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Departments of * Physics and Chemistry, McGill University, Montreal, Quebec, Canada; and MEMPHYS, Center for Biomembrane Physics, Department of Physics, University of Southern Denmark, Odense, Denmark
Correspondence: Address reprint requests to Nela Durisic, E-mail: nduris{at}po-box.mcgill.ca.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSUPPLEMENTARY MATERIALACKNOWLEDGEMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSUPPLEMENTARY MATERIALACKNOWLEDGEMENTSREFERENCES |
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–3). The QDs typically consist of an inorganic semiconductor core and shell (e.g., CdSe/ZnS) with an outer organic coating for water solubility and biocompatibility. Recent improvements in QD synthesis and surface functionalization strategies have made the conjugation of QDs to various biomolecules more feasible, thus increasing their applications to cell and animal biology (4–8). Some of the photophysical properties of QDs are superior to conventional organic fluorophores. In particular, their broad absorption spectra and high quantum yields make them significantly brighter than many common fluorescent dyes (9), while their greater photostability permits longer observation times than conventional organic fluorophores (10,11). Additionally, experiments have shown that QDs have very large two-photon absorption cross sections, which make them promising labels for multiphoton microscopy applications (12).
These photophysical properties of luminescent nanoparticles would also be advantageous for optimizing fluorescence fluctuation measurements of macromolecular transport coefficients using techniques such as fluorescence correlation spectroscopy (FCS) and its imaging analog temporal image correlation spectroscopy (TICS) (13–16). In fluorescence fluctuation methods, the signal/noise ratio increases as the number of fluorescence photons emitted per molecule per second increases (17,18), so having a label with a large quantum yield and absorption cross section is desirable. The enhanced photostability of the QDs is also advantageous for fluorescence fluctuation measurements because photobleaching of the fluorophore can lead to systematic errors in transport coefficients measured by temporal correlation analysis (19).
However, the photophysics of QDs is also characterized by nonstationary emission or fluorescence intermittency that is commonly referred to as luminescent "blinking" (20). As techniques such as FCS and TICS measure molecular transport parameters by temporal correlation analysis of fluorescence fluctuations, it is not surprising that the blinking emission of QDs will contribute to the decay of the calculated time correlation function (21,22). The usual goal of an FCS or TICS experiment is to measure the transport coefficients of a labeled macromolecule by correlation analysis of the detected fluorescence fluctuations arising from changes in the number of fluorophores in a laser beam focus as the macromolecules move in and out of the focal region (see Fig. 1, A and B). However, the luminescent blinking of the QDs will contribute additional fluctuations to the intensity time record (Fig. 1 B).
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). However, unlike many organic dyes (24) and fluorescent proteins (25) (where similar blinking fluctuations have exponential kinetics with time constants usually one order of magnitude smaller than the characteristic molecular diffusion time), QD blinking is especially difficult to separate from other fluctuations of interest since the probability distribution function (PDF) of the "on" and "off" blinking time durations has a form of inverse power law (26,27):
 | (1) |
This power law distribution entails that fluctuations due to blinking will occur over many timescales, and this prevents any characteristic correlation time from being linked with the blinking emission via correlation analysis. We thus predict that QD blinking will contribute a systematic error to mobility measurements made by TICS depending on the actual PDF of the nanoparticle blinking.
In our previous work, we showed that the blinking of static QDs immobilized on glass substrates could be studied by TICS to characterize the decay rates of blinking autocorrelation (22). In this work, we show that fluctuations due to luminescent blinking of the QDs will systematically bias transport measurements made by TICS when such nanoparticles are employed as labels. Using a model system of QDs diffusing between two coverslips in a glycerol medium, we were able to obtain total internal reflection fluorescence (TIRF) microscopy image time series with different laser excitation powers to systematically adjust the exponent of the blinking power law (20,28). Analysis of these image series by TICS illustrated that the change in blinking clearly affected the correlation function decay; moreover, a simple two-dimensional (2D) diffusion model fit the decays well but yielded different characteristic diffusion times for the different excitation powers. The experimental results were corroborated by computer simulations of image series of blinking/diffusing point emitters where the blinking, transport, and collection conditions were systematically controlled. The experimental and simulation image series were also analyzed using the new k-space image correlation spectroscopy (kICS), which separates the contributions of fluctuations due to photophysics from those due to transport (29). We show that the transport coefficients can be accurately recovered by kICS without the systematic and hidden bias of the photophysical fluctuations that perturb the temporal image correlation. Finally we demonstrate the application of TICS and kICS to measure the diffusion of a glycosyl phosphatidylinositol (GPI)-anchored protein, CD73, in the membrane of IMR-90 fibroblasts and compare the results to those obtained for the model system and the simulations.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSUPPLEMENTARY MATERIALACKNOWLEDGEMENTSREFERENCES |
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150 QDs per 1 µL of glycerol water mixture. The mixture was then sonicated for 30 min before being deposited on the etched wells. A second coverslip was placed on top to close the wells, and the assembly was sealed and mounted on a microscope slide for fluorescence imaging. These samples provided a reasonable model for 2D diffusion because the QDs diffused within the 100-nm wells and were imaged by TIRF with an 100 nm depth of field.
