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Updated: May 24, 2026
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Automated Two-dimensional Spatiotemporal Analysis of Mobile Single-molecule FRET Probes
Published on: November 23, 2021
Power spectrum and Allan variance methods for calibrating single-molecule video-tracking instruments.
1Materials Department, University of California Santa Barbara, Santa Barbara, California 93106, USA.
The Review of Scientific Instruments
|March 3, 2012
Summary
We present new methods to precisely calibrate single-molecule instruments, extracting probe drag (α) and spring constant (κ) from Brownian motion. The Allan variance (AV) method offers a simpler, more robust approach for accurate calibration.
Area of Science:
- Biophysics
- Single-molecule manipulation
- Instrument calibration
Background:
- Optical traps and magnetic tweezers use video tracking for probe position measurement.
- Calibration relies on modeling Brownian motion to estimate probe drag (α) and spring constant (κ).
Purpose of the Study:
- To develop accurate and precise time- and frequency-domain methods for extracting α and κ.
- To compare the performance of different calibration techniques.
Main Methods:
- Frequency-domain analysis: Estimating power spectral density (PSD) with windowing, blocking, and accounting for aliasing and video tracking filters.
- Time-domain analysis: Utilizing Allan variance (AV) with a theoretical equation and optimal computation using octave-sampled overlapping bins.
Main Results:
- Both PSD and AV methods, when combined with maximum-likelihood fitting, provide unbiased and low-error extraction of α and κ.
- The Allan variance (AV) approach demonstrates superior simplicity and robustness compared to the PSD method.
Conclusions:
- Accurate calibration of single-molecule instruments is achievable using both time- and frequency-domain analyses.
- The Allan variance (AV) method is recommended for its practical advantages in simplicity and robustness for instrument calibration.
