Analysis of single-molecule kinesin assay data by hidden Markov model filtering

Observations of the position of a microscopic bead attached to a single kinesin protein moving along a microtubule contains detailed information about the position of the kinesin as a function of time, although this information remains obscured because of the fluctuations of the bead. The theory of hidden Markov models suggests a possible theoretical framework to analyze these data with an explicit stochastic model describing the kinesin cycle and the attached bead. We model the mechanical cycle of kinesin using a discrete time Markov chain on a periodic lattice, representing the microtubule, and model the position of the bead using an Ornstein-Uhlenbeck autoregressive process. We adapt the standard machinery of hidden Markov models to derive the likelihood of this model using a reference measure, and use the Expectation-Maximization (EM) algorithm to estimate model parameters. Simulated data sets indicate that the method does have potential to better analyze kinesin-bead experiments. However, analysis of the experimental data of Visscher et al. (1999) indicates that current data sets still lack the time resolution to extract significant information about intermediate states. Considerations for future experimental designs are suggested to allow better hidden Markov model analysis.