Accuracy and Precision in Camera-Based ... - ACS Publications

Mar 22, 2013 - The two parameters that control the accuracy and precision of the estimates from camera-based FCS are time resolution (Δτ) of the cam...
0 downloads 0 Views 747KB Size
Download PDF
Article pubs.acs.org/ac

Accuracy and Precision in Camera-Based Fluorescence Correlation Spectroscopy Measurements Jagadish Sankaran,†,‡,§ Nirmalya Bag,‡ Rachel Susan Kraut,§ and Thorsten Wohland*,†,‡ †

Singapore−MIT Alliance, E4-04-10, 4 Engineering Drive 3, Singapore-117576 Centre for BioImaging Sciences, Departments of Biological Sciences and Chemistry, National University of Singapore, 14 Science Drive 4, Singapore-117546 § School of Biological Sciences, Nanyang Technological University, 60 Nanyang Drive, Singapore-637551 ‡

S Supporting Information *

ABSTRACT: Imaging fluorescence correlation spectroscopy (FCS) performed using array detectors has been successfully used to quantify the number, mobility, and organization of biomolecules in cells and organisms. However, there have not been any systematic studies on the errors in these estimates that are introduced due to instrumental and experimental factors. State-of-the-art array detectors are still restricted in the number of frames that can be recorded per unit time, sensitivity and noise characteristics, and the total number of frames that can be realistically recorded. These limitations place constraints on the time resolution, the signal-to-noise ratio, and the total measurement time, respectively. This work addresses these problems by using a combination of simulations and experiments on lipid bilayers to provide characteristic performance parameters and guidelines that govern accuracy and precision of diffusion coefficient and concentration measurements in camera-based FCS. We then proceed to demonstrate the effects of these parameters on the capability of camera-based FCS to determine membrane heterogeneity via the FCS diffusion laws, showing that there is a lower length scale limit beyond which membrane organization cannot be detected and which can be overcome by choosing suitable experimental parameters. On the basis of these results, we provide guidelines for an efficient experimental design for camera-based FCS to extract information on mobility, concentration, and heterogeneity.

F

simulations have been carried out to understand the effects of various parameters on the accuracy and precision of estimates.21−29 The noise has also been experimentally quantified, and the effects of concentration, intensity, and measurement times on the autocorrelation function were studied.30 The mobility obtained by camera-based FCS was compared with existing techniques and revealed that imaging FCS yielded the same diffusion coefficients (D) within margin of error31 as confocal FCS, SPT, and FRAP. The effects of two experimental parameters (laser power and time resolution) on the precision of mobility in camera-based FCS has been tested recently.32 To the best of our knowledge, no systematic investigation on the effects of these and other instrumental and experimental factors (including total acquisition time (T), time resolution (Δτ), point spread function (PSF), pixel size (a), number of particles (N), and maximum lagtime (τmax)) on camera-based FCS has been performed. Hence, this work encompasses simulations and experimental studies, aimed at investigating the effects of different parameters on the estimates of mobility, concen-

luorescence correlation spectroscopy (FCS) is a tool that is used to measure the transport and binding properties of molecules.1 FCS is most commonly implemented in a confocal system and uses point detectors. Multiplexing has been achieved by the creation of several well-separated focal volumes and the use of multiple2 or array detectors.3−5 The use of EMCCDs6,7 or the more recent scientific CMOS8 (sCMOS) cameras for detection led to the development of imaging FCS. Apart from the implementations in confocal mode,6,7,9−12 imaging FCS has been extended to other illumination schemes including total internal reflection fluorescence microscopy (TIRFM), 13−15 single plane illumination microscopy (SPIM),16,17 and critical angle illumination.18 These experiments established camera-based FCS as a quantitative bioimaging technique that provides contrast based on functional parameters.19 A variety of theoretical studies have been performed in FCS to understand the effects of different factors in the collection, analysis, and the interpretation of data. Pioneering work on the statistical accuracy of FCS was performed by Koppel who proved that the signal-to-noise (S/N) ratio in FCS is proportional to the counts per molecule per second (cps) and not the total counts per second and is independent of the number of particles.20 Apart from theoretical studies, © 2013 American Chemical Society

Received: December 1, 2012 Accepted: March 22, 2013 Published: March 22, 2013 3948

dx.doi.org/10.1021/ac303485t | Anal. Chem. 2013, 85, 3948−3954

Analytical Chemistry

Article

with various diffusion coefficients and trapping probabilities and demonstrate their influence on the diffusion laws (Supporting Information, Section S1C).

