Step Measurement - Theory and Simulation for Tethered Bead Constant-Force Single Molecule Assay

¹ University of Helsinki

^* To whom correspondence should be addressed. E-mail: anders.wallin{at}helsinki.fi.

Submitted on September 21, 2006
Revised on December 6, 2006
Accepted on 11 April 2007

	Abstract

Linear molecular motors translocate along polymeric tracks using discrete steps. The step length is usually measured using constant-force single molecule experiments in which the polymer is tethered to a force-clamped microsphere. During the enzymatic cycle the motor shortens the tether contour length. Experimental conditions influence the achievable step length resolution, and ideally experiments should be conducted with high clamp-force using slow motors linked to small beads via stiff short tethers. We focus on the limitations that the polymer track flexibility, the thermal motion of the microsphere, and the motor kinetics pose for step length measurement in a typical optical tweezers experiment. An expression for the signal-to-noise ratio in a constant-force, worm-like chain tethered particle, single molecule experiment is developed. The signal-to-noise ratio is related to the Fourier transform of the pair-wise distance distribution, commonly used to determine step length from a time-series. Monte Carlo simulations verify the proposed theory for experimental parameter values typically encountered with molecular motors (polymerases and helicases) translocating along single- or double-stranded nucleic acids. The predictions are consistent with recent experimental results for double-stranded DNA tethers. Our results map favorable experimental conditions for observing single motor steps on various substrates but indicate that principal resolution limits are set by thermal fluctuations.

Key Words: molecular motor, optical tweezers, single molecule experiment, step detection, thermal noise, worm-like chain