1. Introduction

Since its proposal [1] and first experimental demonstration [2], dual-color confocal fluorescence cross-correlation spectroscopy (FCCS) has proven to be a versatile and valuable tool, accessing a wide range of molecular parameters such as local concentrations, mobility, association/dissociation kinetics and enzymatic activity (for a review, see references [3] and [4]). The basic principle of FCCS consists in labeling each reaction partner with different (spectrally separable) fluorophores and cross-correlating the fluorescence signals to get a measure of the association and colocalization efficiency. This achieves a high signal specificity while following molecular interactions of different species. For instance, FCCS has been applied to monitoring kinetics of enzymatic reactions [5] and enzymatic activity screening [6, 7]. Despite a fast and simple data analysis, the experimental realization of a dual-color FCCS setup is demanding, as it requires exact and stable superposition of the two confocal observation volumes. One solution is to use a multi-line laser [7, 8], but this technique requires perfect chromatic corrections and wavelength-selective beam expanders to achieve similar excitation volumes. Another solution uses two-photon excitation to simultaneously excite two carefully selected distinct dyes within one infrared laser line [9]. This technique yields significant advantages, and has been successfully applied to probing enzymatic activity [9] as well as intracellular protein binding [10, 11]. However, determining the two-photon excitation spectra of different dyes turns out to be quite difficult, as selection rules for two-photon excitation greatly differ from those for single-photon. This, combined with the rather expensive pulsed laser required, somehow balances the attractiveness of this method. Recently, new experiment designs have been introduced to confocally excite multiple dyes with a single laser line and single-photon transitions [12, 13, 14]. Let us also mention the implementation of dual-color total internal reflection fluorescence (TIRF) for FCCS applications with a high molecular brightness [15]. Altogether, this shows that the FCCS field is presently very active, and still looking for experimental innovations.

As FCCS is based on fluctuations analysis of the number of detected molecules, the observation volume size determines the maximum concentration suitable for FCCS experiments, often ten to hundred nanomolar. FCCS is thus limited to high-affinity reactions, in which susbtantial effects are obtained even at low concentrations. Reduced observation volumes open the way for analysis of reactions with weaker affinity which generally require concentrations in the microto millimolar range. In single molecule fluorescence spectroscopy, nanoapertures milled in a metallic film (so-called “zero-mode waveguides”) have been used to reduce the observation volume down to 10 zeptoliter (10^-20 L), gaining up to 5 orders of magnitude from the volume commonly obtained in confocal microscopy and allowing single molecule resolution at 100 µM concentration [16]. This has stimulated many experimental work on single-color fluorescence correlation spectroscopy, either on solutions [17, 18, 19, 20] or on lipid membranes [21, 22, 23]. Properly optimized nanoapertures have also been reported to enhance the fluorescence brightness [18, 19, 24]. This effect appears especially interesting because it allows for a significant analysis volume reduction while still providing an efficient signal-to-background discrimination, even with attoliter volumes and single molecule resolution.

Surprisingly, even if the concept of nanoapertures to perform FCCS measurements has been proposed in [16] and to some extent earlier in [6], no experimental implementation has ever been reported. In this article, we describe the first FCCS applications of single nanometric apertures. This design provides a simple and robust setup to perform dual-color FCCS at high concentrations. In particular, the optical alignment and specifications for chromatic aberrations correction are greatly eased, as no confocal pinhole is used. As applications of this technique, we monitor the kinetics of an enzymatic DNA cleavage reaction. We also report that FCCS in nanoapertures can be applied to fast sample screening for dual-labeled species at high concentrations, offering new possibilities for biotechnology.

 

Fig. 1. Scheme of the experimental setup for dual-color FCCS with a nanoaperture (APD: avalanche photodiode, DPSSL : diode-pumped solid state laser).

