Quantifying Lipid Diffusion by Fluorescence Correlation Spectroscopy

Article pubs.acs.org/Langmuir

Quantifying Lipid Diffusion by Fluorescence Correlation Spectroscopy: A Critical Treatise Fabian Heinemann,†,‡,§ Viktoria Betaneli,†,‡ Franziska A. Thomas,‡ and Petra Schwille*,‡,§ ‡

Biophysics Institute, Biotec/Technische Universität Dresden, Tatzberg 47-51, 01307 Dresden, Germany Max Planck Institute of Biochemistry, Am Klopferspitz 18, 82152 Martinsried, Germany

§

S Supporting Information *

ABSTRACT: Fluorescence correlation spectroscopy (FCS) measurements are widely used for determination of diffusion coefficients of lipids and proteins in biological membranes. In recent years, several variants of FCS have been introduced. However, a comprehensive comparison of these methods on identical systems has so far been lacking. In addition, there exist no consistent values of already determined diffusion coefficients for well-known or widely used membrane systems. This study aims to contribute to a better comparability of FCS experiments on membranes by determining the absolute diffusion coefficient of the fluorescent lipid analog 1,1′-dioctadecyl3,3,3′,3′-tetramethylindodicarbocyanine (DiD) in giant unilamellar vesicles (GUVs) made of dioleoylphosphatidylcholine (DOPC), which can in future studies be used as a reference value. For this purpose, five FCS variants, employing different calibration methods, were compared. Potential error sources for each particular FCS method and strategies to avoid them are discussed. The obtained absolute diffusion coefficients for DiD in DOPC were in good agreement for all investigated FCS variants. An average diffusion coefficient of D = 10.0 ± 0.4 μm2 s−1 at 23.5 ± 1.5 °C was obtained. The independent confirmation with different methods indicates that this value can be safely used for calibration purposes. Moreover, the comparability of the methods also in the case of slow diffusion was verified by measuring diffusion coefficients of DiD in GUVs consisting of DOPC and cholesterol.

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INTRODUCTION The fluidity of the plasma membrane and thus lateral diffusion of lipids and membrane proteins is an essential property of living cells. Diffusion enables the distribution of membrane constituents and is a prerequisite for diffusion-limited chemical reactions inside the membrane plane.1 According to the influential 40 year old Singer and Nicholson fluid-mosaic model2 and its biophysical description according to Saffman and Delbrück,3 the plasma membrane can be described as a twodimensional viscous fluid with a free lateral diffusion of lipids and embedded proteins. Nowadays, it is known that the situation is more complex.4 Lateral diffusion of membrane proteins and lipids is modulated by various factors, such as crowding due to the high protein content in the membrane (for example, 23% of the area in the erythrocyte membrane is occupied by proteins).5 Furthermore, the proposed sphingolipid- and cholesterol-enriched lipid nanodomains6 represent dynamic obstacles or traps for diffusing membrane species.7−9 Also, membrane-associated parts of the cytoskeleton are supposed to interfere with membrane diffusion 8,10 by dividing the membrane into compartments of typically 40−200 nm in diameter.11,10 The question of how precisely lateral membrane diffusion is modulated is currently under intensive investigation. Minimal systems as well as native cell membranes are used for these studies. © 2012 American Chemical Society

A widely used technique to measure lateral diffusion coefficients D in biological membranes is fluorescence correlation spectroscopy (FCS), as recently discussed.12−14 Besides the classical method of “point” FCS with a steady confocal volume,15−18 several modifications like dual-focus FCS,19−21 z-scan FCS,22 one or two focus scanning FCS (1f SFCS, 2f SFCS),23 circular scanning FCS, 24 and line-scan FCS (LSFCS)25 have been developed. These new variants of FCS address some of the notorious problems related to FCS on membranes: membrane movements, fluorophore bleaching, and the requirement of a calibration of the detection volume. Despite this diversity of methods, there is a lack of consensus values of diffusion coefficients. This is reflected in the discrepancy of published diffusion coefficients for equivalent experimental conditions. As an example, the reported diffusion coefficients D of the frequently used fluorescent lipid analog 1,1′-dioctadecyl-3,3,3′,3′-tetramethylindodicarbocyanine (DiD) in giant unilamellar vesicles (GUVs) composed of 1,2-dioleoylsn-glycero-3-phosphocholine (DOPC) range from D = 5.8 ± 0.3 18 to 8.7 ± 0.7 μm2 s−1 26 (in both cases using point FCS). Another result for DOPC GUVs was obtained by nuclear Received: June 27, 2012 Revised: August 13, 2012 Published: August 14, 2012 13395

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Figure 1. Schematic representation of various FCS techniques to study membrane diffusion. (A) In point FCS, the focal spot is positioned on the membrane. (B) In z-scan FCS, several FCS measurements are performed with different z positions relative to the membrane. (C) For LSFCS, the focal spot is moved in the membrane plane by repeatedly scanning a line with a scan speed ν. (D) In 1f SFCS, the focal spot is scanned in a linear manner perpendicular to the membrane across the equator of a GUV. (E) For 2f SFCS, two focal spots separated by a distance d are scanned linearly and perpendicular to the GUV membrane.

magnetic resonance, where a value of D ≈ 9 μm2 s−1 was reported.27 In order to obtain a comparability of results when characterizing membrane diffusion, it is obviously important to obtain absolute values of D. In this study, a precise determination of the diffusion coefficients of the lipid analog DiD in GUVs composed of DOPC is performed. Independent measurements with five different FCS variants (point FCS, two types of z-scan FCS, 1f SFCS, 2f SFCS, and LSFCS, see Figure 1) are used to accurately determine the value of D. In the case of methods relying on calibration of the focal volume with a dye of known D, a recently published high-precision value for the red dye Atto 655 was used.19 In the case of 2f SFCS, which is very sensitive to the distance of the two foci, the distance was precisely determined by atomic force microscopy (AFM) on a photoreactive polymer. Finally, the novel methods 1f SFCS, 2f SFCS, and LSFCS are compared with point FCS and z-scan FCS. Potential error sources and application ranges of the different FCS variants are discussed. Since all techniques independently resulted in identical values of D, the overall average value for DiD in DOPC represents a precise measurement of the absolute diffusion coefficient in this system.