tration, and heterogeneity in camera-based FCS and providing guidelines for efficient experimental design. The image of a single point-like particle on an array detector is described by the PSF. Therefore, the signal of the particle can be detected over an extended area and can contribute to different pixels. The observation area is therefore given by the convolution of the PSF with the pixel area. This also implies that neighboring pixels will have overlapping observation areas in which the overlap will be dependent on the size of the pixel and PSF. Hence, we derive an analytic equation for the effective observation area (Aeff), which is the convolution of the square area of the pixel (a2) with the PSF. This helps to define the diffusion time τd (τd = Aeff/4D), similar to confocal FCS, which represents the average time a particle needs to traverse the observation area. On the basis of these results, the optimal ranges for Δτ and T are provided in terms of τd. The results indicate that the accuracy is primarily determined by the time resolution while the total measurement time and the number of frames per acquisition determines the precision. One major advantage of camera-based FCS is the ability to multiplex, or observe many different contiguous areas at the same time. This property allows access to spatiotemporal correlations that exist over large areas and therefore gives insight into another dimension of organization. This helps in understanding heterogeneity in diffusion in the system under study. Heterogeneity in camera-based FCS can also be analyzed via the so-called FCS diffusion laws.33 Therefore, we investigate in the last part of the article how the experimental constraints in camera-based FCS affect the smallest detectable heterogeneities in FCS diffusion law analysis.

■

RESULTS AND DISCUSSION Effective Area in Camera-Based FCS. The PSF was modeled as a Gaussian function with w0 as its e−2 radius. The Gaussian PSF was convolved with a square pixel, and an expression for the effective area, Aeff, was obtained. The details of the derivation are provided in the Supporting Information, Section S2: Aeff =

a2

(erf( ) + a w0

w0 a π

2

2

(e−a /w0 − 1)

2

)

, τd =

Aeff 4D (1)

Simulation studies of FCS concerning the optimal time resolution25 (Δτ) typically report the optimal Δτ values in terms of the diffusion time τd. The definition of τd = Aeff/4D with the help of the effective observation area in camera-based FCS in this article facilitates the comparison of the constraints derived in this study with those in FCS literature, which mostly concern confocal FCS. Accuracy and Precision of Number and Mobility Estimates from Camera-Based FCS. The two parameters that control the accuracy and precision of the estimates from camera-based FCS are time resolution (Δτ) of the camera and the total measurement time (T), respectively. The time resolution mentioned in the article is the acquisition time per frame, which is the sum of the exposure time and the read out time. The read out time increases with increasing number of pixels per camera chip and varies for each camera model. Typical readout times per frame are 0.25 ms or longer for current EMCCD camera models but can be as low as 10−40 μs for sCMOS. It should be noted that the recorded signal intensity is related only to the exposure time. T is related to the time resolution (Δτ) and the total number of frames (n) captured during the acquisition (T = nΔτ). The mean and standard deviation (SD) reported here are those calculated across the pixels from a single image stack, if not indicated otherwise. The relative error is calculated from 100 × (Dsim − Dfit)/Dsim, where Dsim is the simulated diffusion coefficient and Dfit is the diffusion coefficient obtained by fitting the simulated correlation function. The next two sections discuss the dependence of accuracy and precision of the estimates on experimental and sample parameters. Values with a difference of at most 10% between the simulated and the obtained values and those with a coefficient of variation (100 × SD/mean) of at most 20% were considered as accurate and precise, respectively. A precision value of 20% was chosen for two reasons. First, typical experimental estimates of mobility on membranes using FCS have a coefficient of variation of 20%.32,35 Second, in order to decrease the error to less than 20%, simulations need to be carried out with more than 60 000 frames, which is above the typical number of collected frames in imaging FCS and is also not achievable with all systems mainly due to limited storage capacity and data transfer. Typically, we collect 10 000 frames for a measurement, which is a good compromise between accuracy and precision on one side and the inherent variability of the sample on the other side. For the rest of the article, we will assume measurements of 10 000 frames unless otherwise stated.

