Total internal reflection fluorescence microscopy (TIR-FM) is an important tool in life science. Taking advantage of a very thin $(<100\mathrm{nm})$ optical excitation depth formed by an evanescent wave above a glass substrate, TIR fluorescence detection achieves an exceptional axial resolution and allows for the study of important cellular processes, in particular at or near the cellular membrane.¹ Prominent biological applications of TIR-FM include real-time in vivo observations of dynamics of molecular motors,^{2, 3} or of various membrane trafficking events, such as vesicle fusion or signal transduction after receptor binding.^{4, 5} To extend the sensitivity and observation of such cellular assays, it is important to combine TIR-FM with fluorescence measurement and single-molecule fluctuation analysis. Fluorescence correlation spectroscopy enables to expose biological reactivity such as binding events on the basis of temporal fluctuations in the fluorescence emission of single molecules.^{6, 7} Dual-color fluorescence cross-correlation spectroscopy (FCCS) represents a further development of fluctuation spectroscopy, which achieves a significantly improved selectivity and applicability.⁸ FCCS institutes two differently colored labels and realizes the distinction between coinciding and separated occurrence of these labels. It thus introduces a useful tool to monitor various biological assays including molecular binding between two differently labeled binding partners. Typically, FCCS is based on a confocal epi-illumination microscope with multicolor laser excitation and single-photon detection. Nonetheless, for several applications, TIR illumination can provide further benefits, for instance when ligands interacting with receptors immobilized onto a surface are to be studied.^{9, 10, 11, 12} First, in TIR-FCCS the molecules are only excited near the glass-sample interface, which simplifies the discrimination between freely diffusing and immobilized particles. Second, the most important prerequisite for efficient single-molecule detection is a high fluorescence count rate per molecule (CPM). Using TIR excitation and exploiting the anisotropic emission of the fluorescence generated at the glass-sample interface, much higher can be extracted from the investigated molecules.¹³

In this work, we present for the first time a dual-color excitation scheme for TIR single-molecule detection, which enables us to perform FCCS at glass-sample interfaces with high sensitivity. The improved performance of TIR-FCCS was verified on a synthetic binding assay, including dual-labeled double-stranded DNA molecules in aqueous solution, demonstrating its potential for biological and cellular applications.

Figure 1 shows our dual-color TIR-FCCS setup. Two linear polarized laser beams were expanded to an ${\mathrm{e}}^{-2}$ diameter of $\approx 2\mathrm{mm}$ and collinearly aligned to the microscope objective (BE & BS; beam expansion $2.5\times$ ). The laser powers were controlled by neutral density filters. An achromatic lens focused the beams into the back-focal plane (BFP) of the high numerical aperture (NA) oil immersion objective ( $\alpha$ -Plan-Fluar $100\times 1.45$ with Immersoil™ 518F, Carl Zeiss Jena, Jena, Germany), which resulted in circular spots with ${\mathrm{e}}^{-2}$ diameters at the cover slide-sample interface of $\approx 16\mu \mathrm{m}$ (blue) and $\approx 20\mu \mathrm{m}$ (red), respectively. In the BFP, a beam foci offset of $\approx 2.3\mathrm{mm}$ from the optical axis resulted in a super-critical angle illumination, i.e., a $z$ -confinement below $100\mathrm{nm}$ resulting from the evanescent field excitation.

Due to the epi-illumination, the fluorescent light was collected with the same high NA objective toward the pinholes and the single-photon detectors. The pinholes were realized by two multimode fibers with a core diameter of $50\mu \mathrm{m}$ . Dichroic mirrors and bandpass filters blocked the back-reflected laser light by more than OD10 and provided an excellent filtering of the green and red fluorescence. The fluorescence photons were detected by fiber-coupled single photon counting modules (SPCM-AQR-14-FC, PerkinElmer Optoelectronics, Wiesbaden, Germany; ASY50/105 silica fibers, Thorlabs Inc., Grünberg, Germany), whose signals (number of photons over time) were recorded and correlated with a USB hardware correlator (Flex02-08D, Correlator.com, Bridgewater, New Jersey). A focusing lens, a $\lambda ∕4$ plate, and a dichroic mirror were moved in one block by a linear translator for adjusting the position of the beam foci in the BFP of the objective. In this way, the excitation angle could be adjusted without altering the optical path length between the focusing lens and the objective. The configuration can easily be changed to a conventional confocal epi-illumination by removing the focusing lens and by centering the collimated beams in the BFP.

As a synthetic binding assay, we used free rhodamine green (RhG) and Cy5 fluophores, and a 40 base pair double-stranded DNA labeled with Alexa488 and Cy5 (Zeiss cross-correlation standard). The laser powers were optimized with the dsDNA sample and the background was measured with a NaCl/EDTA/TRIS pH 8.0 buffer. The cross talk between the detection channels was calibrated with free $10\text{-}\mathrm{nM}$ RhG and $50\text{-}\mathrm{nM}$ Cy5, respectively. For cross-correlation measurements, different mixtures of the double-labeled dsDNA sample and free $9\text{-}\mathrm{nM}$ RhG/ $50\text{-}\mathrm{nM}$ Cy5 solutions were used and investigated with identical laser powers during a time interval of $20\mathrm{s}$ . Plasma cleaning of the cover slides improved the results due to a strong suppression of unspecific binding at the glass surface.

