Optical tweezer (OT) single-molecule force spectroscopy is a powerful method to map out the energy landscape of biological complexes and has found increasing applications in academic and pharmaceutical research. The dominant method to extract molecular conformation transitions from the thermal diffusion-broadened trajectories of the microscopic OT probes attached to the single molecule of interest is through hidden Markov models (HMMs). In standard applications, the HMMs assume a white noise spectrum of the probes superimposed onto the molecular signal. Here, we demonstrate, through theoretical derivation, computer modeling and experimental measurements that this standard white noise HMM (wnHMM) misses key features of real OT data. The deviation is most pronounced at higher frequencies because the white noise model does not account for the overdamped nature of particle diffusion in an OT harmonic potential in aqueous environments. To address this, we derive how to incorporate autoregression between consecutive data points into a HMM, and demonstrate through modeling and experiment that such an autoregressive HMM (arHMM) captures real OT data behavior across all frequency ranges. Through analysis of real OT data we recorded on a single DNA hairpin undergoing folding and unfolding transitions, we show that the wnHMM extracts lifetimes that are at least a factor of 2 faster and less consistent than the arHMM results, which match expectations and prior measurements. Overall, our work suggests that arHMM should be the default model choice for analysis OT single-molecule transitions and that its use will improve the fidelity and accuracy of single-molecule force spectroscopy measurements.

中文翻译：

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自回归 HMM 解决了被动光镊力测量的生物分子转变


光镊 （OT） 单分子力谱是绘制生物复合物能量景观的强大方法，在学术和制药研究中得到了越来越多的应用。从附着在目标单个分子上的微观 OT 探针的热扩散展宽轨迹中提取分子构象转变的主要方法是通过隐藏马尔可夫模型 （HMM）。在标准应用中，HMM 假设探针的白噪声频谱叠加在分子信号上。在这里，我们通过理论推导、计算机建模和实验测量证明，这种标准白噪声 HMM （wnHMM） 错过了真实 OT 数据的关键特征。这种偏差在较高频率下最为明显，因为白噪声模型没有考虑水环境中 OT 谐波电位中粒子扩散的过阻尼性质。为了解决这个问题，我们得出了如何将连续数据点之间的自回归合并到 HMM 中，并通过建模和实验证明这种自回归 HMM （arHMM） 捕获了所有频率范围内的真实 OT 数据行为。通过分析我们在经历折叠和去折叠转变的单个 DNA 发夹上记录的真实 OT 数据，我们表明 wnHMM 提取物的寿命比 arHMM 结果快至少 2 倍且一致性更低，这与预期和先前的测量结果相匹配。总体而言，我们的工作表明 arHMM 应该是分析 OT 单分子跃迁的默认模型选择，它的使用将提高单分子力谱测量的保真度和准确性。