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Some fluorophores show fast transitions between fluorescent and nonfluorescent states (so-called ‘blinking’), for example, caused by triplet transitions.30 The typical ‘on state’ time of these fluorescent species causes an additional component in the autocorrelation function. In this case a modified fitting function has to be used G(τ ) =

τD =

−1 τ⎞ 1⎛ ⎜1 + ⎟ τD ⎠ N⎝

(4)

The focal waist ω0 corresponds to the lateral e radius of the intersection of the detection volume with the membrane under the assumption of a Gaussian-shaped effective detection area

⎛ x2 + y2 ⎞ ⎟ W (x , y) = exp⎜ − 2 ω02 ⎠ ⎝

(5)

If ω0 is known, the diffusion coefficient can be calculated from τD with eq 4. Calibration of the waist is performed by measuring τD for a freely diffusing reference dye with known diffusion coefficient D and using eq 4. z-Scan FCS. In z-scan FCS,22 the membrane with the diffusing fluorescent species is placed perpendicular to the optical axis and a vertical stack of autocorrelation curves G(τ) is recorded at different distances z from the center of the focal spot and the membrane (Figure 1B). This method utilizes the divergence of the detection area waist ωxy(z) along the optical axis z, with ωxy(0) = ω0. In contrast to the approximation of a 3D Gaussian, the waist ωxy(z) increases with the distance to the center of the focal spot at z = 031−33

(1)

⎛ λ ⎞2 2 ωxy(z)2 = ω02 + ⎜ ⎟z ⎝ nπω0 ⎠

For two-dimensional diffusion in the membrane, the theoretical autocorrelation function is28,29 G(τ ) =

ω02 4D −2

THEORY

⟨δF(t )δF(t + τ )⟩ ⟨F(t )⟩2

(3)

with f t as the average fraction of molecules in the nonfluorescent state and τt the typical duration of a fluorescent ‘on state’ state. The diffusion time τD is related to the diffusion coefficient D and the focal waist ω0 by

Point FCS. In this method, the center of the focal spot is placed on the membrane, with the membrane perpendicular to the optical axis (Figure 1A). The measured fluorescence fluctuations δF(t) = F(t) − ⟨F(t)⟩ around the average ⟨F(t)⟩ are analyzed by calculation of the autocorrelation function, where the brackets ⟨⟩ represent the temporal average and the variable τ is the correlation time

G(τ ) =

−1 1 − ft + ft e−τ / τt 1 ⎛ τ⎞ ⎜1 + ⎟ 1 − ft N⎝ τD ⎠

(6)

λ is the excitation wavelength, n the refractive index of the medium, and ω0 the beam waist at the focal plane at z = 0. By combining eqs 4 and 6 the dependency τD(z) can be obtained

(2)

Here, N is the average particle number in the focal area and τD the diffusion time. Both parameters are obtained by fitting eq 2 to the experimentally obtained autocorrelation data.

τD(z) = 13396

ω02 λ 2z 2 + 2 2 2 4D 4n π ω0 D

(7)

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The first term corresponds to the minimal diffusion time at z = 0. The experimentally obtained dependence of the diffusion times τD on the vertical position z is fitted with eq 7. Beam waist ω0 and the diffusion coefficient D are directly obtained as fitting parameters without using an external standard. Equation 6 was obtained assuming a small angle of the laser beam with respect to the optical axis (paraxial approximation). However, small angles are not realistic for objectives with high numerical aperture (e.g., α = 64° for a numerical aperture NA = 1.2 and water), and it is unclear how this affects the validity of eqs 6 and 7. Another use of the z-scan is therefore to fit the observed τD(z) dependence empirically with a quadratic polynomial and use the minimal diffusion time and eq 4 to obtain the diffusion coefficient after a calibration of the focal volume. This approach can compensate for a slight vertical mispositioning of the focal volume with respect to the membrane. 1f SFCS. In the single-focus variant of scanning FCS (1f SFCS), the detection volume is moved perpendicular to the membrane across the equator of a GUV (Figure 1D).23 For each scanned line, the intensity is collected along the scan path, resulting in a scan vector f i. The membrane passage can be easily identified as the maximum intensity of this vector. Typically, more than 105 scans across the membrane are performed, each resulting in a single-scan vector. These scan vectors can be combined in a matrix f ij, where j represents the index of the scanned line and i the acquired fluorescence along the single scans. Membrane movements can be corrected by shifting the scan vectors relative to each other and aligning the maximum signals in a row. For each aligned scan vector, the contributions of the membrane are summed up (typically the maximum ± 2.5 standard deviations) and an intensity value F(t) for each line is obtained. From the resulting intensity trace F(t), the autocorrelation G(τ) is calculated according to eq 1. For two-dimensional diffusion, the experimental autocorrelation data can be fitted with the function

1⎛ τ⎞ ⎜1 + ⎟ N⎝ τD ⎠

−1/2

G(τ ) =

−1/2 ⎛ τ ⎞ ⎜1 + 2 ⎟ S τD ⎠ ⎝

Photons in the two foci are collected with a delay td, which is given by the scan repetition time. This delay has to be taken into account while evaluating the corresponding cross-correlation curves.23 A calibration measurement in solution is not required to determine the diffusion coefficient, but the distance between the two lines has to be precisely known. LSFCS. Another variant of FCS is line-scan FCS,25 which belongs to the class of image correlation techniques. In LSFCS, a line is repeatedly scanned in the membrane plane of a GUV (Figure 1C). The detected fluorescence intensity traces of the line scans i are arranged vertically to form a pseudoimage F(x,ti), where ti = iT (T is the scanning period). Due to scanning, the intensity F(x,ti) is acquired at the time ti + x/ν, where ν is the scan speed. The horizontal axis of the obtained pseudoimage describes the position x in the sample and the vertical axis the time ti. This image is used to calculate the spatiotemporal correlation curve G(ξ, τi) using the following equation G(ξ , τi) =

