3.1.

Setup

The experimental configuration for parallel excitation and detection is displayed in Fig. 1 (a single-point measurement is realized without the DOE in the illumination part). The laser beam from a diode-pumped solid state laser (532 nm, Kimmon DPSS Laser, model-5526) was enlarged by a beam expander [L₁(f=25 mm),L₂(f=400 mm)] to fully illuminate the diffractive optical element (for details on DOEs see Ref. 22) and to overfill the back aperture of the microscope objective. Using the collimating lenses [L₃(f=150 mm),L₄(f=150 mm)], the DOE, and the microscope objective, the expanded beam was reshaped into a 2×2 -foci pattern and focused into the sample. The intensity in a single spot was measured to be 1.7 mW at the entrance of the objective. The excitation light was reflected by a dichroic mirror (Chroma, 565LP) into a 40× numerical aperture (NA) 1.15 water immersion objective (Olympus, Uapo/340, cover slip corrected). The fluorescence emission was collected by the same objective and transmitted through a bandpass filter (Chroma HQ585/40) that discriminated the signal from Rayleigh- and Raman-scattered light. Finally, the fluorescence emission was focused by the tube lens [L₅ (f=180 mm)] and a 4× demagnifying lens [L₆ (f=35 mm)] onto either one detector (∅ 7 to 8 μm, see Fig. 2) of the 2×2 CMOS SPAD array or onto the optical fiber (∅ 9 μm) connected to the SPCM-AQR-13. An XYZ translation stage holding the 2×2 CMOS SPAD array or the fiber connected to the SPCM-AQR-13 enabled spatial fine adjustment of the detector(s). The photoinduced pulses from the detectors were registered by a hardware correlator (Correlator.com, Flex99OEM-12C), which calculated the autocorrelation function. The calculated functions were stored in computer memory and then analyzed with an in-house computer program based on the Marquardt-Levenberg nonlinear least-squares minimization algorithm weighted after Koppel²³ that produces the number of molecules and the molecular diffusion times as fitting parameters.

Figure 1

Experimental configuration for parallel FCS measurements.

Figure 2

(a) Geometrical configuration of a single CMOS SPAD, where the effective diameter of the sensitive area corresponds to 7 to 8 μm; (b) single CMOS SPAD with integrated electronics; and (c) chip having a 2×2 CMOS SPAD array: OUT 1 to OUT 4 show the positions of the active areas; the distance between each is 1.1 mm.

3.2.

Single-Photon Detectors

APDs and PMTs are presently used for measuring fluorescence signals in FCS experiments. The detection efficiency of APDs (typically 70) is higher than that of PMTs (around 10). APDs have a higher dark count rate (250 to 500 Hz versus 15 Hz for PMTs), a higher afterpulsing probability (1 to 3 versus 0.1 for PMTs) and a longer dead time (50 versus 25 ns for PMTs). All of these parameters (dead time, afterpulsing, detection efficiency, and dark count) cause artifacts influencing the accuracy and/or precision of FCS measurements. Dead time and afterpulsing limit the shortest time lag accessible in a photon correlation experiment and also introduce correlated signal contribution to the modeled autocorrelation curve. Detection efficiency and dark counts influence the SNR of the measurement. Due to technological limitations, APDs and PMTs alike cannot be used directly in multispot FCS systems incorporating large numbers of spots. These detectors are not compatible with integration of processing electronics and the photodetector on the same chip. However, CMOS technology enables the design of photodetector arrays and the simultaneous integration of necessary electronics onto a single chip. Recently, the first array of Geiger APDs made by an industrial CMOS process (CMOS SPAD) was designed and successfully tested in the Microsystems Laboratory of the Swiss Federal Institute of Technology, Lausanne¹⁸ (Switzerland). A similar CMOS SPAD detector and its performance in FCS measurements is described in this paper.

3.3.