■

METHODS The simulations of imaging FCS experiments are based on the algorithm described elsewhere.28 Nine hundred particles were uniformly distributed inside a circle with radius R = 4 μm and were allowed to diffuse freely. Diffusion was simulated with time step Δτ. At each position, displacements drawn from a normal distribution defined by zero mean and standard deviation √(2DΔτ) were added to the position of each particle in the x and y directions. Whenever a particle left the circular region, another particle was added at a random position on the perimeter, thus maintaining a constant number of particles inside the circular region. The number of photons emitted by each particle was decided by a Poisson-distributed random number with the counts per particle per second (cps = 60 kHz) as the mean. The position at which the photons were detected was determined by a random number distributed with a probability proportional to the PSF around the particle position. The PSF was modeled as a Gaussian distribution function (w0 = e−2 radius = 320 nm). To simulate EMCCD-based detection, a 20 × 20 square pixel grid with pixel size a = 240 nm was superimposed onto the circular region. The fluorescence intensity at each pixel was calculated as the sum of photons falling onto that particular pixel. This procedure was repeated for 10 000 frames to create one image stack. The stacks were analyzed using ImFCS.34 The typical values for the parameters used for the simulations are listed in this section unless mentioned otherwise. A detailed description of the simulations, the experimental protocols to prepare supported lipid bilayers and perform imaging FCS measurements32 are provided in the Supporting Information, Section S1. In the Supporting Information, we also provide simulations of possible heterogeneities by including domains 3949

dx.doi.org/10.1021/ac303485t | Anal. Chem. 2013, 85, 3948−3954

Analytical Chemistry

Article

in the same order of Δτmax for other techniques. For instance, Δτmax has been reported to be 2/3 × τd and 1/2 × τd for confocal FCS25 and TICS38 for error limits of 10%. The effect is more drastically seen for D than for N. The value of N is predominantly determined by the shorter correlation times of the autocorrelation curve. N is inversely related to G(0), which can be determined by the extrapolation of the shorter correlation times to τ = 0. In order to test the validity of the constraints for experiments, two different lipid bilayers (DOPC and DOPC/ DPPC/Chol-5:5:2) with diffusion coefficients of ∼2.2 and 0.6 μm2/s (τd = 45 and 167 ms, respectively) were measured at different time resolutions. In the case of DOPC bilayers with τd = 45 ms (D = 2.2 μm2/s), the accuracy drops for Δτ > 5 ms, that is, Δτ/τd > 0.1, as in Figure 2A, which is in agreement with the results obtained from the simulations.

Accuracy of Mobility and Number Estimates. First, we investigated the accuracy of D and N obtained from the simulations in terms of the parameters Δτ, n, and T, assuming the sample has certain values of τd. The plot of percent error versus Δτ/τd in Figure 1A indicates that a broad range of values

Figure 1. Dynamic range of time resolution in camera-based FCS: (A) The errors in D and N obtained at various time resolutions (simulation parameters: n = 10 000, D = 1 μm2/s, cps = 60 kHz, and Nt = 900 in a circular area of R = 4 μm; EMCCD detection grid is 20 × 20 pixels; a = 240 nm and PSF = 320 nm). The parameters were chosen to approximate actual experiments as closely as possible. (B, C) The error can be overcome by increasing T or n as in B and C, respectively. The white and gray shaded areas indicate 10% and 20% errors from the simulated value. (D) A typical correlation curve is shown here highlighting the three different regions that determine the accuracy and precision of the estimate. The precision is determined by T and n. For accurate estimation of D and N, the first point of correlation should be in the white region and not in the gray region. The standard deviation from the mean across all the pixels is shown in the error bars in A, B, and C.

Figure 2. Experimental demonstration of the dynamic range of time resolution in camera-based FCS: (A) is a plot of D obtained from DOPC bilayer imaged at different time resolutions. The coefficient of variation (CV) is defined as the ratio between the standard deviation (SD) to the mean. Here, Δτ = 1 ms (shown in red) is in the “n” controlled region, and an increase in the number of frames leads to better precision as shown in the inset. (B) Plot of D obtained from DOPC/DPPC/Chol (5:5:2) at different time resolutions. As seen in simulations, the D values here are not as precise as in A (i.e., the CV is larger), since the SD is inversely related to mobility. In this case, the time resolution of 1 ms (shown in red) is in the “T” controlled region, and hence, an increase in T leads to estimates with increased precision as shown in the inset. The standard deviation from the mean across all the pixels is shown in the error bars.