Total internal reflection fluorescence microscopy imaging
All fluorescence microscopy measurements on the model QD samples were conducted on a home-built total internal reflection microscope described in detail previously (22). The samples were mounted on an inverted microscope (Zeiss Axiovert S100TV, Jena, Germany) equipped with a Zeiss Planapo 63x 1.45 numerical aperture oil immersion objective lens and illuminated by through-objective evanescent mode with the 488-nm line from a CW Ar+ laser (Melles Griot 35 LAP 431, Ottawa, Ontario, Canada). The excitation power was attenuated using neutral density filters. A Q 495 Lp dichroic mirror and 605/55 nm emission filter combination (Chroma Technology, Rockingham, VT) were used for all measurements. The back collected fluorescence was focused onto an intensified PentaMax charge-coupled device (CCD) camera (Princeton Instruments, Trenton, NJ) with 50–70 ms integration time and 13 ms readout time for imaging. Rectangular subregions chosen for correlation analysis were all selected from within the center of the imaged field of view where the evanescent excitation intensity was fairly (10%) constant.
Computer simulations
Computer simulated image time series of point emitters were generated using programs written in either IDL (RSI, Denver, CO) or MATLAB R14 (The MathWorks, Natick, MA). The programs placed point emitters at random pixel positions with a set particle density of six emitters/µm2. The particle matrix was convolved with a 2D Gaussian function of defined radius to yield an image matrix. In all simulations, we set the image size either to 64 x 64 or to 128 x 128 pixels with 0.1-µm pixel diameter, and the radius of the Gaussian convolution function was set to three pixels (i.e., 0.3 µm). An image time series was generated in which the diffusion coefficients and the on/off emission statistics of the point emitters were input by the user. For diffusion simulations, periodic boundary conditions were used at the image boundaries, and displacements in x and y were computed at every time step for each particle, according to normally distributed, floating-point, pseudorandom numbers with a mean of zero and a standard deviation of 
where D is the diffusion coefficient and 
the time step between images. The "on" and "off" time durations for particle emission were randomly selected according to inverse power law probability distributions with a set off time distribution exponent (moff) of 1.5 and on-time distributions exponents (mon) varying between 1.5 and 2. The minimum "on" and "off" times were set to the image time step of the simulation and for each set of distribution exponents, we varied the time step between images between 2.25 and 100 ms. The simulation image series were then analyzed by both temporal and k-space image correlation techniques.
Cell tissue culture, labeling, and imaging
IMR-90 human fibroblasts (ATCC) were grown in Dulbecco's modified Eagle's medium (D-MEM; Invitrogen, Carlsbad, CA) supplemented with 10% fetal bovine serum (FBS), 100 units/mL penicillin, 100 µg/mL streptomycin, and 0.1 mM minimum essential amino acids. One to two days before an experiment cells were plated in 35-mm glass bottom culture dishes (MatTek, Ashland, MA).
Cells in glass bottom dishes were washed in phosphate buffered saline (PBS) containing 1 mM CaCl2 and 1 mM MgCl2. Cells were subsequently stained with 1 mL of 9.5 µg/mL monoclonal mouse anti-human CD73 (clone AD2, kind gift of N. L. Thompson, Oklahoma Medical Research Foundation, Oklahoma City, OK) and 0.5 µg/mL of the same biotinylated antibody (3.8 biotin/IgG (immunoglobulin G)) in PBS with 1% BSA for 10 min. Cells were then washed in PBS and stained with 100 µL of 2 nM steptavidin-conjugated 605-nm QDs (sAv605-Qdots; Invitrogen) in PBS with 1% BSA for 1 min after which a few drops of a biotin blocking solution (Streptavidin/Biotin Blocking Kit, Vector Laboratories, Burlingame, CA) was added to prevent further cross-linking. Cells were then washed three times in PBS containing free biotin, as before, and finally in D-MEM/F-12 containing 15 mM HEPES but no phenol red (Invitrogen) additionally supplemented with 10% FBS and free biotin. All of these steps were done at room temperature.
