Single Plane Illumination Fluorescence Correlation Spectroscopy (SPIM-FCS) probes inhomogeneous three-dimensional environments

Thorsten Wohland; Xianke Shi; Jagadish Sankaran; Ernst H.K. Stelzer

doi:10.1364/OE.18.010627

1. Introduction

Most optical technologies are applied to two-dimensional cellular systems, i.e. they are used in a cellular context that is defined by hard and flat surfaces. However, physiological meaningful information relies e.g. on the morphology, the mechanical properties and the biochemistry of a cell’s context [1,2]. A physiological context is certainly not found in single cells cultivated on cover slips. It requires the complex three-dimensional relationship of cells cultivated e.g. in an ECM-based gel or in naturally developing small embryos of flies or embryos and, of course, in tissue sections [1]. Therefore there is an urgent need for the development of imaging techniques which provide more information on the state of a particular system than mere average fluorescence intensities and consequently there have been many new developments in imaging spectroscopy. A particularly powerful spectroscopic approach is fluorescence correlation spectroscopy (FCS), which has been used over the years to measure many biochemical and physiological parameters [3–8]. However, FCS poses a particular difficult problem for the recording of images in a three dimensional sample. FCS records the signal from a small observation volume (~1 fl) with single molecule sensitivity and correlates the signal in time to obtain sample concentrations and characteristic times of processes, which underlie the signal fluctuations [9]. Two important conditions are necessary for the recording of FCS data. The signal has to be recorded with sufficiently good time resolution to be able to observe molecular processes and the detection volume has to be small to allow the recording of the signal with single molecule sensitivity and a low background. The first condition was met with the advent of electron multiplying charge coupled device (EMCCD) cameras, which are capable of recording images at high frame rates (~1000 per second), with high quantum efficiency (>90%) and a good signal to noise ratio. Using single lines of the EMCCD chip even allows time resolutions in the μs range [10,11]. However, the second condition, i.e. the creation of multiple small observation volumes in 3D, was more difficult to solve. In the past, several solutions were attempted. Raster Image Correlation Spectroscopy (RICS) uses the inherent time information in a laser scanning confocal image to obtain information on particle concentrations and movements [12]. This system suffers from low collection efficiency since only one point is illuminated at any particular time. Using a spinning disk confocal microscope allowed the scanning of a whole sample with a multitude of pinholes [13]. However, again due to the scanning process the light collection efficiency is also low and limits the applications of this system [14]. Another possibility is the use of many fixed pinholes and laser beams [14–16]. This technique has the disadvantage that it does not provide contiguous pixels in an image. In addition, confocal systems illuminate much larger parts of the specimen than are actually observed. This is particularly problematic in FCS in which relatively high laser powers are used on a single spot for an extended period of time causing photo-toxic effects which can lead to malfunction of death of the biological sample [1]. Another approach is the use of excitation by total internal reflection, which limits the exposure of the specimen but simultaneously restricts the detection to the interface between sample and sample chamber [17,18].

To solve this problem we use Single Plane Illumination Microscopy (SPIM) [19] which creates a thin, diffraction limited light sheet in the whole focal plane of a detection objective, and thus provides the necessary z-sectioning to create small observation volumes (Fig. 1 ) [19,20]. In the case of SPIM all illuminated parts of the sample are as well observed, dramatically reducing the exposure of the specimen to light and reducing the photo-toxicity. This potentially allows much longer observation times at the same energy dose delivered to the specimen. Simultaneously many more measurements can be taken per time interval since SPIM records a whole plane simultaneously while confocal systems require single spots. At best in spinning disk systems a number of non-contiguous spots are taken but this happens at the expense of light collection efficiency [14]. SPIM was already used recently to perform single particle visualization and tracking [21]. In this work we combine SPIM and camera-based FCS to provide for the first time contiguous FCS images in 3D. We provide the fitting functions for this configuration and prove with different microsphere solutions that we can distinguish diffusion coefficients of different particles with good spatial and temporal resolution. In addition, we show the first imaging FCS measurements within a living zebrafish embryo by measuring the diffusion of microspheres injected into the zebrafish blood circulation system.

Fig. 1 Schematic drawing of the SPIM sample chamber. The sample chamber can contain both, illumination and detection, objectives as shown here. In our case only the water dipping detection objective was contained in the sample chamber while the light sheet from the illumination objective was coupled over a thin glass window into the sample chamber. The particular setup can be adapted to the NA required for the application. The sample chamber itself is filled with aqueous solution which is chosen according to the nature of the sample. The yellow 3D specimen, held in agarose by a capillary coming from the top (capillary is not shown for clarity), is positioned in the excitation light sheet (cyan). The emitted light (green) from the illuminated plane is collected by the detection objective and imaged over a tube lens on an EMCCD camera (camera not shown).

