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© 2011 John Wiley & Sons A/S doi:10.1111/j.1600-0854.2011.01264.x
Accurate Quantification of Diffusion and Binding Kinetics of Non-integral Membrane Proteins by FRAP Ronen Berkovich1,2,† , Haguy Wolfenson3,† , Sharon Eisenberg3 , Marcelo Ehrlich4 , Matthias Weiss5 , Joseph Klafter1 , Yoav I. Henis3,∗ and Michael Urbakh1,∗ 1 School
of Chemistry, Raymond and Beverley Sackler Faculty of Exact Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel 2 Present address: Department of Biological Sciences, Columbia University, New York, NY 10027, USA 3 Department of Neurobiology, George S. Wise Faculty of Life Sciences, Tel Aviv University, Tel Aviv 69978, Israel 4 Department of Cell Research and Immunology, George S. Wise Faculty of Life Sciences, Tel Aviv University, Tel Aviv 69978, Israel 5 Experimental Physics I, University of Bayreuth, D-95440 Bayreuth, Germany *Corresponding author: Yoav I. Henis,
[email protected] or Michael Urbakh,
[email protected] † These authors contributed equally to this work. Non-integral membrane proteins frequently act as transduction hubs in vital signaling pathways initiated at the plasma membrane (PM). Their biological activity depends on dynamic interactions with the PM, which are governed by their lateral and cytoplasmic diffusion and membrane binding/unbinding kinetics. Accurate quantification of the multiple kinetic parameters characterizing their membrane interaction dynamics has been challenging. Despite a fair number of approximate fitting functions for analyzing fluorescence recovery after photobleaching (FRAP) data, no approach was able to cope with the full diffusion–exchange problem. Here, we present an exact solution and MATLAB fitting programs for FRAP with a stationary Gaussian laser beam, allowing simultaneous determination of the membrane (un)binding rates and the diffusion coefficients. To reduce the number of fitting parameters, the cytoplasmic diffusion coefficient is determined separately. Notably, our equations include the dependence of the exchange kinetics on the distribution of the measured protein between the PM and the cytoplasm, enabling the derivation of both kon and koff without prior assumptions. After validating the fitting function by computer simulations, we confirm the applicability of our approach to live-cell data by monitoring the dynamics of GFP-N-Ras mutants under conditions with different contributions of lateral diffusion and exchange to the FRAP kinetics. Key words: binding kinetics, diffusion analysis, FRAP, membrane interactions, simulations Received 19 May 2011, revised and accepted for publication 1 August 2011, uncorrected manuscript published online 2 August 2011, published online 30 August 2011
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Non-integral membrane proteins are important mediators of signaling events from the plasma membrane (PM) downstream into the cell. They can be triggered by cues from upstream receptors (1–3), apoptosis inducers (4) or other signals, and can amplify, branch and diversify extracellular stimuli. In many cases, their biological activity requires tethering to the membrane, and depends on dynamic binding/unbinding (exchange) processes between membrane-associated and cytoplasmic populations. A prominent example is supplied by the Ras small GTPase superfamily, whose members regulate multiple cellular processes, from cell proliferation, apoptosis or differentiation to cell motility and metastatic potential (5–7). In spite of the critical role of membrane interactions in the signaling of non-integral membrane proteins, their local association/dissociation kinetics at the PM and their transport coefficients in the membrane and cytoplasm have been notoriously difficult to determine in vivo. Using green fluorescent protein (GFP)-tagged proteins, fluorescence recovery after photobleaching (FRAP) has frequently been employed to determine some of the above-mentioned dynamic parameters. In FRAP, the recovery of the fluorescence signal in a region of interest (ROI) after an initial period of bleaching is monitored. As a consequence of (diffusive) transport and/or exchange between membrane and cytoplasmic pools, the fluorescence in the bleached ROI recovers, and fitting with an appropriate theoretical model may be used to determine the dynamic parameters. While FRAP had been originally developed for a laser beam at a fixed location (8), it was later adapted for laser scanning confocal microscopes (LSMs) using non-synchronous stepwise bleaching of larger ROIs (9). We will refer to this approach, which found numerous applications in cell biology (10), as non-synchronous FRAP (NS-FRAP). The pixel-wise stepwise bleaching of relatively large areas in NS-FRAP gives rise to problems and artifacts that can only be cured partially. As scanning of a typical ROI takes tens to hundreds of milliseconds, bleaching in the ROI does not occur instantaneously but takes a finite time during which diffusion and binding kinetics continue. As a result, the initial conditions from which the recovery starts may be incompatible with the assumptions underlying the derivation of the fitting function (11), leading to large systematic errors in the dynamic coefficients obtained from the fit. Several approaches have aimed at tackling this technical challenge (12,13), but all had shortcomings in that they relied on limiting assumptions concerning the bleaching profile (13) and/or the rate and contribution of cytoplasmic diffusion (12,13). Moreover, two intrinsic problems of NS-FRAP remain: first, since bleaching and imaging in an LSM is typically done pixel by pixel, the locus in the upper left corner of the ROI is bleached tens to hundreds of
Analysis of Diffusion and Binding Kinetics by FRAP
milliseconds before the region in the lower right corner. Including this systematic anisotropy into fitting functions is possible, yet far beyond a user-friendly method, as it requires the input of microscope-specific details for each measurement. Second, NS-FRAP averages over a wider spatial range, potentially masking local heterogeneities in the membrane interaction dynamics of the proteins (e.g. association with cellular structures/scaffolds such as focal adhesions). The above problems do not apply to Gaussian spot FRAP (GS-FRAP), which employs a fixed-localization Gaussian laser beam focused on a small membrane area for both the bleaching and recovery periods. The fact that no stepwise scanning is required at either stage results in better time resolution, typically a few milliseconds or less. Implementation of GS-FRAP via commercial LSMs is straightforward since only the scanning process is left out. Still, determining the dynamics of non-integral membrane proteins with this approach crucially depends on the availability of an exact solution that can be fitted in a robust way to the experimental data. Here, we extended the GS-FRAP solution developed for integral membrane