of Δτ/τd yields simultaneously accurate estimates of D and N (errors within 10%) for a fixed number of frames (10 000). There is a critical value of Δτ/τd (0.1), above which the error increases beyond 10%. Hence, the first constraint governing the accuracy in camera-based FCS is provided in eq 2:

Δτ < 0.1 τd

Precision of Mobility Estimates. As mentioned in the previous section, the error is high when the values of Δτ/τd are low ( 0.1. This analysis suggests the accuracy is determined primarily by the time resolution of the camera at optimal T and n. The estimate of Δτmax, that is, the maximum value for Δτ compatible with accurate camera-based FCS measurements, is 3950

dx.doi.org/10.1021/ac303485t | Anal. Chem. 2013, 85, 3948−3954

Analytical Chemistry

Article

photon correlation spectroscopy23 and in rotational correlation spectroscopy40 where simulations and experiments yielded a value of 100τd . The error decreased as a function of 1/T in the case of experiments, which were performed using spinning disc confocal based imaging FCS.10 For a D = 1 μm2/s captured at Δτ = 5 ms, 2000 frames are sufficient according to the above guidelines. Similarly, 20 000 frames are necessary for D = 0.1 μm2/s. But, Figure 1C shows that, apart from T, the number of frames (n) in the stacks affected the precision of the estimates as well. Similar to the data presented here, it was observed in TICS that, for Δτ within the suggested regime, the total number of sampled images in the stack determined the precision.38 As seen in Figure 1C, for a given Δτ/τd < 0.1 (here, Δτ = 5 ms, τd ∼= 100 ms), the minimum number of images in the stack required to obtain a precision of at least 20% is 10 000. Hence, the second constraint governing the precision in camera-based FCS can be summarized as T ≥ max(100τd , 10 000Δτ)

number of frames is required for obtaining the same level of error (Supporting Information, Figure S2E). Hence, it is advisable to acquire the images at the lowest Δτ for a given T. The effect of changing τmax is discussed in detail in the Supporting Information, Section S3C and Figures S4 and S5. The inherent assumption in the entire discussion on accuracy and precision is that the experiments are performed using optimal concentrations for FCS.21 In the case of surfaces, previous reports32 suggest a working concentration range 0.1− 100 μm−2. The effects of surface concentration on accuracy and precision are studied here. In the case of N, surface concentrations up to 2000 μm−2 yield estimates within 10% error (Supporting Information, Figure S2F). For surface concentrations larger than 2000 μm−2, there is a loss in accuracy due to the decrease in amplitude of the correlation functions. The simulations suggest a working concentration level larger than 100 μm−2, since experimental noise has not been included in the simulations. It is also known that the finite exposure time during acquisition leads to a broadening in the PSF.41,42 These reports state that the effect is observed only when the exposure time is greater than 21 ms for a D = 1 μm2/s (PSF ∼ √DΔτ/3). Applying the first constraint for obtaining accurate estimates of D, camera-based FCS has to be performed at time resolutions below 10 ms, since the τd value corresponding to D = 1 μm2/s is 100 ms. This shows that effects of PSF broadening due to particle motion during the finite exposure time are negligible in the time scale of experiments typically performed in camerabased FCS. Accuracy and Precision in Lipid Bilayer Measurements. The lipid bilayers with D = 0.6 and 2.2 μm2/s were imaged with a time resolution of 1 ms. The D values obtained for the slow bilayer are not as precise as the fast bilayer, since the standard deviation is inversely related to mobility (Figure 2A,B). This corresponds to Δτ/τd = 0.006 and 0.022, respectively. Δτ/τd = 0.006 lies in the “T-controlled” region of the graph, and hence, an increase in T is needed to reduce the error (Figure 2B inset). The value Δτ/τd = 0.022 lies in the “n-controlled” region of the graph. Since the 1 ms acquisition time of the camera has an exposure time of only 0.75 ms (readout time 0.25 ms) and assuming the S/N ratio is proportional to the exposure time, applying the second constraint (eq 3), one expects that at least 6000 frames are required to reach the desired precision. However, from the inset in Figure 2A, it is clear that a precision of 20% is not reached before at least 10 000 frames are recorded, and beyond 10 000 frames, the precision increases, and the error decreases as expected. The larger number of frames required in experiments compared to the simulations is a result of the exclusion of the experimental noise in the simulations. The guidelines provided here help to increase precision through the design of suitable experiments. The protocol of a typical camera-based FCS experiment is provided in the Supporting Information, Section S5. The effects of the various parameters in camera-based FCS are summarized in Table S2 (Supporting Information). In essence, the accuracy and precision of D and N are affected by the choice of pixel size, PSF, total measurement time, time resolution, surface concentration, and the maximum lagtime up to which the correlation curve is fitted. Note that, if the PSF is itself experimentally estimated from the measurements,32 then the accuracy of PSF is also dependent upon the total measurement time and the pixel size. After the detailed analysis of mobility