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2. Materials and methods

1.1 SPIM-FCS setup

A detailed description of the SPIM setup is given in Huisken et al. and Greger et al. [19,22]. Briefly, the 488 nm line of a multiline Argon-Krypton laser (35 LTL 835, Melles Griot, CA) is selected by an acousto-optic tunable filter (AOTF, AA.AOTF.8C + AAMOD.8C, Pegasus Optik GmbH, Germany), reflected by a mirror on a gimbal mount (26.306.038, OWIS GmbH, Germany), passes a beam expansion (1−8 × , S6ASS2075-067, Sill Optics GmbH, Germany) and is then focused into the back aperture of an illumination objective by a cylindrical lens (f = 100 mm, Melles Griot). The illumination objective produces a light sheet in the focal plane of the detection objective which is mounted at 90° to the illumination objective (Fig. 1). As illumination objectives we used either an Epiplan 10x/0.2 or an LD Achroplan 20x/0.4 objective (Carl Zeiss, Goettingen, Germany); for detection we used an Achroplan 40x/0.75 W or Achroplan 100x/1.0 W objective (Carl Zeiss). A self-built sample chamber of aluminum contained windows on three sides for the illumination objective and for viewing of the sample while the fourth side contained a mounting hole for the water dipping detection objective with a sealing ring. In this way the light sheet of the illumination (air) objectives can penetrate through the window into the sample chamber. The water immersion detection objectives are mounted inside the sample chamber, which is then filled with de-ionized water or PBS, and have unhindered access to the sample. With a set of three orthogonally mounted motorized translation stages (M-111.DG, Physik Instrumente (PI) GmbH, Germany) the sample, mounted at the end of a glass capillary, can be scanned through the light sheet. An additional stage (M-116.DG, PI GmbH, Germany) allows rotating the sample around an axis parallel to the light sheet. The system is controlled by a program written in LABVIEW (Version 7.1, National Instruments, Austin, TX). For FCS measurements the signal from the microscope, which passed a long-pass RazorEdge LP01-488RU-25 (Semrock, Rochester, NY) emission filter, was imaged by a tube lens (45 29 60, Zeiss, Germany) onto an EMCCD camera. Here we used two different models. Either we used an iXon DU860 (Andor Technology, Belfast, Northern Ireland, UK) containing a 128 × 128 chip with a pixel size of 24 × 24 μm² (corresponding to a pixel side length of 0.24 or 0.6 μm in object space using the 100x or 40x objectives, respectively) which was controlled by Solis Software (Andor Technology); or we used an Evolve (Roper Scientific, Munich, Germany) containing 512 × 512 pixel chip with a pixel size of 16 × 16 μm² (corresponding to a pixel side length of 0.16 or 0.4 μm in object space using the 100x or 40x objectives, respectively) which was controlled by Micromanager (Version 1.2.39). Both cameras have a quantum efficiency of over 90% but differ in achievable time resolution.

2.2 SPIM-FCS measurements

If not stated otherwise we acquired regions of interest of 32 × 32 pixels, for which the readout time is 0.82 ms for the camera used here. The camera is cooled to −80°C, and the EM gain is set to 150-200. The laser power used before the objective is 60 μW. We collected up to 20,000 frames with exposure times of 1-5 ms, resulting in frame rates between 171 and 549 frames per second. The first frames can contain a non-stable decreasing background due to camera artifacts, resulting in an extra decay of the autocorrelation function at long times. Care has to be taken to either correct or exclude these frames from data treatment to avoid artificial correlations from camera artifacts. In our measurements we used at least 10,000 frames of each measurement for FCS evaluations. The data is correlated and evaluated in a self-written program including a software correlator in C (Microsoft Visual Studio .NET 2003, Redmond, WA, USA) and a user front end and data fitting routine in IgorPro 6.0 (Wavemetrics, Lake Oswego, OR, USA).

2.3 Theory

The autocorrelation function of a fluorescence signal is given by

G (τ) = \frac{〈 F (t) F (t + τ) 〉}{{〈 F (t) 〉}^{2}} = g (τ) + G_{\infty}

where the fluorescence signal at time t is given by

F (t)

and τ is the correlation time. Angular brackets

〈 \dots 〉

denote a time average. Here

g (τ)

is the general functional form of the autocorrelation function and

G_{\infty}

is the convergence value of the autocorrelation function for long times, which is 1 for infinitely long measurement times. We keep this as an independent fitting parameter since this improves the fit. However, in most cases

G_{\infty}

does not deviate from 1 more than a few percent.

The 2D fitting model for a CCD camera with square pixels was recently derived by Ries et al. [23] and an approximation for large pixels compared to the microscope point spread function (PSF) derived by Guo et la [24]. Its extension to the cross-correlation for general shapes of pixel areas on a CCD and for flow and diffusion was derived by Sankaran et al. [25]. In our experiments we assume only diffusion and no flow. However, particle diffusion is observed in 3D and the illumination profile, as given by the light sheet, is constant in the xy-direction and has a Gaussian profile in the z-direction. In this case, since the integration for the three directions are separable, the solution is the product of the autocorrelation function for 2D diffusion in the xy-plane as seen by a CCD camera with square pixels and a constant illumination intensity in the xy-plane, and the solution of the diffusion in the z-direction with a Gaussian illumination profile. The first is given by [23,25]:

g_{x y} (τ) = \frac{1}{4 〈 C 〉 a^{4}} {(2 a \cdot \erf (\frac{a}{2 \sqrt{D τ + σ_{x y}^{2}}}) + \frac{4 \sqrt{D τ + σ_{x y}^{2}}}{\sqrt{π}} (e^{- \frac{a^{2}}{4 (D τ + σ_{x y}^{2})}} - 1))}^{2}

where

〈 C 〉

is the average concentration, a is the side length of a square pixel in object space (in our case 0.24 or 0.6 μm), D is the diffusion coefficient, and