proteins, which can only diffuse in the PM (8), by deriving an analytical expression from first principles for fitting GS-FRAP curves of non-integral membrane proteins that undergo PM–cytoplasm exchange, lateral diffusion in the membrane and cytoplasmic diffusion. We confirm the applicability of the analytical result by computer simulations and apply the method to measure the dynamic parameters of GFP-N-Ras mutants in COS-7 cells under conditions that result in highly different contributions of lateral diffusion versus membrane binding/unbinding kinetics. N-Ras is highly suitable as a test model, because its dynamic association with the PM and intracellular membranes can be modulated by mutations and/or natural modifications in its C-terminal hypervariable region (HVR) (5,14,15). It displays a significant cytoplasmic pool, and its association with specific cellular membranes is regulated by a palmitoylation/depalmitoylation cycle (16,17). Our studies show the feasibility of the method for determination of the diffusion coefficient in the PM (DM ) and the binding/unbinding kinetic parameters of non-integral membrane proteins. To reduce the number of fitting parameters, we employ the following steps: (i) Determine directly by three-dimensional (3D) confocal imaging the relative numbers of molecules of the measured protein in the PM and the cytoplasm (a value denoted by RM ; see eqn 8). (ii) Measure separately the cytoplasmic diffusion coefficient (DC ) using a GFP-N-Ras mutant lacking the membrane anchor under identical GSFRAP conditions; this is advantageous over introducing this value as measured by another technique with nonidentical experimental setup and conditions (13), because the contribution of cytoplasmic diffusion to the FRAP measurement (effective DC ) depends on the instrument setup and the efficiency of fluorescence collection from the confocal volume (18,19). (iii) Estimate the fraction of mobile
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proteins within the experimental timescale (Rf ) by fitting the experimental data to the fitting function (eqn 9), into which the measured RM and DC values are introduced as fixed input. (iv) We then improve the error bounds by refitting the data to eqn 9, introducing also the Rf value determined in step (iii) as a fixed input. Together with the MATLAB (The Mathworks) fitting programs, our approach yields high-quality data for the dynamic parameters of nonintegral membrane proteins with a robust and user-friendly fitting protocol.
Results and Discussion We have dissected the derivation of the fitting equation, the numerical test of its validity and the application of our approach to experimental data into subsections. In the first part, we outline the derivation of the fitting function. Details on the math can be found in the Supporting Information. The central result of this part is eqn 7, which lies at the heart of the downloadable fitting routine described in the second subsection. The third part is a numerical test of the fitting approach by computer simulations. The fourth subsection reports on the application of our approach to several GFP-N-Ras mutants in COS-7 cells.
Derivation of the analytical fitting function To derive an analytical fitting model for GS-FRAP curves, we start with the general equations of motion of nonintegral membrane proteins. To that end, the flux of molecules between the 3D cytoplasm and the twodimensional (2D) membrane can be described in protein numbers instead of concentrations. These two quantities differ only by a scaling factor due to the constant volume element illuminated by the laser beam in GSFRAP measurements. We denote by NM the number of the membrane-bound proteins with a diffusion coefficient DM . The number of proteins in the cytoplasmic pool (diffusion coefficient DC ) is denoted by NC . The exchange between the two pools is governed by the rate constants kon (binding to the PM) and koff (dissociation from the PM). It should be noted that kon depends on the number of molecules available for exchange from the cytoplasmic layer in a single average step, and therefore depends on DC , the time interval and the depth of the GS-FRAP volume element (for details, see Supporting Information, end of Appendix S1). The equations of motion thus read: ∂ NM = DM ∇ 2 NM − koff NM + kon NC ∂t ∂ NC = DC ∇ 2 NC + koff NM − kon NC ∂t
(1) (2)
The Laplacian operator ∇ 2 is best evaluated in polar coordinates (cf. Supporting Information). In GS-FRAP, both the bleaching and observation beams have a Gaussian intensity profile I (r ), given by: 2 2 2P0 −2 r −2 r e w 2 = I0 e w 2 I (r ) = (3) 2 πw 1649
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where w is the Gaussian radius (half-width at e−2 height), P0 is the total laser power and r 2 = x 2 + y 2 . Bleaching only changes the state of the fluorophore that is attached to the protein of interest but does not perturb the steady state of the protein’s binding and motion. The bleaching can be described as a first-order reaction with a rate constant αI (r ), where α is a proportionality constant reflecting the sensitivity of the fluorophore to bleaching (8). Hence, bleaching for a period T much shorter than the typical time required for a protein to travel through the beam width induces an initial condition for the recovery immediately after the bleach: −αTI (r )
NM (r , t = 0) = NM,0 e NC (r , t = 0) = NC,0 e−αTI (r )
(4) (5)
Here, NM,0 and NC,0 are the initial uniform values of the total sum of fluorescent proteins in the membrane and in the cytoplasm, respectively. For convenience, we define by κ = αTI0 the ‘amount’ of bleaching during the period T . As boundary conditions, we assume NM (r → ∞, t ) = NM,0 and NC (r → ∞, t ) = NC,0 , i.e. the entire system is much larger than the area illuminated by the beam so that boundary regions are not affected by the bleaching. The equations of motion can be solved with the above initial and boundary conditions in Fourier space (i.e. with a transformation x , y → μx , μy , indicated via the superscript ‘F’; see Supporting Information for details): ⎤ ⎡ δ(μx )δ(μy ) + − ) ( 1 2 ⎣ ∞ (−κ)n w 2 − w 2 (μ2x +μ2y )⎦ N F (μ, t ) = 8n (1 − 2 ) 8π e n=1 n!n (6)
w2
qI0 8Aπ
=
(1 −2 ) (1 −2 )
∞
n=1
(−κ)n n!n
w2 8π
2
−w μ2 8n
e
2,1 t
1,2 = [NM,0 (1,2 + μ DM ) + NC,0 (1,2 + μ DC )]e 2
2
and 1,2 =
1 (−μ2 DM − koff − μ2 DC − kon ± 2 (−μ2 DM − koff + μ2 DC + kon )2 + 4koff kon )
From this result, we obtain the total fluorescence at time ∞ q I (r )N (r , t )d 2 r , where A
t > 0 by recalling that F (t ) =
−∞
N (r , t ) is the sum of the number of protein molecules in the cytoplasm and in the membrane, q is the quantum efficiency parameter and A is the attenuation factor of the beam during the recovery phase. Then, the solution of the equations of motion gives the following expression for the normalized fluorescence (see Supporting Information): f (t ) =
F (t ) = f0 + 2π φ
∞ 0
NμF (μ, t )e−
w 2 μ2 8 μdμ
(7)
,
φ=
and f0 = 4π2 (NM,0 + NC,0 ).
