Evaluation of Exponential Distributions Measured from Single Fluorescent Molecules

Abstract

Characterizing a Poisson process is very important in biology, because most of the underlying processes are influenced by finite on- and off-rates. However, accessing the complete distribution often proves difficult due to limitations in time and spatial resolution. Additionally, the experimental setup often introduces systematic errors, which require correction. Here, we use numerical simulations to estimate the statistical and systematic errors that commonly occur when evaluating exponential distributions obtained from measurements. With regard to measurements on the stepping of fluorescently-labeled motor proteins on cytoskeletal filaments, we additionally test methods to correct for photobleaching and the limited lengths of the filaments. Results of the simulations are compared to experimental data on kinesin-1 motors walking along microtubules. Our work will not only improve the error estimation for experimental data, but will also allow for better statistical comparison of two or more populations of motor proteins (e.g. motors with distinct mutations or motors linked to different cargos).