Fluorescence time-lapse movies were acquired on an Olympus IX-81 microscope equipped with a XR/MEGA-10Z ICCD (Stanford Photonics, Palo Alto, CA). We used a 100-W Hg-arc lamp and a 460/50 nm excitation filter for exciting the QDs and a 610/20 nm emission filter (Chroma, Rockingham, VT) for detection. Time-lapse sequences were imaged at 30 frames per second.
Image analysis
Temporal image correlation spectroscopy
For a given image time series, i(x, y, t), we define a temporal intensity fluctuation autocorrelation function:
 | (2) |
= i(x, y, t) – 
i(x, y, t)
t is the fluorescence intensity fluctuation at pixel location (x, y) in the image recorded at time t, 
is the temporal lag variable, and " " denote spatial averaging over all pixel positions in an image (16).
The temporal autocorrelation decay can be fit by a variety of models depending on the dynamic processes that contribute fluctuations on the timescale of the image sampling. We fit our data to the standard 2D diffusion model (16):
 | (3) |
The fit parameters are the zero lag amplitude, g(0,0,0), the characteristic diffusion time, 
and an offset, g
. The diffusion coefficient, D, is calculated from the characteristic diffusion time and the mean beam radius:
 | (4) |
The mean beam radius, 
o, is calculated from the beam radii obtained by fitting spatial correlation functions to each image in the series as has been described previously (16).
k-Space image correlation spectroscopy
The details of the kICS method were recently published (29). Briefly, a k-space time correlation function, rk(k,
), is obtained by temporal correlation of the image series after 2D spatial Fourier transforms have been calculated for each image:
 | (5) |
is the Fourier transform of the image acquired at time t, 
denotes its complex conjugate, and the angular brackets denote temporal averaging in this case. For a system undergoing 2D diffusion, rk(k,) has the following analytical form:
 | (6) |
(k) is the optical transfer function of the imaging system. The fluorescence emission function, 
(t) (= 1 for on and = 0 for off), does not depend on spatial coordinates and it models the photophysics of the fluorophore assuming that fluorescence emission is independent of other dynamic processes. By dividing rk(k,) by rk(k,0) and log transforming, we obtain a point spread function-independent k-space time correlation function:
 | (7) |
For each image series analyzed, D was calculated as follows. First, ln[rk(k,)/rk(k,0)] was circularly averaged. Next, a linear regression of ln[rk(k,)/rk(k,0)] as a function of |k|2 was performed for each discrete value of , yielding slopes of D. Finally, the slope of a linear regression of a plot of these slopes as a function of was equal to D. Since the diffusion coefficient is calculated independently of fluorescence emission function, the kICS method yields a transport coefficient that is free of systematic errors caused by blinking or other photophysics contributions.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSUPPLEMENTARY MATERIALACKNOWLEDGEMENTSREFERENCES |
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,28,30). Using the same type of QDs as employed in this study, we have shown previously that temporal correlation functions measured by TICS from samples of static QDs decay more rapidly as the illumination laser power is increased (22). We found that the decay of the temporal autocorrelation function measured for an ensemble of immobilized blinking QDs was fit well by a power law:
 | (8) |
The fitting exponent 
reflects the variation in the underlying "on" time distribution and it can be related to the "on" time blinking PDF exponent mon as = 2 – mon (31,32), and it decreases as excitation laser power increases (22). At higher laser powers the QDs blink more frequently and shorter "on" events are observed on average, which leads to the observed increased rate of correlation function decay.