It is convenient to rephrase the above expression by defining a new parameter, RM , which is a function of the number of the molecules of the measured protein in the membrane-bound and cytoplasmic pools:
RM =
NM NM + NC
(8)
Since part of the membrane protein population in a cell may be immobile on the timescale of the FRAP measurement, another parameter that has to be incorporated is the fraction of mobile proteins within this time frame, defined by Rf . Introducing this, the normalized fluorescence will be expressed by:
F (t ) = F 0 Rf f ∗ (t ) + FB (1 − Rf )
(9)
Where F 0 is the initial average fluorescence before the bleach and FB is the fluorescence immediately after the bleach, and
f ∗ (t ) =
f (t ) w2 =1+ 2 4π (NM,0 + NC,0 ) 4
∞ 0
(ω1 − ω2 ) Sn μdμ (1 − 2 ) (10)
Here ω1,2 =
1,2 R ( + μ2 DM ) + = M 1,2 e2,1 t (1 − RM )(1,2 + μ2 DC ) (NM,0 + NC,0 ) (11)
and ∞ (−κ)n − w82 1n +1 μ2 Sn (μ) = e n!n
with
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NμF (μ, t )
(12)
n=1
With these definitions, the fit formula [eqn 9, with f ∗ (t ) defined by eqn 10] is expressed entirely in terms of experimentally accessible quantities (cf. Supporting Information). This central result provides the basis for the fitting procedure (see next subsection). The analytical result in eqns 7 and 10 does not invoke any of the assumptions that are frequently found in the literature. In particular, there is no need to restrain the analysis to binding-limited or diffusion-limited cases. Rather, all contributions are considered in the formula, including cytoplasmic diffusion. Clearly, the somewhat complex form of the result cannot be implemented directly into commercial fitting programs but requires a more elaborate framework that will be discussed in the next subsection.
Formulation of a fitting procedure Given the complexity of the general solution of the equations of motion, it is important to outline a straightforward way to fit experimental data to this expression. While in many cases FRAP data are analyzed Traffic 2011; 12: 1648–1657
Analysis of Diffusion and Binding Kinetics by FRAP
by commercial fitting programs that are typically restricted to closed analytical fitting formulas, we discuss here a more powerful alternative in terms of a MATLAB code that is provided for download in the Supporting Information. Notably, performing a fit using the above analytical expression is surprisingly simple. Essentially the fit code supplied does the following: after attaining from the user the time-points and normalized FRAP values in a twocolumn ASCII format, the program estimates an initial value for κ similar to previous approaches (8). The program then fits an inverse Fourier transform to all the acquired data and depicts the experimental data, the best-fit curve and the extracted values for the different parameters (given also in a text file) as a graph. The fit itself is based on a Levenberg–Marquardt approach that always uses Fourier transforms. Hence, the complex math is transparent to the user.
Testing the applicability of the analytical fitting function by simulations To test the applicability of the fitting approach and procedure, we performed a series of FRAP simulations. In brief, we implemented a diffusion-binding model on a 3D lattice (see Materials and Methods for details) that includes the relevant dynamic parameters and hence mimics the association/dissociation cycle of non-integral membrane proteins. To this end, the proteins (particles in a 3D grid) were referred to as random walkers that diffuse and undergo exchange between two distinct phases (bound and free, NM and NC ) according to the parameters that govern their motion (diffusion, rate constants and number of particles). The system is at steady state at all times (before, during and after bleaching). The random walk simulations employed 20 000 particles (protein molecules) distributed at a 4:1 ratio between one face of a 3D grid (the membrane) and the grid volume (the cytoplasm; Figure 1). DM and DC were chosen in the range reported for DM of lipid-anchored proteins (e.g. Ras) and for DC of several peripheral membrane proteins: DM = 0.15 μm2 /second, DC = 20 μm2 /second. The exchange between the cytoplasm and the membrane was modeled with kon = 82.8/second and koff = 3.1/second. We first probed whether simple diffusion in the cytoplasm or the membrane was correctly reproduced by the fitting procedure. To generate simulation data where diffusion is limited to the cytoplasm, the random walk of the particles was limited to the 3D grid volume (see Materials and Methods); these data were then fitted to the general solution (eqn 9) after introducing DM = koff = NM,0 ≡ 0 to reflect the lack of binding to the membrane. Under these conditions, eqn 9 becomes similar to the equation for lateral diffusion (8); this equation is valid for the 3D diffusion in the grid, since the 3D diffusion is projected onto a 2D space (19,20). Indeed, the simulated data yielded a good fit to this equation (R 2 = 0.93; Figure 2A). A similarly good fit (not shown) was obtained when an analogous simulation was employed to probe diffusion
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Figure 1: Schematic representation of the model for simulations of non-integral membrane protein dynamics. The particles (molecules of non-integral membrane proteins) undergo fast 3D diffusion (random walk; characterized by DC ) in a cubic volume, and bind reversibly (with the kinetic rate constants kon and koff ) to one of the volume boundaries (shaded area), representing the PM. A subpopulation of the bound molecules is allowed to be immobile on the simulation timescale. To simulate a FRAP experiment, a Gaussian laser beam, whose radius is very small relative to the size of the cube face, is focused at the PM. Bleaching is performed throughout the z -axis of the simulated cubic volume. The details of the model (not drawn to scale) are given under Simulations (Materials and Methods). The full description of the derivation of the analytical expression derived from this model is given under Supporting Information.
in the membrane, limiting the random walk to the face of the grid representing the membrane, and introducing DC = koff = NC,0 ≡ 0 into the fitting equation. Next, we simulated the general case, in which all processes discussed above occur: diffusion in two phases (bound and free) and exchange between them, and a fraction of the surface-bound particles that is immobile on the experimental timescale (taken here to be 0.1, leaving the mobile fraction as Rf = 0.9). The output of this simulation and its fit to the model are presented in Figure 2B. As can be seen, the fit is excellent (R 2 = 0.997), and the fitted parameters are very close to the input simulation values.