For free diffusion the following model equation was used:¹³

Here, indices $m$ and $n$ represent the green and red detection channels; hence $G_{gg}$ and $G_{rr}$ are the autocorrelations of the signals in the green and red detection channels, respectively, and $G_{gr}$ is the cross-correlation of both signals. The index $i$ represents the diffusing species: $g$ for RhG, $r$ for Cy5, and $c$ for the dsDNA. Also, $B$ is the measured background count rate, $I$ is the total count rate, $Q_{mi}$ is the CPM in channel $m$ of species $i$ , $N_i$ are the number of molecules in the effective sampling volume, $G_{mnt}$ and ${\tau }_{mnt}$ are the triplet amplitudes and the triplet correlation times, respectively, $G_{mn\infty }\approx 1$ are the offsets at infinite lag time $\tau$ , and $D_{mni}$ describes the diffusion and is given by¹³ where ${\tau }_{iz}$ and ${\tau }_{ixy}$ are the axial and lateral diffusion times of species $i$ , respectively, and the scaled complementary error function is $\mathrm{erfcx}\left(x\right)=\exp \left(x^2\right)\times \mathrm{erfc}\left(x\right)$ . A multidimensional least-squares Gaussian-Newtonion algorithm was used to fit the experimental data to these model equations.

For these first experiments, only relative concentrations of the species were of interest. Therefore, a unique diffusion time was used, neglecting channel differences due to an imperfect overlap of the excitation and detection volumes. The triplet term accounts for the triplet contribution in the initial correlation amplitude $G_{\left(0\right)}$ .

The measured background signals were $B_g=7.54\mathrm{kHz}$ and $B_r=19.6\mathrm{kHz}$ , respectively. Typically, autofluorescence from the immersion oil as well as from the glass slide were the main contributions to $B_g$ and $B_r$ , respectively. The crosstalk CPM of RhG in the red channel was found to be $Q_{rg}=0.032\times Q_{gg}$ and assumed constant during the following evaluations. Cy5 did not show any crosstalk in the green channel, hence $Q_{gr}=0$ . Therefore, the CPM were replaced by the crosstalk factor $Q_{rg}∕Q_{gg}=0.032$ for simplification.

Figure 2 shows the correlation results for a mixture of the free fluorophores (negative control). The count rates of this control sample were $I_g=40.2\mathrm{kHz}$ and $I_r=66.0\mathrm{kHz}$ . The CPMs were $Q_{gg}=(I_g-B_g)∕N_g=13.1\mathrm{kHz}$ and $Q_{rr}=[I_r-B_r-0.032\times (I_g-B_g)]∕N_r=18.9\mathrm{kHz}$ , respectively. Figure 3 shows the results for the Cy5 and Alexa488 labeled dsDNA correlation (positive control). We measured $I_g=39.3\mathrm{kHz}$ and $I_r=44.2\mathrm{kHz}$ , from which $Q_{gc}=13.3\mathrm{kHz}$ and $Q_{rc}=27.0\mathrm{kHz}$ were extracted. The increased count rate for bound Cy5 is attributed to a reduction of conformational changes leading to higher fluorescence emission.^{14, 15} For $\tau >10\mu s$ , the fit residuals were lower than ${10}^{-2}$ . For smaller lag times, shot noise and afterpulsing reduced the signal-to-noise ratio.

Figure 4 summarizes the TIR-FCCS measurements on a titration series of double-labeled dsDNA in a mixture of free $9\text{-}\mathrm{nM}$ RhG/ $50\text{-}\mathrm{nM}$ Cy5, such that the total fluorophore concentration was approximately constant. The measured fraction of dsDNA scaled linearly with the mixed fraction from $\approx 1\%$ (negative control) to $\approx 28\%$ (positive control). The measurements showed a relative scatter of $\approx \pm 15\%$ . The measured fraction was at best one-third of the mixed fraction. This can be explained by an excess of molecules with a single green label, possibly further enhanced by photobleaching of the red label during the two-color excitation.¹⁵ The overlap of the sampling volumes was estimated to $\approx 60\%$ , which is close to the theoretical maximum. To reduce the influence of photobleaching, we used excitation intensities of $\approx 10\mu \mathrm{W}∕\mu {\mathrm{m}}^2$ . The measured CPM were about two times higher than with a confocal epi-illumination and a 1.20 NA water immersion objective at identical excitation intensities.^{13, 16}

The diffusion times of the dsDNA were ${\tau }_z=51\mu \mathrm{s}$ axially and ${\tau }_{xy}=2.3\mathrm{ms}$ laterally, respectively. Given a penetration depth of $80\mathrm{nm}$ and a waist radius of $370\mathrm{nm}$ , the diffusion constant was calculated to $\mathrm{D}\approx 1.5\times {10}^{-7}{\mathrm{cm}}^2∕\mathrm{s}$ , which is about 22% of the estimation ${\mathrm{D}}_{\mathrm{DNA}}\approx 6.8\times {10}^{-7}{\mathrm{cm}}^2∕\mathrm{s}$ for a rodlike molecule with a diameter of $24\mathrm{\AA }$ and a length of $140\mathrm{\AA }$ . We attribute this to an increased hydrodynamic drag near the interface and weak unspecific binding, respectively.

This study demonstrates for the first time single-molecule FCCS measurements based on an epi-illumination TIR concept. This TIR-FCCS concept offers distinct advantages to confocal FCCS for coincidence assays at solid/liquid surfaces, in particular by virtue of the much higher fluorescence collection efficiencies and the confinement of the excitation field to the surface of interest.