σ_{x y}

is the radius of the PSF in the xy-plane. The second, z-dependent, term can be derived from

\int_{- \infty}^{\infty} \int_{- \infty}^{\infty} P (z | z') I (z) I (z') d z d z' = \frac{1}{2 \sqrt{π (D τ + σ_{z}^{2})}}

where we used

P (z | z') = \frac{1}{2 \sqrt{π D τ}} e^{- \frac{(z - z')}{4 D τ}}

I (z) = \frac{1}{\sqrt{2 π} σ_{z}} e^{- \frac{{(z - m)}^{2}}{2 σ_{z}^{2}}}

m is the central position and

σ_{z}

is the 1/e² radius of the Gaussian profile in z-direction. The total function for SPIM, for diffusion is then:

G (τ) = \frac{1}{4 a^{2} \sqrt{π} N} {(\begin{array}{l} 2 a \cdot \erf (\frac{a}{2 \sqrt{D τ + σ_{x y}^{2}}}) \\ + \frac{4 \sqrt{D τ + σ_{x y}^{2}}}{\sqrt{π}} (e^{- \frac{a^{2}}{4 (D τ + σ_{x y}^{2})}} - 1) \end{array})}^{2} {(1 + \frac{D τ}{σ_{z}^{2}})}^{- \frac{1}{2}} + G_{\infty}

We have defined the number of particles in an observation volume as $N = 〈 C 〉 \cdot a^{2} \cdot 2 σ_{z}$ . This function contains only 3 free fitting parameters, namely the diffusion coefficient D, the number of particles N, and the convergence value of the autocorrelation function for long times $G_{\infty}$ . All other parameters are known or are fixed to their theoretical values.

Similarly, the correlation function for 3D diffusion and flow (with flow limited to the xy-plane) is

G (τ) = G_{\infty} + \frac{1}{4 a^{2} N} {(1 + \frac{D τ}{σ_{z}^{2}})}^{- \frac{1}{2}} \times G_{x} \times G_{y}

\begin{array}{l} G_{x} = \\ \frac{2 \sqrt{D τ + σ_{x y}^{2}}}{\sqrt{π}} (e^{- \frac{{(a + r_{x} - v_{x} τ)}^{2}}{4 (D τ + σ_{x y}^{2})}} + e^{- \frac{{(a - r_{x} + v_{x} τ)}^{2}}{4 (D τ + σ_{x y}^{2})}} - 2 e^{- \frac{{(r_{x} - v_{x} τ)}^{2}}{4 (D τ + σ_{x y}^{2})}}) + (a + r_{x} - v_{x} τ) \erf (\frac{(a + r_{x} - v_{x} τ)}{2 \sqrt{D τ + σ_{x y}^{2}}}) \\ + (a - r_{x} + v_{x} τ) \erf (\frac{(a - r_{x} + v_{x} τ)}{2 \sqrt{D τ + σ_{x y}^{2}}}) - 2 (r_{x} - v_{x} τ) \erf (\frac{(r_{x} - v_{x} τ)}{2 \sqrt{D τ + σ_{x y}^{2}}}) \end{array}

\begin{array}{l} G_{y} = \\ \frac{2 \sqrt{D τ + σ_{x y}^{2}}}{\sqrt{π}} (e^{- \frac{{(a + r_{y} - v_{y} τ)}^{2}}{4 (D τ + σ_{x y}^{2})}} + e^{- \frac{{(a - r_{y} + v_{y} τ)}^{2}}{4 (D τ + σ_{x y}^{2})}} - 2 e^{- \frac{{(r_{y} - v_{y} τ)}^{2}}{4 (D τ + σ_{x y}^{2})}}) + (a + r_{y} - v_{y} τ) \erf (\frac{(a + r_{y} - v_{y} τ)}{2 \sqrt{D τ + σ_{x y}^{2}}}) \\ + (a - r_{y} + v_{y} τ) \erf (\frac{(a - r_{y} + v_{y} τ)}{2 \sqrt{D τ + σ_{x y}^{2}}}) - 2 (r_{y} - v_{y} τ) \erf (\frac{(r_{y} - v_{y} τ)}{2 \sqrt{D τ + σ_{x y}^{2}}}) \end{array}

The parameters $〈 C 〉$ , N, a, D, $σ_{z}$ , and $G_{\infty}$ have the same definitions as above. The variables r_x and r_y describe the distance in x and y-direction between two pixels which are cross-correlated (the autocorrelation can be achieved by setting r_x = r_y = 0). The parameters v_x and v_y are the transport or flow velocities along the x and y directions, respectively. There are only six free fitting parameters: N, D, v_x, v_y, σ and $G_{\infty}$ . We use these functions to fit all data. Fits are performed using a self-written program in IgorPro 6.0 (Wavemetrics).