Quantifying the dynamics of N-Ras proteins in living cells To confirm the applicability of our fitting approach to measure the dynamics of non-integral membrane proteins in live cells, we conducted GS-FRAP studies on GFP-NRas mutants at the periphery of COS-7 cells. The ability to modulate the membrane interactions of N-Ras by cellular cues or specific mutations enables to shift its FRAP kinetics between lateral diffusion-dominated, bindingdominated and mixed recovery modes. In untreated cells, constitutively active GFP-N-Ras(G13V) displays a relatively stable association with the PM (5,21). We have recently found that immunoglobulin G (IgG)-mediated clustering 1651
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Figure 2: GS-FRAP simulations (black circles) and fittings (red lines) to diffusion in the cytoplasm and to the general case. A) Diffusion in the cytoplasm (no binding to the upper boundary). A random walk algorithm was used to simulate GSFRAP while limiting the particles to the 3D grid volume. The parameters used to generate the simulation were DC (sim) = 20 μm2 /second and Rf (sim) = 1.0. The simulation data were fitted to eqn 9 using MATLAB, introducing DM = koff = NM,0 ≡ 0 (no binding to the surface; see text). The best-fit parameters derived, DC (fit) and Rf (fit), are shown ± SEM (see Materials and Methods). The values of these parameters are very close to the simulation parameters. B) Simulation of the general case (diffusion in the cytoplasm and membrane, and exchange). Simulation was as above, except that the particles were allowed to bind to and dissociate from the upper boundary (20 000 particles in total distributed at a 4:1 ratio between the upper boundary and the grid volume, so that NM = 16 000 and NC = 4000 particles, yielding RM = 0.8; see Materials and Methods), and diffuse both in the cytoplasm and in the membrane (the upper boundary). The parameters used to generate the simulation were DC (sim) = 20 μm2 /second, DM (sim) = 0.15 μm2 /second, kon (sim) = 82.8/second, koff (sim) = 3.1/second and Rf (sim) = 0.90. To reduce the degrees of freedom and the number of parameters derived from the fit, DC , RM and Rf were inserted as fixed values into eqn 9 and all other parameters [DM (fit), kon (fit), koff (fit)] were determined by the fitting procedure. For derivation of eqn 9 and the MATLAB fitting code, see Supporting Information.
of a raft-localized protein, glycosylphosphatidylinositolanchored influenza hemagglutinin (HA-GPI), enhances the depalmitoylation of GFP-N-Ras(G13V), shifting its FRAP mechanism to exchange (S. Eisenberg, M. Ehrlich and Y. I. Henis, unpublished observations). In addition, GFPHVR-N-DA, an N-Ras-based mutant comprised of GFP fused to the N-Ras HVR region with a double Asp to Ala mutation (DD175,176AA), displays significantly reduced palmitoylation and PM association (15); this mutant is a good candidate for measuring FRAP by mixed recovery (lateral diffusion and exchange). This experimental setup allowed us to probe the dynamics of the different regimes using closely related proteins with specific modifications in their membrane-interacting moieties. Prior to applying a full-parameter analysis using our fitting approach, it was advantageous to get an estimate for the relative contribution of lateral diffusion and exchange to the FRAP of the GFP-N-Ras proteins tested. To this end, we employed FRAP beam-size analysis, a FRAP variation that we developed and applied to study the dynamics of several non-integral membrane proteins (22–24). In this method [detailed in Ref. (25)], the 1652
apparent characteristic recovery times τ for two different Gaussian laser beam sizes (obtained by using a 63× and a 40× objective) are compared. For FRAP by lateral diffusion, τ is directly proportional to the area illuminated by the beam, i.e. τ(40×)/τ(63×) = w 2 (40×)/w 2 (63×) = 2.28, the measured ratio between the areas illuminated by the beams (26). In contrast, when FRAP occurs by exchange, τ reflects the chemical relaxation time, which is independent of the dimensions of the bleached area [τ(40×)/τ(63×) = 1]. Intermediate τ ratios are indicative of a mixed recovery mode (25). In line with the stable association of constitutively active GFP-N-Ras(G13V) with the PM in untreated cells, FRAP beam-size analysis yielded τ(40×)/τ(63×) essentially identical to the 2.28 beam-size ratio (Figure 3), indicating a negligible contribution of exchange to the recovery. In sharp contrast, following IgG-mediated clustering of HA-GPI, the FRAP dynamics of GFP-N-Ras(G13V) were shifted to recovery by exchange, as shown by a τ ratio essentially similar to 1 (Figure 3). Finally, in accord with the reduced palmitoylation and lower PM binding of GFP-HVRN-DA (15), this mutant yielded an intermediate τ ratio (1.9), suggesting a mixed contribution of diffusion and exchange to the FRAP curves (Figure 3). Next, we turned to accurately analyze the FRAP kinetics of the GFP-N-Ras proteins by a full-fitting approach using eqn 9. To improve the signal-to-noise ratio of the experimental data, 40–60 normalized GS-FRAP curves were averaged in each case by summing up the intensities of each individual curve, starting from the bleach point for synchronization (the prebleach level was set to unity). Due to the large number of parameters in eqn 9, it is highly desirable to increase the stability of the fitting procedure by introducing some of the parameters as predetermined fixed input. These parameters are DC and RM , which can be directly determined experimentally. We preferred to determine DC using the same GS-FRAP setup in order to obtain the effective DC under the exact conditions that apply for the full fitting for the proteins of interest. The small illuminated area in GS-FRAP enables a higher temporal resolution sufficient for studies of diffusion in the cytoplasm, unlike NS-FRAP. To measure DC without any contribution of PM interactions, we expressed in COS-7 cells a GFP-N-Ras mutant lacking the membrane anchor (last 10 amino acid residues; GFP-N-Ras-10). As this mutant does not bind to the PM, we fitted the results to eqn 9 with DM = koff = NM,0 ≡ 0, leaving only DC and Rf as fitting parameters. Equation 9 is applicable for 3D diffusion analysis, since the 3D diffusion is projected onto a 2D space (19,20). This procedure yielded Rf of 1.0 ± 0.02 (as expected), and DC = 8.0 ± 0.6 μm2 /second, in the range reported for a closely sized GFP-ARF1 (small GTPase ADP-ribosylation factor) using fluorescence correlation spectroscopy (28). It should be noted that in the absence of a pinhole in the collection path, the expansion of the Gaussian laser beam along the z -axis can lead to an underestimate of DC in the FRAP analysis
