Structured Illumination Fluorescence Correlation Spectroscopy for Velocimetry in Zebrafish Embryos Paolo Pozzia, Leone Rossettia, Laura Sironia, Stefano Freddia, Laura D'Alfonsoa, Michele Cacciaa, Margaux Bouzina, Maddalena Collinia, Chirico Giuseppe*a. a Physics Department, Università degli Studi di Milano Bicocca, Piazza della Scienza 3, I-20126, Milano, Italy. ABSTRACT The vascular system of Zebrafish embryos is studied by means of Fluorescence Correlation and Image Correlation Spectroscopy. The long term project addresses biologically relevant issues concerning vasculogenesis and cardiogenesis and in particular mechanical interaction between blood flow and endothelial cells. To this purpose we use Zebrafish as a model system since the transparency of its embryos facilitates morphological observation of internal organs in-vivo. The correlation analysis provides quantitative characterization of fluxes in blood vessels in vivo. We have pursued and compared two complementary routes. In a first one we developed a two-spots two-photon setup in which the spots are spaced at adjustable micron-size distances (1-40 m) along a vessel and the endogenous (autofluorescence) or exogenous (dsRed transgenic erythrocytes) signal is captured with an EM-CCD and cross-correlated. In this way we are able to follow the morphology of the Zebrafish embryo, simultaneously measure the heart pulsation, the velocity of red cells and of small plasma proteins. These data are compared to those obtained by image correlations on Zebrafish vessels. The two methods allows to characterize the motion of plasma fluids and erythrocytes in healthy Zebrafish embryos to be compared in the future to pathogenic ones. Keywords: Fluorescence Correlation; velocimetry; Zebrafish
1. INTRODUCTION Fluorescence correlation spectroscopy is a well-established technique[1] that is based on the detection of the fluctuations of the fluorescence signal of molecules or cells diffusing or passing through a tiny volume determined by the laser beam waist,
0 . The most relevant sources of these fluctuations are translational diffusion of the fluorophores
through the observation volume and those arising from the chemical kinetics that involve changes in the quantum yield. Additional sources of fluctuation are the rotational diffusion of molecules[2] and drift motions.[3,4] These different phenomena have different signature in the fluorescence auto-correlation function: the hyperbolic decay of translational diffusion, intrinsically slower than the exponential decay related to the chemical kinetics, may be sometimes superimposed on the decay that characterizes the drift motion. [5,6] In the present study two different times characterize the correlation functions of the emitted signal: the diffusion time, D , and the drift time V , related to the laser beam waist, 0 , to the translational diffusion coefficient, D, and to the amplitude of the molecular drift velocity, V. It is often very difficult to determine both the diffusion and the drift components on experimental data based on single volume detection.[7,8,9] Cross-correlation measurements of the fluorescence signal coming from two laser foci lying along the drift current greatly improve the sensitivity in the measurement of both the diffusion coefficient and the drift speed.[10] *
[email protected]; Phone:0039-0264482440: Fax:0039-0264482585;
However this methodology has not been widely applied due to the technical difficulty of gathering signals from different spatial locations on two separated light detectors.[10,11] This technical issue has motivated in the past the choice of fixed inter-spots distance configurations that limits the capabilities of the setup to investigating widely varying drift conditions. This contribution shows how dual foci correlation spectroscopy can be performed at variable distance of the two focal spots, by employing an EMCCD camera, in a wide field dual foci fluctuation spectroscopy. The recent advance of pixelated light detectors, such as EMCCD cameras, has made the spatial separation of signals easier, so that dual foci correlation spectroscopy can be easily performed. We test this method in-vitro and show preliminary validation results on the characterization of the blood flow of embryos of zebrafish (Danio rerio), a model organism widely used in developmental biology[12] and oncology.[13] Finally we point out to what extent direct image correlation methods in wide field transmission microscopy can be applied to characterize visually the drift motion.