Beam Quality on the Detector

Our experimental configuration shows off-axis aberrations (mainly coma and astigmatism) due to the fact that the DOE generates the confocal spots beside the optical axis. Since the microscope system itself is aberration corrected, the strongest aberrations are expected from the demagnifying lens (L₆) placed in the detection arm of the system. The small size of the active area of the CMOS detectors makes the detection system sensitive to the contribution of aberrations, merely affecting the total collection efficiency. Our simulations utilizing ZEMAX (Focus Software, Inc.) showed that for a 2×2 -foci system, we could expect a decrease in the collection efficiency of a factor 2 to 5 in comparison to an onaxis single-point illumination scheme.

3.4.

Samples

A nucleotide triphosphate (tetramethylrhodamine-6-dCTP, New England Labs-425) henceforth referred to as TMR, diluted from a stock solutions (1 μM) in Millipore water to concentrations of 0.5, 2.5, and 1 nM, was used for single-component diffusion measurements.

For two-component diffusion measurements, the binding of different biological molecules to each other can be detected with FCS only when the difference in diffusion time is sufficiently high.^{24 25} Therefore, an high-performance liquid chromatograph (HPLC) pure primer template with 42 nucleotides (CTCGGGCTAAGGAGATTGTGTGGAATGGTCCTGT-GGGGGTAT, Thermo Hybaid, Ulm, Germany) tagged on the 5^′ -end with a TAMRA dye was chosen. The molecular weight given is M _prime =13,822 g/mol and M _{free_dye} ≈500 g/mol. A 10-nM primer concentration was mixed with a 10-nM dye concentration in different ratios (between 10/0 and 1/9) and each mixture was measured with the two detectors, CMOS SPAD and SPCM-AQR-13, in triplicates.

4.1.

CMOS SPAD versus SPCM-AQR13: Dead Time, Afterpulsing, Dark Counts, and Detection Efficiency

In this subsection we compare the performance of the CMOS SPAD with the SPCM-AQR-13 commercial single-photon counting module normally used in FCS experiments.

Figure 3 shows autocorrelation curves (averaging time is 60 s) and trace signals of dark counts measured with our CMOS SPAD [OUT 1, see Fig. 2(c)] and the SPCM-AQR-13. As we can see from the figure, our detector does not have any measurable afterpulsing effect. The SPCM-AQR-13 module shows an afterpulsing signal expanding up to τ=10 μs in the correlation curve. For dynamical processes in the microsecond range (e.g., triplet states), this afterpulsing could bias the result significantly. The corresponding signal traces, shown in the bottom plots, demonstrate the dark count level for both photodetectors, which is about 50 Hz for the CMOS SPAD and around 500 Hz for the SPCM-AQR13.

Figure 3

Measured autocorrelation curves and trace signals of dark counts obtained from the CMOS SPAD and the SPCM-AQR-13 for a 60-s measurement.

Figure 4 demonstrates typical autocorrelation function curves (averaging time is 60 s) of freely diffusing TMR nucleotide measured with our CMOS SPAD and the SPCM-AQR13. The dye-labeled molecules were dispersed in a droplet on a cover glass at a concentration of 2.5 nM. The autocorrelation curves are distorted differently by the effects of dead time and afterpulsing. The CMOS SPAD exhibits only a small distortion due to dead time, which is not higher than 30 ns, visible as a gap at lower values of τ. For the SPCM-AQR13 module, one can see distortions caused by afterpulsing, the sharp peak at 100 ns, as well as the dead time, which is estimated to be approximately 50 ns.

Figure 4

Typical autocorrelation curves and trace signals of TMR solution (2.5 nM) measured with the CMOS SPAD and the SPCM-AQR-13 for 60 s.

The analytical autocorrelation function [Eq. (1)] was fitted to the obtained data. The autocorrelation function for τ<10 μs was not taken into account to exclude the triplet state and afterpulsing effects for the SPCM-AQR13. From the fits, the average number of molecules per volume element is N=1.54 for the CMOS SPAD and N=2.0 for the SPCM-AQR13. The radial diffusion times are τ_D=86 and 118 μs, respectively. These differences are caused by the fact that the measured confocal volumes V for the SPCM-AQR-13 coupled to a 9-μm optical fiber and our detector, which has an effective diameter of 7 to 8 μm (see Fig. 2), are slightly different. In addition, the afterpulsing probability of the SPCM-AQR-13 is also higher. Therefore, a systematic error can be introduced by the measurement as well.