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2. Materials and methods

2.1. Biochemical system

We describe here the preparation of the green- and red-labeled molecules used to calibrate our cross-correlation setup. Two complementary 66-nt DNA oligonucleotides were custom-synthesized and HPLC purified by Eurogentec. Both oligonucleotides are labeled by a fluorescent dye at their 5’ ends, respectively Cyanine-5 (Cy5; excitation/emission maxima 650/670 nm; Amersham) and Rhodamine Green (RhGr; excitation/emission maxima 500/525 nm; Invitrogen). When the two complementary sequence are hybridized, they contain cleavage site for the restriction endonuclease EcoRI (purchased at an activity of 10 u/µL; Invitrogen). The sequences were chosen following Ref. [5] : Cy5-5’-ATGGCTAATGACCGAGAATAGGGATCCGAATTCAATATTGGTACCTACGGGCTTTGCGCTCGTATC-3’ and RhGr-5’-GATACGAGCGCAAAGCCCGTAGGTACCAATATTGAATTCGGATCCCTATTCTCGGTCATTAGCCAT-3’. Complementary strands were annealed at concentration of 10 µM in a buffer containing 100 mM KOAc, 25 mM Tris-acetate (pH 7.6), 10 mM MgOAc, 0.5 mM β -mercaptoethanol and 10 µg/ml BSA, by heating the solution at 95 °C for 2 min and cooling it down to 23 °C with a gradient of 1.2 °C/min. Cross-correlation experiments on oligonucleotides were performed in a phosphate-buffered saline (PBS 1x) solution. The activity of restriction endonuclease EcoRI was recorded in a buffer containing 50 mM Tris-HCl (pH 8.0), 10 mM MgCl2 and 100 mM NaCl.

2.2. Experimental setup

In this study, we use circular apertures of 340 nm diameter to provide a simple way of superposing the two analysis volumes for dual-color FCCS. Our experimental setup for single-color FCS with a sub-wavelength aperture has already been described in [18, 19]. Focused Ga+ ion beam (FEI Strata DB235) is used to mill circular nanometric apertures in an opaque aluminium film (thickness 250 nm) deposited on a standard microscope glass coverslip (thickness 150 µm). The metallic film masks the fluorescent molecules diffusing in the droplet above the aperture. Seen from below (glass side), the fluorescence only originates from the illuminated aperture.

The experimental setup for FCCS is displayed on Fig 1. It is based on a Zeiss Axiovert 35M inverted microscope. Two-color excitation is obtained by combining the 488 nm laser line of a Sapphire 488LP (Coherent) with the 633 nm beam of an helium-neon laser (Melles Griot 25LHP991) using dichroic mirrors (Chroma Z488RDC and Omega Filters 640DRLP). Tightly focusing the two laser beams with a Zeiss C-Apochromat objective (40×/NA=1.2/infinite corrected) and positioning the sample with a 3-axis piezo stage (Polytek PI P527) allows to excite a single nanoaperture. Fluorescence from both dyes is collected by the same objective and filtered by the dichroic mirrors. A set of a long-pass (Omega Filters 493AELP) and holographic Notch filter (Kaiser Optical HNF-632.8-1.0) provides an efficient rejection of the two laser lines. The detection is performed by focusing on two avalanche photodiodes (Perkin-Elmer SPCM-AQR-13) through a 50/50 beamsplitter and bandpass filters (green : Omega Filters 535AF45, red : Omega Filters 670DF40).

Let us emphasize that except the active surface of the photodiodes (170 µm diameter which is almost three times the size of the optical spot at its best focus), no confocal pinhole is used in this setup. The nanoaperture provides directly the reduced observation volume needed in FCS. In the experiments reported below, special care was taken to calibrate the background noise within the apertures. Photobleaching was avoided, as the average number of detected molecules and diffusion time remained constant when we increased the excitation power by a factor of two.

The choice of an aperture diameter of 340 nm is a compromise so that the two excitation beams sense the same volume set by the aperture. For a smaller hole, the 633 nm would be evanescent inside the structure, leading to a reduced overlap between the laser beams, while for a larger hole, we would lose the observation volume confinement (see discussion in section 3.1).

2.3. Fluorescence cross-correlation analysis

Analysis of the fluorescence intensity fluctuations is performed by computing temporal autoand cross-correlations on a ALV6000 hardware correlator. The general expression for fluctuations auto- and cross-correlation functions is given by [2, 3]:

where F_i(t), F_j(t) are the fluorescence photocount signals for species i, j and 〈·〉 stands for time averaging. We experimentally investigate a mixture of green-only (G), red-only (R) and greenred (GR) molecules, with average concentrations C _G, C _R and C _GR [2]. The total concentration of green- and red-labeled species are noted C _G,tot=C _G+C _GR and C _R,tot=C _R+C _GR. In case of negligible fluorescence emission/absorption overlap and cross-talk, cross-correlation is sensitive to dual-labeled molecules GR, while green and red autocorrelations are sensitive to all green or red labeled molecules, that is the combination of G (resp. R) and GR species. For free Brownian three-dimensional diffusion in the case of a Gaussian molecular detection efficiency and equal two-color illumination, auto and cross-correlation functions can be expressed as [2, 5]:

 

Fig. 2. Autocorrelation functions of Alexa-647 dye excited at 633 nm (red) and 488 nm (blue) in a 340 nm diameter nanoaperture. Thin solid lines correspond to raw experimental data, while thick lines refer to numerical fits assuming Eq.(5). The dashed curve is the 488 nm autocorrelation after correction for the background noise. Amplitudes and characteristic times of the 633 nm and corrected 488 nm autocorrelations are almost equal, showing that the effective observation volumes for each laser line accurately overlap inside the nanoaperture, even without minute alignment.

