Statistics of Molecular Ensemble Blinking Fluorescence

Abstract

Fluorescence of M noninteracting molecules, each of which exhibits blinking fluorescence with on- and off-intervals, is considered. Theoretical expressions suitable for statistical analysis of fluorescence of M molecules are derived. The derivation of (i) the distribution functions Pon,off(t) for on- and off-interval duration, (ii) the distribution function wN(t) for the number N of photons emitted at a time interval t, and (iii) the fluorescence autocorrelation function g(2)(t) is carried out with the help of the formulas previously derived for single molecule blinking fluorescence. The statistical treatment of intensity fluctuations in fluorescence of several molecules is carried out to find the three types of the above-mentioned functions. The coincidence of the functions “measured” in blinking fluorescence and those calculated with the help of the theoretical formulas derived proves the validity of the latter.