We, therefore, expect that the same excitation intensity-dependent decay due to blinking will be manifest in the temporal decay of correlation functions measured by TICS for the diffusing QDs, similar to what has been shown by Weiss and co-workers for faster timescale FCS measurements on semiconductor nanoparticles (21). As with all fluctuation/correlation methods, the relative contribution is going to depend on the sampling timescale, the characteristic transport time, and the blinking time(s). Fig. 2 shows normalized temporal autocorrelation functions measured by TICS from the same sample of diffusing QDs but at two different laser excitation powers: 4.5 W/cm2 and 13.5 W/cm2. The overall shape of the autocorrelation functions does not change significantly, but fits of these decays to the standard 2D diffusion model (Eq. 3) yield two different characteristic diffusion times: 1 = 7.38 ± 0.05 s and 2 = 5.96 ± 0.06 s which correspond to D = (1.88 ± 0.02) x 10–2 µm2/s and (2.15 ± 0.01) x 10–2 µm2/s, respectively, for the lower and higher powers. The average fluorescence intensity per image remained constant throughout the entire stack of 2000 images, thus eliminating the possibility that the differences in the measured D are due to changes in the brightness or bleaching of QDs with time (see inset Fig. 2). Transient heating effects caused by 488 nm excitation laser light were examined earlier for immobilized QDs of similar size (26). As conclusions reached in that study suggest negligible temperature changes due to QD absorption, we expect the diffusion coefficient to be the same for both samples. Clearly, the fluorescence intermittency introduces a systematic error into the TICS measurement obtained with the standard 2D diffusion fit model. More importantly, under these measurement conditions, the temporal autocorrelation functions fit reasonably well to the simple 2D model (see residuals in Fig. 2 B) so an experimenter might erroneously assume that blinking was not significant and remain unaware of this systematic deviation due to blinking.
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). It might be argued that the difference between the TICS measured D at the two different laser powers is really reflecting contributions of the blinking of the static QD population to the decay of the temporal autocorrelation function as we have previously measured this effect for stationary nanoparticles (22). To test whether or not this is the case, we imaged two different model systems of QDs while systematically increasing the excitation laser power. One sample was prepared so that the QDs diffused relatively slowly and were intermixed with a significant fraction (40%) of immobile nanoparticles. The second sample was prepared so that the QDs were diffusing more quickly (approximately an order of magnitude faster) with almost no static nanoparticles present. Furthermore we analyzed all sets of measurements for both samples by TICS and the reciprocal space variant kICS. It has been previously shown that the transport coefficients measured by kICS are independent of fluorophore photophysics (29). We did not calculate a Stokes-Einstein diffusion coefficient for these samples because it is known that glycerol readily absorbs water, making it difficult to know the true viscosity of the sample, and because our sample chamber geometry was effectively a thin film of 0.1 µm thickness.
Fig. 3 shows the D as measured by TICS and kICS for the slow/static QD sample as a function of excitation laser power. At the lowest excitation power of 3 W/cm2 where the contribution of blinking fluctuations should be minimized, there is a systematic difference between the measured DTICS = (1.6 ± 0.2) x 10–2 µm2/s, the TICS measured diffusion coefficient at the same power, and the average diffusion coefficient calculated from the kICS measurements at each power sampled (DkICS = (0.8 ± 0.2) x 10–2 µm2/s). This difference, where the DTICS is systematically at least 50% greater than DkICS, is constant for low to moderate laser powers and then begins to increase for powers >31 W/cm2. This trend shows the interplay between the characteristic transport fluctuation time and the timescales of the nanoparticle blinking which change as a function of laser power. More importantly, it demonstrates that even at the lowest excitation power, there is a systematic error in the TICS measured D for this sample because the measurement did not account for the blinking.
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DkICS = (8.6 ± 0.2) x 10–2 µm2/s, and this value differed from the TICS measured D by almost 50% for the highest powers used. At the lowest laser power, the DTICS is slightly greater than DkICS, but the error bars for these points overlap so the difference is within the statistical uncertainty. This overlap in DTICS and DkICS was not observed at the lowest laser power for the slow/static sample. For both of these samples, we assume that the exponent of the blinking power law distribution will be the same (identical excitation powers), and hence the timescales of the QD emission intermittency will be similar. However, for the slow/static QD sample, the characteristic diffusion time is approximately an order of magnitude larger than that of the rapid/mobile sample. Consequently the blinking fluctuations make a greater contribution to the decay of the TICS autocorrelation function for the slow/static sample because more on/off events can occur during the longer residency time of the QDs within each correlation area. In the rapid/mobile sample, the shorter characteristic diffusion time entails that fewer on/off blinking events are sampled before the QDs exit each correlation area by diffusive transport. Hence the blinking contributes less to the decay of the TICS autocorrelation function and the DTICS and DkICS are the same within the statistical uncertainty. As the laser excitation power is increased, the QD blinking becomes more rapid and the nanoparticles exhibit on/off blinking events of shorter duration so more blinking fluctuations are sampled over the timescale of the characteristic transport time. Hence, we observe that DTICS is systematically greater than DkICS for the higher laser powers for this sample.