G(ξ , τi) =

D(T ) =

1⎛ 4Dτ ⎞ ⎟ Gx(τ ) = ⎜1 + N⎝ ω02 ⎠

⎛ 4Dτ ⎞ ⎜1 + 2 2 ⎟ ω0 S ⎠ ⎝

kBT 6πrη(T )

D(T ) = D(T0)

(15)

T η(T0) T0 η(T )

(16)

Typically, water is used as a solvent for calibration of dyes. To obtain the viscosity of water at any temperature in the range 0−100 °C, the following approximation can be used34

(10)

2

η(T ) = η2010((A(T20− T ) − B(T − T20) )/(T − C))

⎛ ⎞ d ⎟ exp⎜− 2 ⎝ ω0 + 4Dτ ⎠ (11) Also, the area concentration C of the molecules can be obtained from N = CπSω20. −1/2

(14)

Here, r is the hydrodynamic radius of the molecule and kB the Boltzmann constant. The diffusion coefficient depends on the absolute temperature T both directly and indirectly via the viscosity η(T). The diffusion coefficient D(T0) at a temperature T0 can be corrected to a value D(T) at a different temperature T by

To determine the values of D and ω0, the two autocorrelation curves and the cross-correlation curve are globally fitted to the following functions for two-dimensional diffusion

−1/2

⎛ ⎞ 1 ξ2 ⎟ exp⎜ − 2 2 Cπω0 ⎝ ω0 + 4D(τi + ξ /ν) ⎠

The concentration of molecules C, the diffusion coefficient D, and the waist of the focal volume ω0 are obtained as fit parameters. This method relies on knowledge of the scanning velocity ν and does not require a dye with known diffusion coefficient for calibration. Temperature Dependence of the Reference Dye Diffusion Coefficient. For the FCS variants which require determination of the focal waist using eq 4, it is essential that dyes with precisely known diffusion coefficients are used. Recently, reliable values for several dyes such as Alexa Fluor 488, Alexa Fluor 546,24 and Atto 65519 have been published. For an accurate determination of the focal waist, it is important to correct the diffusion coefficient to the temperature of the system that should be calibrated.13 This temperature dependence is often omitted, although it is strong. In the case of three-dimensional diffusion, the temperature dependence of the diffusion coefficient D of a molecule is described by the Stokes−Einstein equation

(9)

−1/2 −1/2 ⎛ 1⎛ 4Dτ ⎞ 4Dτ ⎞ ⎟ ⎜1 + 2 2 ⎟ G(τ ) = ⎜1 + N⎝ ω02 ⎠ ω0 S ⎠ ⎝

(13)

−1 ⎛ 4D ⎛ ξ ⎞⎞ ⎜1 + 2 ⎜τi + ⎟⎟ ν ⎠⎠ ω0 ⎝ ⎝

(8)

⟨δF1(t )δF2(t + τ )⟩ ⟨F1(t )⟩⟨F2(t + τ )⟩

⟨F(x , ti)⟩2

where δF(x, ti) = F(x,ti) − ⟨F(x,ti)⟩, ξ is the spatial correlation variable, and τi = iT is the discrete lag time. The obtained correlation curve can be fitted to the equation

The model function was derived for an elliptical two-dimensional Gaussian intersection of the focal volume and the membrane with focal waists ω0 and Sω0. The so-called structural parameter S is defined as the ratio of axial and lateral size of the detection volume S = ωz/ω0. Diffusion coefficients are obtained from the diffusion time τD using eq 4 after calibration of the focal radius ω0 with a reference dye with a precisely known diffusion coefficient. Due to the limited scan speed with maximum repetition times of below 1 ms, triplet blinking with a typical time range of a few microseconds cannot be resolved and is therefore neglected. 2f SFCS. In two-focus SFCS (2f SFCS), two lines separated by a distance d are scanned perpendicular to the equator of a GUV (Figure 1E).23 The alignment of the data is identical to 1f SFCS with the difference that two intensity traces F1(t) and F2(t) are obtained. The autocorrelation functions for each focus G1(τ), G2(τ) are calculated using eq 1. The cross-correlation Gx(τ) between the two foci is defined as Gx(τ ) =

⟨δF(x , ti)δF(x + ξ , ti + τi)⟩

2

(17)

η20 corresponds to the viscosity at T20 = 293.15 K (20 °C) with η20 = 0.001002 Pa s and the constants A = 1.1709, B = 0.001827 K−1, C = 183.22 K. If required, η(T) can also be directly measured. This might be important in cases when a buffer solution with an unknown temperature dependency of the viscosity is used during calibration. 13397

