Biochemical assays can identify potential protein–protein interactions in cell extracts, but studying these interactions in living cells is a more challenging task. The most promising approach for the measurement of molecular interaction dynamics exploits the energy transfer between fluorophores over short distances (Fluorescence Resonance Energy Transfer; FRET) (1). This transfer occurs only if both molecules are in close proximity to one another (typically less than 10 nm) (2).

Several strategies are used to obtain this measurement which are mainly based on fluorescence intensity (3), anisotropy (4), and lifetime (5) measurements. The latter is rather accurate, especially when using a Time Correlated Single Photon Counting (TCSPC) system (6) and an instrumental setup with a narrow Instrumental Response Function (IRF) (7). This spectroscopy technique can either be used for the measurement of fluorescence lifetime of selected areas or for the acquisition of complete images; in which case it is referred to as FLIM (Fluorescence lifetime imaging microscopy). TCSPC is an indirect method that allows determination of the fluorescence lifetime species by fitting measured photon decay curves using the following equation:

With “*b*” the background level, “IRF”, IRF of the acquisition system, “*i*” an index associated with each exponential, “*a*” the proportion of each component and “τ” the corresponding lifetime.

A mean fluorescence lifetime defined as in Eq. (2) is used to facilitate comparison between experiments (8),

With “*a*” the proportion and “τ” the lifetime of each fluorescent component.

In general, fluorescence lifetime analysis is performed based on the Least squares method relying on the iterative minimization of the χ^{2} parameter (9, 10). Parameters that according to Marquardt (11) describe the difference between the model and the measured data are:

and

With “*i*” the time channel, “*V*” the photon number, “*b*” the background, “IRF”, IRF of our system, “*j*” an index associated with each exponential, “*a*” the proportion of each component and “τ” the corresponding lifetime.

Using a least squares based fit procedure implies the choice of the fluorescence species used in Eq. (1). This choice is usually achieved based on the fit curve residual distribution.

To accurately calculate the fluorescence lifetime, the choice of “*n”* in Eq. (1) is essential as demonstrated in Figure 1. On one hand, a missing exponential term leads to an overestimation of fluorescence lifetime (Fig. 1A). On the other hand, an overestimation of the model's degree of freedom, i.e. exponential terms results in instability of the fitting algorithm (12), and so, in higher dispersion of estimated lifetimes (Fig. 1B). The Occam's or Ockham's razor (13), also referred to as parsimony law, states a preference for simple theories. Consequently, the fit model that describes the photon decay curve with the lowest number of exponentials is preferred.

The choice of the optimal fit model based on the residual statistics has a strong theoretical foundation in literature of both statistics and information theory fields (14, 15). However, the information that is crucial to apply this theory is not easily accessible from the FLIM analysis software. Moreover, it cannot be directly used for the generation of lifetime images.

In this article, we describe an easy-to-use analysis procedure based on the χ^{2} variation that allows for best model choice on a pixel-by-pixel basis. It uses information available in all FLIM analysis systems without complex modification of the fitting algorithm. We demonstrate its robustness throughout the analysis of series of simulated photons decay curves. We then show the improvement gained when applied to FRET investigation in living cells.