Lansdorp Bob M, Saleh Omar A
Materials Department, University of California Santa Barbara, Santa Barbara, California 93106, USA.
Rev Sci Instrum. 2012 Feb;83(2):025115. doi: 10.1063/1.3687431.
Single-molecule manipulation instruments, such as optical traps and magnetic tweezers, frequently use video tracking to measure the position of a force-generating probe. The instruments are calibrated by comparing the measured probe motion to a model of Brownian motion in a harmonic potential well; the results of calibration are estimates of the probe drag, α, and spring constant, κ. Here, we present both time- and frequency-domain methods to accurately and precisely extract α and κ from the probe trajectory. In the frequency domain, we discuss methods to estimate the power spectral density (PSD) from data (including windowing and blocking), and we derive an analytical formula for the PSD which accounts both for aliasing and the filtering intrinsic to video tracking. In the time domain, we focus on the Allan variance (AV): we present a theoretical equation for the AV relevant to typical single-molecule setups and discuss the optimal manner for computing the AV from experimental data using octave-sampled overlapping bins. We show that, when using maximum-likelihood methods to fit to the data, both the PSD and AV approaches can extract α and κ in an unbiased and low-error manner, though the AV approach is simpler and more robust.
单分子操纵仪器，如光镊和磁镊，经常使用视频跟踪来测量产生力的探针的位置。通过将测量到的探针运动与谐波势阱中的布朗运动模型进行比较来校准仪器；校准结果是探针阻力α和弹簧常数κ的估计值。在这里，我们提出了时域和频域方法，以准确、精确地从探针轨迹中提取α和κ。在频域中，我们讨论了从数据中估计功率谱密度（PSD）的方法（包括加窗和分块），并推导了一个考虑了混叠和视频跟踪固有滤波的PSD解析公式。在时域中，我们关注阿伦方差（AV）：我们给出了与典型单分子设置相关的AV理论方程，并讨论了使用倍频程采样重叠区间从实验数据计算AV的最佳方式。我们表明，当使用最大似然方法拟合数据时，PSD和AV方法都可以以无偏且低误差的方式提取α和κ，尽管AV方法更简单、更稳健。