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where the temporal dependence is given by:

In the expression above (for each species i), V_eff is the effective analysis volume, n _T,i stands for the triplet amplitude, τ _T,i the triplet time, 〈I_i〉 the mean intensity, 〈B_i〉 the mean background, τ _d,i the diffusion time and s_i the ratio of transversal to axial dimensions of the observation volume.

These expressions assume a 3D Brownian diffusion, which is strictly speaking not fulfilled with a nanoaperture. To account for this discrepancy, the aspect ratio s was let to vary freely in the numerical fits, and converged to a value almost equal to one for each run (this comes close to the naive guess of the nanoaperture diameter vs. height ratio which is close to 1.3). This model may appear very crude, and yet the experimental data is remarkably well fitted by this 3D model, as already noticed in [18, 19]. Deriving a complete mathematical expression for g ⁽²⁾(τ) within a single nanoaperture such as the one used here is a challenging task, as it amounts to describing the local excitation and collection efficiencies and the molecular concentration correlation, which are all affected by the nanostructure. Such an analysis is beyond the scope of this paper. Instead, we will rather focus on detecting the presence of cross-correlations and changes in the amount of total cross-correlation signal.

3. Dual-color FCCS in a single nanoaperture

3.1. Observation volume calibration

Before performing cross-correlation studies on labeled DNA strands, we aim at calibrating the observation volume inside the nanohole for both excitation wavelength. Ideally, these volumes should perfectly overlap in order to get the highest cross-correlation signal. The observation volume calibration is achieved by exciting a drop of Alexa Fluor 647 fluorescent dyes (Invitrogen) in a phosphate-buffered saline solution. Though Alexa-647 has its peak absorption at 650 nm, it can still be excited at 488 nm provided the 488 nm laser power is high enough. To this end, the excitation power is set to 600 µW at 488 nm and 15 µW at 633 nm. For FCCS carried on oligonucleotides, the 488 nm laser power was set to 25 µW, while the red laser power was unchanged. This ensures that the contribution of the green excitation to the red detection remains negligible.

 

Fig. 3. Auto- and cross-correlation curves for labeled DNA oligonucleotides at 2 µM concentration in a 340 nm diameter nanoaperture. Thin lines correspond to raw experimental data, thick lines are numerical fits.

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Figure 2 displays the autocorrelation functions for Alexa-647 with the two laser excitations. As the signal-to-noise ratio for the 488 nm excitation of Alexa-647 dye is pretty low (SNR_A647,488≃2 whereas SNR_A647,633≃80), the 488 nm autocorrelation is lowered by a factor of (1-〈B〉/〈I〉)²≃0.42 as indicated in Eq.(5). This effect can be easily corrected numerically, yielding the dashed blue curve in Fig. 2, which can be directly compared to the 633 nm autocorrelation. Numerical fits based on Eq.(5) yield comparable average numbers of molecules N ₄₈₈≃50, N ₆₃₃≃54 and diffusion times τ ₄₈₈≃τ ₆₃₃≃100 µs (with s=1). Given the dye concentration of 4 µM, one can estimate an effective volume of 0.02 fL, which closely corresponds to the aperture geometrical volume. The slight discrepancy between the two curves at short times seen on Fig. 2 is related to a different triplet excitation at each wavelength n _T,488≃0.3 while n _T,633≃0.7. We can thus assume that the illuminated volumes satisfactorily overlap inside the nanoaperture. Let us point out that this result was achieved without requiring extensive optical alignment.

