on the move: insights gained from fluorescent 27. Pautot S, Lee H, Isacoff EY, Groves JT. Neuronal synapse interaction protein technologies. Nat Rev Mol Cell Biol 2011;12:656–668. reconstituted between live cells and supported lipid bilayers. Nat 5. Kenworthy AK, Nichols BJ, Remmert CL, Hendrix GM, Kumar M, Chem Biol 2005;1:283–289. Zimmerberg J, Lippincott-Schwartz J. Dynamics of putative raft- 28. Jacobson K, Hou Y, Derzko Z, Wojcieszyn J, Organisciak D. Lipid lateral associated proteins at the cell surface. J Cell Biol 2004;165:735–746. diffusion in the surface membrane of cells and in multibilayers formed 6. Axelrod D, Koppel DE, Schlessinger J, Elson E, Webb WW. Mobility from plasma membrane lipids. Biochemistry 1981;20:5268–5275. measurement by analysis of fluorescence photobleaching recovery 29. James PS, Hennessy C, Berge T, Jones R. Compartmentalisation kinetics. Biophys J 1976;16:1055–1069. of the sperm plasma membrane: a FRAP, FLIP and SPFI analysis 7. Soumpasis DM. Theoretical analysis of fluorescence photobleaching of putative diffusion barriers on the sperm head. J Cell Sci recovery experiments. Biophys J 1983;41:95–97. 2004;117:6485–6495.

Trafﬁc 2012; 13: 1589–1600 1599 Kang et al.

30. Wang Z, SWang Z, Shah JV, Sun CH, Berns MW. Fluorescence 33. Conrad C, Wunsche¨ A, Tan TH, Bulkescher J, Sieckmann F, Verissimo correlation spectroscopy investigation of a GFP mutant-enhanced F, Edelstein A, Walter T, Liebel U, Pepperkok R, Ellenberg J. cyan ﬂuorescent protein and its tubulin fusion in living cells with Micropilot: automation of ﬂuorescence microscopy-based imaging two-photon excitation. J Biomed Opt 2004;9:395–403. for systems biology. Nat Methods 2011;8:246–249. 31. Dragestein KA, van Cappellen WA, van Haren J, Tsibidis GD, 34. Cremona ML, Matthies HJ, Pau K, Bowton E, Speed N, Lute BJ, Akhmanova A, Knoch TA, Grosveld F, Galjart N. Dynamic behavior Anderson M, Sen N, Robertson SD, Vaughan RA, Rothman JE, Galli of GFP-CLIP-170 reveals fast protein turnover on microtubule plus A, Javitch JA, Yamamoto A. Flotillin-1 is essential for PKC-triggered ends. J Cell Biol 2008;180:729–737. endocytosis and membrane microdomain localization of DAT. Nat 32. Niv H, Gutman O, Kloog Y, Henis YI. Activated K-Ras and H-Ras display Neurosci 2011;14:469–477. different interactions with saturable nonraft sites at the surface of live cells. Cell Biol 2002;157:865–872.

1600 Trafﬁc 2012; 13: 1589–1600