Background: When modeling single-molecule fluorescence lifetime experimental data, the analysis often involves fitting a biexponential distribution to binned data. When dealing with small sample sizes, there is the potential for convergence failure in numerical optimization, for convergence to local optima resulting in physically unreasonable parameter estimates, and also for overfitting the data.
Results: To avoid the problems that arise in small sample sizes, we have developed a gamma conversion method to estimate the lifetime components. The key idea is to use a gamma distribution for initial numerical optimization and then convert the gamma parameters to biexponential ones via moment matching. A simulation study is undertaken with 30 unique configurations of parameter values. We also performed the same analysis on data obtained from a fluorescence lifetime experiment using the fluorophore Cy3. In both the simulation study and the real data analysis, fitting the biexponential directly led to a large number of data sets whose estimates were physically unreasonable, while using the gamma conversion yielded estimates consistently close to the true values.
Conclusions: Our analysis shows that using numerical optimization methods to fit the biexponential distribution directly can lead to failure to converge, convergence to physically unreasonable parameter estimates, and overfitting the data. The proposed gamma conversion method avoids these numerical difficulties, yielding better results.