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times averaged to obtain the dependency τD(z). Measurement time for single measurements was 20 s and the laser power 0.95 μW. 1f SFCS and 2f SFCS. The fluorescence image of a GUV was acquired on the equatorial plane of the vesicle. For 1f SFCS, a line was scanned perpendicular to the membrane plane with a length of 19.2 μm in the unidirectional scan mode. In 2f SFCS, two lines separated by a distance d = 0.54 μm were scanned perpendicular to the membrane plane. For this a scan frame with a size of 32 × 2 pixels and a length of 19.2 μm was used in the multitrack mode of the microscope software. The bidirectional scanning mode was chosen, and lasers were switched on only during the back scanning. For both SFCS variants, measurements were conducted at the maximum scan speed of the instrument (768 μs/line for 1f SFCS, 1536 μs/scan for 2f SFCS) for 300−900 s with a laser power of 8.25 μW, except for the laser power variation experiments. Data were analyzed using software developed in house in MatLab (version R2007b) (the MathWorks, Natick, USA) as described.23 The value of S was fixed during the data fitting (S = 5). LSFCS. The fluorescence image of a GUV was acquired at the upper pole of the vesicle (with a diameter of at least 30 μm). The position of the membrane was found by detecting the maximal intensity. The line was scanned using the line scan mode of the microscope software with zoom 15 and line length of 512 pixels (15.36 μm). Each measurement was conducted for at least 30 s with a laser power of 5 μW. LSFCS data were analyzed using software developed in MatLab as described.25 The spatial variable ξ was restricted to ξ = −0.8, ..., 0.8 μm. The discrete lag time τi was restricted to τi = τ1, ..., τ100, with T = 768 μs. Experiments yielding a focal waist from the LSFCS fit exceeding the waist from a 3D calibration by more than 20% were discarded since this indicates a wrong vertical positioning. To avoid evaluation of experiments with vertical drift, only measurements without change in intensity were used for further analysis. Calibration of Scan-Line Distance for 2f SFCS. Polymer Synthesis. Polymer was synthesized by a modification of the procedure of Ho et al.35 The following chemicals were used without further purification: dimethylformamide (DMF), sodium sulfate (Acros-Organics, Geel, Belgium); dichloromethane (DCM), Disperse Red, methylacryloyl chloride, sodium carbonate, tetrahydrofuran (THF) (Sigma-Aldrich, St. Louis, MO, USA); α,α′-azoisobutyronitrile (AIBN), ethanol, methanol, and triethylamine (VWR International, Darmstadt, Germany). All reactions were carried out under argon atmosphere at room temperature (22−23 °C). NMR spectra were recorded on a Bruker DRX 500 (Bruker BioSpin, Rheinstetten, Germany). Monomer (Disperse Red 1 methacrylate (DR1M)) was prepared as follows. Disperse Red (3.28 g, 10.4 mmol, 1.0 equiv) was dissolved in THF (50 mL) at 0 °C, and triethylamine (1.5 mL, 10.8 mmol, 1.03 equiv) was added. After stirring for 10 min at this temperature methylacryloyl chloride (1.1 mL, 11.3 mmol, 1.1 equiv) in THF (10 mL) was added dropwise, and the dark red solution was stirred at room temperature overnight. Solvent was removed under reduced pressure, and residue was redissolved in a solution of 1.0 g of sodium carbonate in 100 mL of deionized water. Aqueous phase was extracted with DCM (4 × 50 mL). Combined organic extracts were dried over sodium sulfate, and solvent was removed under reduced pressure. Crude product was recrystallized from 100 mL ethanol to yield the monomer (2.86 g, 7.5 mmol, 72%) as a red powder. 1H NMR (500 MHz, CDCl3): δ (ppm) = 8.32 (d, J = 9.0 Hz, 2 H, CHarom−CNO2), 7.93 (d, J = 9.0 Hz, 2 H, CHarom), 7.92 (d, J = 8.5 Hz, 2 H, CHarom), 6.83 (d, J = 9.0 Hz, 2 H, CHarom−N), 6.11−6.09 (m, 1 H, CH), 5.60− 5.58 (m, 1 H, CH), 4.37 (t, J = 6.0 Hz, 2 H, CH2−O), 3.74 (t, J = 6.0 Hz, 2 H, CH2−CH2−O), 3.55 (q, J = 7.0 Hz, 2 H, CH2−CH3), 1.93 (t, J = 1.0 Hz, 3 H, CH3−C), 1.26 (t, J = 7.0 Hz, 3 H, CH2−CH3). Polymerization (pDR1M) was performed as follows. Monomer DR1M (500.7 mg, 1.3 mmol, 1.0 equiv) was dissolved in DMF (50 mL) and degassed by two freeze−pump−thaw cycles. Afterward, AIBN (48.1 mg, 0.3 mmol, 0.22 equiv) dissolved in DMF (5 mL) was added dropwise. The reaction mixture was heated to 60 °C for 48 h and then poured into methanol (500 mL). Precipitated polymer was filtered off, redissolved in THF (45 mL), and again precipitated by

MATERIALS AND METHODS

Preparation of GUVs. Giant unilamellar vesicles were prepared from pure 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) and in mixture with 20%, 30%, 40%, and 50% cholesterol (chol) (Avanti Polar Lipids, Alabaster, USA). The fluorescent lipid dye 1,1′dioctadecyl-3,3,3′,3′-tetramethylindodicarbocyanine, 4-chlorobenzenesulfonate salt (DiD) (Invitrogen, Darmstadt, Germany), in some articles also referred to as DiIC18(5), was added at 0.01 mol % to the lipid dissolved in chloroform. GUVs were prepared by the electroformation method in a custom-made Teflon chamber with two electrodes made of platinum wires. The lipid mixture (5 μL, 1 mg/mL) in chloroform was spread on both wires. The chamber was filled with 300 mM sucrose (350 μL). An ac electric field of 2 V (corresponding to a rms field strength of 400 V m−1) was applied across the chamber at a frequency of 10 Hz for 1 h. To detach the vesicles from the electrodes, the frequency was reduced to 2 Hz for 0.5 h. The vesicles (25 μL) were transferred into an observation chamber (#1.5 cover slide, Nunc, Lab-Tek, Ashland, USA) coated with albumin from bovine serum (Sigma-Aldrich, St. Louis, MO, USA) and containing 400 μL of phosphate-buffered saline (PBS) (137 mM NaCl, 2.7 mM KCl, 4.3 mM Na2HPO4, 1.4 mM KH2PO4, pH 7.4). Fluorescence Correlation Spectroscopy. Optical Setup. Fluorescence correlation spectroscopy measurements were carried out using a confocal microscope equipped with a 40× water immersion objective (C-Apochromat, NA 1.2 UV−vis−IR, Zeiss, Jena, Germany). Samples were excited by the 633 nm line of a He−Ne laser. A λ/4 plate was used to achieve excitation by circularly polarized light. Fluorescence was detected by avalanche photodiodes (PerkinElmer, San Jose, CA, USA). In scanning FCS measurements, photon arrival times were recorded in the photon mode of a Flex 02-01D hardware correlator (correlator.com, Bridgewater, USA), and correlation curves were obtained using specific software as described below, whereas for point and z-scan FCS measurements, correlation curves were directly calculated by a hardware correlator. Atto 655 (Atto-Tec, Siegen, Germany) in water (∼50 nM) was used to align the setup. The objective correction collar and the pinhole position (d = 90 μm) were adjusted to maximize the fluorescence intensity. Calibration of the focal radius ω0 was performed using the FCS model function for 3D diffusion without triplet correction. The diffusion coefficient of Atto 655 D = 426 ± 8 μm2 s−1 (25 °C)19 was corrected to the temperature measured over the objective with an electrode thermometer (Voltcraft 302 JKJ, Conrad electronics, Hirschau, Germany). All experiments were carried out in the interval 23.5 ± 1.5 °C. Point FCS, z-scan FCS (except for two measurements shown in Figure S1, Supporting Information), LSFCS, 1f SFCS, and 2f SFCS measurements were carried out on a LSM 510 Meta system (Zeiss, Jena, Germany) using a homemade detection unit at the optical fiber output channel. A dichroic mirror HFT 488/543/633 and a band-pass filter HQ700/75 (AHF Analysentechnik, Tübingen, Germany), positioned behind a collimating achromat, were used to reject scattered or reflected laser light. Partly, point FCS, 1f SFCS, and LSFCS measurements were also carried out on a LSM 510, ConfoCor3 system (Carl Zeiss, Jena, Germany). HFT 488/633 and NFT 635 dichroic mirrors and a LP655 long-pass filter were used to split excitation and emission. Point FCS. The focus was positioned at the top pole of a GUV at the position of the minimal diffusion time and maximum fluorescence intensity. Before the experiments it was verified that these points coincide. Correct vertical position was controlled after each measurement; measurements with visible vertical drift were rejected. Measurement time was 30 s. Except for the measurements with varying laser power, a low laser power of 0.95 μW was used to avoid photobleaching. z-Scan FCS. For each z-stack, nine FCS measurements were performed around the maximum of the fluorescence intensity with a vertical distance between the individual measurements of 0.2 μm. In total, six z-stacks were aligned to the maximum intensity and the diffusion 13398

