Statistics of single‐molecule measurements: Applications in flow‐cytometry sizing of DNA fragments

<jats:title>Abstract</jats:title><jats:sec><jats:title>Background</jats:title><jats:p>The measurement of physical properties from single molecules has been demonstrated. However, the majority of single‐molecule studies report values based on relatively large data sets (e.g., <jats:italic>N</jats:italic> > 50). While there are studies that report physical quantities based on small sample sets, there has not been a detailed statistical analysis relating sample size to the reliability of derived parameters.</jats:p></jats:sec><jats:sec><jats:title>Methods</jats:title><jats:p>Monte Carlo simulations and multinomial analysis, dependent on quantifiable experimental parameters, were used to determine the minimum number of single‐molecule measurements required to produce an accurate estimate of a population mean. Simulation results were applied to the fluorescence‐based sizing of DNA fragments by ultrasensitive flow cytometry (FCM).</jats:p></jats:sec><jats:sec><jats:title>Results</jats:title><jats:p>Our simulations show, for an analytical technique with a 10% CV, that the average of as few as five single‐molecule measurements would provide a mean value within one SD of the population mean. Additional simulations determined the number of measurements required to obtain the desired number of replicates for each subpopulation within a mixture. Application of these results to flow cytometry data for λ/<jats:italic>Hind</jats:italic>III and <jats:italic>S</jats:italic>. <jats:italic>aureus</jats:italic> Mu50/<jats:italic>Sma</jats:italic>I DNA digests produced accurate DNA fingerprints from as few as 98 single‐molecule measurements.</jats:p></jats:sec><jats:sec><jats:title>Conclusions</jats:title><jats:p>A surprisingly small number of single‐molecule measurements are required to obtain a mean measurement descriptive of a normally‐distributed parent population. © 2004 Wiley‐Liss, Inc.</jats:p></jats:sec>