2.4 Microsphere sample preparation

We used either 0.2 or 1 μm Fluoresbrite multifluorescent microspheres (Polysciences, Eppelheim, Germany) which contained 2 −3% solids. The 0.2 μm microspheres were used in a 10 times dilution from stock, while the 1 μm microspheres were used in the same concentration as the stock solution, giving both solutions a microsphere concentration in the nM range. The microspheres were immersed in phosphate buffered saline (PBS) within in a small sample bag made from a water refractive index-matched foil (bioFOLIE 25, Greiner bio-one, Frickenhausen, Germany). To observe the diffusion of 0.2 μm microspheres into agarose, we filled the sample bag to about 1/3 with 1.5% low melting agarose before deposition of the microsphere solution on top. The sample bags were then mounted at the tip of a glass capillary and immersed in the sample chamber of the microscope filled with PBS.

2.5 Zebrafish preparation

Zebrafish (Danio rerio) were maintained as previously described [26]. Embryos of a wild-type strain (Tupfel long fin) were used for beads injection. The embryos were incubated at 28.5 °C for optimal development till 48 hr postfertilization (hpf) and PTU (0.003% 1-phenyl-2-thiourea in 10% Hanks’ saline; Invitrogen, Carlsbad, CA) was added at 24 hpf to reduce pigmentation. The 48 hpf wild-type embryos were dechorionated, anesthetized with 0.01% tricaine (Sigma-Aldrich, St. Louis, MO) and placed onto a molded agarose holder for beads injection. 200 - 400 picoliters of 0.2 μm Fluoresbrite multifluorescent microsphere beads stock solution (5.68 × 10¹² particles/ml, Polysciences) were injected into the blood circulation through the common cardinal vein. The injected embryos were further treated with tricaine to reduce the blood flow velocity in order to accommodate the time resolution of the EMCCD. The prepared zebrafish embryo was then mounted in 1% low melting temperature agarose (Invitrogen) inside a 100 μL glass micropipette (Blaubrand, Brand, Wertheim, Germany). The glass micropipette was mounted in the SPIM stage and a piece of wire was used to push the agarose cylinder that contained the embryo into the immersion water in the SPIM chamber for SPIM-FCS measurements.

2.6 Zebrafish measurements

The embryo was imaged with a 40 times objective (Achroplan 40 × /0.75 W, Carl Zeiss, Jena, Germany) in the SPIM-FCS system. The sample was positioned through the SPIM stage so that the dorsal aorta of the injected embryos was in the focus of the objective. The sample was illuminated with ~200 μW of 488 nm laser and a long-pass 488 emission filter was used. The movement of the 0.2 μm multifluorescent beads along with the blood fluid is directly visible in the EMCCD camera and a ROI of 20 × 20 pixel was selected inside the vessel for SPIM-FCS measurements. The Evolve camera was operated in a non-overlap mode with an exposure time of 1.0 ms and an interval time of 4.6 ms. An EM gain of 300 was applied during measurements.

3. Results

3.1 Light sheet characterization

The dimensions of the FCS observation volume are determined by the pixel size of the camera (16 µm and 24 μm for the two cameras), by the magnification of the detection objective, and by the point spread function (PSF) of the optical system. We used an Achroplan 40x/0.75 W or an Achroplan 100x/1.0 as a detection objective lens. They provide a pixel size in object space between 0.16 µm and 0.6 μm and a PSF with a radius of 0.61λ/NA = 0.415 μm and 0.61λ/NA = 0.311 μm for an emission wavelength of $λ =$ 0.51 μm, respectively. An Epiplan 10x/0.2 or an LD Achroplan 20x/0.4 objective create light sheets with axial widths of the PSF of $σ_{z} =$ 1.5 μm and 0.75 μm for an excitation wavelength $λ =$ 0.488 μm, respectively. The actual values for of the light sheets as detected by the EMCCD camera and fitted with a Gaussian function are 1.9 µm and 1.4 μm [Fig. 2(A) ] The depth of focus for the light sheet is between 7 and 29 μm. The intensity of the light sheet is constant across the 32 × 32 pixel region of interest (corresponding to square regions with a side length of 5-19 μm). Across the total field of view, the intensity variations in the light sheet are less than 10%. These dimensions indicate an observation volume of about 1.7 - 2.3 fl compared to typically 0.3 fl in a confocal FCS setup with an NA of 1.2. Since the properties of the CCD are known, a camera based FCS system does not require the calibrations of a confocal FCS, but provides absolute diffusion coefficients as well as the size of the point spread function of the system directly [24,25].