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pouring the solution into methanol (450 mL). After filtration, the product was dried under vacuum to yield the polymer (61.3 mg) as red crystals. Polymer Coating of Slides. Polymer pDR1M was dissolved in THF (0.5% w/v). Polymer clusters were disrupted by sonication. A glass coverslip was plasma cleaned and coated with the dissolved polymer using a spin coating device (KW-4A, Chemat Northridge, USA). The coated slide was dried at 70 °C, and a homogeneous flat polymer film with a thickness of 20−40 nm was obtained. Generation of Optically Inscribed Scan Lines. Photoreactive polymer pDR1M exhibits maximal absorbance at 458 nm,35 and topography changes can be induced by the 488 nm laser line of the argon laser of the LSM 510 Meta system. The laser was focused on the polymer film using a laser power of 20 μW. All optical parts and scan settings were identical to 2f SFCS. Elevated scan lines were obtained after 30 s of scanning. Atomic Force Microscopy. Elevated lines were imaged in air using a NanoWizard AFM (JPK Instruments, Berlin, Germany). Imaging was performed in contact mode with minimized force. Rectangular cantilevers with a nominal tip radius of 10 nm and a nominal spring constant of 30 mN m−1 were used (CSC38/noAl, MicroMash, Tallinn, Estonia). Average line profiles over the elevated lines with a width of ∼4 μm were obtained from flattened images using the software gwyddion (http://gwyddion.net/). The distance between the elevated lines was determined as the peak to peak distance of two Gaussian functions fitted to the individual peaks using the software IgorPro (Wavemetrics, Portland, USA).

waist it is convenient to use the maximum in fluorescence as an indicator. However, it has to be ensured that for a given sample and setup the maximum of the fluorescence intensity and the minimum of the diffusion time coincide as shown in Figure 3A.

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RESULTS AND DISCUSSION Point FCS on a membrane corresponds to conventional FCS with the focal volume positioned at the membrane. A typical autocorrelation curve and corresponding fit (eq 3) of DiD diffusing in GUVs composed of DOPC is shown in Figure 2. Figure 3. z-scan FCS. (A) Measured diffusion times (black circles) and fit (solid line) for DiD in DOPC GUVs at different vertical positions. Corresponding normalized fluorescence count rate is shown in gray with an empirical Gaussian fit (dashed line). (B) Plot of the common 3D Gaussian approximation for the effective detection volume. (C) Plot of a more accurate approximation of the focal volume, showing the vertical divergence around z = 0, which is utilized in z-scan FCS.

Optical aberrations, for example, induced by deviations in cover slide thickness or buffers with a slightly different refractive index than water, can induce an offset in the positions.22,21 In these cases or when the maximum in fluorescence is not well pronounced it is recommended to perform a series of FCS measurements along z and measure at the position of the highest counts per molecule.21 Alternatively, the z-scan approach with external calibration, as described below, can be used, where the minimum in diffusion time is determined by fitting the observed dependence τD(z) with a quadratic polynomial. Another important source of error is a too high excitation power. Even though by increasing the laser power the signal-tonoise ratio of the autocorrelation curves can be increased,36 laser powers above a certain threshold introduce new artifacts: photobleaching and saturation. For membrane diffusion, photobleaching is typically the major problem. Compared to free 3D diffusion, single fluorophores stay 1 or 2 orders of magnitude longer in the focus. Therefore, bleaching of fluorophores in the focal spot occurs at much lower power compared to fast 3D diffusion. In-focus photobleaching reduces the diffusion time, since fluorophores are removed before they leave the detection area. Moreover, infocus bleaching can also cause a noticeable depletion of the total number of fluorophores in the system. This decay of fluorophores during a measurement results in distorted autocorrelation curves.

Figure 2. Representative autocorrelation curves (experimental data with corresponding fits) obtained by point FCS (circles) and 1f SFCS (triangles) for DiD diffusion in DOPC GUVs. Both autocorrelation curves were normalized to the particle number. For 1f SFCS, the autocorrelation curve has a lower temporal resolution and is shifted toward longer correlation times compared to the point FCS curve.

