Processive molecular motors, such as kinesin, myosin, or dynein, convert chemical energy into mechanical energy by hydrolyzing ATP. The mechanical energy is used for moving in discrete steps along the cytoskeleton and carrying a molecular load. Single-molecule recordings of motor position along a substrate polymer appear as a stochastic staircase. Recordings of other single molecules, such as F1-ATPase, RNA polymerase, or topoisomerase, have the same appearance. We present a maximum likelihood algorithm that extracts the dwell time sequence from noisy data, and estimates state transition probabilities and the distribution of the motor step size. The algorithm can handle models with uniform or alternating step sizes, and reversible or irreversible kinetics. A periodic Markov model describes the repetitive chemistry of the motor, and a Kalman filter allows one to include models with variable step size and to correct for baseline drift. The data are optimized recursively and globally over single or multiple data sets, making the results objective over the full scale of the data. Local binary algorithms, such as the t-test, do not represent the behavior of the whole data set. Our method is model-based, and allows rapid testing of different models by comparing the likelihood scores. From data obtained with current technology, steps as small as 8 nm can be resolved and analyzed with our method. The kinetic consequences of the extracted dwell sequence can be further analyzed in detail. We show results from analyzing simulated and experimental kinesin and myosin motor data. The algorithm is implemented in the free QuB software.
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