Fig. 2 (A) Comparison of the light sheet profiles of the 10x/0.2 and 20x/0.4 illumination objective lenses. An image of the light sheet was recorded with the EMCCD camera by placing a mirror at an angle of 45° into the focal plane of the detection objective (100x/1.0 W). The full widths at half maximum (FWHM) of the light sheets are 2.4 µm and 1.4 μm, respectively. The 1/e² radii are 1.9 µm and 1.4 μm, respectively. (B) Comparison of the normalized autocorrelation functions obtained with three different combinations of illumination and detection objectives. The measurement with the 10x/0.2 illumination objective was taken at an exposure time of 1 ms. The two measurements with the 20x/0.4 objective were taken with an exposure time of 5 ms. All three measurements result in similar diffusion coefficients between 0.9 μm²/s and 1.5 μm²/s. Using the same detection objective (100x/1.0 W) but different illumination objectives (10x/0.2 or 20x/0.4), the autocorrelation functions show little difference since diffusion along the z-direction contribute less significantly to the autocorrelation function than along the xy-directions. However, for different detection objectives (100x/1.0 W or 40x/0.75 W), but the same illumination objective (20x/0.4), the differences are significant since the detection objective influences the xy resolutions of the system. (C) The 0.2 μm bead sample is homogeneous. All 1024 ACFs are very similar. (D) The ACFs of the 1.0 μm bead sample allow us to distinguish single microspheres as well as aggregates. (E) Examples of the different ACFs for the 1.0 μm bead sample (solid gray lines) including their fits (black lines). (F) Comparison of ACFs for single 0.2 µm and 1.0 μm microspheres quantitate the different ACFs. The average diffusion coefficients are 1.1 ± 0.5 μm²/s and 0.28 ± 0.18 μm²/s for the two bead populations.

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The system was calibrated using multicolor microspheres with diameters of 0.2 µm and 1.0 μm in an aqueous solution [Figs. 2(B)–2(F)]. First we calibrated the system with 0.2 µm microspheres using different combinations of illumination and detection objectives. Table 1 shows experimental diffusion coefficients of a sample of 0.2 µm multicolour microspheres recorded with three different combinations of illumination (Obj_Ill) and detection (Obj_det) objectives using the 24 μm pixel CCD chip. All measurements result in very similar diffusion coefficients as would be expected, demonstrating that the system is calibration free and provides absolute diffusion coefficients. In addition, Fig. 2 shows that for the same detection objective but different illumination objectives the autocorrelation functions (ACFs) are very similar since the z-direction (optical axis of the detection objective) contributes significantly less to the ACF than the xy-direction [Eq. (6)]. However, for the same illumination objective but different detection objectives, the ACFs differ significantly since different illumination objectives influence the xy-dimensions of the observation volume.

Table 1. Diffusion coefficients in μm²/s for 0.2 μm multicolor microspheres in aqueous solution measured by the 128 × 128 pixel chip (24 μm pixel size) with different combinations of illumination and detection objectives.

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For further measurements we used the combination of a 20x/0.4 illumination objective lens and a 100x/1.0 detection lens as this gives the smallest observation volume. The field of view in this case corresponds to ~30 µm on the 128 × 128 pixel chip. We recorded a 32 × 32 pixel sub-region with an excitation power of 60 μW in front of the objective lens. This resulted in 1024 ACFs with a time per frame between 1.82 – 5.82 ms. The average diffusion coefficient determined from 1024 correlation curves of the 0.2 μm microsphere sample was 1.1 ± 0.5 μm²/s [Fig. 2(C)] and showed little or no aggregation. The 1.0 μm microsphere sample seemed to partially aggregate. During a typical measurement, ACFs with very different widths and amplitudes were observed [Fig. 2(D) and 2(E)] thus single particles as well as a range of aggregates could be clearly distinguished. The diffusion coefficient for 1.0 μm microspheres was 0.28 ± 0.18 μm²/s according to the 48 ACFs that correspond to the central area of the region of interest, in which the ACFs were homogeneous and narrow. The expected diffusion coefficients are 2.1 μm²/s and 0.43 μm²/s for the 0.2 and 1.0 μm microspheres, respectively (see discussion for possible reasons of the deviations). Figure 2(F) shows a comparison of the ACFs measured for the two types of microspheres. Both experimental diffusion coefficients are close to the theoretical values and their experimental ratio of diffusion coefficients of 4 +/− 1.1 is also close to the theoretical value of 5.

Particular attention should be paid to the side lobes of the light sheet. In confocal microscopy they contribute usually less than ~5% to the intensity (11% are in the side lobes of the Airy disk, but the contribution is limited by the pinhole) and due to the limited dynamic range of confocal microscopy (~5 bit) do not play an important role. This is not true for SPIM which has a much higher dynamic range and the side lobes cannot be neglected anymore [27]. Here we aimed at minimizing the side lobes of the light sheet by spatial filtering of the laser beam to approximate as close as possible a Gaussian shape of the intensity profile in the z-direction. This is important for FCS measurements in which a Gaussian intensity profile in z-direction was used for the derivation of the fitting function. However, when using image de-convolution before the calculation of the correlations this is not necessary and might even be disadvantageous if the de-convolution algorithms take account of the side lobes.