Compared to the other investigated methods, this technique has the highest temporal resolution. The autocorrelation curve shows a decay in the millisecond range, due to the diffusion of DiD, as well as fast ‘blinking’ dynamics in the microsecond range. Diffusion coefficients obtained by point FCS are prone to several sources of error. First, due to the z-dependence of the focal waist (eq 6), the correct positioning of the focal volume on the membrane is crucial. Wrong positioning results in too high diffusion times and too low diffusion coefficients. Especially in the case of slow diffusion, for example, in cellular membranes, where longer measurement times are required, this is a disadvantage. Here, membrane movements hamper the accuracy of the method. For a vertical positioning at the minimal focal 13399

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The other relevant laser power-dependent phenomenon is saturation. It can occur when the excitation intensity is so high that the fluorescence is not anymore proportional to the excitation intensity, due to an increasing number of molecules in a nonexcitable state. Since the highest excitation intensity is at the center of the focal volume, saturation results in an effective flattening of the combined excitation and detection volume and, as a consequence, leads to an increase in the effective observation volume and diffusion time.37 Figure 4 shows the

Table 1. Absolute Diffusion Coefficients (mean values and standard deviations) of DiD in DOPC GUVs Obtained by Different FCS Methodsa FCS method point FCS z-scan FCSb z-scan FCSc 1f SFCS 2f SFCS LSFCS all techniquesd

diffusion coefficient, D (μm2 s−1) 10.2 10.4 9.6 9.9 10.5 9.6 10.0

± ± ± ± ± ± ±

1.1 0.9 1.2 0.9 1.5 0.9 0.4

no. of measurements calibration based on 39 6 6 13 14 19

D of standard vertical focal step size D of standard D of standard distance between foci scanning speed

Measurements were carried out at 23.5 ± 1.5 °C. No significant difference between the diffusion coefficients measured by the different methods was found (p ≥ 0.01, two-sided Wilcoxon−Mann−Whitney Test of all possible pairs). bFit to the observed τD(z) dependency with eq 6. cWith external calibration dMean and standard deviation of the mean values from the individual FCS methods. a

acquisition of the z-stack, which typically takes a few minutes. The experimentally obtained z-dependency of the diffusion times is shown in Figure 3A, and the principle of the method is illustrated in Figure 3B and 3C (cf. point FCS), where the common approximation of a 3D Gaussian function for the effective detection volume is shown in comparison with the more realistic divergent effective volume calculated according to Dertinger et al.19 Two different approaches to analyze the z-scan data were used. In the first method, the experimental data τD(z) were fitted with eq 7 resulting in a diffusion coefficient of 10.4 ± 0.9 μm2 s−1 (mean ± sd, n = 6). This value was not different from the diffusion coefficients obtained by the other methods (Table 1). Also, the obtained minimal waist ω0 = 265 ± 11 nm (mean ± sd, n = 6) was very close to the value of ω0 = 258 ± 6 nm (mean ± sd, n = 31) obtained by external calibration with Atto 655. This agreement of the results for D and ω0 indicates that for our setup eq 6 describes the beam waist accurately, although a high NA objective was used, which clearly violates the paraxial approximation. This is in accordance to findings by Dertinger et al., who confirmed eq 6 for a high NA objective by measuring the point spread function.19 However, in another work it was reported that diffusion coefficients determined by the z-scan without external calibration were ∼1.5-fold higher compared to other FCS methods.38 There it is discussed that for high NA objectives the conventional z-scan using eqs 6 and 7 is not necessarily valid. In the Supporting Information, Figure S1, we show that for two other commercially available setups the z-scan indeed yielded strongly differing values for the beam waist and the diffusion coefficient compared to the expected values. Therefore, eqs 6 and 7 should be applied very carefully and only if for a given setup it can be confirmed that the obtained beam waist ω0, as well as the diffusion coefficient D, are identical to the results from other methods. Another possibility to analyze z-scan FCS data is to determine the minimum diffusion time by fitting the observed dependence τD(z) with a quadratic polynomial. This approach allows compensating for slight vertical mispositioning with respect to the minimum diffusion time. In our experiments, the diffusion coefficient obtained by z-scan with external calibration was 9.6 ± 1.2 μm2 s−1 (mean ± sd, n = 6) and not different from any of the other methods (Table 1).

Figure 4. DiD diffusion coefficients measured by point FCS (circles) and 1f SFCS (triangles) at various laser powers in DOPC GUVs. At higher laser powers, in-focus bleaching results in increased diffusion times in the case of point FCS. In contrast, 1f SFCS is insensitive to photobleaching.

determined diffusion coefficients for DiD in GUVs composed of DOPC at different laser powers. Above 2 μW, the apparent diffusion coefficient increases with increasing laser power, showing that initially photobleaching is the dominant laser power-dependent error for this system. The appropriate laser power without saturation or bleaching should be determined before measuring diffusion coefficients in a given system. A further potential error source when performing point FCS on membranes is related to the shape of the observation volume. Diffusion coefficients for two-dimensional membrane diffusion were obtained using the effective focal waist ω0 from a calibration in three dimensions using the Gaussian approximation (Figure 3B). However, the real observation volume has a more complex shape (Figure 3C), and the possible effect of the difference in the e−2 waist of the intersection of a membrane with the observation volume and the effective e−2 waist ω0 obtained from the calibration in three dimensions was unclear. However, by carefully considering the aforementioned limitations of the technique and eliminating the potential source of errors (e.g., by precise vertical positioning of the membrane in a stable setup and using a moderately low laser power (0.95 μW)) one can obtain correct values of the diffusion coefficients. The determined average diffusion coefficient was 10.2 ± 1.1 μm2 s−1 (mean ± standard deviation (sd), n = 39) and did not show a significant difference to any other method (Table 1). This shows that precise diffusion coefficients can be obtained by point FCS on a membrane. Moreover, it shows that potential deviations caused by determination of ω0 in three dimensions and measuring in two dimensions are negligible. z-scan FCS was performed by acquisition of a vertical set of FCS measurements on the GUV membrane. For this method it is a prerequisite that the membrane is vertically stable during the whole 13400

