Statistical analyses of the impact of X-ray damage effects on conformational heterogeneity in room temperature (277 K) and cryo-cooled (100 K) protein crystals

Ringer analysis. Ringer profiles were obtained for each residue in each protein as follows. The final structural models and diffraction data were used to calculate composite omit maps to reduce potential model bias (Liebschner et al., 2019). For comparison of Ringer profiles from the least and most damaged datasets, composite omit maps for both the least and most damaged datasets were calculated at the resolution of the most damaged dataset. The resulting map and refined models were then submitted to Ringer as implemented in the phenix suite using a 5° sampling angle (Lang et al., 2010; Liebschner et al., 2019). Because the absolute amount of electron density (σ) can vary between datasets irrespective of changes in rotameric distributions, we normalized all Ringer profiles prior to comparison. The normalized Ringer profiles were then used to calculate Pearson correlation coefficients (PCC) (see below). Calculating Pearson correlation coefficients (PCC) and mean square errors (MSE). The Pearson correlation coefficient (Pcc, also known as Pearson's r) between normalized Ringer profiles was calculated using the scipy.stats.pearsonr function of the SciPy package in Python 3 (Virtanen et al., 2020). Mean square errors were calculated between normalized Ringer profiles using the sklearn.metrics. mean_squared_error function of the scikit-learn package in Python 3, with the non-default parameter "squared = False" (Pedregosa et al.) Crystallographic disorder parameter (1-S2) calculation. Crystallographic and solution NMR order parameters (S2) have been shown to correlate well and range between 1 for a completely rigid residue and 0 for a completely unrestrained residue (Fenwick et al., 2014). Here we used the opposite of order parameters and calculated disorder parameters (1-S2). High resolution data (generally better than ~1.7 Å) is required for crystallographic (1-S2) analysis (Fenwick et al., 2014), and the high resolution of the datasets obtained in this work (1.02 to 1.54 Å, Tables S1-S4) makes the (1-S2) analyses in this work reliable. Crystallographic disorder parameters, (1-S2), were obtained from the 277 K multi-conformer models as previously described (Fenwick et al., 2014; Russi et al., 2017). These disorder parameters include both harmonic and anharmonic contributions as captured by the crystallographic atomic displacement parameters (B-factors) and by the occupancies of alternative rotameric states. The analysis was applied to the bond most closely associated with the first side-chain dihedral angle (χ1), using Cβ—H for all amino acids other than Gly and Cα—H for Gly. For each residue, the extrapolation to zero-dose (1-S2) was done by fitting a linear equation to the plot of (1-S2) as a function of absorbed X-ray dose and extracting the y-intercept. All fits were of good quality with average R2 and standard deviation of 0.91±0.09, 0.96±0.06, and 0.93±0.05 for thaumatin, proteinase K, and lysozyme, respectively