Tweezepy: A Python package for calibrating forces in single-molecule video-tracking experiments.

Ian L Morgan,Omar A Saleh,Kerstin G Blank

doi:10.1371/journal.pone.0262028

Abstract

Single-molecule force spectroscopy (SMFS) instruments (e.g., magnetic and optical tweezers) often use video tracking to measure the three-dimensional position of micron-scale beads under an applied force. The force in these experiments is calibrated by comparing the bead trajectory to a thermal motion-based model with the drag coefficient, γ, and trap spring constant, κ, as parameters. Estimating accurate parameters is complicated by systematic biases from spectral distortions, the camera exposure time, parasitic noise, and least-squares fitting methods. However, while robust calibration methods exist that correct for these biases, they are not always used because they can be complex to implement computationally. To address this barrier, we present Tweezepy: a Python package for calibrating forces in SMFS video-tracking experiments. Tweezepy uses maximum likelihood estimation (MLE) to estimate parameters and their uncertainties from a single bead trajectory via the power spectral density (PSD) and Allan variance (AV). It is well-documented, fast, easy to use, and accounts for most common sources of biases in SMFS video-tracking experiments. Here, we provide a comprehensive overview of Tweezepy's calibration scheme, including a review of the theory underlying thermal motion-based parameter estimates, a discussion of the PSD, AV, and MLE, and an explanation of their implementation.

Highlights

Single-molecule force spectroscopy (SMFS) instruments are powerful tools with a wide variety of experimental applications
Most force calibration methods fall into two categories: methods that calibrate against known forces, such as Stokes drag or sedimentation [29], and methods that calibrate based on the thermal motion of the bead [9]
We find that fixing γ with the power spectral density (PSD) and Allan variance (AV) removes the increase in the error and slight bias for κ at high corner frequencies (Fig 5C and 5D)

Summary

Introduction

Single-molecule force spectroscopy (SMFS) instruments are powerful tools with a wide variety of experimental applications. Force calibration relies on comparing the thermal motion of a trapped bead to a model derived from the Langevin equation [9] These methods have limitations; notably, at times, t ≲ 10−4 s, the standard Langevin equation does not account for certain. Thermal motion-based calibration methods are advantageous because they only rely on the temperature of the system, which is much easier to measure and control in most experiments. These methods model the trap as a harmonic potential in which the bead undergoes random, diffusive motion (Fig 1B–1D). The spring constant of the trap can be related to the standard variance of the bead position, s2x: s2x

Objectives

Results

Conclusion