Trujillo Justin, Fung Russell, Shankar Madan Kumar, Schwander Peter, Hosseinizadeh Ahmad
Department of Physics, University of Wisconsin-Milwaukee, 3135 N. Maryland Ave, Milwaukee, Wisconsin 53211, USA.
Department of Chemistry-BMC Biochemistry, Uppsala University, Husargatan 3, Uppsala 75237, Sweden.
Struct Dyn. 2025 Jan 21;12(1):014101. doi: 10.1063/4.0000280. eCollection 2025 Jan.
There is a growing understanding of the structural dynamics of biological molecules fueled by x-ray crystallography experiments. Time-resolved serial femtosecond crystallography (TR-SFX) with x-ray Free Electron Lasers allows the measurement of ultrafast structural changes in proteins. Nevertheless, this technique comes with some limitations. One major challenge is the quality of data from TR-SFX measurements, which often faces issues like data sparsity, partial recording of Bragg reflections, timing errors, and pixel noise. To overcome these difficulties, conventionally, large volumes of data are collected and grouped into a few temporal bins. The data in each bin are then averaged and paired with the mean of their corresponding jittered timestamps. This procedure provides one structure per bin, resulting in a limited number of averaged structures for the entire time interval spanned by the experiment. Therefore, the information on ultrafast structural dynamics at high temporal resolution is lost. This has initiated research for advanced methods of analyzing experimental TR-SFX data beyond the standard binning and averaging method. To address this problem, we use a machine learning algorithm called Nonlinear Laplacian Spectral Analysis (NLSA), which has emerged as a promising technique for studying the dynamics of complex systems. In this work, we demonstrate the power of this algorithm using synthetic x-ray diffraction snapshots from a protein with significant data incompleteness, timing uncertainties, and noise. Our study confirms that NLSA is a suitable approach that effectively mitigates the effects of these artifacts in TR-SFX data and recovers accurate structural dynamics information hidden in such data.
X射线晶体学实验推动了人们对生物分子结构动力学的日益深入理解。利用X射线自由电子激光进行的时间分辨串联飞秒晶体学（TR-SFX）能够测量蛋白质中超快的结构变化。然而，这项技术存在一些局限性。一个主要挑战是TR-SFX测量数据的质量，其常常面临数据稀疏、布拉格反射的部分记录、定时误差和像素噪声等问题。为了克服这些困难，传统上会收集大量数据并将其分组到几个时间区间。然后对每个区间的数据进行平均，并将其与相应抖动时间戳的平均值配对。这个过程每个区间提供一个结构，导致在实验所跨越的整个时间间隔内平均结构的数量有限。因此，高时间分辨率下超快结构动力学的信息就丢失了。这引发了对超越标准分箱和平均方法的先进TR-SFX实验数据分析方法的研究。为了解决这个问题，我们使用一种名为非线性拉普拉斯谱分析（NLSA）的机器学习算法，它已成为研究复杂系统动力学的一种有前途的技术。在这项工作中，我们使用来自一个存在大量数据不完整、定时不确定性和噪声的蛋白质的合成X射线衍射快照来展示该算法的强大功能。我们的研究证实，NLSA是一种合适的方法，能够有效减轻这些伪影对TR-SFX数据的影响，并恢复隐藏在这类数据中的准确结构动力学信息。
