1. Introduction

An increasing number of research fields in biology and medicine requires spectroscopic techniques with single molecule sensitivity in order to understand biochemical or microbiological processes. One of the technological milestones for spectroscopy was therefore the development of the confocal principle, which subsequently resulted in a very high signal to noise ratio in many applications. The implementation of the confocal principle, known from microscopy, in fluorescence correlation spectroscopy (FCS) [1, 2, 3] in the early 90’s, was a technical innovation that dramatically enhanced the sensitivity of FCS [4]. From this moment on, FCS was used in an ever increasing number of applications to investigate dynamic and kinetic properties of molecular systems including measurements of diffusion inside cells [5], investigations of receptor - ligand binding kinetics [6, 7] and enzyme binding and reaction kinetics [8, 9]. The latter applications generally require the molecular system under investigation to be attached to a surface. In this case, the use of total internal reflection FCS (TIR-FCS) [10] can be advantageous over confocal FCS. In contrast to confocal FCS where fluorophores are excited inside the waist of a laser beam, TIR-FCS uses an evanescent wave to excite molecules. This leads to a reduced axial extent of the observation volume and hence to a decreased background from Raman scattered light and from unwanted fluorescence of molecules in solution. However, both techniques, when used for measurements on surfaces, have disadvantages. For instance, confocal FCS suffers from a large axial extent of the excitation- and hence observation volume, while for classical TIR-FCS, the light collection efficiency is comparably low. To circumvent these inadequacies we propose a new technique that combines several aspects of TIR-FCS and confocal FCS [11]. Based on an objective-type TIRF setup [12, 13, 14], the proposed system uses epi-illumination through the periphery of a high NA oil-immersion objective to generate an evanescent wave on the surface of a microscope slide. The fluorescence signal is collected by the same objective, which leads to an excellent light collection efficiency while retaining the advantage of a reduced detection volume. In the present paper, we demonstrate the high performance of ‘objective-type TIR-FCS’ by investigating diffusion and binding of free dye molecules on surfaces, respectively. Our results show that the proposed technique has superior performance compared to classical FCS methods with respect to the signal to background ratio and counts per molecule (cpm). The parameter cpm is a frequently used figure of merit in FCS, which denotes the detection rate of photons, emitted by a single fluorophore inside the observation volume. Furthermore, the molecule detection efficiency (MDE) function and the size of the observation volume was calculated using high-angle vectorial diffraction integrals. The calculations incorporate the influence of the dielectric interface on the emission properties of fluorophores. Parameters derived from experimental data, in particular the structure parameter and diffusion times, agree with the calculated MDEs.

2. Instrumentation

 

Fig. 1. Schematic representation of the ‘objective-type TIR-FCS’ setup (left). L1 - L4: lenses; F1, F2: fluorescence filters; GP: glass plate; D: dichroic mirror; Obj: microscope objective; bfp: back focal plane of the objective; MS: motorized scanning stage. An enlargement of the ray-path inside the microscope objective (right). d: evanescent wave depth; Θ_c: critical angle.

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The setup (Fig. 1) is essentially an objective-type (‘prismless’) total internal reflection fluorescence (TIRF) setup adapted to measure FCS. Here, the beam of an argon ion laser (model 2214-25ML, Cyonics, Sunnyvale, CA) is enlarged by means of a telescope formed by lenses L1 and L2. Lens L3 focuses the beam onto the back focal plane (BFP) of an oil-immersion objective (α-Plan-Fluar, 1.45 NA, 100×, Carl Zeiss Jena GmbH, Jena, Germany) in order to get a collimated beam emerging from the objective. A pivotable glass-plate GP enables lateral shifting of the laser beam with respect to the optical axis. By shifting the beam, the angle of incidence at the glass-sample interface can be adjusted to exceed the critical angle _Θc, thereby introducing total internal reflection. In this way, an evanescent wave with an intensity distribution that is Gaussian in the xy plane (parallel to the interface) and exponential in the z direction (along the optical axis) is generated at the glass-sample interface. The intersection of the beam with the interface is elliptical, with a lateral dimension (full width at half maximum of the intensity distribution in the plane of incidence) of roughly 15μm. Fluorescence light is collected by the same objective and focused onto the end of a fiber, which is connected to a single photon avalanche diode (SPAD) (SPCM-AQR-13-FDC, PerkinElmer, Wellesley, MA). The core of the fiber acts as a pinhole assuring the lateral confinement of the observation volume. In our measurements we used a fiber with a core diameter of 50μm, unless otherwise stated, which was a convenient choice for the experimental investigations. The signal of the SPAD is processed by a hardware correlator or a single photon counting module (SPCM, SPC-630, Becker & Hickl GmbH, Berlin, Germany) to record the intensity versus time trace with high time resolution.

