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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.more » « less
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null (Ed.)Abstract Background Asymmetric gait post-stroke is associated with decreased mobility, yet individuals with chronic stroke often self-select an asymmetric gait despite being capable of walking more symmetrically. The purpose of this study was to test whether self-selected asymmetry could be explained by energy cost minimization. We hypothesized that short-term deviations from self-selected asymmetry would result in increased metabolic energy consumption, despite being associated with long-term rehabilitation benefits. Other studies have found no difference in metabolic rate across different levels of enforced asymmetry among individuals with chronic stroke, but used methods that left some uncertainty to be resolved. Methods In this study, ten individuals with chronic stroke walked on a treadmill at participant-specific speeds while voluntarily altering step length asymmetry. We included only participants with clinically relevant self-selected asymmetry who were able to significantly alter asymmetry using visual biofeedback. Conditions included targeting zero asymmetry, self-selected asymmetry, and double the self-selected asymmetry. Participants were trained with the biofeedback system in one session, and data were collected in three subsequent sessions with repeated measures. Self-selected asymmetry was consistent across sessions. A similar protocol was conducted among unimpaired participants. Results Participants with chronic stroke substantially altered step length asymmetry using biofeedback, but this did not affect metabolic rate (ANOVA, p = 0.68). In unimpaired participants, self-selected step length asymmetry was close to zero and corresponded to the lowest metabolic energy cost (ANOVA, p = 6e-4). While the symmetry of unimpaired gait may be the result of energy cost minimization, self-selected step length asymmetry in individuals with chronic stroke cannot be explained by a similar least-effort drive. Conclusions Interventions that encourage changes in step length asymmetry by manipulating metabolic energy consumption may be effective because these therapies would not have to overcome a metabolic penalty for altering asymmetry.more » « less