In Fig. 4, the count traces of the measured fluorescence signal demonstrate the sensitivity of the two systems. As one can see from the traces, the sensitivity of the CMOS SPAD is about one order of magnitude lower than that of the SPCM-AQR13. The efficiency of the SPCM-AQR13 is given in the technical specifications to be around 70, which provided a count rate of ν=59700 Hz in the experiment. The CMOS SPAD has only 6 to 7 detection efficiency, which resulted in ν=5400 Hz. Table 1 lists the characteristics of the two investigated detectors.

Table 1

4.2.

CMOS APD versus SPCM-AQR13 Module: Fitting Error versus Sampling Time for Measurements on the Single-Molecule Level

In the following experiment we measured the influence of the averaging time on the statistical reliability of an FCS measurement. The statistical reliability of the FCS measurements for the two detectors was tested with diffusing-dye-labeled nucleotides. The number of molecules in the sample volume never exceeded 1, which means that on average at the most one molecule was present in the detection volume.

For most biological applications, the concentration of fluorescent molecules in the sample is important to know. With FCS the average concentration of fluorescent molecules (C∝N) and the diffusion time (τ_D) can be obtained by fitting the measured correlation curve with the described analytical autocorrelation function [see Eq. (1) or (2)]. The number of photons per molecule detected within a certain time interval influences the FCS statistical reliability, or the “smoothness,” of the correlation function, and thus decreases the standard deviation, which, in turn, finally influences the precision of the estimated values of τ_D and N.

Measurements were performed with the CMOS SPAD and the SPCM-AQR-13 detector on two different concentrations of TMR molecules (2.5 nM and 500 pM). The measurements on the 500-pM solution are displayed in Fig. 5, which shows the measured number of molecules in the detection volume element and the diffusion time as functions of the acquisition time (averaging time) chosen to be 1, 3, 5, 7, 10, 15, 20, 30, 45, and 60 s. The dependence of the fitting error (standard deviation in fitting coefficient) on the acquisition time is shown on the right Y axis for each graph.

Figure 5

Left Y axes: measured number of molecules (N) in the sampling volume and diffusion time (τ_D) as functions of the averaging time; right Y axes: fitting error (standard error in fitting coefficient). Measurements were performed with the CMOS SPAD and a commercial single-photon counting module (SPCM-AQR-13) on TMR at a 500-pM concentration. The solid line is a fit of the error data points with the equation $y=a+b/\sqrt{T};$ see text for details.

The measurements performed with the SPCM-AQR13 gave a better statistical reliability and consequently a smaller fitting error; the latter of is always less than 0.6 for N and 2.5 for τ_D. The maximal fitting errors obtained with the CMOS SPAD are 8 and 16, respectively (see Fig. 5). However, for longer averaging times, the fitting error is strongly reduced, and even in the sub-single-molecule measurement regime (N<1) our detector showed a good statistical reliability with fitting errors smaller than 1.2 for N and smaller than 5 for τ_D for a 20-s acquisition time. The different statistical accuracies that we obtained with the two detectors are explained by the SNR for FCS measurements, which is given by^{23 26 27}

In our measurements, the error data points (“stars” in Fig. 5) were fitted with $y=a+b/\sqrt{T},$ in accordance with Eq. (4). Here, the parameter a is due to a systematic error of the measurements. The parameter b is inversely proportional to the count rate (ν) and had an approximately order of magnitude higher value for the CMOS SPAD than for the SPCM APD, a difference clearly resulting from the lower detection efficiency of the CMOS SPAD. However, the measurements performed with the CMOS SPAD at a 500-pM concentration gave results with an error rate of <5 after only 5 s for the determination of the number of molecules N and after 15 s for the diffusion time τ_D. For applications where the relative difference in number of molecules or diffusion time is decisive, such an error might be acceptable.

4.3.