The illuminated region at the glass-water interface is several times larger than the observation volume, whose lateral extent is delimited by a pinhole in the microscope’s image plane. The actual size of the illuminated region is adjustable by changing the magnification of the telescope used to enlarge the beam. Because of the large illuminated region, TIRF imaging using a camera and spectroscopic measurements can be performed at the same time. For spectroscopic measurements, locating a position of interest in the sample, e.g. a single receptor attached to the glass surface, may be achieved by scanning the fiber end in the image plane. There is no need to move the sample in this case, which makes the system very stable under experimental conditions. However, for some applications, where the residence time of fluorophores on the surface is large, illuminating a whole area may be disadvantageous due to the risk of photo-bleaching.

The advantages of the objective-type configuration with respect to prism-based configurations are, in particular, a higher light collection efficiency and easier handling of the system. In conventional (prism-based) TIR-FCS [10, 15], the evanescent wave is generated by means of a prism, placed on top of an objective that resides, in general, in an inverted microscope. A microscope slide is interfaced to the lower surface of the prism using immersion oil. The biological system (e.g. a membrane containing receptors) is attached to the lower surface of this glass slide, where fluorescence is excited by the evanescent wave. The sample, containing the biological system and some type of aqueous solution is sandwiched between the glass slide and another microscope-, or coverslide. An objective (typically a water immersion objective), placed below the coverslide is used to collect fluorescence light. The objective therefore focuses into an aqueous solution.

For objective-type TIR-FCS, the coverslide carrying the biological system is situated directly upon the objective and focusing into an aqueous solution is avoided. Only in such a case does the use of high NA oil immersion objectives become senseful because these objectives are designed to collect light in a high refractive index environment. They perform poorly, due to aberrations, if the focal plane is not right at the surface of the coverglass [3]. Using an oil immersion objective with NA 1.45 in the proposed configuration guarantees that almost all of the light from fluorescent particles at the focus position, emitted into the lower half-space falls into the cone of light accepted by the objective. The portion of light that is accepted even exceeds 50% because the light emission for dipoles near a dielectric interface is anisotropic, favoring emission into the medium with the higher refractive index [16, 17]. A further advantage of the present system is easier sample access. In particular, there is no hindrance by a prism as is the case in prism-based TIRF or TIR-FCS instruments [14].

3. Observation volume

In order to determine the shape and estimate the size of the detection volume, we calculated the normalized molecule detection efficiency (MDE) function [18], based on a wave-vectorial approach [19]. The MDE expresses the relative intensity seen by the detector as a function of the position of a point-emitter in the sample space; it is therefore the correct mathematical representation of the detection volume.

Figure 2 shows the normalized MDEs for a confocal FCS system (left) and for our TIR-FCS system (right). The MDE is calculated by multiplying the intensity distribution, I(r), by the collection efficiency function (CEF), the CEF being proportional to the probability for a photon to be detected as a function of the position of the emitter:

 

Fig. 2. The normalized MDEs for confocal FCS (left) and TIR-FCS (right). The confocal FCS case was calculated for a 1.15 NA, 40 × water-immersion objective. For the TIR-FCS case a 1.45 NA, 100 × oil-immersion objective was considered. A diameter of the pinhole (core of the fiber) of 50μm was assumed in both cases. The excitation wavelength was 488 nm and the fluorescence emission wavelength was 542 nm.

