  Tethered particle experiments use light microscopy to measure the position of
a micrometer-sized bead tethered to a microscope slide via a ~micrometer length
polymer, in order to infer the behavior of the invisible polymer. Currently,
this method is used to measure rate constants of DNA loop formation and
breakdown mediated by repressor protein that binds to the DNA. We report a new
technique for measuring these rates using a modified hidden Markov analysis
that directly incorporates the diffusive motion of the bead, which is an
inherent complication of tethered particle motion because it occurs on a time
scale between the sampling frequency and the looping time. We compare looping
lifetimes found with our method, which are consistent over a range of sampling
frequencies, to those obtained via the traditional threshold-crossing analysis,
which vary depending on how the raw data are filtered in the time domain. Our
method does not involve such filtering, and so can detect short-lived looping
events and sudden changes in looping behavior.