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The two lines scanned in 2f SFCS across the GUV membrane are in close proximity to each other, with the distance d between them on the order of the resolution limit of the optical microscope. To determine this distance independently with high precision, a new AFM-based approach was used, since it allows a higher spatial resolution compared to optical calibration methods. To measure the distance between the two scanned lines by AFM, a system which changes its topography upon irradiation with light was required. The azo polymer pDR1M40 was used to this end. It was previously shown that topography changes can be optically induced in a layer of this polymer, due to the transition from the trans to the cis configuration of pDR1M upon laser irradiation at an absorbing wavelength (Figure 5A). This

1f SFCS is conducted by continuously scanning a linear path perpendicular to the equator of a GUV and subsequent correlation of the fluorescence signal corresponding to the membrane passages.23 Due to this procedure 1f SCFS does not depend on a precise positioning of the focus. This is an advantage, for example, compared to point FCS, which gives systematic errors in the case of wrong vertical focus positioning. Therefore, 1f SFCS is robust against membrane movements, which are compensated during data analysis. This is important in the case of undulating vesicle membranes or measurements on cell membranes, especially in the case of slow diffusion, which requires longer measurement times.39 In Figure 2, the autocorrelation of a 1f SFCS measurement of DiD in DOPC GUVs is shown. Compared to point FCS, the autocorrelation is shifted toward longer diffusion times, since the detection area is elliptical with an area of πSω02, compared to πω02 for point FCS. Due to the limited scan speed, the temporal resolution of the autocorrelation curve is several orders of magnitude lower than for point FCS. Fast processes such as triplet blinking are not resolved and can be neglected in the fit model, since they are 3 orders of magnitude below the temporal resolution of 1f SFCS. Due to the short membrane passage of the scanning laser, the method is not sensitive to in-focus bleaching and the determined diffusion coefficients are stable over a wide range of laser powers (Figure 4). In addition, out of focus bleaching of the vesicle can be reduced, as the scanning laser is typically 50% of the time located outside the vesicle. Compared to point FCS, higher laser powers and longer measurement times are required for stable results, since the short membrane passage reduces the counts per molecule in 1f SFCS. A further drawback of 1f SFCS compared to point FCS is the additional dependence on the structural parameter S. In order to get stable results for τD it was required to fix the structural parameter S to the value obtained from the threedimensional calibration. Moreover, for derivation of the FCS autocorrelation function (eq 8) the intersection of the observation volume and the membrane was approximated as a twodimensional Gaussian elongated along z, but in fact, the real intersection is better represented by the double cone-like shape shown in Figure 3C. Similar to point FCS, it is unclear how using effective values for S and ω0 obtained from a threedimensional calibration using the Gaussian approximation would affect the precision of the results. However, despite aforementioned limitations and concerns, in the case of sufficiently long measurements (e.g., ∼300 s in Figure 2) using a moderate laser power (5 μW) and fixing the structural parameter a diffusion coefficient of 9.9 ± 0.9 μm2 s−1 (mean ± sd, n = 13) was obtained, which did not differ significant from any of the other methods (Table 1). 2f SFCS is a variant of scanning FCS, where two lines parallel to each other separated by a known distance are scanned across the membrane of a GUV or cell.23 Two spatial channels are used to obtain the corresponding autocorrelation curve for each channel and the cross-correlation curves between the two channels. Compared to 1f SFCS, this method does not require an external calibration using a solution of a fluorophore with a known diffusion coefficient. However, precise determination of the distance between two foci is required. Once this distance is known, absolute values of diffusion coefficient, concentration, and focal volume size can be obtained from analysis of autoand cross-correlation curves.

Figure 5. Calibration of the distance d between two foci for 2f SFCS. (A) Structure of polymer pDR1M and its transition from the trans to the cis configuration upon irradiation by the 488 nm argon laser beam. (B) AFM height image of a surface coated with the polymer pDR1M with two lines separated by a distance d obtained by laser irradiation.

transition increases the average free volume occupied by the polymer and therefore leads to formation of surface elevations. The polymer was spin cast on a cover glass and irradiated by scanning two lines of a 488 nm argon laser using an identical beam path and identical scan settings as for 2f SFCS. Two protruding lines were recognized by AFM (Figure 5B). The distance d between the lines was determined as d = 0.54 ± 0.09 μm (mean ± sd, n = 8). Subsequently, this distance was used for analysis of the correlation curves obtained by 2f SFCS. The representative auto- and cross-correlation curves along with their fits are presented in Figure 6. The resulting diffusion coefficient was 10.5 ± 1.5 μm2 s−1 (mean ± sd, n = 14) and did not differ from the results obtained by other methods (Table 1). 2f SFCS is a useful technique which avoids external standard calibration, does not require precise focal volume positioning, and allows correcting for membrane movements. However, the technique is very sensitive to the distance between the two foci, which, therefore, has to be determined with high precision. 13401

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Figure 6. Representative 2f SFCS auto- (crosses) and cross-correlation (triangles) curves (experimental data with corresponding fits) for DiD diffusion in DOPC GUVs.