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Figure 3: FRAP beam-size analysis of GFP-N-Ras mutants reveals different FRAP modes. A) Average τ values from FRAP beam-size analysis of GFP-N-Ras proteins. The ratio between the two beam sizes generated by the two objectives (40× and 63×) was 2.28 ± 0.17 (n = 59). Therefore, this is the τ(40×)/τ(63×) ratio expected for FRAP by lateral diffusion. A τ ratio of 1 is indicative of recovery by exchange (see Materials and Methods; 27). Bars are means ± SEM of 40–60 measurements. IgG crosslinking (CL) of HA-GPI resulted in a much shorter τ(40×) for GFP-N-Ras(G13V) (***p < 10−13 , Student’s t -test). B) Bootstrap analysis of the τ(40×)/τ(63×) ratio for GFP-N-Ras(G13V) showed that it is not significantly different from the 2.28 beam-size ratio expected for FRAP by lateral diffusion under the experimental conditions employed (p > 0.3, bootstrap analysis). CL of HAGPI strongly reduced the τ(40×)/τ(63×) ratio to a value not significantly different from 1, as expected for FRAP dominated by exchange (p > 0.06, bootstrap analysis). On the other hand, GFPHVR-N-DA displayed a τ ratio of 1.9, significantly different from both 2.28 (the value expected for lateral diffusion; *p < 0.05) and 1 (p < 10−15 ), suggesting a mixed recovery mode.
by a factor of ∼2; however, with a pinhole radius up to twofold larger than w (in our case, this ratio is 1.65), the underestimation is negligible (less than 1%) (19,20). To experimentally determine the second input parameter, RM , we measured for the GFP-N-Ras proteins, under each experimental condition, the relative numbers of molecules in the PM and the cytoplasm by 3D confocal imaging, identifying the PM by a specific membrane-associated fluorescent marker (see Materials and Methods). These measurements yielded RM = 0.68 ± 0.02, 0.67 ± 0.02 and
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0.69 ± 0.01 for GFP-N-Ras(G13V), GFP-N-Ras(G13V) with cross-linked HA-GPI and GFP-HVR-N-DA, respectively (n = 20 in all cases; the errors indicate SEM values). Inserting the above RM values and DC = 8.0 μm2 /second as fixed input into eqn 9, we analyzed the FRAP kinetics of the GFP-N-Ras proteins (Figure 4). For GFP-N-Ras(G13V), the best-fit values obtained were koff = 0.0014/second, kon = 0.003/second and DM = 0.25 μm2 /second (Figure 4A). Because the dimensions of koff and kon are different from that of DM , one has to compare the characteristic recovery times of FRAP by exchange (τex ) and by lateral 2 diffusion (τD ). While τD = 4wD , we define τex as kon +1 k . M off This definition is based on the fatty acid-dependent membrane anchorage of N-Ras, which does not rely on association with saturable binding sites. Therefore, the flux between the cytoplasmic and membrane-bound pools dN is described by dtM = kon NC − koff NM . The solution to this differential equation has the form NM = a0 + a1 e(kon +koff )t with appropriate constants a0 , a1 that keep track of the steady-state values and the amount of bleaching at time t = 0. Hence, τex depends on both kon and koff , and no assumptions are made about the rate-limiting step. Numerous previous studies assumed binding to saturable sites at the PM, which then require dissociation from occupied sites prior to association of cytoplasmic molecules, resulting in dissociation being the rate-limiting step. Since the fitting to eqn 9 yields both kon and koff without prior assumptions, our method is applicable also for cytoplasmic proteins that bind to saturable sites at the PM (e.g. to integral membrane proteins). The analysis in such a case is the same, yielding kon and koff . The only difference is in translating the rate constants into τex , which is then taken simply as k 1 . off
Getting back to the kinetic rate constants and DM of GFP-N-Ras(G13V) (Figure 4A), we obtain τex /τD = 380, showing that GFP-N-Ras(G13V) diffusion in the PM is much faster than its exchange. Therefore, GFP-NRas(G13V) diffusion dominates the fluorescence recovery, in accord with the beam-size analysis results (Figure 3). Moreover, the DM value thus obtained is in good agreement with D values determined for other Ras proteins by fitting to lateral diffusion only (21,23,29). It should be noted that eqn 9 employs a single DM value, since allowing multiple values would increase the degrees of freedom beyond the sensitivity of the measurement. If multiple diffusion coefficients exist (e.g. due to partitioning into different membrane domains), the fitted DM value would represent a weighted average. IgG-mediated clustering of HA-GPI, which was found by FRAP beam-size analysis to be dominated by exchange, yielded best-fit values (fitting to eqn 9) of koff = 1.34/second, kon = 2.89/second and DM = 0.14 μm2 /second (Figure 4B), yielding τex /τD = 0.22. This indicates that under these conditions, the major contribution to the FRAP is by exchange, in agreement with the beam-size analysis results. Finally, to show that both the lateral diffusion and exchange parameters can be 1653
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Figure 4: Analysis of the FRAP kinetics of GFP-N-Ras proteins by the full-fitting approach. GS-FRAP experiments were conducted as described under Materials and Methods, using the 63× objective. For each GFP-N-Ras protein or condition, 40–60 FRAP curves were normalized and averaged. To reduce the number of parameters in the fit, DC = 8.0 μm2 /second (determined experimentally with the same GS-FRAP setup using GFP-N-Ras-10; see text) and RM (determined separately for each N-Ras mutant/condition by 3D imaging) were introduced as fixed values. The experimental data (black circles) were then fitted (red curves) to eqn 9 using MATLAB (see Supporting Information). The Rf (fit) values were around 0.90 in all cases. Therefore, to obtain improved error bounds, the mean Rf estimated by averaging the Rf values from the individual FRAP curves was re-entered as fixed input. Importantly, such calculation of Rf yielded essentially identical results to those obtained when performing the full fit. Entering Rf as fixed input results in reduction of the degrees of freedom and enables to avoid numerical issues in the fit. The best-fit parameters ± SEM values thus obtained are shown. A) GFP-N-Ras(G13V) in untreated cells. B) GFP-N-Ras(G13V) following IgG-mediated clustering (CL) of HA-GPI. C) GFP-HVR-N-DA.
