Mean fluorescence lifetime and its error Eva Fiˇ serova ´ a,1 , Martin Kubala b,n,1 a Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacky University in Olomouc, tr. 17. listopadu 12, CZE-77146 Olomouc, Czech Republic b Department of Biophysics, Faculty of Science, Palacky University in Olomouc, tr. 17. listopadu 12, CZE-77146 Olomouc, Czech Republic article info Article history: Received 24 November 2011 Received in revised form 2 March 2012 Accepted 8 March 2012 Available online 18 March 2012 Keywords: Fluorescence Mean lifetime Error Confidence interval TCSPC Histogram abstract Mean excited-state lifetime is one of the fundamental fluorescence characteristics and enters as an important parameter into numerous calculations characterizing molecular interactions, such as e.g. FRET or fluorescence quenching. Our experiments demonstrated that the intensity-weighted mean fluorescence lifetime is very robust characteristic, in contrast to the amplitude-weighted one, which value is dependent on the data quality and particularly on the used fitting model. For the first time, we also report the procedure for the error estimation for both the intensity- and amplitude-weighted mean fluorescence lifetimes. Furthermore, we present a method for estimation of the mean fluorescence lifetime directly from the fluorescence-decay curve recorded by TCSPC (Time-Correlated Single-Photon Counting) method. For its simplicity and low computational demands, it could be a useful tool in the high-throughput applications, such as FACS, FLIM-FRET or HPLC detectors. & 2012 Elsevier B.V. All rights reserved. 1. Introduction Due to the extreme sensitivity, non-invasivity and availability of wide range of techniques, fluorescence spectroscopy became a very useful tool for monitoring of molecular features and inter- actions in modern biology. However, the fluorescence intensity, which is the easiest-to-get characteristic, is also the least repro- ducible one, because its value is dependent on the instrument setup (and consequently on the instrument stability) or precise knowledge of the fluorophore concentration. The latter becomes important in applications, which are based on the comparison of the fluorescence from two samples, e.g. FRET (F ¨ orster Resonance Energy Transfer), where one compares the fluorescence of a donor in the absence or the presence of an acceptor. Unfortunately, in many samples the information about the concentration is esti- mated with an error, which largely exceeds an error of spectro- scopic measurement, in some cases it is even unavailable (e.g. in microscopy). For these reasons, fluorescence characteristics that are independent on the fluorophore concentration are preferable. Kinetic of the fluorescence decay is independent on the fluor- ophore concentration, and its measurement has been implemented also in fluorescence microscopes (FLIM—Fluorescence Lifetime IMaging, or FLIM-FRET—Fluorescence Lifetime IMaging used for monitoring of F ¨ orster Resonance Energy Transfer) [1], flow-cyt- ometers [2] or chromatography detectors [3]. Although it is not straightforward to interpret fluorescence kinetic parameters they are used in more complex calculations of molecular features. For example, in the dynamic fluorescence quenching the fluorescence lifetime delimits the time-window, within which the collisions between the fluorophore and quencher molecules cause effective fluorescence quenching. Hence, the parameter, which can be used for calculation of diffusion coefficients [4] or fluorophore steric accessibility [5] is given by k Q ¼ K SV =t 0 , ð1Þ where K SV is the well-known Stern–Volmer quenching constant, t 0 is the fluorescence lifetime in the absence of the quencher and k Q is denoted as bimolecular quenching constant. Similarly, in FRET experiments the formula E ¼ 1t DA =t D , ð2Þ where t DA denotes the donor fluorescence lifetime in the presence of acceptor and t D the lifetime in its absence, is used for estimation of the energy transfer efficiency (E), which is further used for the calculation of the donor–acceptor distance [6]. In the simplest case, the fluorescence decay of a homogenous population of single fluorophore following the d-pulse excitation can be described by an exponential function. However, many commonly used organic fluorophores [7], fluorescent proteins [1] or semiconductor quantum dots [8] display more complex kinetic Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/jlumin Journal of Luminescence 0022-2313/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jlumin.2012.03.038 n Corresponding author. Tel.: þ420 585634179; fax: þ420 585634002. E-mail address: mkubala@prfnw.upol.cz (M. Kubala). 1 Both authors contributed equally to this work. Journal of Luminescence 132 (2012) 2059–2064