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The constant c is a normalization coefficient introduced to make MDE(0) = 1. The fiber core diameter in both cases was 50μm and the excitation wavelength was 488 nm, corresponding to the blue line of the argon laser. The fluorophore under consideration was fluorescein. We assumed an emission wavelength of 542 nm, which is the average of the emission spectrum of fluorescein multiplied by the transmission function of the emission filter. In the confocal FCS case, we calculated the MDE for a 1.15 NA, 40× water immersion objective, which is standard. For confocal FCS, the intensity distribution was approximated by the point-spread function (PSF) of the system. The intensity distribution for TIR-FCS was assumed to be constant in the xy plane on the length scale of the typical diameter of the observation volume. It was further assumed to decay exponentially in the z direction with a penetration depth, d, of the intensity distribution given by:

This was calculated for a maximal lateral displacement of the excitation beam, implying a minimal angle of incidence θ = 71°. Here, n ₁ and n ₂ are the refractive indices of water and of the glass slide, respectively. The angle of incidence at the glass-water interface, θ, was measured by out-coupling the beam with the aid of a prism.

In the proximity of a dielectric interface the emission of a dipole with random orientation becomes highly anisotropic. This results in an apparent increase of the fluorophores brightness with decreasing distance to the interface [16, 17]. To take this effect into account we introduce the function P(z), the fraction of power emitted by a single dipole at a distance z from the interface into the cone of light accepted by the objective. This is calculated for a dipole with random orientation situated at the optical axis according to [20]. The CEF may then be approximated by

This is a convolution of the systems point spread function, PSF(r), calculated according to [19], with the transmission function of the pinhole represented by a disk function, circ(q/a), and multiplied by P(z). The convolution is carried out in the focal plane in object space (z = 0). The symbol q denotes a vector in the focal plane and a is the pinhole size divided by the magnification of the microscope. Results in Fig. 2 are consistent with experimental results, which we discuss later in section 5.

Given the MDE, we numerically calculated the W ₁ volume and the effective volume, V_eff ≡ $W_1^2$/W ₂, using [18]

where V is the half-space containing the sample. The quantityW ₁ is the size of the geometrical volume that would produce the given count-rate if the detection efficiency were equal to the maximum of the MDE and constant inside the volume. The numerical calculations give W ₁ = 17al (17 attoliter), V_eff = 57al for TIR-FCS andW ₁ = 26al, V_eff = 134al for confocal FCS.

The numerically calculated MDE for TIR-FCS is close to the analytical approximation given by

The calculations of the autocorrelation function in section 5 are based on this approximation. Here, h is the axial displacement at which the normalized MDE decreases to 1/e. This is smaller than the evanescent field depth, since the MDE, being the product of two in z monotonically decreasing functions (I and CEF), decreases faster with z than the intensity I.

4. Single molecule binding

Several groups were able to show the single fluorophore detection capabilities of objective-type TIRF (see [21] and references therein).We would expect that the proposed TIR-FCS setup features similar sensitivity since it differs from an objective-type TIRF setup essentially in the way the detected signal is processed and in the fact that for FCS only a single-point detector is used. Using our TIR-FCS setup, we performed measurements on single rhodamine 6G molecules undergoing adsorption and desorption on glass coverslides. Thereby we were able to examine the performance of our system; in particular, from high resolution intensity time traces we could estimate a lower bound for the maximal cpm that can be achieved in objective-type TIR-FCS experiments on binding kinetics. Dye molecules, present at a low concentration, diffused through the sample and eventually adsorbed at some location at the surface. For dyes entering the observation volume, and especially for binding events inside the observation volume, intensity peaks or bursts were observed. In general, the height of a burst depends on the lateral location of the bound dye within the observation volume or, for a diffusing dye, on its trajectory. It further depends on the dyes residence time inside the observation volume in the case that this is shorter than the binning time. Therefore, the cpm inferred from single molecule bursts are in general lower than the maximal cpm. For example, the maximal cpm would be obtained in experiments investigating binding kinetics of a single receptor, perfect alignment presumed; in other words, if the receptor is situated at the position where the MDE is maximal.