2. THEORETICAL BACKGROUND 2.1 Autocorrelation Function. Fluorescence correlation techniques are based on the analysis of the fluctuations occurring on the fluorescence signal gathered from a confocal volume in a fluorophores solution at low concentration. The typical source of fluctuations is the variation in local concentration of the sample in the focal volume, due to translational diffusion. In standard FCS the autocorrelation function ( ) of the signal I(t) is considered:[1]
G
I t I t t I t
(1)
2 t
( ) ( ) 〈 ( )〉. For simple three dimensional Brownian diffusion, the autocorrelation function is a where monotonically decreasing hyperbolic function, in which the decay time is proportional to the mean time spent by each molecule in the excitation volume (the parameter is the excitation volume form factor):
GBrown G0
1 1
1
D
(2)
1 D 2
In the case of a drift motion the autocorrelation function is modulated with an exponential factor [4] that is related to the drift time,
V , taken by the fluorophore to run through the excitation volume:
Gdrift ; D , V G Brown ; D exp V G Brown ; D S ; D , V
2
1 1 D
(3)
As seen in Fig.1A, for diffusion times (D) similar to drift times (V) or longer, the shape of the autocorrelation function is extremely similar in both situations and an “a posteriori” determination of the kind of motion is difficult, if not impossible, as soon as the data are affected by a few percent of uncertainty, a figure that is primarily determined by the
molecular brightness. To the above considerations one should add also the possibility of fast exponential decays determined by the chemical fluctuations of the fluorescence signal.[14,15] The diffusion and drift times are related to the diffusion coefficient, D, the focal beam waist, 0, and the modulus of the drift speed V according to (notice that we are employing two-photon excitation):
02 D 8D V 0 V
(4)
and a beam waist 0 0.8 m, V D for speeds
For a dye diffusion coefficient of D 220 m2/s
V
8D
0
0.5 1.5mm / s . The shape of the GBrown ; D and the Gdrift ; D , V correlation functions are
very similar for large drift times (for example G Brown() Gdrift() for V = 8 ms and D 0.8 ms, solid line and open squares in Fig.1A), while one can easily discern the two correlation functions when V D (for example V = 1 ms and D 0.8 ms, solid line and open circles in Fig.1A). From this plot we can conclude that one can easily discern the drift component S(;D,V) from the global correlation function only when |V| 8D/0 0.1 – 0.3 mm/s. A final consideration regards the lack of sensitivity to the direction of the drift motion with a single spot autocorrelation function. 2.2 Cross-correlation Function. Regarding the above issues, we have a few advantages when computing the cross-correlation GX12() of the signals ( ) and ( ), gathered from two observation volumes spaced by the vector R (see sketch in Fig.1). The crosscorrelation, defined as,
G X 12
I 1 t I 2 t t I 1 t
t
I 2 t
(5)
t
depends on the diffusion and the drift relaxation times. It now takes the form of a Gaussian modulation of the hyperbolic decay typical of the Brownian motion:
1 G X 12,drift ; D , V , R G Brown ; D exp 2 0 G Brown ; D S R ; D , V , R
R V 1 D 2
(6)
where V is the flow drift. For collinear R and V vectors, the cross-correlation shows a clear maximum for =
V ,R
R V
, as visible in Fig.1B. The dependence of the peak position of the cross-correlation is evident in Fig.1B
where the cases corresponding to |R| = 2 m (symbols) and to |R| = 10 m (solid lines) are reported. The diffusion and drift relaxation times are then decoupled (see Eq.4). Moreover, the cross-correlation function displays a cross-correlation factor if the two volumes are distant enough (i.e.
V ,R
is larger than 500 ns - 1 s, the minimum lag time in correlator
boards) and the two volumes (Wobs2 and Wobs1, sketch in Fig.1) lie along the flux direction, or mean time taken by the fluorescent molecules to drift from Wobs1 to Wobs
2
R V 0 . V , R is the
and the FWHM of
S R ; D , V , R
is
proportional to the diffusion coefficient (see Fig.1C open and filled black squares). The determination of the type of motion from the function is then straightforward, and it becomes easier to obtain both the diffusion coefficient and the drift speed from a curve fit.
