Correctly validating results from single molecule data: The case of stretched exponential decay in the catalytic activity of single lipase B molecules

The question of how to validate and interpret correctly the waiting time probability density functions (WT-PDFs) from single molecule data is addressed. It is shown by simulation that when a stretched exponential WT-PDF, φ{symbol}_off (t) = φ{symbol}₀ e^{- (t / τα}, generates the off periods of a two-state trajectory, a reliable recovery of the input φ{symbol}_off(t) from the trajectory is obtained even when the bin size used to define the trajectory, dt, is much larger than the parameter τ. This holds true as long as the first moment of the WT-PDF is much larger than dt. Our results validate the results in an earlier study of the activity of single lipase B molecules and disprove recent related critique.