For these measurements, we have chosen experimental conditions described in the following. We used standard microscope coverslides previously cleaned by sonication in 2% Helmanex. The applied laser power incident on the microscope slide was approximately 10 - 15 mW. We used a dye solution containing 1 nM rhodamine 6G in buffer (potassium phosphate, pH 7.0), a concentration, low enough to assure that only single molecule events are observed. Due to adsorption, this concentration of free dye drops to smaller values immediately after applying the solution to the coverslide. Using a conventional confocal FCS system (Confocor I, Zeiss Jena GmbH), we checked the sample to exclude further that bursts are due to aggregated molecules. No aggregation could be inferred from the FCS data.

 

Fig. 3. Typical time trace for single rhodamine 6G molecules binding to a microscope slide (left). The right picture shows an enlargement of the two highest bursts. The binning time is 100μs.

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Figure 3 shows a typical time trace (left) and an enlargement of the highest photon bursts (right). The threshold for identifying a burst was set to 10 counts per 100μs (given a background of 2 counts per 100μs), in order to keep the probability for false positives (bursts due to variations of the background) low. Given this threshold, one can expect about one false positive in a time window of ten seconds. Intensity peaks, lasting on average for about 400μs, occurred with a frequency of about 7 per second. The average number of overlaps of two or more bursts in a time interval of 10 s was calculated to be approximately one, for about 70 bursts in total. The probability to observe two molecules residing at the same time in the observation volume was therefore small. For broader bursts the binning time (100μs) was small compared to the lasting of the bursts (sometimes several milliseconds). Bursts due to two (or more) molecules could in this case be easily distinguished from single molecule events by the necessary existence of steps or spikes. This is because a timely overlap of two binding events will never be exact; two molecules will not adsorb to, and desorb from the surface at exactly the same time, presumed that there is no aggregation (see above). In the example shown, inspection of the enlargement confirms the assumption that the observed event was caused either by a single molecule, or two, but successively binding molecules. In particular no spikes or steps are observed during the photon bursts lasting for about 10 ms. In general, burst heights frequently exceeded 70 counts, which implies cpm of more than 700 kHz. The background was approximately 20 kHz, which implies a signal to background ratio of 35 for the highest burst shown in Fig. 3. These values are further supported by FCS measurements of diffusing dyes as is shown in the following section.

5. FCS on diffusing molecules

We performed TIR-FCS measurements on rhodamine 6G molecules freely diffusing near a coverglass surface. To prevent unspecific binding, the microscope slides were treated with oxygen plasma before use. This renders the surface of the slides highly hydrophilic and lowers the probability to observe binding events. As a result, the correlation time becomes orders of magnitude smaller compared to measurements on slides not specially prepared. Furthermore, after cleaning with oxygen plasma no bursts are observed in the time traces, given a binning time of 100 ms and a fluorophore concentration,C, of 1 nM.

Figure 4 shows an autocorrelation curve and the corresponding time trace obtained for a solution of 100 nM rhodamine 6G in water. To fit the data, we used the model presented in [11] and further discussed in [22]:

 

Fig. 4. Autocorrelation for diffusing rhodamine 6G molecules (upper left) and time trace (right). The overall measurement time was 30 s. Fitting the data with the model represented by equation 6 yields the following parameters: N = 1.2, τ_z = 21.1μs, ω =0.38, p=15.4%, τ_t =1.6μs and cpm = 1.77 MHz. The red curve represents the fit to the autocorrelation data.