Figure 1. Simulation of the Auto- (G()) and Cross-correlation (GX1,2()) functions of the fluorescence emitted by a dye (D=220 m2/s) subject to a drift motion with speed, |V|, in modulus. The diffusion characteristic time D = 745 s for all the simulation data sets but for dot-dashed and filled squares data in panel C for which D = 7.450 ms. A 2% Gaussian distributed uncertainty was added to all the simulated correlation functions. The sketch represent the cross-correlation setup with a drift velocity that is not collinear with the distance vector R between the two observation volumes Wobs1 and Wobs2. Panel A reports the autocorrelation functions for drift velocity values |V| =0.1, 1, 2 mm/s (squares, circles and triangles respectively). The solid line represent the Brownian diffusion autocorrelation function, GBrown(). Panel B reports the cross-correlation functions for different drift velocity values and for the spots distance |R| =2 m (|V|=0.1, 1, 2 mm/s, open squares, circles and triangles, respectively) and |R| = 10 m (|V| = 1, 2 mm/s, filled circles and triangles respectively). Panel C: The solid and dashed lines represent the Brownian diffusion autocorrelation function, GBrown() for D =745s and D = 7.45 ms, respectively. The open and filled squares correspond instead to the cross-correlation functions computed for the drift speed |V|= 0.1 mm/s.
3. MATERIALS AND METHODS. 3.1 Optical Setup. The Dual beam FCS (DFCS) experiments were performed on a home-made setup in which a Ti:Sa Mode locked laser source (Tsunami, Spectra Physics) is used to perform two photon excitation on the sample. A wide field image of the
focal plane is collected by a EM-CCD. The same setup can provide also single photon excitation images with an additional Argon laser (2050, Spectra Physics), since each pixel of the EMCCD detector filters spatially the signal similarly to a confocal setup. The laser beam is split in two independently steerable beams by a Twyman-Green interferometer. The plane of the two mirrors of the interferometer is conjugated to the objective back aperture by two lenses arranged in a telescope position. Such setup allows to easily position the two focal volumes in the sample, by tilting the mirrors of the interferometer. The microscope objective (Olympus, 20X 0.95N.A.) is used for epifluorescence illumination and to obtain a bright field image of the sample. Fluorescence emission is gathered from the same objective and an image is formed on the EMCCD detector. The EMCCD (Cascade II 512B, Photometrics, USA) has a 512x512 pixel sensible chip and is designed to acquire in frame transfer mode, reaching a frame rate of 250 fps for subregions with less than 20 pixel lines. Such frame rate determines a maximum time resolution, for the cross correlation measure, of 4 ms. For cross correlation test measurements a borosilicate capillary tube (CM Scientific Ltd., UK) with square section was used, with an inner section of 800x800 µm (160 m wall thickness). The square section was chosen to minimize aberrations in the focal volume. The laminar flow of the solutions in the capillary was obtained by connecting both sides of the capillary tube to 4 cm3 glass cylinders used as sample reservoir. These cylinders where set horizontally at different heights, so that the solution flow from the upper cylinder to the lower through the capillary tube was regulated by a micrometric change in the difference of altitude of the two reservoirs. Surface tension prevents the sample solution from spilling from the cylinders. 3.2 Chemicals and embryos. Rhodamine 6G was purchased from Sigma-Aldrich and used without further purification. Stock solutions (ethanol) were diluted to 20-40 nM concentration for the correlation measurements. Gold Nanorods were synthesized by means of seed growth method in presence of the CTAB surfactant as described elsewhere. [16] For characterization of the vascular system, the sample consisted of a juvenile Casper zebrafish[17] transgenic for tg(fli1:GFP)y1[18] (30 days postfertilization, ∼1 cm long) that does not present skin pigmentation and is optically weakly scattering. The zebrafish is anesthetized with Tricaine mesylate, mounted in a 2-mm-diam fluorinated ethylene propylene (FEP) tube (FT2X3, Adtech Polymer Engineering, UK) with 1.5% low melting point agarose and then immersed in a water cell.[19]