Figure 5: Sensitivity analysis of the fitting method to changes in the values of the fitted parameters. The normalized averaged GS-FRAP curve of GFP-HVR-N-DA (Figure 4C) was fitted to eqn 9 using the full-fit procedure (A); to determine the sensitivity to the values of DM or koff , these parameters were introduced as fixed values into the fit, and all the other parameters were allowed to adjust accordingly [B, koff (fixed); C, DM (fixed)]. The values chosen for the fit were 1.5-fold higher than the values obtained by performing the full fit on the same data. Presented for each fit is the initial rise of the curve, which entails ∼2/3 of the recovery and is the most sensitive region for the fit. For both DM (fixed) and koff (fixed), the fittings were worse than in panel (A), resulting in large deviations in the fitted values of the other fitting parameters; e.g. fixing DM at 1.5-higher value shifted koff to a 3.5-fold lower value, with error bounds of ∼200% [koff (fit) = 0.093 ± 0.2]. Similar results were obtained when assigning values 1.5-fold lower than those obtained when performing the full fit.
determined for a protein whose FRAP is governed by a mixed contribution of lateral diffusion and exchange, we conducted a full fit on the FRAP data of GFP-HVR-NDA, which had an intermediate τ ratio (1.9) in the FRAP beam-size analysis. The parameters derived from this fit were koff = 0.32/second, kon = 0.75/second and DM = 0.27 μm2 /second (Figure 4C), i.e. τex /τD = 1.7. This indicates a significant contribution of both processes to the fluorescence recovery. A further support for the validity of the analysis is provided by the fact that the DM value derived for GFP-HVR-N-DA is essentially similar to the DM value derived for GFP-N-Ras(G13V) in untreated cells, which is mainly dominated by diffusion. Notably, the analysis of 1654
the experimental data presented here by our fitting procedure is sensitive to the values of the fitted parameters. The sensitivity limits were evaluated by performing fits for GFP-HVR-N-DA, assigning fixed values for either DM or koff 1.5-fold above or below the values derived from the full fit and allowing all other parameters to adjust accordingly. As shown in Figure 5, this resulted in unsatisfactory fits. Importantly, from the steady-state assumption it follows that kon /koff = CM /CC (where CM and CC are the membrane and cytoplasmic concentrations, respectively). Comparison between the kon /koff ratios obtained from the fits and the CM /CC ratios measured independently using
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3D confocal imaging (see Materials and Methods) yielded comparable values. For GFP-N-Ras(G13V), kon /koff = 2.25 and CM /CC = 2.27 ± 0.16; for GFP-N-Ras(G13V) with cross-linked HA-GPI, kon /koff = 2.15 and CM /CC = 2.24 ± 0.26 and for GFP-HVR-N-DA, kon /koff = 2.34 and CM /CC = 2.51 ± 0.15. In conclusion, our studies present a fitting approach for GS-FRAP using an equation describing the full diffusion–exchange model for non-integral membrane proteins. The approach was validated by computer simulations and by testing its applicability on several N-Ras protein mutants, whose FRAP dynamics are dominated by either lateral diffusion, exchange or a mixture of both. Going beyond previous NS-FRAP approaches, our approach employs a very short bleach time and avoids gradual bleaching and scanning, eliminating the need to introduce complex corrections for recovery during the bleach (13). Moreover, we do not assume that cytoplasmic diffusion is almost instantaneous (12), making the approach applicable also for cases where the FRAP kinetics at the membrane are fast and get close to the range of cytoplasmic diffusion. Importantly, the approach presented here takes into account the distribution of the protein of interest between the PM and the cytoplasm, enabling the derivation of both koff and kon without having to rely on any assumptions. Having given a set of tools for accurately quantifying dynamic parameters of non-integral membrane proteins via GS-FRAP, we hope that these will enable many investigators to determine the dynamic parameters of non-integral membrane proteins in the living cell.
Materials and Methods Cell culture and materials COS-7 cells (American Type Culture Collection) were grown as described (27). IgG of HC3 mouse monoclonal anti-X:31 HA was from J. J. Skehel (National Institute for Medical Research). Cy3 goat antimouse IgG (Fc specific) was from Jackson ImmunoResearch Laboratories. SynaptoRed™ reagent (FM 4-64) was from Sigma.