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). One might be tempted to use higher laser powers to increase the signal/noise ratio in such imaging studies because the QDs are more resistant to photobleaching. However, this would result in a greater systematic error for a TICS diffusion measurement that would not be detected if the standard diffusion fitting model is used. A kICS measurement would detect changes in the blinking statistics as variations in the intercept of the k-space time correlation function and would measure an unbiased diffusion coefficient from the slope of this function (29).
Computer simulation results
We generated computer simulated image time series of point emitters with user set 2D diffusion and on/off emission probability distribution parameters for direct comparison with the model system experimental results and to investigate the role of temporal sampling in more detail. As was observed for the TICS experiments on the model QD samples, the normalized intensity fluctuation time autocorrelation functions calculated from the simulated image time series were well fit by the 2D diffusion model (data not shown), and the characteristic diffusion time decreased as mon increased. Fig. 5 presents the simulation results for the measurement of DTICS and DkICS as a function of mon. As mon increases, the systematic overestimation of the diffusion coefficient measured by TICS increases, whereas the kICS measured transport coefficient matches the set D within statistical error. This trend is completely in accord with our experimental measurements.
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d, to the image acquisition time) can determine the precision with which the characteristic correlation time can be measured by TICS (19). It was found that precision was optimized with sampling of two image frames per characteristic time and higher sampling rates did not increase the precision. However, since the QDs have no characteristic blinking timescale, we decided to use the computer simulations to generate image series with a variety of image frame sampling times to determine how this parameter would affect TICS measurements with this type of label. In practice, the frame-to-frame image sampling time can be adjusted over several orders of magnitude in imaging systems equipped with area detectors, by changing the CCD integration time. We adjusted the number of images sampled per characteristic diffusion time from 2.25 to 100 while keeping the total number of images in the time series constant. Fig. 6 shows the TICS measured D as a function of the number of image frames sampled per characteristic diffusion time for two sets of simulations with mon set at 1.5 and 1.8 whereas D was fixed at 0.10 µm2/s. The results show that the TICS measurement can recover this D within error for a temporal sampling ratio of 2. However, as the sampling ratio is increased, the measured D deviates as an increasing systematic overestimation from the set value. This is due to the fact that it is the faster timescale blinking fluctuations which are now being sampled as the temporal sampling ratio is increased and this contributes to a more rapid decay of the autocorrelation function. In experimental applications, it would not be possible to optimize the temporal sampling without a priori knowledge of the characteristic diffusion time.
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) and lymphocyte adhesion to the endothelia (35), and its activity has been found to be upregulated in a variety of tumor types (36). Along with other GPI-anchored proteins, CD73 is thought to reside in hypothesized lipid raft nanodomains in the cellular plasma membrane. As such it is one of many potential molecular markers in the ongoing search for in vivo lipid rafts.
To date, most quantitative studies of molecular dynamics with QDs as probes have focused on single particle tracking (SPT) techniques (37). One of the great strengths of fluorescence fluctuation techniques such as TICS is their ability to measure the dynamics of fluorescent particles at a relatively high density. In contrast, SPT can only be performed on samples in which the average particle spacing is significantly greater than the frame-to-frame particle displacements. The region of the membrane of the IMR-90 cell where the analysis was performed is outlined in Fig. 1 C. To verify that the CD73 protein is diffusing freely in that region, we examined the trajectories of several QDs whose traces could be resolved using SPT and did not find signs of confined diffusion (data not shown).
We made an effort to minimize QD blinking during data collection, so we could expect TICS and kICS methods to give similar results. The temporal autocorrelation function measured by TICS from the analyzed region of the cell is shown in Fig. 8 A. We calculated the diffusion coefficient to be DTICS = (0.109 ± 0.008) µm2/s from a fit of the 2D diffusion model to this correlation function. Analysis of the same image substack using kICS gave DkICS = (0.088 ± 0.008) µm2/s. Once again, kICS measures a smaller diffusion coefficient, which is expected since the transport coefficient measured by the reciprocal space method is not affected by photophysical fluctuations. Thus, even for a sample where QD blinking did not appear by eye to be significant, luminescent blinking of the nanoparticles leads to a small systematic error.
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CONCLUSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSUPPLEMENTARY MATERIALACKNOWLEDGEMENTSREFERENCES |
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SUPPLEMENTARY MATERIAL |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSUPPLEMENTARY MATERIALACKNOWLEDGEMENTSREFERENCES |
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ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSUPPLEMENTARY MATERIALACKNOWLEDGEMENTSREFERENCES |
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FOOTNOTES |
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Submitted on February 20, 2007; accepted for publication April 16, 2007.
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REFERENCES |
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