Biologically Relevant Two-Component Analysis with CMOS SPAD

The two-component analysis is interesting for many different biological applications. This analysis method has been applied previously to investigate the hybridization of DNA strands to each other and to RNA and the binding of ligands to their receptors and to other proteins.^{1 28} We investigated if molecules having different diffusion times could be identified equally well with both detectors: the CMOS SPAD and the SPCM-AQR-13. The 10-nM primer concentration was mixed with a 10-nM dye concentration in different ratios between 10/0 and 1/9 and measured with the two detectors in triplicate. The autocorrelation curves of the measured samples were fitted in the time interval from approximately 10 μs to 30 s. The autocorrelation signal at times less than 10 μs was excluded to diminish the effect of afterpulsing (which is only present in the SPCM-AQR-13 detected autocorrelations) as well as to exclude the contribution of the triplet states. To evaluate the performance of the two detectors, the percentage of molecules with the slower diffusion component (primer) in relation to the more rapidly diffusing molecules (dyes) was determined as follows:

First, the autocorrelation curve obtained on a pure dye solution was analyzed with Eqs. (1) and (3) to estimate the ratio of the axial and radial dimensions R=ω_z/ω_xy, the diffusion time (τ_D1), and the count rate per molecule (ν₁) of the free dye. The values were determined to be R=8, τ_D1=τ=100 μs, and ν₁=3900 Hz for the CMOS SPAD and R=9, τ_D1=τ=110 μs, and ν₁=48,600 Hz for the SPCM-AQR-13.

Second, the purity of the HPLC pure primer was determined by an HPLC (Spectra Systems, ThermoFinnigan with Vydac 214TP reverse phase column, Dionex). Here, free TAMRA dyes could still be identified in the sample. Therefore, the count rate per molecule of the primer ν₂, could not be measured experimentally. Instead, we estimated the count rate per molecule of the HPLC pure primer to be one third of the count rate per molecule of the free dye ν₁. Following Eq. (2) we get

Third, the recorded autocorrelation curves of the different primer-dye mixtures from both detectors were analyzed (see Fig. 6) with the described in-house fitting program. Here, the ratio of the axial and radial dimensions of the detection volume element (R), the diffusion time of the free dye (τ_D1), and the coefficient q=0.3 were fixed. The fitting of Eq. (5) gave the diffusion time of the primer (τ_D2=0.7 and τ_D2=0.6 for the CMOS SPAD and the SPCM APD, respectively), the coefficients n, and the number of molecules N₁. Finally, the primer fraction was determined as PF=N₂/(N₁+N₂). Figure 7 shows this ratio with reference to the theoretically calculated fraction of the primer (from the mixing of the two components).

Figure 6

Measured two-component diffusion autocorrelation curves obtained with the CMOS SPAD (left), the mean count rate was around I=30 kHz, N₁=5.2, and N₂=30.6, and SPCM-AQR-13 (right), the mean count rate was around I=380 kHz, N₁=2.8, and N₂=23.3. The primer fraction (more slowly diffusing component) was in both cases determined to be around PF=85. The dotted lines in both plots show the curve fitted to the experimental data. Due to the lower detection efficiency of the CMOS SPAD detector, the noise in the autocorrelation function is worse than for the SPCM-AQR-13. However, the residuals of the CMOS SPAD, with no afterpulsing, show lower and more consistently varying values than for the SPCM-AQR-13.

Figure 7

Experimentally measured fraction of primer molecules (PF) as a function of the estimated primer fraction in solution (determined by the volumetric ratio of the primer and dye solutions).

It turned out that the estimated ratio of the count rates per molecule q=0.3 was not exactly correct. In consideration of Eq. (3) (where I is the mean count rate obtained in one measurement), the ratio of the count rates per molecule was probably even lower. The reason for this increment count rate lies in the oversimplification of the biological compound model. Here, obviously, more than two compounds with different count rates per molecule ν were present in the sample (e.g., free dyes, dye-labeled primer, and primer with intercalated dyes) making the determination of the exact absolute values of N₁ and N₂ difficult. However, the relative values based on measurements with the CMOS SPAD are quite similar compared to the relative values obtained by the measurements with the SPCM-APD. Thus, both detectors can be used for, for instance, concentration determinations of unknown mixtures giving a calibration curve, as in Fig. 7. The experimentally obtained primer fractions do not differ systematically, but only stochastically, between the two different detectors, the CMOS SPAD and the SPCM-AQR-13. Despite the fact that the detection efficiency of the CMOS SPAD is approximately 10 times lower than that of the SPCM-AQR13, the measurement time for the CMOS SPAD was only two times longer and very similar results are found for both detectors. In conclusion, the CMOS detector as well as the commercially available high-performance single-photon detector (as APD) can be used in FCS.