3.2 The influence on binning on the ACF

As shown in Fig. 2 calibrations with different particle sizes successfully distinguished between properly dissolved and aggregated samples and recovered diffusion coefficients close to the expected values. In addition, for different applications the pixels in every image can be binned, which is similar to changing to different laser foci and pinhole sizes in confocal FCS, and can be used to determine any spatial dependence of the diffusion coefficient. Binning per software done on our measurements from 1 × 1 to 8 × 8 all resulted in the same diffusion coefficient, within the margins of error, of 1.1 ± 0.5μm²/s, while the number of particles increased linearly with the area of the binned region (Table 2 ). It is also possible to use larger regions of interest for SPIM-FCS. We have used areas up to 64 × 64 pixels, providing 4096 FCS measurements in one experiment of less than 1 minutes duration. However, the larger region of interest increases the read-out time to 1.27 ms and thus reduces the time resolution to 2.27 ms if at least a 1 ms exposure is assumed. Until faster cameras are available the increase of the region of interest to 64 × 64 pixels or even to the whole chip can only be used in slowly diffusing particles, as e.g. membrane proteins.

Table 2. Dependence of diffusion coefficient and particle in the observation volume on binning

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3.3 Correlations of spatially non-homogeneous samples

We used 0.2 μm microspheres in samples containing both water and agarose to confirm the applicability of correlation images to the analysis of spatially non-homogeneous samples. We filled ~1/3 of a sample bag with 1.5% low melting agarose. Once the agarose had solidified, we added the 0.2 μm microsphere solution. The field of view in the SPIM-FCS setup (17 × 79 pixels resulting in 1343 FCS measurements) covered the diffusion of the microspheres at the border between aqueous solution and agarose. Intensity images and images of particle number and diffusion coefficient are depicted in Figs. 3(A) –3(C). Clearly, correlations can be seen in the microsphere solution [Fig. 3(E)]. However, no correlation can be seen in the bulk of the agarose, into which the microspheres did not penetrate [Fig. 3(G)]. At the border between the aqueous solution and the agarose, the diffusion coefficient changes by a factor of 5 from 1.2 ± 0.1 μm²/s in the bulk to 0.23 ± 0.02 μm²/s [Fig. 3(F)]. We attribute these changes to the agarose/water interface, at which the diffusion coefficient of the microspheres will decrease with an increase of the agarose concentration. It should be noted that the images representing N and D [Fig. 3(B) and 3(C)] show the same trends, i.e. medium values for N and D in the bulk solution (positions 1-20), decreased N and D at the transition zone (positions 21-54), and erratic values within the bulk of the agarose (positions 55-79). The values in agarose are a reflection of the fact that the ACFs cannot be fitted in that region. The differences in the N and D images reflect the different influence of the sample characteristics (viscosity, concentration, bleaching) on N and D, i.e. the amplitude and the width of the ACF.

Fig. 3 Diffusion measurement of 0.2 μm microspheres at a water/agarose border. During the course of the experiment, the microspheres were injected into the aqueous medium. (A) Intensity image averaged over 10,000 frames. (B) Particle number N extracted from the single fits to each ACF of the 1343 pixels. (C) The diffusion coefficient D extracted from the fits to each ACF. (D) Diffusion coefficients of all 17 lines (each with 79 pixels). The diffusion coefficient D within the aqueous phase sample agree well while D decreases towards the water/agarose border (from left to right). Beyond the border (pixel position ~50), no consistent diffusion coefficients can be found due to a lack of correlations. (E-G) Depicted are all experimental ACFs for areas from position 0-20 (solution, E), 21-54 transition region from solution to agarose (F), and 55-79 (agarose, G). The average D for position 1-5 (solution) is D = 1.2 ± 0.1 μm²/s, while the average D for position 30-35 (transition region) is D = 0.23 ± 0.02 μm²/s due to the decrease in diffusion towards the water/agarose border. Beyond position 55 no correlations are discernible.

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In addition, measurements were performed at the border of the sample where the microsphere solution is separated from the surrounding aqueous solution by the bioFolie foil bag. In this case we used a region of interest of 81 × 16 (data not shown). Within the sample, N and D have a continuous uniform distribution with very similar values for each pixel as would be expected from a homogeneous solution. At the border a slow increase of D can be seen possibly due to some influence of the electrostatics of the foil on the carboxylated microspheres [28]. However these changes are not larger than a factor of 2. Once outside the sample, N becomes very large, corresponding to very low or no correlations and D changes erratically over almost 2-3 orders of magnitude. All ACFs Outside the sample are flat, indicating a lack of correlation.

3.4 SPIM-FCS in living zebrafish

For in vivo measurements we used the detection objective lens with the smaller magnification to provide for an easier orientation of the plane within the sample (Obj_ill = 20x/0.4 and Obj_det = 40x/0.75). For the detection, we used the 512 × 512 pixel camera with a pixel size of 16 μm. We injected 0.2 μm microspheres into the blood stream of living zebrafish embryos 48 hours post fertilization (hpf). The fish were anesthetized with ~1 mM tricaine to avoid movements of the embryo during the measurements. The blood flow was measured either in the dorsal aorta or close to the heart. The ACFs measured in the dorsal aorta [Fig. 4(A) ] are narrow and steep. This is expected by an active transport mechanism or flow, in which the particles are moved through the observation volume in a directed manner. The flow speed of the particles can be extracted by fitting the data to Eq. (7), and result in a blood flow of about 60-170 μm/s. This is consistent with movements of single beads as estimated from the image time series. The measured velocities are similar to previously measured data in zebrafish embryos treated with 1 mM tricaine. The peak velocities were about 500 μm/s and the minimal velocities about 200 μm/s [29]. For the measurement of the flow velocity, i.e. speed and direction of flow, we cross-correlated a central pixel within the aorta with surrounding 24 pixels [Fig. 4(B)]. The cross-correlation functions show a typical peak if the flow moves from the central pixel to the outlying pixel but show no peak if the flow is in the opposite direction [25,30]. In Fig. 4(B) the flow direction is from the right to the left of the image in an anterior-posterior direction within the embryo as expected in the dorsal aorta. Measurements closer to the heart are dominated by the heart movement resulting in peaks at the heartbeat rate and at higher harmonics [Fig. 4(C)]. The heartbeat is ~3 beats per second, which is again similar in the publication mentioned previously [29]. A comparison of measurements within the blood circulation and within aqueous solutions is given in Fig. 4(D).