(3)

Which of the two terms (100τd or 10 000Δτ) is larger in the second constraint varies depending on the circumstances. Equation 3 leads to two different regions in the correlation curve namely a T-controlled and an n-controlled region. The first possibility 100τd > 10 000Δτ can be rewritten as Δτ/τd < 0.01. This region of the correlation curve is referred to as the “T-controlled” region. The second possibility 100τd < 10 000Δτ can be rewritten as Δτ/τd > 0.01. Incorporating eq 2, this region is given by 0.01 < Δτ/τd < 0.1. Here, irrespective of the mobility, the number of frames must be at least 10 000. This is the “n-controlled” region. Given that Δτ is constrained by the diffusion time, τd, of the sample, fixing one T or n automatically decides the other (T = nΔτ). These results are summarized in Figure 1D. In the Tcontrolled region, the diffusion time is much larger than Δτ, and thus, T needs to be increased to produce a sufficient S/N ratio for the correlation function. In the n-controlled region, the number of frames must be fixed to at least 10 000, irrespective of sample mobility. If the first point of the experimental correlation function is located in the third region (Δτ/τd > 0.1), then accurate estimates of mobility cannot be obtained (gray area in Figure 1D). The error associated with the estimate of D decreases with an increase in D (Supporting Information, Figure S2A) or a decrease in τd for a fixed n. Because τd is directly related to Aeff, a reduction in the PSF or the pixel size will lead to a decrease in Aeff and hence will lead to a decrease in τd. The effects of decreasing the Aeff are discussed in detail in Sections S3A and S3B in the Supporting Information. In short, decreasing the PSF leads to a decrease in error of the estimate of D (Supporting Information, Section S3A and Figure S2C). The choice of the pixel size is dependent upon two different effects. First, a reduction in the pixel size (a) in object space provides better precision because it provides increased sampling (Supporting Information, Figure S2D). Second, in cases where imaging is performed at suboptimal signal-to-noise ratio, an increase in the pixel size leads to an increase in the S/ N ratio (higher photon count) and therefore an increase in precision of the estimate (Supporting Information, Section S3B and Figure S3). These competing effects must be borne in mind while choosing the pixel size. For a given T, D, and Aeff, in a non-shot-noise limited regime, the error increases with increasing Δτ, and as a result, a larger 3951

