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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. 

Förster resonance energy transfer (FRET) spectrometry is a method for determining the quaternary structure of protein oligomers from distributions of FRET efficiencies that are drawn from pixels of fluorescence images of cells expressing the proteins of interest. FRET spectrometry protocols currently rely on obtaining spectrally resolved fluorescence data from intensity-based experiments. Another imaging method, fluorescence lifetime imaging microscopy (FLIM), is a widely used alternative to compute FRET efficiencies for each pixel in an image from the reduction of the fluorescence lifetime of the donors caused by FRET. In FLIM studies of oligomers with different proportions of donors and acceptors, the donor lifetimes may be obtained by fitting the temporally resolved fluorescence decay data with a predetermined number of exponential decay curves. However, this requires knowledge of the number and the relative arrangement of the fluorescent proteins in the sample, which is precisely the goal of FRET spectrometry, thus creating a conundrum that has prevented users of FLIM instruments from performing FRET spectrometry. Here, we describe an attempt to implement FRET spectrometry on temporally resolved fluorescence microscopes by using an integration-based method of computing the FRET efficiency from fluorescence decay curves. This method, which we dubbed time-integrated FRET (or tiFRET), was tested on oligomeric fluorescent protein constructs expressed in the cytoplasm of living cells. The present results show that tiFRET is a promising way of implementing FRET spectrometry and suggest potential instrument adjustments for increasing accuracy and resolution in this kind of study.