Accurate Drift-Invariant Single-Molecule Force Calibration Using the Hadamard Variance

Single-molecule force spectroscopy (SMFS) techniques play a pivotal role in unraveling the mechanics and conformational transitions of biological macromolecules under external forces. Among these techniques, multiplexed magnetic tweezers (MTs) are particularly well suited to probe very small forces, ≤1 pN, critical for studying non-covalent interactions and regulatory conformational changes at the single-molecule level. However, to apply and measure such small forces, a reliable and accurate force calibration procedure is crucial.

Here, we introduce a new approach to calibrate MTs based on thermal motion using the Hadamard variance (HV). To test our method, we develop a bead-tether Brownian dynamics simulation that mimics our experimental system and compare the performance of the HV method against two established techniques: power spectral density (PSD) and Allan variance (AV) analyses. Our analysis includes an assessment of each method’s ability to mitigate common sources of additive noise, such as white and pink noise, as well as drift, which often complicate experimental data analysis. Our findings demonstrate that the HV method exhibits overall similar or even higher precision and accuracy, yielding lower force estimation errors across a wide range of signal-to-noise ratios (SNR) and drift speeds compared to the PSD and AV methods. Notably, the HV method remains robust against drift, maintaining consistent uncertainty levels across the entire studied SNR and drift speed spectrum. We also explore the HV method using experimental MT data, where we find overall smaller force estimation errors compared to PSD and AV approaches.

Overall, the HV method offers a robust method for achieving sub-pN resolution and precision in multiplexed MT measurements. Its potential extends to other SMFS techniques, presenting exciting opportunities for advancing our understanding of mechano-sensitivity and force generation in biological systems. Therefore, we provide a well-documented Python implementation of the HV method as an extension to the Tweezepy package.

Statement of Significance

Single-molecule force spectroscopy techniques are vital for studying the mechanics and conformations of bio-macromolecules under external forces. Multiplexed magnetic tweezers (MTs) excel in applying forces ≤ 1 pN, which are critical for examining non-covalent interactions and regulatory changes at the single-molecule level. Precise and reliable force calibration is essential for these measurements. In this study, we present a new force calibration method for multiplexed MTs using Hadamard variance (HV) based on thermal motion. The HV method shows similar or even higher precision and accuracy to established techniques like power spectral density and Allan variance. Most significantly, it is drift-invariant, maintaining consistent performance across varying experimental conditions. This robustness against drift ensures reliable force application and measurements at sub-pN resolution.