dx.doi.org/10.1021/ac303485t | Anal. Chem. 2013, 85, 3948−3954

Analytical Chemistry

Article

estimates, the next section is focused on the accuracy and precision of heterogeneity metrics. Characterizing the Heterogeneity by Diffusion Laws. The cell membrane is a complex two-dimensional fluid made up of hundreds of lipid and protein species. Current models of membrane organization state that certain lipids and proteins arrange themselves into domains of various sizes below the optical resolution limit bringing heterogeneity into the structure of the cell membrane.43,44 The organization of the membrane can be characterized using the FCS diffusion laws33 that state that the average transit time through areas of different sizes scale linearly with the size of the area in the case of free diffusion. Theoretically, when extrapolated to an area of size zero, a transit time of zero is expected. Any nonzero intercept upon extrapolation is an indication of heterogeneity. Specifically, a positive intercept is an indication of domains leading to hindered diffusion. FCS diffusion law analysis in camera-based FCS was used to probe domain formation in phase-separated bilayers,32 which had the advantage that the entire FCS diffusion law plot could be obtained from a single experiment, since post acquisition binning of pixels provides detection areas of different sizes.32 Upper and lower limits of confinement times in microdomains accessible by FCS diffusion laws have been reported.33 The next section is an exploration of the effects of various experimental and sample parameters (D, Δτ, T, w0, and a) on the intercepts obtained from diffusion laws in camera-based FCS. Effect of Experimental Parameters on FCS Diffusion Laws. In order to investigate the influence of heterogeneous systems on the intercepts in a model system, FCS diffusion laws were calculated for the same set of data as in Figure 1. Five different binning areas (1 × 1−5 × 5) were used, and for each binning, all possible areas in a measurement were used for the evaluation. The FCS diffusion law was visualized by plotting Aeff/D versus Aeff, where the parameter Aeff/D is proportional to the time taken for a molecule to cross the observation area. The standard error of the mean at each binning condition was used to perform a weighted linear least-squares fit. Typical FCS diffusion laws for D = 1 and 0.1 μm2/s are shown in Figure S7 (Supporting Information). The slope is inversely proportional to D. The accuracy of D obtained from simulations is described in Section S6A in the Supporting Information. Figure S8B (Supporting Information) shows the intercept values obtained from the FCS diffusion laws. There is a certain range of Δτ/τd values that yields intercepts close to zero as expected. The gray box indicated an error of 100 ms. As in the case above, the intercepts at smaller Δτ/τd are limited by the number of frames, and hence, nonzero intercepts are seen. Intercepts from camera-based FCS greater than 100 ms for D = 1 μm2/s are an indication of heterogeneity. This lower limit of the intercept above which heterogeneity can be identified will depend on D, PSF, T, and a (Figure 3). Effect of Total Measurement Time, PSF, and Pixel Size on Intercepts in the FCS Diffusion Law. An increase in n effectively leads to an increase in T, and this leads to a reduction in the intercept value as seen in Figure 3B. It was shown earlier in Figure 1B that an increase in T reduces the error observed with the estimates of D from autocorrelations. Furthermore, the pixel size and PSF also affect the intercepts obtained from the FCS diffusion law plot (Figure 3C,D). A reduction in pixel size or the PSF leads to a reduction in the observation area thereby reducing the values of Aeff/D, and

Figure 3. (A) Intercepts for the FCS diffusion laws at different time resolutions for a fixed measurement time obtained from the FCS diffusion laws are inversely related to the mobility. (B) Shows that an increase in T leads to a decrease in intercepts. The nonzero intercepts obtained due to lower mobility can be reduced with a reduction in the detection area. (C, D) Show two different ways to reduce the detection area. The detection area can be reduced by either reducing the PSF or the pixel size. The FCS diffusion laws at two different PSFs or pixel sizes are shown in the insets in blue or green or red corresponding to those values with bars filled with the same color. The error bars in the intercept values are the errors obtained from the weighted linear fitting of the different points in the FCS diffusion laws.

hence, the intercepts obtained are close to the expected value of zero (Figure 3C,D). There are two factors governing the precision of the FCS diffusion law, the distance of the first point on the x axis from zero and the spacing between the points. Both factors stated above are determined by Aeff. The primary factor affecting the distance of the first point from zero and the spacing between them are PSF and pixel size, respectively. Figure 3C,D shows that a two times reduction in PSF at a given pixel size (a = 240 nm, w0 = 160 and 320 nm) is more effective in reducing the intercept than a two times reduction in pixel size at a given PSF (a = 120 and 240 nm, w0 = 320 nm). The effect of the error in PSF in FCS diffusion law analysis is discussed in greater detail in Section S6B in the Supporting Information (Figure S9). The validity of the limits from simulations stated above was tested in experiments performed using the slow and fast diffusion bilayers mentioned earlier. No phase separation was observed in both the bilayers in accordance with previous reports.32 Hence, null intercepts in FCS diffusion laws are expected in both cases. The fast diffusing bilayer yielded intercepts within ±100 ms for acquisition times ranging from 0.5 to 10 ms whereas the slow diffusing bilayer yielded intercepts within ±300 ms (Supporting Information, Figure S10A,B). In agreement with the results from simulations (Figure 3A), the error limits increase from 100 to 300 ms with a decrease in D. In both experimental samples, the intercept decreases with an increase in T (Supporting Information, Figure S10C,D) as expected (Figure 3B). The effect of varying the pixel size in FCS diffusion laws was tested in experiments by reducing the pixel size to 150 nm from 240 nm as in Figure S10E (Supporting Information). The intercepts reduced with a decrease in pixel size in accordance with the data presented from simulations (Figure 3D). In order to test for heterogeneity, simulations of hindered diffusion in the presence of domains were performed. The details of the simulations are presented in the Supporting 3952

dx.doi.org/10.1021/ac303485t | Anal. Chem. 2013, 85, 3948−3954

Analytical Chemistry

Article

Institute (NUS)−Baden-Württemberg Initiative (LSI-BW: BE2010-02).