Moreover, due to the limited scan speed, cross-correlation below the millisecond range cannot be resolved. In addition, the initial part of the correlation curve contains considerable noise, which can be reduced by comparatively long measurement times (typically 1 order of magnitude longer than for point FCS). This noise in the cross-correlation data affects the precision of 2f SFCS, particularly for fast diffusion in fluid model membranes, since in this case the maximum in crosscorrelation is at low correlation times. Consequently, the standard deviation of D measured by 2f SFCS was higher compared to the other methods (Table 1). Better accuracy is obtained when 2f SFCS measurements are performed with slower diffusing species, for example, on lipids diffusing in membranes containing cholesterol.23 LSFCS is another technique not directly depending on an external calibration, which allows determination of diffusion coefficients and concentrations in lipid membranes.25 In contrast to other FCS methods investigated here, LSFCS belongs to the class of image correlation techniques. Compared to 2f and 1f SFCS, LSFCS, as well as point FCS and z-scan FCS, is performed on the pole of the GUV and parallel to the membrane plane. Therefore, this method can be performed not only on GUVs but also on supported lipid membranes (SLBs) or cell membrane patches. It was shown that LSFCS is not sensitive to photobleaching, even for relatively high laser power, because fluorophores spend less time in the detection volume, due to the continuous scanning. Another advantage is that short measurement times comparable to point FCS already yield precise results for diffusion coefficients.25 In addition, LSFCS allows excluding membrane areas with nonhomogeneous fluorophore distribution, caused by aggregation or clustering of the molecules. This is achieved by the possibility of area selection in the pseudoimage obtained using the LSFCS analysis software before the correlation curves are generated. This feature is particularly useful while studying diffusion in cell membranes. LSFCS is also convenient for measurements in membranes exhibiting phase separation. Information about diffusion coefficients and concentrations of molecules in the membrane can be obtained from the different lipid phases simultaneously by scanning a line over different phases. Spatiotemporal correlation curves can be computed individually for the different phases by manual selection of the differently bright phases in the pseudoimage.25 In Figure 7, a set of spatiotemporal correlation curves of DiD in GUVs made of DOPC for one LSFCS measurement is presented. For a more distinct display, only 18 spatial correlation curves corresponding to τi = τ1, ..., τ18 (see eqs 13 and 14) are shown. In total, 100 spatiotemporal correlation curves were generated and fitted for each measurement to determine the diffusion

Figure 7. Spatiotemporal correlation curves (gray) with corresponding fits (black) for discrete lag times τi obtained by LSFCS for DiD diffusion in DOPC GUVs. Data for one measurement. Eighteen correlation curves (out of 100) corresponding to τi = τ1, ..., τ18 are presented.

coefficient. In our experiments, a careful vertical positioning during line scanning turned out to be important. Wrong positioning or vertical drift were indicated by a too large focal waist from the LSFCS fit (eq 14) and resulted in a larger spread of diffusion coefficients. This was presumably induced by the loss in molecular brightness caused by a wrong vertical positioning, which as a consequence resulted in a higher noise in the spatiotemporal correlation curves. Therefore, we used the waist ω0 from the LSFCS fit as a semiempirical criterion to identify results measured at a slightly wrong position. Curves, which showed a waist exceeding ω0 from the 3D calibration by more than 20%, were discarded. As a result, a diffusion coefficient of 9.6 ± 0.9 μm2 s−1 (mean ± sd, n = 19) was obtained. No additional calibration measurements were required to determine the diffusion coefficient. The only requirement was knowledge of the scan speed, which is generally known for confocal microscope systems. However, the focal waist from a 3D calibration was required as a control parameter to test the correct vertical positioning. In this respect LSFCS cannot be considered as completely independent from a 3D calibration. A further limitation of LSFCS, which also applies to 1f SFCS and 2f SFCS, is the lower spatial (in terms of localization of the diffusion measurement) and temporal resolution compared to

Figure 8. Precise diffusion coefficients D for DiD diffusion in GUVs consisting of DOPC with increasing amounts of cholesterol. Points are the average values obtained by different FCS variants; error bars represent standard deviations. 13402

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Notes

point FCS due to the requirement to scan a line and the limited scanning speed of the confocal microscope. To verify the comparability of the different FCS variants also in the case of slower diffusing species we performed an additional set of measurements on membranes containing cholesterol. Therefore, we used GUVs consisting of DOPC with increasing amounts of cholesterol (20%, 30%, 40%, and 50%), which show a uniform liquid phase at the resolution of the confocal microscope.41 We measured the diffusion coefficient D of DiD in these GUVs by point FCS, z-scan FCS, 1f SFCS, 2f SFCS, and LSFCS. The average diffusion coefficients D are shown in Figure 8. For a given lipid mixture we obtained comparable results by all methods. The individual results for the methods are given in the Supporting Information (Table S1).

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Dr. Remigiusz Worch (Polish Academy of Sciences, Warsaw, Poland) and Dr. Zdeněk Petrásě k (Max-Planck Institute of Biochemistry, Martinsried, Germany) for helpful comments. Financial support was provided by the DFG-funded DIGS-BB graduate school at the TU Dresden to V.B. and the ESF in the EuroMEMBRANE program (LIPIDPROD) to F.A.T.

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CONCLUSION For a direct comparison of lateral membrane diffusion coefficients it is important to consider not only relative changes but also absolute values. Despite the multitude of methods to measure lateral diffusion coefficients, to the best of our knowledge, no diffusion coefficient has been reported so far, which was verified by independent FCS variants. Here, we measured the membrane diffusion coefficient for GUVs composed of the single lipid DOPC and the dye DiD at 23.5 ± 1.5 °C. This system is easy to reproduce and therefore might be used as a standard for diffusion coefficient measurements in lipid membranes. It was possible to obtain statistically not different values (p ≥ 0.01, two-sided Wilcoxon−Mann− Whitney Test of all possible pairs) with all five FCS variants based on four types of calibration (Table 1). Also, when slowing down the diffusion to biologically more relevant diffusion coefficients by adding cholesterol to the lipid mixture, we obtained comparable values for all investigated FCS variants. Deviations from previously published values measured in the same system by point FCS18,26,27 are most likely related to the only recently solved problem of calibration standards with precisely known diffusion coefficients (for a discussion, see ref 13). Moreover, the strong exponential temperature dependence of lipid diffusion42 has to be considered when comparing diffusion coefficients. In conclusion, all of the compared FCS variants allow one to obtain precise and absolute values for membrane diffusion coefficients. However, the choice of a particular method has to be made depending on the specific experimental conditions, such as the expected value of the diffusion coefficient, membrane orientation, and stability.

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ASSOCIATED CONTENT

S Supporting Information *

z-scan FCS measurements of DiD in DOPC GUVs acquired on three commercial setups; diffusion coefficients measured with different FCS methods for DiD in GUVs consisting of DOPC/ chol mixtures are enlisted. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*Phone: +49-89-8578-2900. Fax: +49-89-8578-2903. E-mail: [email protected]. Author Contributions †

These authors contributed equally. 13403

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