3.2. Fluorescence cross-correlation in a nanoaperture

Figure 3 shows the results of FCCS experiments performed on a mixture of green-, red- and dual-labeled DNA oligonucleotides in a 340 nm nanoaperture without any further confocal filtering. In this particular experiment, the DNA oligonucleotide concentration was set to 2 µM, but it could be increased further by using smaller apertures. While FCS is generally performed at nanomolar concentrations, this experiment highlights that nanoapertures allow to reach much higher concentration regimes, as already pointed out by Levene and coworkers in [16]. Even without extra confocal filtering, we could achieve sufficiently high signal to noise ratios. For the experiment reported on Fig. 3, we detected average signals of 68,000 and 140,000 photons per second on the green and red detectors respectively, while the background noise was of 1,500 and 4,000 counts per second. The signal to noise ratios were thus of SNR₄₈₈≃45 and SNR₆₃₃≃35. No cross-talk was measurable in the green detection channel, as the excitation of the green dye by the red laser and the green emission of the red dye are both negligible. In the red detection channel, we measured a pure signal (red detection/red dye/red excitation) of 136,000 cts/s, and cross-talks of red detection/red dye/green excitation=3,000 cts/s and red detection/green dye/green excitation=1,000 cts/s. Following Ref. [2], the critical cross-talk parameter is the red fluorescence of the green dye versus the total red channel. Here this ratio equals 1,000/140,000=0.7%, which appears negligible.

 

Fig. 4. Cross-correlation curves during an endonucleotic cleavage reaction carried on a droplet containing 20 µL DNA substrate at 2 µM, 2 µL EcoRI of activity 10 u/µL and 2 µL Tris-HCl/MgCl2/NaCl buffer (10×) in a 340 nm diameter nanoaperture. Thin lines correspond to raw experimental data, thick lines are numerical fits.

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The ratio of doubly-labeled species can be evaluated from Eqs.(2–4):

From the numerical fits on Fig. 3, we estimate C _GR/C _G,tot≃41% and C _GR/C _R,tot≃49%.

As noted in [2] and seen on Fig. 3, the triplet amplitude seen on the cross-correlation curves is significantly lower than for the auto-correlation case. From numerical fits, we have n _T,G≃0.3 and n _T,R≃1.1, while n _T,GR≃0.1. These observations can be explained by a purely statistical model. The probability of having a dye in the triplet state is proportional to the triplet fraction F_T=n_T/(1+n_T). From our data, we have F _T,G≃0.23, F _T,R≃0.52. Since both dyes on a doubly-labeled molecule are independent, the probability of having both dyes in a triplet state simultaneously is thus proportional to F _T,GR=F _T,G×F _T,R≃0.12 yielding n _T,GR≃0.14. This is close to the measured value.

3.3. Enzymatic cleavage observation

EcoRI enzyme breaks the chemical link between the two different fluorophores on the doublestranded DNA molecule, resulting in loss of the cross-correlation signal. This effect was monitored at different reaction times inside a 340 nm nanoaperture (see Fig. 4). During cleavage, the amplitude of the cross-correlation decreases gradually, while the diffusion time and average fluorescence intensity remain constant. This indicates the specific detection of doubly-labeled DNA molecules by our experiment.

FCS and FCCS generally require nanomolar concentrations of fluorophores for optimal correlation measurements. To get a high enough substrate concentration for enzymatic reactions, extra unlabeled substrate is usually added to the reaction sample. Here, thanks to the low analysis volume set by the nanoaperture, direct cross-correlation analysis on labeled species at high concentration was possible, making useless the step of adding extra unlabeled substrate.

4. Rapid FCCS in subwavelength apertures

We now turn on to examining the applicability of FCCS in nanoapertures as a tool for rapid assay processing. This follows the idea proposed in Ref.[6] to accurately detect the presence of doubly-labeled species within short analysis times thanks to FCCS in a yes-or-no test. Rapid dual-color FCCS measurements were carried within 1 s integration time in a 340 nm nanoaperture either on a 2 µM double-labeled DNA mixture or on a solution containing free Rhodamine green and Alexa Fluor 647 dyes at the same fluorophore concentration (but showing obviously no cross-correlation). Let us point out that the concentration of the free RhGr/Alexa-647 solution was easily and accurately monitored using 488 and 633 nm autocorrelations. To evaluate the statistics of rapid FCCS, sets of 250×1 s cross-correlations were measured. Figure 5 shows typical cross-correlation functions with 1 and 100 s integration.

