Hidden-Markov Methods for the Analysis of Single-Molecule Actomyosin Displacement Data: The Variance-Hidden-Markov Method

Abstract

In single-molecule experiments on the interaction between myosin and actin, mechanical events are embedded in Brownian noise. Methods of detecting events have progressed from simple manual detection of shifts in the position record to threshold-based selection of intermittent periods of reduction in noise. However, none of these methods provides a "best fit" to the data. We have developed a Hidden-Markov algorithm that assumes a simple kinetic model for the actin-myosin interaction and provides automatic, threshold-free, maximum-likelihood detection of events. The method is developed for the case of a weakly trapped actin-bead dumbbell interacting with a stationary myosin molecule (Finer, J. T., R. M. Simmons, and J. A. Spudich. 1994. Nature. 368:113-119). The algorithm operates on the variance of bead position signals in a running window, and is tested using Monte Carlo simulations to formulate ways of determining the optimum window width. The working stroke is derived and corrected for actin-bead link compliance. With experimental data, we find that modulation of myosin binding by the helical structure of the actin filament complicates the determination of the working stroke; however, under conditions that produce a Gaussian distribution of bound levels (cf. Molloy, J. E., J. E. Burns, J. Kendrick-Jones, R. T. Tregear, and D. C. S. White. 1995. Nature. 378:209-212), four experiments gave working strokes in the range 5.4-6.3 nm for rabbit skeletal muscle myosin S1.