4. RESULTS. 4.1 In vitro experiments. The capability of the setup to provide a measure of the drift speed for objects of various sizes was tested in borosilicate capillaries on two samples: rhodamine 6G in water (high diffusion coefficient sample), and 16x48 nm gold nanorods in water (low diffusion coefficient sample). Fluorescence emission in both samples was primed by two-photon absorption at = 800 nm since gold nanorods are known to present strong luminescence under two photon excitation.[20] We first performed a test of the invariance of the flow speed measurement on the distance between the two spots. The actual value of the speed, Vexp = 0.28 ± 0.05 mm/s, was obtained by measuring directly the flow of the hydraulic system (see M&M). The same measurement was taken with different distances between the focal points, obtaining a linear dependence of the mean drift time, VR, on the distance between the two excitation spots, |R|, for distances |R| < 20 m, corresponding to the case VR D (see Fig.2). Above this value the modulation of the cross-correlation function due to the Brownian motion leads to a progressive loss of information on the cross-correlation peak at lag times VR. Also for small inter-spots distances a limitation exists, consisting in an insufficient sampling of the cross-correlations for sampling times > VR/2. The result of the linear regression (according to the relation
V ,R R / V ) on the data for |R| < 20 m gives us a value of the flow speed, V =
0.3 ± 0.02 mm/s, in agreement with the expected one. We further investigated the possibility to recover information on the diffusion coefficient of the fluorophore from the width of the cross-correlation peak. To this purpose we measured the cross-correlation of solutions of Rhodamine 6G and compared them to that measured on suspensions of gold nanorods (see Fig.3). The values of the diffusion coefficients recovered from the fit are 270±30 µm2/s for Rhodamine and 23±6 µm2/s for gold nanorods, respectively. Both results are compatible with literature and theoretical estimates. It is to be noted that the Rhodamine 6G diffusion time, only six times larger than our sampling time, could not be easily measurable with EMCCD detectors in an single spot autocorrelation mode. Spatial cross correlation circumvents the limit imposed by the time resolution, as long as the
two focal points are distant enough. It is noteworthy that the position of the peak in the cross-correlation function is very similar when measured for the Rhodamine and for the gold Nanorods suspensions, and this corresponds to very close values of the flux speed measured in the two cases.
(B)
60
1.0 40
VR [ms]
GX12()
(A)
GX12()
0.5 0.10
0.00
0.0
10 lag times [ms]
100
0
20
0.05
10 100 lag time [ms]
10
20
0
|R| [m]
Figure 2. Experiments on gold nanorods (16 x 48 nm; D = 10 ± 1 m2/s). Panel A: normalized cross-correlation functions acquired from spots at distances |R| = 2, 4, 14, 20 m (squares, circles, up and down triangles respectively), collinear to the flux. Solid lines are best fit of Eq. 6 to data. Panel B reports the best fit values of the flux speed obtained from VR as a function of |R|. The solid line is the best fit to the three lowest values of the speed. Inset: un-normalized cross-correlation functions (same symbol code as in Panel A).
4.2 Experiments on Zebrafish embryos. We then investigated the blood flux in the vein vessels of Zebrafish embryo by setting two spots of the infrared laser along the vein axis and computing the cross-correlation function of the luminescence signal collected from the two laser spots. We have measured the drift speed by detecting the blood auto-fluorescence signal (short pass filter at 670 nm to block NIR excitation) and the dsRed signal from engineered red cells (emission filter at 600nm, band width 40nm) in casper Zebrafish embryos.
GX12()
1.0
0.5
0.0
10
100 lag times[ms]
Figure 3. Normalized cross correlation signal from luminescent 16x48 nm gold nanorods (circles), and rhodamine 6G (squares) in water solution, distance between focuses is 16 µm. Fitted diffusion coefficent is 270±30 µm2/s for Rhodamine 6G and 23±6 µm2/s for gold nanorods, respectively.