Fig. 4 SPIM-FCS measurements within a live zebrafish 48 hpf. Microspheres with adiameter of 0.2 μm were injected into the blood circulation 68 seconds prior to the start of the experiment. (A) Fast blood flow within a blood vessel. The ACFs are narrower and steeper compared to solution measurements since flow transports the molecules with a speed of about 60-170 μm/s through the observation volumes. (B) This figure shows cross-correlation functions (CCFs) between the central pixel of the 20 × 20 pixel ROI and the surrounding pixels at a distance of 3 pixels (same experiments as A). A prominent peak in the CCF confirms the transport of particles from the central pixel to the surrounding pixels. The development of the peak is direction dependent, with the flow going from the green marked pixels to the central pixel in the direction of the red marked pixels, giving the blood flow profile. (C) The ACFs were been recorded close to the heart and show dominant peaks due to the heart beat, which is about 3 per second in this example as observed from the ACFs. They show little transport since flow is slow in the large vessels. (D) Comparison between measurements of 0.2 μm microspheres in solution and at different parts in the zebrafish.

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4. Discussion

Imaging techniques which employ other contrast mechanisms than simple time averaged light intensities have been implemented for several fluorescence parameters, including spectral imaging, fluorescence lifetime imaging (FLIM), and fluorescence polarization/anisotropy. These techniques have different and often higher information content than simple fluorescence images. FCS, however, has particularly stringent requirements due to the necessity to record fluorescence signals with single molecule sensitivity and low noise at very fast speeds. In this article we have combined SPIM [19] with camera based FCS [25] to produce SPIM-FCS, capable of collecting images with good spatial and temporal resolution in 3D. SPIM as an illumination mode has several advantages in particular for FCS. SPIM illuminates only that part of a sample which is actually measured and thus reduces photobleaching compared to confocal setups. The reduced photobleaching allows longer measurement times which are important for FCS which usually has to measure on a longer time scale than normal imaging. SPIM uses the light source more efficiently and can therefore be implemented with the existing low power lasers. In this paper we use a laser power before the objective of 60 μW. This corresponds to about the same laser power used in FCS on single spots. Considering that we illuminate at least all 128 × 128 pixels in the EMCCD, this corresponds to a reduction of laser power delivered to the specimen of at least 4 orders of magnitude compared to the case where confocal FCS would be used for the same purpose.

We provide here the fitting functions for SPIM-FCS for the case of diffusion. The extension to more complicated models including flow, and cross-correlations between pixels is straight forward using the functions derived for ITIR-FCS and ITIR-FCCS as described by Sankaran et al. [25], and the fits to the different data do freely converge and describe the data well. One of the advantages of SPIM-FCS, similar to Two-focus FCS [31] and other camera based approaches [24], is that it determines directly diffusion coefficients and does not need an extra calibration measurement. This is shown with two different sized microspheres of 0.2 and 1 μm diameter whose absolute diffusion coefficient are similar to the theoretically expected and at least for the 1.0 μm microspheres do agree within the margins of error. And this agreement is found although microspheres pose special problems for FCS measurements since i) FCS is sensitive to larger and brighter particles, i.e. to aggregates and the larger particles of the size distribution of the microspheres [32] and ii) the size of the microspheres comparable or larger than the PSF will increase the apparent PSF [33]. Therefore we expect even better agreement in the case of molecular fluorophores, which here couldn’t be measured due to the still limited speed of EMCCD cameras.

The capability of SPIM-FCS to provide accurate diffusion coefficient and concentration maps is demonstrated with the help of three separate measurements. In one case we recorded the diffusion of 0.2 μm microspheres close to the border of a sample (data not shown). Consistent concentrations are found only within the sample while outside the sample no correlations exist. In addition the diffusion coefficients in this case do not vary strongly within the sample, possibly with the exception of some electrostatic, repulsive border effects which increased the diffusion coefficient by not more than a factor 2. In the second example we observe the diffusive behavior of 0.2 μm microspheres in aqueous solution at the border of an interface to low melting agarose (Fig. 3). Again the microspheres can only be found within the aqueous solution. However, close to the interface a clear decrease of the diffusion coefficient by a factor 5 can be detected. Both examples show that measurements are consistent over the whole field of view and can be used to differentiate between areas of different concentrations and diffusion coefficients. In the last example we demonstrate that we can take SPIM-FCS measurements within living zebrafish and determine blood flow profiles. The values obtained from SPIM-FCS are in accord with literature values [29]. But due to the spatial resolution in SPIM-FCS we can measure as well flow directions to give flow profiles within zebrafish.

