Power spectrum and Allan variance methods for calibrating single-molecule video-tracking instruments
Power spectrum and Allan variance methods for calibrating single-molecule video-tracking instruments
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DOI：
10.1063/1.3687431
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发表时间：
2012-02-01
影响因子：
1.6
通讯作者：
Saleh, Omar A.
中科院分区：
文献类型：
--
作者：
Lansdorp, Bob M.;Saleh, Omar A.
单分子操纵仪器，如光阱和磁镊，经常使用视频跟踪来测量力产生探针的位置。通过将测得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;校准的结果是探针阻力a和弹簧常数K的估计。在这里，我们提出了时域和频域方法来从探头轨迹中准确、精确地提取a和K。在频域中，我们讨论的方法来估计的功率谱密度（PSD）的数据（包括开窗和分块），我们推导出一个解析公式的PSD占混叠和滤波固有的视频跟踪。在时域中，我们专注于Allan方差（AV）：我们提出了一个理论方程的AV相关的典型的单分子设置和讨论的最佳方式计算AV从实验数据使用倍频程采样重叠箱。我们表明，当使用最大似然方法来拟合数据时，PSD和AV方法都可以以无偏和低误差的方式提取a和K，尽管AV方法更简单，更鲁棒。(C)2012年美国物理学会。[http：//dx.doi.org/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, a, and spring constant, K. Here, we present both time- and frequency-domain methods to accurately and precisely extract a and K 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 a and K in an unbiased and low-error manner, though the AV approach is simpler and more robust. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3687431]