Time-Integrated Fluorescence Cumulant Analysis in Fluorescence Fluctuation Spectroscopy

¹ University of Minnesota

^* To whom correspondence should be addressed. E-mail: binwu{at}physics.umn.edu.

Submitted on March 28, 2005
Revised on May 15, 2005
Accepted on 27 June 2005

	Abstract

We introduce a new analysis technique for fluorescence fluctuation data. Time-integrated fluorescence cumulant analysis (TIFCA) extracts information from the cumulants of the integrated fluorescence intensity. TIFCA builds on our earlier FCA theory, but in contrast to FCA or photon counting histogram (PCH) analysis is valid for arbitrary sampling times. The motivation for long sampling times lies in the improvement of the signal-to-noise of the data. Because FCA and PCH theory are not valid in this regime, we first derive a theoretical model of cumulant functions for arbitrary sampling times. TIFCA is the first exact theory that describes the effects of sampling time on fluorescence fluctuation experiments. We calculate factorial cumulants of the photon counts for various sampling times by rebinning of the original data. Fits of the data to models determine the brightness, the occupation number, and the diffusion time of each species. In order to provide the tools for a rigorous error analysis of TIFCA, expressions for the variance of cumulants are developed and tested. We demonstrate that over a limited range rebinning reduces the relative error of higher order cumulants, and therefore improves the signal-to-noise ratio. The first four-cumulant functions are explicitly calculated and are applied to simple dye systems to test the validity of TIFCA and demonstrate its ability to resolve species.

Key Words: Cumulant, Fluorescence Fluctuation Spectroscopy, Photon Counting Histogram, Photon Statistics, Single molecule spectroscopy, Two-photon spectroscopy

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