Analysis of kinetics in noisy systems: application to single molecule tethered particle motion

In the tethered particle motion method the length of a DNA molecule is monitored by measuring the range of diffusion of a microsphere tethered to the surface of a microscope coverslip through the DNA molecule itself. Looping of DNA (induced by binding of a specific protein) can be detected with this method and the kinetics of the looping/unlooping processes can be measured at the single molecule level. The microsphere's position variance represents the experimental variable reporting on the polymer length. Therefore, data windowing is required to obtain position variance from raw position data. Due to the characteristic diffusion time of the microsphere, the low-pass filtering required to attain a good signal/noise ratio (S/N) in the discrimination of looped versus unlooped state impacts significantly the measurement's time resolution. Here we present a method for measuring lifetimes based on half-amplitude thresholding and then correcting the kinetic measurements, taking into account low S/N (leading to false events) and limited time resolution (leading to missed events). This method allows an accurate and unbiased estimation of the kinetic parameters under investigation, independently of the choice of the window used for variance calculation, with potential applications to other single molecule measurements with low S/N.