Information in Section S1C. As expected, positive intercepts above the level expected from measurement errors were obtained indicating the presence of domains (Supporting Information, Section S6C). The intercepts obtained from FCS diffusion laws deviate from zero depending on the experimental conditions used. In order to obtain intercepts as close to zero as possible, the smallest pixel size accessible above the shot noise limit for the microscope and the camera need to be used. The PSF should be minimized by employing high NA objectives, and the longest possible measurement time should be used.

■

(1) Digman, M. A.; Gratton, E. Annu. Rev. Phys. Chem. 2011, 62, 645. (2) Brinkmeier, M.; Dorre, K.; Stephan, J.; Eigen, M. Anal. Chem. 1999, 71, 609. (3) Gosch, M.; Serov, A.; Anhut, T.; Lasser, T.; Rochas, A.; Besse, P. A.; Popovic, R. S.; Blom, H.; Rigler, R. J. Biomed. Opt. 2004, 9, 913. (4) Gosch, M.; Blom, H.; Anderegg, S.; Korn, K.; Thyberg, P.; Wells, M.; Lasser, T.; Rigler, R.; Magnusson, A.; Hård, S. J. Biomed. Opt. 2005, 10, 054008. (5) Colyer, R. A.; Scalia, G.; Rech, I.; Gulinatti, A.; Ghioni, M.; Cova, S.; Weiss, S.; Michalet, X. Biomed. Opt. Express 2010, 1, 1408. (6) Kannan, B.; Har, J. Y.; Liu, P.; Maruyama, I.; Ding, J. L.; Wohland, T. Anal. Chem. 2006, 78, 3444. (7) Burkhardt, M.; Schwille, P. Opt. Express 2006, 14, 5013. (8) Hashmi, S. M.; Loewenberg, M.; Dufresne, E. R. Opt. Express 2007, 15, 6528. (9) Sisan, D. R.; Arevalo, R.; Graves, C.; McAllister, R.; Urbach, J. S. Biophys. J. 2006, 91, 4241. (10) Needleman, D. J.; Xu, Y.; Mitchison, T. J. Biophys. J. 2009, 96, 5050. (11) Bestvater, F.; Seghiri, Z.; Kang, M. S.; Groener, N.; Lee, J. Y.; Im, K.-B.; Wachsmuth, M. Opt. Express 2010, 18, 23818. (12) Song, W.; Moon, S.; Lee, B. C.; Park, C. S.; Kim, D. Y.; Kwon, H. S. Appl. Opt. 2011, 50, 3529. (13) Kannan, B.; Guo, L.; Sudhaharan, T.; Ahmed, S.; Maruyama, I.; Wohland, T. Anal. Chem. 2007, 79, 4463. (14) Sankaran, J.; Manna, M.; Guo, L.; Kraut, R.; Wohland, T. Biophys. J. 2009, 97, 2630. (15) Boening, D.; Groemer, T. W.; Klingauf, J. Opt. Express 2010, 18, 13516. (16) Wohland, T.; Shi, X.; Sankaran, J.; Stelzer, E. H. K. Opt. Express 2010, 18, 10627. (17) Capoulade, J.; Wachsmuth, M.; Hufnagel, L.; Knop, M. Nat. Biotechnol. 2011, 29, 835. (18) Matsumoto, M.; Sugiura, T.; Minato, K. Jpn. J. Appl. Phys. 2010, 49, 3. (19) Editorial.. Nat. Methods 2012, 9, 627. (20) Koppel, D. E. Phys. Rev. A 1974, 10, 1938. (21) Nishimura, G.; Kinjo, M. Anal. Chem. 2004, 76, 1963. (22) Ye, F.; Collinson, M. M.; Higgins, D. A. Anal. Chem. 2007, 79, 6465. (23) Nijman, E. J.; Merkus, H. G.; Marijnissen, J. C. M.; Scarlett, B. Appl. Opt. 2001, 40, 4058. (24) Milon, S.; Hovius, R.; Vogel, H.; Wohland, T. Chem. Phys. 2003, 288, 171. (25) Tcherniak, A.; Reznik, C.; Link, S.; Landes, C. F. Anal. Chem. 2009, 81, 746. (26) He, J.; Guo, S.-M.; Bathe, M. Anal. Chem. 2012, 84, 3871. (27) Guo, S.-M.; He, J.; Monnier, N.; Sun, G.; Wohland, T.; Bathe, M. Anal. Chem. 2012, 84, 3880. (28) Wohland, T.; Rigler, R.; Vogel, H. Biophys. J. 2001, 80, 2987. (29) Meseth, U.; Wohland, T.; Rigler, R.; Vogel, H. Biophys. J. 1999, 76, 1619. (30) Starchev, K.; Ricka, J.; Buffle, J. J. Colloid Interface Sci. 2001, 233, 50. (31) Guo, L.; Har, J. Y.; Sankaran, J.; Hong, Y. M.; Kannan, B.; Wohland, T. ChemPhysChem 2008, 9, 721. (32) Bag, N.; Sankaran, J.; Paul, A.; Kraut, R. S.; Wohland, T. ChemPhysChem 2012, 13, 2784. (33) Wawrezinieck, L.; Rigneault, H.; Marguet, D.; Lenne, P. F. Biophys. J. 2005, 89, 4029. (34) Sankaran, J.; Shi, X.; Ho, L. Y.; Stelzer, E. H. K.; Wohland, T. Opt. Express 2010, 18, 25468. (35) Ries, J.; Schwille, P. Phys. Chem. Chem. Phys. 2008, 10, 3487. (36) Degiorgio, V.; Lastovka, J. B. Phys. Rev. A 1971, 4, 2033.

