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Confining the sampling volume for Fluorescence Correlation Spectroscopy using a sub-wavelength sized aperture

Marcel Leutenegger, Michael Gösch, Alexandre Perentes, Patrik Hoffmann, Olivier J.F. Martin, and Theo Lasser

Open Access Open Access

Abstract

For the observation of single molecule dynamics with fluorescence fluctuation spectroscopy (FFS) very low fluorophore concentrations are necessary. For in vitro measurements, this requirement is easy to fulfill. In biology however, micromolar concentrations are often encountered and may pose a real challenge to conventional FFS methods based on confocal instrumentation. We show a higher confinement of the sampling volume in the near-field of sub-wavelength sized apertures in a thin gold film. The gold apertures have been measured and characterized with fluorescence correlation spectroscopy (FCS), indicating light confinement beyond the far-field diffraction limit. We measured a reduction of the effective sampling volume by an order of magnitude compared to confocal instrumentation.

©2006 Optical Society of America

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Figures (11)
Fig. 1.
Fig. 1. Left: SEM image of a 420 nm aperture after evaporation of the 150 nm thick gold film. We noticed small gold particles around the aperture edge. Nanoscale particles and fibers were also found at the border of the gold cap. Right: SEM image of a single 230 nm aperture within a 6×6 array. This aperture was exempt of nearby gold particles.

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Fig. 2.
Fig. 2. Mask layout with orientation triangles and aperture arrays. Every square represents an array with 6×6 apertures of identical diameter. In each array, the apertures are located on a square grid with 5 μm period. We selected 21 array pairs in order to cover aperture diameters between 115 nm and 520 nm. Inset: Trans-illumination image and scheme of an array pair with 2×6×6 apertures of 300 nm diameter in the 150 nm gold film. The central apertures in the selected arrays were measured with FCS.

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Fig. 3.
Fig. 3. Confocal trans-illumination setup. The 40x0.9 objective and the multimode fiber were mounted on xyz-translation stages. The aperture mask was aligned with a piezo xyz-translation stage.

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Fig. 4.
Fig. 4. Simulated excitation fields for aperture diameters of 150 nm (left), 250 nm (center) and 400 nm (right) in a gold film of thickness h = 150 nm. All dimensions are given in nanometers. The coordinate origins are located in the center at the bottom of each aperture. A Gaussian beam with 633 nm wavelength was focused with an opening angle equivalent to a numerical aperture of 0.6 on the apertures. The graphs show three surfaces of equal intensity at e -1 Imax (inner surfaces), e -1.5 Imax (middle surfaces) and e -2 Imax (outer surfaces). Imax is the maximal excitation intensity at z = h. On top of the apertures, the average intensity was reduced to 22%, 73% respectively 87% of the incident intensity at the bottom.

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Fig. 5.
Fig. 5. Afterpulsing corrected auto-correlations G (τ) versus lag time τ for aperture diameters of 125 nm, 230 nm, 340 nm and 490 nm at a Cy5 concentration of 12 nM. The correlation amplitude for the 490 nm aperture was multiplied by 3. For the 125 nm and the 230 nm aperture, the correlation amplitudes show a different slope for delays between 0.1 ms and 1 ms. We interpret this as constrained diffusion of molecules entering into the 150 nm deep aperture.

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Fig. 6.
Fig. 6. Auto-correlations and fits G (τ) versus lag time τ for aperture diameters of 125 nm (blue circles), 490 nm (red points) and for free liquid (black dotted) at a Cy5 concentration of 30 nM. Inset: Fit residuals r (τ) = Gfit /G (τ) - 1.

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Fig. 7.
Fig. 7. Auto-correlations G (τ) versus lag time τ measured on a 125 nm aperture at a Cy5 concentration of 12 nM. The blue dotted line is the measured auto-correlation. The solid line shows the afterpulsing corrected amplitude. The circles trace a second measurement on the same aperture. Inset: intensity trace.

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Fig. 8.
Fig. 8. Diffusion time τd versus aperture diameter d. The data points show the average and the error bars the standard deviation of 10 measurements per aperture diameter. For clarity, the standard deviation is shown for one case only (12 nM Cy5, 50 μm pinhole). The black dotted line was calculated with Eq. (6) for τ ∞ = 240 μs and dτ = 450 nm. In free liquid, the diffusion time was 160 μs to 170 μs. Inset: concentration of Cy5 and pinhole diameter of all cases.

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Fig. 9.
Fig. 9. Number of molecules N versus aperture diameter d for a Cy5 concentration of 30 nM and a 50 μm pinhole. The data points show the average and the error bars the standard deviation of 10 measurements per aperture diameter. The dotted line is for guiding the eyes. In free liquid, we measured about 72 molecules in the confocal volume.

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Fig. 10.
Fig. 10. Background count rates IB , mean intensity 〈I〉 and SNR = 〈I〉/IB - 1 versus aperture diameter d for a Cy5 concentration of 30 nM and a 50 μm pinhole. The data points show the average and the error bars the standard deviation of 10 measurements per aperture diameter. In free liquid, we measured an intensity of 4.7 MHz and a background of 6 kHz.

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Fig. 11.
Fig. 11. Background corrected count rate per molecule CPM versus aperture diameter d for a Cy5 concentration of 30 nM and a 50 μm pinhole. The data points show the average and the error bars the standard deviation of 10 measurements per aperture diameter. The dotted line is for guiding the eyes. In free liquid, we obtained a CPM ≈ 65 kHz for this experiment.

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Tables (1)

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Table 1. Calculated extensions of the excitation fields along the x,y and z axes, respectively excitation volumes Vex = W 1 + Vap and effective sampling volumes Veff = W 2 1/W 2 + Vap for different aperture diameters d. The extensions are understood as e -2 “half-axes” for comparison with the e -2 xy-waist w 0 = 350 nm of the incident beam.

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Equations (7)

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G ( τ ) = 〈 I ( t ) I ( t + τ ) 〉 〈 I ( t ) 〉 〈 I ( t + τ ) 〉 = ( T − τ ) ∫ 0 T − τ I ( t ) I ( t + τ ) d t ∫ 0 T − τ I ( t ) d t ∫ τ T I ( t ) d t
W n = I max − n ∫ ∫ ∫ I ( r → ) n d r →
k z 2 = k 2 − k xy 2
G ( τ ) = G ∞ + ( 1 − I B 〈 I 〉 ) 2 γ N { ( 1 + τ τ d ) − 1 ( 1 + τ K 2 τ d ) − 1 2 + P t 1 − P t exp ( − τ τ t ) }
G ap ( τ ) = 〈 ( G uc ( τ ) − 1 ) 〈 I uc ( t ) 〉 1.02 〉
τ d ≈ τ ∞ d 2 d τ 2 + d 2
N = C N A V eff
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