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One often observes small but measurable differences in the diffraction data measured from different crystals of a single protein. These differences might reflect structural differences in the protein and may reveal the natural dynamism of the molecule in solution. Partitioning these mixed-state data into single-state clusters is a critical step that could extract information about the dynamic behavior of proteins from hundreds or thousands of single-crystal data sets. Mixed-state data can be obtained deliberately (through intentional perturbation) or inadvertently (while attempting to measure highly redundant single-crystal data). To the extent that different states adopt different molecular structures, one expects to observe differences in the crystals; each of the polystates will create a polymorph of the crystals. After mixed-state diffraction data have been measured, deliberately or inadvertently, the challenge is to sort the data into clusters that may represent relevant biological polystates. Here, this problem is addressed using a simple multi-factor clustering approach that classifies each data set using independent observables, thereby assigning each data set to the correct location in conformational space. This procedure is illustrated using two independent observables, unit-cell parameters and intensities, to cluster mixed-state data from chymotrypsinogen (ChTg) crystals. It is observed that the data populate an arc of the reaction trajectory as ChTg is converted into chymotrypsin. 

Abstract We present optical, infrared, ultraviolet, and radio observations of SN 2022xkq, an underluminous fast-declining Type Ia supernova (SN Ia) in NGC 1784 (D≈ 31 Mpc), from <1 to 180 days after explosion. The high-cadence observations of SN 2022xkq, a photometrically transitional and spectroscopically 91bg-like SN Ia, cover the first days and weeks following explosion, which are critical to distinguishing between explosion scenarios. The early light curve of SN 2022xkq has a red early color and exhibits a flux excess that is more prominent in redder bands; this is the first time such a feature has been seen in a transitional/91bg-like SN Ia. We also present 92 optical and 19 near-infrared (NIR) spectra, beginning 0.4 days after explosion in the optical and 2.6 days after explosion in the NIR. SN 2022xkq exhibits a long-lived Ci1.0693μm feature that persists until 5 days post-maximum. We also detect Ciiλ6580 in the pre-maximum optical spectra. These lines are evidence for unburnt carbon that is difficult to reconcile with the double detonation of a sub-Chandrasekhar mass white dwarf. No existing explosion model can fully explain the photometric and spectroscopic data set of SN 2022xkq, but the considerable breadth of the observations is ideal for furthering our understanding of the processes that produce faint SNe Ia.