Plasmids and cell transfection The pEGFP-C3 expression vectors for GFP-N-Ras(G13V) (30) and GFP-HVRN-DA (a gift from I. A. Prior, Physiological Laboratory, School of Biomedical Sciences, University of Liverpool; 15) were described. Expression vector for HA-GPI (the ectodomain of X:31 HA fused to the GPI anchor addition signal of DAF) in pEE14 (originally designated BHA-PI; 31) was a gift from J. M. White (University of Virginia,). GFP-N-Ras-10 was created from GFP-N-Ras in pEGFP-C3 (30) by adding a stop codon right after Gln180 using site-directed mutagenesis. COS-7 cells growing on glass coverslips in 35-mm dishes were transfected by jet-PEI (PolyPlus Transfection) with 0.6 μg of a GFP-N-Ras vector alone or together with the HA-GPI vector (0.6 μg), completing the DNA to 1.2 μg by empty vector where needed.
Antibody-mediated cross-linking Cells were transfected with one of the GFP-N-Ras vectors alone or together with HA-GPI. After 24 h, cell-surface HA-GPI proteins were cross-linked at 4◦ C by IgGs (30 μg/mL HC3 anti-X:31 HA followed by 30 μg/mL Cy3 goat anti-mouse IgG). All antibody incubations (30 min each)
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and washes between incubations were in Hank’s balanced salt solution (HBSS; Biological Industries) supplemented with 20 mM HEPES, 2% BSA (Sigma-Aldrich), pH 7.2 (HBSS/HEPES/BSA).
FRAP beam-size analysis GS-FRAP studies were conducted in HBSS/HEPES/BSA on COS-7 cells transfected with a GFP-N-Ras vector alone or together with HA-GPI. To minimize internalization, FRAP measurements were performed at 22◦ C, replacing samples within 10 min. An argon ion laser beam (Innova 70C, Coherent) was focused through a fluorescence microscope (Axio Imager.D1, Carl Zeiss MicroImaging) to a Gaussian spot of 0.77 ± 0.03 μm [Plan Apochromat 63×/1.4 numerical aperture (NA) oil-immersion objective] or 1.17 ± 0.05 μm (C apochromat 40×/1.2 NA water-immersion objective), and experiments were conducted with each beam size (25,26). The ratio between the illuminated areas (26) was 2.28 ± 0.17 (n = 59). The setup was confocal, with a pinhole set at the image plane on route to the photomultiplier tube, which operated at a photon-counting mode (32). After a brief measurement at monitoring intensity (488 nm, 1 μW), a 5-mW pulse (5–10 milliseconds) bleached 60–75% of the fluorescence in the spot, and recovery was followed by the monitoring beam. In the FRAP beam-size analysis experiments, aimed to obtain an estimate of the relative contribution of lateral diffusion and exchange rather than fit to the full solution of diffusion and exchange (see below), the apparent characteristic fluorescence recovery time τ and Rf were extracted from the GS-FRAP curves by non-linear regression analysis, fitting to a lateral diffusion process (33). Studies on the effects of IgG-mediated clustering of HA-GPI on GFP-N-Ras(G13V) FRAP dynamics were conducted similarly, except that HA-GPI cross-linking by IgG preceded the measurement. The significance of differences between τ values measured in this manner with the same beam size was evaluated by Student’s t -test. To compare ratio measurements [τ(40×)/τ(63×) and w 2 (40×)/w 2 (63×)], we employed bootstrap analysis, which is preferable for comparison between ratio values (34). The τ(40×) and τ(63×) values were resampled with replacement using Excel, and average values from each group of resampled data [τ(40×)Boot and τ(63×)Boot ] were derived. For each beam size, 1000 averaged samples were generated, followed by calculation of the bootstrap ratio dividing τ(40×)Boot by τ(63×)Boot . To evaluate whether the τ ratios thus obtained differ significantly from the beam-size ratio calculated by the same method [w 2 (40×)Boot /w 2 (63×)Boot ], the set of the τ bootstrap ratios was divided by the set of beam area bootstrap ratios, and the p value was derived from the spread of the resulting histogram around 1.
Analysis of FRAP kinetics using a full-fitting approach GS-FRAP experiments were performed as described in the preceding section, using the 63× objective. To reduce the noise present in single curves, each curve was normalized by setting the prebleach intensity to 1, and 40–60 curves were then averaged (summing up the intensities), starting from the bleach point for synchronization. The resulting curve was fitted (see Supporting Information) to eqn 9, entering as fixed inputs the DC value (measured for GFP-N-Ras-10, which lacks a membrane anchor) and the RM value (measured for each condition/mutant by 3D confocal imaging; see following section). The derivation of the analytical expressions, the MATLAB program used for the fitting and the derivation of the best-fit parameters (Rf , DM , koff , kon , and κ) are presented in the Supporting R
Z
Information. Estimation of kon was done using kon = koff (1−M ×Z C . RM ) CM
Here, ZC is the fluorescence collection depth upon focusing the beam at the PM in a given GS-FRAP setup (depending on the objective, system geometry and pinhole size), and ZCM = 4DC dt is the thickness of the single-step layer beneath the membrane from which cytoplasmic proteins are available for exchange with the PM (see Supporting Information). The time resolution of the FRAP measurements (dt , given by the dwell time) is selected such that ZCM ≤ ZC . Measurement of ZC for the 63× objective was done according to Ref. (35), and yielded 0.6 μm. In brief, a planar fluorescent sample was prepared using a glass coverslip coated with polylysine (Sigma; 100 μg/mL, 1 h) and labeled with Alexa 488 goat
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Berkovich et al. anti-mouse IgG (Invitrogen; 20 μg/mL, 30 min). Using this sample, the fluorescence intensity as a function of the distance from the objective focal plane (identified by the fluorescence maximum) was calculated. The best linear least-squares fit of these data to eqn 25 in Ref. (35) yielded a fluorescence collection depth of 1.2 μm. This value should be divided by a factor of 2 since when the laser beam is focused at the PM, half of this collection depth is outside the cell and therefore does not include any fluorescent molecules. Notably, implementation of the fitting method presented here for standard LSMs does not require such a measurement, since the collection depth (ZC ) in an LSM can be obtained from the software controlling the microscope, according to the pinhole size and objective used in the FRAP experiments. The goodness-of-fit of the GS-FRAP data to the analytical expression was evaluated by calculating the coefficient of determination, R 2 . The error bounds for the fitted parameters were evaluated by computing the Jacobian for each parameter using the built-in MATLAB function (given in the MATLAB fitting code, Supporting Information). To obtain improved error bounds, the mean Rf estimated by averaging the Rf values from the individual FRAP curves was re-entered as fixed input. Importantly, such a calculation of Rf yielded essentially identical results to those obtained when performing the full fit. Entering Rf as fixed input results in reduction of the degrees of freedom and enables to avoid numerical issues in the fit.
