Quantifying the Resolution of Single-Molecule Torque Measurements by Allan Variance

Abstract

Single-molecule manipulation techniques have provided unprecedented insights into the structure, function, interactions, and mechanical properties of biological macromolecules. While many single-molecule manipulation techniques naturally operate in the space of (linear) extension and force, recently a number of techniques have been developed that enable measurements of rotation angle and torque. Examples include the rotor bead tracking assay, the optical torque wrench (OTW), and magnetic torque tweezers (MTT). While systematic analyses of the position and force resolution of single-molecule techniques have attracted considerable attention (see e.g. [1,2]), detailed analysis of the angle and torque resolution is currently lacking.Here, we propose Allan variance as a criterion to systematically quantitate the angle and torque resolution in single-molecule measurements. We apply the Allan variance method to experimental data from our implementations of MTT [3,4,5] and an OTW [6]. Both magnetic and optical torque tweezers can achieve a torque resolution of better or equal to 1 pN⋅nm. We find that our state-of-the-art OTW outperforms MTT for short measurement times. However, for measurement times > 10 s, drift becomes a limiting factor in the OTW and the superior stability of MTT accomplishes higher ultimate torque resolution for long measurement times.In summary, our Allan variance criterion enables to critically assess the torque resolution as a function of measurement time and across different measurement modalities that rely on distinct physical principles. In addition, the Allan variance method provides a tool to optimize the measurement protocol for a given instrument and system.[1] Czerwinski, et al., Opt. Express (2009).[2] Lansdorp & Saleh, Rev. Sci. Instrum. (2012).[3] Lipfert, et al., Nature Methods (2010).[4] Lipfert, Wiggin, et al., Nature Communications (2011).[5] Janssen, Lipfert, et al., Nano Letters (2012).[6] Pedaci, et al. Nature Physics (2010).