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, , generates the off periods of a two-state trajectory, a reliable recovery of the input α τ φ φ ) / ( 0 ) ( t off e t − = ) (t off φ 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. Introduction Advances in single molecule experimental techniques allow studying at room temperature the dynamics of a large number of processes in real time. Examples include the flux of ions through individual channels [1], conformational fluctuations of biopolymers [2-5], and kinetics of single enzymes [6-9]. The aim of such sophisticated measurements is to learn about the underlying mechanism of the process to an extent that is unattainable from bulk measurements due to averaging. In the simple scenario, the first step in the analysis of the data turns it into a trajectory of on and off periods (waiting times), FIG 1A. A frequently used assumption describes the mechanism of the observed process by a multi-substate on-off Markovian kinetic scheme (KS) [10-17], Fig. 1B; see also [18-21] for other model types. Using statistical tools of data analysis [22-26], one wishes to learn as much as possible about the underlying KS.