A critical point in rapid-FCCS is to estimate the correlogram value at origin g ⁽²⁾(0), which gives the quantity to test for detecting the presence of a doubly-labeled species. In their 1998 demonstration [6], Koltermann and coworkers derived g ⁽²⁾(0) from a numerical fit of the each correlogram with the function described in Eq.(5), where the diffusion time τ_d and structural parameter s were set to fixed values. Here, we propose an alternative method that does not require any a priori knowledge on the sample nor numerical fit. We compute g ⁽²⁾(0) by directly averaging the 40 first points of the correlogram (displayed for instance on Fig. 5). This corresponds to times below 40 µs, where the cross-correlation function is almost flat. Thanks to averaging on 40 points, we can still get a high sensitivity. The mean standard deviation on the first point of the correlogram is ${\sigma }_{g^{\left(2\right)},\left[1\right]}=0.015$ , which appears useless for rapid assay processing. Averaging on 40 points, we have a significantly reduced dispersion ${\sigma }_{g^{\left(2\right)},\left[40\right]}=0.0035$ which comes close to $\frac{{\sigma }_{g^{\left(2\right)},\left[1\right]}}{\sqrt{40}}$ as one would naively expect. Actually, the limit of averaging on the first 40 µs arises that after this time the correlogram can no more be considered flat, which induces wrong estimates on g ⁽²⁾(0). One interesting aspect of this procedure is that it can in principle be directly implemented on the hardware correlator, as it does not require any fitting or processing of the correlograms.

The left panel of Fig. 6 displays the g ⁽²⁾(0) distribution obtained from a set of 250 FCCS measurements in a nanoaperture with 1 s integration time with and without double-labeled species. It can be clearly seen that our procedure allows for a significant separation between positive and negative samples. For the case of double-labeled species, the histogram displayed on Fig. 6 has an average value of 1.015 and a standard deviation of 0.0034. For no doublelabeled species, the average is 1.0032 and the standard deviation 0.0045. We relate the remaining cross-correlation amplitude of 1.0032 in the case of no double-labeled species to a contribution of cross-talk.

To discriminate between the overlapping distributions for a single 1 s acquisition, we consider a positive result when the evaluated g ⁽²⁾(0) lies above the threshold value T indicated on Fig. 6, while results with g ⁽²⁾(0)<T are discarded. The performance of our system can thus be evaluated by computing the detection and error probability, noted Pr _det and Pr _err. From the positive H ₊ and negative detection H _- histogram distributions, we have:

 

Fig. 5. Typical cross-correlation curves with (green) and without (gray) double-labeled molecules in a 340 nm nanoaperture. For rapid assay processing, the integration time was set to 1 s (dotted line). The cross-correlation obtained after 100 s integration time is displayed in thick line for reference.

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Fig. 6. (Left) Histograms of plots showing the distribution of cross-correlation g ⁽²⁾(0) with (green) and without (gray) double-labeled molecules in a 340 nm nanoaperture. These histograms are obtained from a set of 250 FCCS experiments of 1 s integration time, as displayed on Fig. 5. Line curves represent fitted Gaussian distributions. (Right) Error and detection probability versus the threshold value T.

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and

where N₊ and N_- are normalization factors (respectively equal to the integral of H ₊ and H _-). Pr _det and Pr _err are displayed versus the threshold value T on the right panel of Fig. 6. If one has to detect almost all events but may tolerate some errors, fixing T=1.009 provides Pr _det=95% and Pr _err=11%. Conversely, if one wishes the lowest error rate, but tolerates to lose some events, then T=1.0135 would be a possibility having Pr _err=2.5% and Pr _det=68%. The choice of the optimal T obviously depends on the actual application and signal-to-noise ratio.

5. Conclusion

We have demonstrated that nanometric apertures milled in a metallic film provide a simple and robust mean for studying molecular association and dissociation using dual-color fluorescence cross-correlation spectroscopy. Compared to a conventional confocal microscope setup, nanoapertures bring some useful improvements : (i) the overlap of the two excitation beams and the optical alignment are greatly simplified by the nanoaperture which defines the analysis volume; (ii) no confocal pinhole is needed, relaxing the requirement for accurate correction of chromatic aberrations and accurate alignment; (iii) compared to two-photon excitation, the use of nanoapertures keeps the intrinsic advantages of dual-color FCCS to use standard fluorophore constructions with high absorption cross-section and well-defined absorption/emission spectra with large Stokes shifts and (iv) experiments can be conducted at micromolar concentration, allowing for an increase up to 3 orders of magnitude compared to standard FCS setups. We have also demonstrated that FCCS in nanoapertures can be applied to high-throughput assay processing at high molecular concentration. The limited throughput rate of our present setup is a known limitation of rapid FCS [6], but improving to a dual coincidence setup with a nanoaperture would gain up to 10 times in analysis speed, as demonstrated for confocal detection in [7]. Given the recent technical progress in nanotechnology and the development of nanofabrication facilities, we believe that FCCS can be readily improved by this method. Altogether, this opens the way for fast and parallel probing of biochemical reactions.