Photochemistry and Photobiology, zyxwvuts 1998, zyxwvut 67(5): 475-486 The Correct Use of “Average” Fluorescence Parameters Alain Sillen and Yves Engelborghs* Laboratory of Chemical and Biological Dynamics, Katholieke Universiteit Leuven, Leuven, Belgium Received 11 August 1997; accepted 16 January 1998 ABSTRACT zyxwvutsr When more than one fluorophore is present or when one fluorophore displays a multiple exponential decay “av- erage” fluorescence parameters are derived, which can be combined with “average” lifetimes for further inter- pretation. However, two kinds of average lifetimes are used in this context: the intensity and the amplitude av- erage lifetime. In this paper the different average param- eters are carefully analyzed and their “best” combina- tions are derived. These average parameters are ana- lyzed in the context of external and internal dynamic and static quenching, Foster energy transfer and the calcu- lation of the radiative rate constant. The use of the am- plitude average lifetime for the analysis of multiple fluo- rophore-containing systems and the detection of inter- actions is discussed. INTRODUCTION zyxwvutsr Fluorescence measurements are important tools for the anal- ysis of biological systems as shown by an increasing number of applications. The correct use of the fluorescence param- eters is essential for the understanding of their relevance for the biological system under investigation. The theory of fluo- rescence parameters is well developed for the monoexpo- nential decay of fluorescence. In this case simple equations have been derived that describe situations as dynamic and static quenching, fluorescence energy transfer and its dis- tance dependency and radiative and nonradiative processes. However, in biological systems the situation is usually more complicated. The fluorescence decay is almost always mul- tiexponential, due to heterogeneity of the fluorophores or of their environment. Very often the fluorescence of heteroge- neous systems is analyzed in the same way as a simple sys- tem, At a first glance this seems to be justified because the complex fluorescence behavior of the system can be de- scribed by an average fluorescence lifetime. However, this is not always true. Moreover, two different types of average lifetimes can be calculated (the amplitude and the intensity average lifetime). In this manuscript we analyze the meaning of the different *Author to whom correspondence should be addressed at: Labora- tory of Chemical and Biological Dynamics, Katholieke Univer- siteit Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. Fax: 32-16-327982; e-mail: yves.engelborghs@fys.kuleuven.ac.be zyxwvuts 0 1998 American Society for Photobiology zyxwvutsrqp 0031-8655/98 zyxwvutsrqpo $5.00+0.00 parameters obtained by using these average lifetimes, and we indicate which lifetime is to be used dependent on the situation to be analyzed. When studying dynamic quenching, using an externally added quencher, we show that the use of the amplitude av- erage lifetime leads to a linear Stern-Volmer plot at low quencher concentrations, and the average collisional quench- ing constant zyxwvu (k,) reflects closely the kq of the major com- ponent. A decrease of the amplitude average lifetime upon quenching is usually attributed to dynamic quenching. How- ever, for a heterogeneous system, the amplitude average life- time can also be changed by static quenching. This is the case when the static quenching is selective for some of the components of the heterogeneous system and changes the amplitude ratio. This situation can only be identified by the inspection of the individual lifetimes and amplitude frac- tions. In analyzing heterogeneous fluorescence in the ab- sence of lifetime data one has to be aware of this. For the calculation of the average radiative rate constant (kr) only the amplitude average lifetime can be used. It should be noted, however, that in a heterogeneous system the value of k, can be underestimated by the presence of static quenching. The amplitude average lifetime is also a very useful tool in the analysis of interactions between fluorophores, e.g. the different tryptophan residues within a protein. The amplitude average lifetime of a multitryptophan protein is identical to the amplitude average lifetime calculated from the lifetime data of the individual tryptophan residues, provided no en- ergy transfer occurs. If energy transfer does occur between a pair of tryptophan residues, this pair can be identified. DEFINITIONS Multiexponential fluorescence decay F(t,X) is described as a function of time (t) and wavelength (A) by the following equation: F(t,X) = I(X)z a,(k)exp(-t/T,) (1) where I(X) is the total amplitude, a,(X) are the amplitude fractions and T, are the fluorescence lifetimes. Fluorescence lifetime analysis gives only the amplitude fractions, because I(h) is normalized. On measuring fluorescence lifetimes it is possible to calculate different average lifetimes, the two most commonly used are the intensity average lifetime and the amplitude average lifetime. Intensity average lifetime. Because the fluorescence intensity con- tribution of a component is proportional to the product a?, the in- tensity average lifetime is defined as (T)~ = z a,T,%a,T,. The intensity average lifetime is the average amount of time a fluorophore spends in the excited state (1). This average is given by 475