■

CONCLUSION Imaging FCS, the application of FCS to every pixel in an image, is a powerful tool for measuring molecular dynamics. However, in contrast to confocal FCS, which easily reaches sufficient time resolution for even the fastest fluorescence processes, imaging FCS is limited by the current camera technologies and requires additional experimental planning to acquire quantitative images. We therefore set out in this work to explore the basic technical (in contrast to photophysical) parameters that govern accuracy and precision in imaging FCS applications and provide protocols and guidelines for their implementation. Here, we used a combination of simulations and experiments to test the limits of time resolution, the number of frames recorded, and total measurement time. Our results show that the accuracy in imaging FCS is primarily determined by the time resolution while the total measurement time and the number of frames per acquisition determine the precision. In addition, imaging FCS allows the implementation of the FCS diffusion laws as has been shown before, with the caveat that here, too, there is a limit of the smallest heterogeneity than can be detected in the FCS diffusion laws with imaging FCS due to effects of the finite pixel size and point spread function. The constraints presented here, though specifically performed for camera-based FCS are also valid for other imaging-based FCS modalities. When applying proper guidelines as discussed here, imaging FCS provides reliable estimates of D, N, and heterogeneity of the sample and is a valuable biophysical tool to study membrane dynamics and organization.

■

ASSOCIATED CONTENT

S Supporting Information *

Additional information as noted in the text. This material is available free of charge via the Internet at http://pubs.acs.org.

■

REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS J.S. was supported by a graduate scholarship of the SingaporeMIT Alliance. N.B. is supported by a graduate scholarship of the National University of Singapore. R.S.K. gratefully acknowledges funding from the Ministry of Education (MOE2009-T22-019), and T.W. acknowledges funding from the Life Science 3953

dx.doi.org/10.1021/ac303485t | Anal. Chem. 2013, 85, 3948−3954

Analytical Chemistry

Article

(37) Brenner, S. L.; Nossal, R. J.; Weiss, G. H. J. Stat. Phys. 1978, 18, 1. (38) Kolin, D. L.; Costantino, S.; Wiseman, P. W. Biophys. J. 2006, 90, 628. (39) Saffarian, S.; Elson, E. L. Biophys. J. 2003, 84, 2030. (40) Lu, C. Y.; Vanden Bout, D. A. J. Chem. Phys. 2006, 125, 9. (41) Michalet, X. Phys. Rev. E 2010, 82, 041914. (42) Deschout, H.; Neyts, K.; Braeckmans, K. J. Biophotonics 2012, 5, 97. (43) Pike, L. J. J. Lipid Res. 2006, 47, 1597. (44) Pike, L. J. J. Lipid Res. 2009, 50, S323.

3954

dx.doi.org/10.1021/ac303485t | Anal. Chem. 2013, 85, 3948−3954