The cross-correlation functions reported in Fig.4 allow to easily measure the blood flux from the position of the peak of the cross-correlation function. The fitting of the data to Eq.6 gives very similar values, V = 0.20 ± 0.03 mm/s and V = 0.22 ± 0.03 mm/s for the autofluorescence signal and for the blood red cells (dsRed), respectively, as found in the literature.[21] The width of the auto-fluorescence cross-correlation function is clearly larger than that of the blood cells fluorescence in agreement with our interpretation of the origin of the plasma auto-fluorescence. From the best fit width of the peak of the cross-correlation function we recover the diffusion coefficients D 0.13 m2/s for the blood red cells, corresponding to a size 1.7 – 2 m. The cross-correlation computed on the auto-fluorescence signal, collected with a wide band filter, can instead be described by at least two components with widely different values of D: the slower one corresponds to D 25 m2/s and the faster one is fit to a component with D 0.33 m2/s. The fast diffusion coefficient should then corresponds to 7-9 nm size of spherical objects, indicating that the origin might be small aggregates of auto-fluorescent proteins. The best fit diffusion coefficient obtained for slow diffusion component well represents again the red blood cells visible through their autofluorescence.
GX12()
30
0.2
20
0.1
10
0.0
GX12()
0.3
0 10
100
1000
lag times [ms] Figure 4. Normalized spatial cross-correlation function in live zebrafish dorsal vein. Squares (left scale) report the cross-correlation function for autofluorescent proteins in unstained casper embryos, circles (right scale) correspond to the dsRed engineered blood cells. Solid and dashed lines are the best fit of the data to Eq.6. Distance between the two laser spots was |R| = 40 m. Best fitting of the correlation functions of the dsRed (red cells) data to Eq.6 provides values of the diffusion coefficients D 0.13 µm2/s, which is consistent with the size of a red cell. For plasma auto-fluorescence data at least two components are visible that correspond to D 25 µm2/s (at shorter lag times) and to D 0.33 m2/s, that may correspond to the size of small protein aggregates and to the red cells, respectively. The estimated flow speed is 0.23 and 0.21 mm/s for the dsRed red cell fluorescence and for the auto-fluorescence data.
The motion of blood cells can be brought directly into evidence by wide field transmission image correlation of the embryo’s vein. We have acquired 400 images at 4 ms per frame covering a portion of the vein along the blood flux (Fig.5A). We first analyzed them visually by composing, for each row (), a space-time image in which the horizontal (x) axis stands for a path along the vein axis measured along the row and the vertical (y) axis stands for the time along the time stack of images. The resulting images (see Fig.5), called here Time Carpets (Fig.5B), provides a direct visualization of the drift motion of the red blood cells, visible as skew lines along the carpet (see dotted lines in the blowup of Fig.5B). The slope of these lines corresponds to the cells’ speed. From the analysis of Fig.5B (blow-up) one can recover the value V 0.3 ± 0.1 mm/s for the speed of the blood cells in the transmission images.
The reddish skew stripes correspond to single objects that are followed for part of their motion along the vein because they drift out of focus during their motion in the vein that may also not lie in a plane perpendicular to the optical axis.
Figure 5. Experiments on Zebrafish embryos. Panel A: wide field transmission image of the dorsal embryo vein vessel. The blow up reports one of the 200 images acquired on the embryo vein with details of the blood red cells (black objects). The white dashed line in this blow-up is then used to produce the Carpet Image reported in panel B. Panel B: carpet image (row number 7 out of a total of 30 in each image) of the motion of the blood red cells along a straight line in the embryo vein. The horizontal and vertical axes of this image correspond to the path along the vein and the time (4 ms per frame) in the time stack of images (200 frames total) acquired in transmission wide field mode (pixel size 0.63 m). The blow up reports details of the skew lines that can be used to estimate the drift velocity of the blood cells.
5. CONCLUSIONS. The two spot excitation mode coupled to a sensitive wide field EM-CCD detection allows to investigate fluxes in microcapillaries and in blood vessels. The use of cross-correlation methods coupled to the possibility to have a wide field information of the motion, both in epi-fluorescence and transmission acquisition mode, offer a number of possibilities to obtain detailed information on the complex behavior of objects, proteins and cells, in the blood flux.
ACKNOWLEDGMENTS. This work has been partially funded by the Progetto regionale Accordo Quadro 2005 to G.C. and by the MIUR 2008JZ4MLB PRIN project to M.C. We are also grateful to Andrea Bassi (politecnico di Milano, Milano, I) for providing us with the casper Zebrafish embryos.
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