The disadvantage of the SPIM-FCS is still the limited time resolution of imaging devices. Faster recording in a photon counting mode would allow the calculation of correlations at shorter times and would provide for better fitting especially in cases when more than one particle size is present in the sample or when photophysical properties of dyes are to be investigated. At the moment the system can record only one wavelength and thus dual-color cross-correlation cannot be performed. However, this can be solved with either a second camera [27,34] or by using a wavelength dependent imaging splitter which creates the images at two or more wavelength on different areas of the same camera. Further improvements can be achieved by creating the light sheet by quickly scanning a laser beam across the sample as done in Digital Scanned Laser Light Sheet Microscopy [27,34]. It would allow illuminating and recording single lines of an EMCCD with very high time resolution [10,11]. And if the laser beam can be scanned with a rate on the order of μs per line, it can be used to improve fluorophore brightness by avoiding triplet state population built-up, as already used in pulsed FCS systems [35]. However, the present system should be sufficient in terms of time resolution and sensitivity to allow the measurements of proteins movements within living cells and organisms.

5. Conclusions

The use of a light sheet based fluorescence microscope that is implemented with a single illumination plane (SPIM) provides the z-sectioning capability essential for the performance of imaging FCS applications. In addition, it provides all the advantages SPIM has compared to confocal imaging [36]. In particular, SPIM-FCS allows FCS recordings within whole planes in a 3D sample simultaneously. It, therefore, offers more measurements per sample per time interval with much lower light exposition of the specimen. We recorded up to 4096 FCS measurements within one minute, with a laser power as low as 60 μW across the whole light sheet. This compares favorably with confocal FCS which acquires typically only one spectrum in the same time. SPIM-FCS thus reduces the phototoxicity of the measurements and allows observations over longer time. SPIM-FCS measurements provide concentration and diffusion coefficients in non-homogeneous samples with a clear contrast in non-homogeneous 3D samples and live zebrafish embryos. The use of different combinations of low numerical aperture (NA) illumination objectives for the creation of light sheets with high NA detection objectives for SPIM-FCS, and fast, sensitive EMCCD cameras provides a wide range of flexibility for the SPIM-FCS systems to observe various samples. The limited time resolution of the available cameras with sufficient quantum efficiency and low noise levels still restricts the use of imaging FCS to relatively slow moving particles, but we expect that the next generation of cameras will address this issue. However, large cytosolic proteins and membrane bound molecules, which constitute a large part of the protein machinery of a cell, are currently investigated. SPIM-FCS brings biologists a step closer to the acquisition of quantitative information in a highly multiplexed imaging format with single molecule sensitivity in living specimens.

Acknowledgements

TW gratefully acknowledges funding from the Alexander von Humboldt Foundation. TW and XS acknowledge funding by a grant from the Biomedical Research Council in Singapore (BMRC 07/1/21/19/488, R-143-000-351-305), JS is supported by a scholarship of the Singapore MIT Alliance. We would like to thank Andor Technology and Roper Scientific Germany for the loan of their EMCCD test units.

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	Obj_det
Obj_ill	40x/0.75	100x/1.0
10x/0.2	-	1.5 ± 0.6
20x/0.4	0.9 ± 0.4	1.1 ± 0.5

Binning	1 × 1	2 × 2	3 × 3	4 × 4	8 × 8
D [10⁻¹² cm²/s]	1.1 ± 0.5	1.0 ± 0.3	1.0 ± 0.3	1.0 ± 0.3	1.0 ± 0.4
N	2.0 ± 0.3	7.9 ± 1.1	17.1 ± 2.1	27.9 ± 3.7	77.0 ± 9.7

	Obj_det
Obj_ill	40x/0.75	100x/1.0
10x/0.2	-	1.5 ± 0.6
20x/0.4	0.9 ± 0.4	1.1 ± 0.5

Binning	1 × 1	2 × 2	3 × 3	4 × 4	8 × 8
D [10⁻¹² cm²/s]	1.1 ± 0.5	1.0 ± 0.3	1.0 ± 0.3	1.0 ± 0.3	1.0 ± 0.4
N	2.0 ± 0.3	7.9 ± 1.1	17.1 ± 2.1	27.9 ± 3.7	77.0 ± 9.7

Single Plane Illumination Fluorescence Correlation Spectroscopy (SPIM-FCS) probes inhomogeneous three-dimensional environments

Abstract

1. Introduction

2. Materials and methods

1.1 SPIM-FCS setup

2.2 SPIM-FCS measurements

2.3 Theory

2.4 Microsphere sample preparation

2.5 Zebrafish preparation

2.6 Zebrafish measurements

3. Results

3.1 Light sheet characterization

3.2 The influence on binning on the ACF

3.3 Correlations of spatially non-homogeneous samples

3.4 SPIM-FCS in living zebrafish

4. Discussion

5. Conclusions

Acknowledgements

References and links

Cited By

Figures (4)

Tables (2)

Equations (9)

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