Ten samples with different primer concentrations were measured for 60 s each and the resulting autocorrelation curves were analyzed (see Fig. 7). Even in the HPLC pure primer solution approximately 10 of free dyes were found. Therefore, the highest value of the measured primer fraction resulted only in approximately 90. Independent measurement by HPLC confirmed the existence of free dye molecules also (data not shown). Each data point in Fig. 7 is the average of the three values from the three independent measurements. The error bars indicate the standard deviation for the measurement point. An offset on the abscissa of 0.02 has been introduced for the CMOS SPAD to avoid an overlap of the data points in the graph.

4.4.

Parallel Single-Molecule Detection and Parallel FCS with 2×2 CMOS SPAD Array

In this section the results obtained with the multifocal diffractive optical FCS system are presented. Also here, the concentration of molecules was so low that single-molecule detection could be performed. We utilized one of our 2×2 CMOS SPAD arrays to demonstrate its potential for parallel FCS experiments. Since the manufacturing process is not yet optimized for the homogeneous performance of all four detectors,¹⁸ we chose one of the arrays that has pixels with essentially different dark count rates: 40, 30, 400, and 2000 Hz for OUT1 to OUT4 [Fig. 2(c)], respectively. With this detector, the impact of the nonuniformity of the detector parameters to the measurement accuracy was estimated.

A 1-nM solution of TMR was dispersed in a droplet on a cover glass. The 2×2 fan-out diffractive optical foci were then positioned into four arbitrary points of the drop. The measurement time was 300 s. Figure 8 illustrates the result of the measurements performed with the 2×2 FCS system on a 1-nM TMR sample. The first three detectors show a similar performance: the average number of molecules 〈N〉=0.88±0.04, the average diffusion time 〈τ_D〉=88±8 μs, and the average count rate per molecule 〈ν〉=2000±280 Hz. The relative differences can be explained by the individual response of the four detectors as well as the positioning inaccuracy of the conjugated confocal spots on the detectors. Similar differences (<20) also can be observed in single-spot FCS measurements. The fourth detector has a higher dark count rate (2000 Hz) but the same detection efficiency. This results in a flattening of the autocorrelation trace and the fitting of the curve has to be corrected for this background signal.²⁹ Even with such a correction we get higher values for N=2.6, τ_D=166 μs and an almost fourfold lower ν value (590 Hz). One explanation for these differences could be that aberration occurred, which results in different confocal spots. Another would be that the DOE was somehow tilted and the distance between the spots was no longer optimized toward the distance between the active pixels of the detector array. Thereby, the excitation volume elements did not coincide 100 with the active areas of the CMOS SPAD array, which resulted in a larger confocal volume per spot as well as in lower collection efficiency for the different foci. Finally, we calibrated the confocal volume for each sensor on the basis of the radial diffusion times. With an estimated diffusion coefficient^{5 14} of D=(kT)/(6πηr)=2.6×10⁻¹⁰ m ²/s, and using V=R(4πτ_DD)^3/2, we estimated the detection volume elements for each of the four detectors to be 1.2, 1.4, 1.1, and 3.2 fl, respectively. From these values, the concentration values were determined to be 1.3, 1.1, 1.3, and 1.4 nM, respectively. This calibration method ensures that all detectors give a similar quantitative measure. This result demonstrates the feasibility of our parallel FCS system in the sub-single-molecule (N<1) range.

Figure 8

Autocorrelation functions (left) of fluorescence signals (right) measured in a solution of 1-nM dye-labeled nucleotide triphosphates (TMR) from four DOE-generated foci with a 2×2 CMOS SPAD array.