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The diffusion times are τ _z = h ²/(4D) and τ_xy = ${\omega }_{\mathit{\text{xy}}}^2$/(4D) = ω ²τ_z for the axial diffusion and diffusion parallel to the surface, D is the diffusion coefficient, and ω =ω_xy /h. The parameters h and ω_xy describe the geometry of the observation volume (equation 5). The parameter p denotes the percentage of molecules in the triplet state and τ_t denotes the triplet state decay time. The function w is defined by w ≡ exp(-x ²)erfc(-ix), and γ is a correction factor defined as γ ≡W ₂/W ₁ [18]. This factor describes the deviation of the effective volume, V_eff ∝ 1/(CG(0)), from W ₁. From equations 4 and 5 it follows that γ equals 1/4. However, in the subsequent calculations we used the value γ = 1/3.4, which was obtained from the numerical calculations.

To estimate the cpm from diffusion measurements, we used cpm=r/N where r stands for the total average count-rate. N is the number of molecules in the volumeW ₁, which implies the cpm is the maximal value for a molecule that stays at the position where the MDE is maximal. This deviates from the definition in [11], where cpm describes an averaged value. The value for cpm in the example shown in Fig. 4 reaches almost 1.8 MHz. This is higher than the value obtained from the more direct investigation of the time traces (Fig. 3). The discrepancy may be due to a different alignment, especially of the focus position with respect to the sample and/or a different incident angle of the laser beam. Indeed, the background in these diffusion measurements was higher too; we estimated it to be approximately 45 kHz for FCS measurements in distilled water. This implies a signal to background ratio of about 39, which is close to the value obtained from direct measurements, which is 35.

From inspection of the residuals (Fig. 5, lower left), we conclude that the model still deviates from reality. This may be due to the fact, that there is some interaction of the dye with the surface even after treating the slides with oxygen plasma. In the present model, interaction of dyes with the surface is not taken into account. Nevertheless, fitting of the data with the model represented by equation 6 gives reasonable parameter estimates.

In order to experimentally verify the model given by equation 6, TIR-FCS measurements for three different core diameters (37.5μm, 50μm and 100μm) were performed on diffusing fluorescein. A solution of 50 nM fluorescein in buffer (TRIS, pH 8) was used for these experiments. The results for three typical measurements over 100 s measurement time are shown in Table 1.

Table 1. Parameter estimates for measurements with different pinhole diameters. pd: diameter of the pinhole. D: diffusion coefficient. ωt : theoretically obtained structure parameter. For other symbols refer to the discussion of equation 6. The parameter τ t was fixed to 1μs.

View Table

The diffusion coefficients in Table 1 were calculated from the estimated value of τ_z, using the relation D = h ²/4τ_z. The value of h was estimated from the numerical calculations of the MDE to be 64 nm. Values for the structure parameter,ω, that were derived from the data, are in excellent agreement with valuesω_t , that were obtained from the numerically calculated MDEs. Also values for D coincide to a satisfactory degree with values previously published [23]. For a pinhole diameter of 100μm, the MDE function is not well approximated by equation 5, which explains the deviations of the values τ_z and D in this case. However, these values are all in the same range, which is to be expected, because changing the pinhole diameter should only marginally change the axial extent of the MDE.

6. Conclusion

By adapting an objective-type TIRF setup for FCS measurements, a very sensitive system is obtained. High counts per molecule (cpm) are achieved due to the good light collection efficiency inherent to this system. A small observation volume decreases background and measurement artifacts. The signal to background ratio is excellent, as can be inferred from intensity time traces of single molecules adsorbing to a glass slide, or more indirectly from TIR-FCS measurements. Numerical calculations of the observation volume are in good agreement with experimental TIR-FCS data, obtained for freely diffusing fluorophores. In particular, the diffusion coefficient and structure parameters derived from experimental data are in good agreement with reported and theoretical values. The system allows for simultaneous parallel TIRF imaging by simply connecting a camera to a second port of the microscope. All these features, in addition easy handling and excellent stability, make the proposed set-up perfectly suitable for surface FCS measurements on a single molecule level.