Fluorescence detection of single molecules near a solution/glass interface – an electrodynamic analysis
Introduction
In Ref. [1], Xu and Yeung reported their experiments on the fluorescence detection of single dye-labeled proteins diffusing in an aqueous solution near a surface of fused silica. Their experimental arrangement is schematically depicted in Fig. 1: the fluorescence was excited by the evanescent light of a (decoherent) light beam that was reflected at the solution/glass interface by total internal reflection. Fluorescence detection was achieved from above by a high-speed intensified charge-coupled device camera (ICCD) imaging the light that was collected by a microscope objective (numerical aperture 1.3) and passed through emission filters. The sampling time of one ICCD image was ∼0.4 ms. Because the ICCD was an integrating single-photon detector, the recorded spot sizes traced out the random-walk motion of the single molecules within the exposure time for molecules inside the excitation region.
The main concern of the paper of Xu and Yeung was to gain information about the spatial distribution of molecules in solution above the fused silica surface. Although these authors did not explicitly do so in their paper, it should be possible, by relating momentary fluorescence intensities of the different detected molecules to distance, to deduce a distance distribution of these molecules. Within their paper, Xu and Yeung made the statement that
However, when deriving the correct relationship between fluorescence intensity and distance, one has to take into account not only the spatial profile of the excitation but also that the fluorescence emission of single molecules near the solution/glass interface differs significantly from that of molecules in bulk solution. This leads to a dependence of the detected fluorescence intensity upon molecule/surface distance that is not simply exponential.… as molecules approach a solid surface from solution, the excitation intensity, and thus the fluorescence intensity, should increase exponentially (by a factor of 2.718 from the surface out to 180 nm) …
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Theory and results
To determine the apparent fluorescence intensity of a fluorescing molecule as seen by the objective, two processes have to be considered: the absorption of a photon from the exciting light, and the fluorescence emission of a photon by the excited molecule. The photon absorption rate ka of a molecule at a distance z0 away from the glass surface and absorption dipole orientation â is proportional to the square of the exciting electric field component along â at the molecule's position. For an
Acknowledgements
I thank Martin Böhmer and Thomas Ruckstuhl for many inspiring discussions. I am grateful to Richard Ansell for his linguistic support.
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