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* School of Chemistry, Raymond & Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel; and
Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892
Correspondence: Address reprint requests to Ophir Flomenbom, E-mail: flomenbo{at}post.tau.ac.il.
A time trajectory of an observable that fluctuates between two values (say, on and off), stemming from some unknown multisubstate kinetic scheme, is the output of many single-molecule experiments. Here we show that when all successive waiting times along the trajectory are uncorrelated the on and the off waiting time probability density functions contain all the information. By relating the lack of correlation in the trajectory to the topology of kinetic schemes, we can immediately specify those kinetic schemes that are equally consistent with experiment, and cannot be differentiated by any sophisticated analyses of the trajectory. Correlated trajectories, however, contain additional information about the underlying kinetic scheme, and we consider the strategy that one should use to extract it.
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