The residence probability: Single molecule fluorescence correlation spectroscopy and reversible geminate recombination

Noam Agmon*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

The residence probability of a freely diffusing particle within an open d-dimensional ball is calculated as a function of time, for an initial distribution that is either a spherical delta function or uniform within the sphere. The latter is equivalent to the autocorrelation function (ACF) of fluorescence correlation spectroscopy (FCS) when utilizing near-field scanning optical microscopy (NSOM) probes. Starting from the general equation for the Laplace transform of the residence probability, we solve it in Laplace space for any dimensionality, inverting it into the time domain in one- and three-dimensions. The short- and long-time asymptotic behaviors of the residence probability are derived and compared with the exact results. Approximations for the two-dimensional ACF are discussed, and a new approximation is derived for the NSOM-FCS ACF. Also of interest is an analytic expression for a three-dimensional ACF, which could be useful for two-photon FCS. Analogy with the binding probability for reversible geminate recombination suggests that more information could be extracted from the long-time tails in FCS experiments.

Original languageEnglish
Pages (from-to)16548-16557
Number of pages10
JournalPhysical Chemistry Chemical Physics
Volume13
Issue number37
DOIs
StatePublished - 7 Oct 2011

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