Data acquisition and processing for determination of the RM value by live-cell 3D imaging
Images were acquired at 22◦ C with a motorized spinning disk confocal (Yokogawa CSU-22 Confocal Head) microscope (Axiovert 200 M, Carl Zeiss MicroImaging) under control of SlideBook™ (IntelligentImaging Innovations), using a Plan Apochromat 100×/1.4 NA oil-immersion objective. 3D image stacks were generated by sequential recordings along the z -axis by varying the position of a piezo-controlled stage. A step size of 0.29 μm was used. For excitation of the various GFP-Ras mutants, samples were illuminatedwith a 40-mW solid-state 473-nm laser. For identification of the PM, SynaptoRed™, a lipophilic fluoroprobe, was added to the cells at 20 μM final concentration. To minimize internalization of SynaptoRed™, samples were replaced every 10 min. Excitation of SynaptoRed™ was with a 10-mW solid-state 561-nm laser. Typical exposure times were 0.5–1 seconds. Quantification of the RM value was as follows: 3D images were acquired as described above. Specific signals were identified through intensity-based segmentation of signals significantly above the background intensity. The PM region of cells expressing GFP-N-Ras and labeled with SynaptoRed™ was defined by the segmented SynaptoRed™ signal. NM , a number directly proportional to the number of molecules in this region, was obtained by summing up the fluorescence intensity (arbitrary units) of the specific GFP-N-Ras signal in all the voxels making up the same region. Similarly, NC , proportional to the number of molecules in the cytoplasm, was determined as the sum of the intensities in the voxels that did not overlap with either the PM or the perinuclear Golgi/endosomal NM . compartment. The RM value was calculated by: RM = N + N M
C
To calculate the CM /CC ratio, NM and NC were each divided by the number of voxels defining the PM and the cytoplasm, respectively.
Simulations To confirm the validity of the analytical expression in eqn 9, we employed random walk simulations to a 3D grid model, depicted in Figure 1. In this model, the ensemble of the molecules of the protein is divided into two populations. One population is attached to the upper surface of the grid representing the membrane. The diffusion of this population in the membrane was treated in terms of random walk scheme, using a Monte–Carlo algorithm with an average step size determined by the diffusion coefficient DM : dxM = 4DM dt . The membrane thickness was taken as 0.03 μm, defining the scale of the system. The second population is composed of the protein molecules at any z -axis value below the membrane surface, and represents the cytoplasmic molecules,
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characterized by the cytoplasmic diffusion coefficient DC . Molecules can exchange between the two populations, which are assumed to be at steady state (i.e. the number of molecules leaving the surface representing the membrane equals the number of those reaching this surface from the cytoplasm). At each step of the simulation, the direction of each particle motion in both layers was defined using a stochastic parameter, generated using a Gaussian distribution random number function. The borders were taken to be self-reflecting in every direction. When a protein reaches the interface between the membrane and the cytoplasm, a possibility of exchange was included by generating another stochastic parameter that mimics the kinetic rate constants (koff for dissociation from the membrane and kon for binding to the membrane surface). The distributions of the fluorescence intensity and bleach profiles were assumed to be Gaussian at the surface (PM); the bleaching had no z -axis dependence and the excitation intensity, I (r ), had a Lorentzian distribution along the z -axis. The Gaussian radius of the beam was taken as 0.77 μM. In these simulations, 20 000 particles were distributed randomly along a 3D grid (2000 × 2000 × 100), at a 4:1 ratio between the upper boundary and grid volume (Figure 1). Then, a summation was taken over the entire fluorescence of the system. Following the next iterations, separated by the time interval dt = 0.0002 seconds, some particles changed their location according to the laws described above, and the fluorescence was summed and documented at each iteration. At a given time-point, one time interval was used to simulate bleaching of 50% of the fluorescent particles in the membrane and the cytoplasm, followed by recovery of the fluorescence via the diffusion (DM and DC ) and exchange of the fluorescent particles.
Acknowledgments This study was supported by a DFG-DIP grant (KL 1948/1-1, GA 309/10-1) to M. W., J. K., Y. I. H. and M. U. Y. I. H. is an incumbent of the Zalman Weinberg Chair in Cell Biology. We thank I. A. Prior for the expression vector for GFP-HVR-N-DA.
Supporting Information Additional Supporting Information may be found in the online version of this article: Appendix S1: Derivation of the analytical expression for GS-FRAP dynamics of a non-integral membrane protein. This section includes the mathematical details of deriving the equation employed for the GS-FRAP fits. It is associated both with the main text and with Figures 1, 2 and 4. Appendix S2: MATLAB fitting code. This is the fitting code to run the above fits. It is to be used as a ‘tool’ by interested researchers who can apply it to fit their data. It is associated with Figures 1, 2 and 4. Appendix S3: Sample dataset. This includes two text files containing the averaged and normalized data from FRAP measurements on GFPHVR-N-DA (GFP-HVR-N-DA 63x SUM_fps.txt and GFP-HVR-N-DA 63x SUM_tps.txt ), to be fitted using the MATLAB fitting code. Please note: Wiley-Blackwell are not responsible for the content or functionality of any supporting materials supplied by the authors. Any queries (other than missing material) should be directed to the corresponding author for the article.
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