Effects of radiation damage and inelastic scattering on single-particle imaging of hydrated proteins with an X-ray Free-Electron Laser

We present a computational case study of X-ray single-particle imaging of hydrated proteins on an example of 2-Nitrogenase–Iron protein covered with water layers of various thickness, using a start-to-end simulation platform and experimental parameters of the SPB/SFX instrument at the European X-ray Free-Electron Laser facility. The simulations identify an optimal thickness of the water layer at which the effective resolution for imaging the hydrated sample becomes significantly higher than for the non-hydrated sample. This effect is lost when the water layer becomes too thick. Even though the detailed results presented pertain to the specific sample studied, the trends which we identify should also hold in a general case. We expect these findings will guide future single-particle imaging experiments using hydrated proteins.

signal, as it was explained in the section 'Results and discussion'. Therefore, in our current analysis we will include the total 23 inelastic scattering signal from the water-and-protein sample. 24 The behaviour of R in Fig. 4(a) in the main text in high resolution region can then be explained by the effect of inelastic 25 scattering. The inelastic scattering from the whole sample contributes stronger with the increasing water layer thickness, as the 26 total number of scatterers, both bound and free ones, then also increases. Consequently, the R factor becomes the largest for the 27 sample with 20 Å thick water layer at high resolution D ≤ 10 Å. 28 This is confirmed by comparing the behavior of R in Fig. 4(a) with the behavior of R factor in Fig. 4(b) in the main text, the 29 latter originating from elastic scattering on the protein only. Below we will show that in the latter case, the behavior of the 30 R factor is mostly affected by ion charge fluctuations and to a smaller extent by atomic displacement. To prove this, in two 31 following calculations we will separate the effects of the 'ionization damage' and the 'displacement damage' on the R factor.

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In order to quantify the effect of the 'ionization damage' and to eliminate the effect of the 'displacement damage', in our 33 first calculation we fixed atom positions to their initial positions. The resulting R factor is shown in Fig. S1. We can see that the 34 R factor in Fig. S1 is very close to the R factor in Fig. 4(b) in the main text, where the overall damage has been included.

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In order to evaluate the effect of the 'displacement damage' on the R factor, in our second calculation we fixed the atomic 36 form factors to their initial values representing a neutral sample. Fig. S2 shows that the resulting R factor degradation occurs 37 mostly in the high resolution regime, with a weak dependence on the tamper thickness. After comparison with Fig. 4(b), we 38 realize that the 'displacement damage' has a smaller effect on the overall damage than the 'ionization damage'. affected by two mechanisms: (i) inelastic scattering, and (ii) ion charge fluctuations. The latter mechanism starts to manifest for 49 thinner water layers (thickness ≤ 4-6 Å), where the contribution of elastic signal prevails over that of the inelastic signal.

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Explanation of R factor behavior in low resolution region 51 The low resolution region represents larger features of the imaged object. Therefore, in contrast to the trend in the high 52 resolution region, ion charge fluctuations and tiny differences in displacements observed for water layers of various thickness 53 will not affect the R factor in the low resolution region. In particular, the weak effect of the 'displacement damage' in the low 54 resolution region is demonstrated in Fig. S2.

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The question is, what effect can be responsible for the behavior of the R factor in the low resolution region? Fig. S3 shows 56 the radial profile of the average number of bound electrons on carbon atoms in the irradiated 2NIP protein at the time zero. One 57 can see that the average number of bound electrons per atom, Q(r) , is not uniformly distributed in the sample, but increases 58 towards the sample edge. For thicker water tampers, this quantity becomes more uniformly spread within the sample. The 59 average charge can be fitted with an approximate relation: where r[Å] is the radial coordinate, measured from the particle center, and R = 38 Å is the approximate particle radius. S4. Their behavior matches qualitatively the R factor behaviour in the low resolution range 20-100 Å in Fig 4(b), supporting 79 our explanation that it is determined by the non-uniformity of bound electron distribution in the sample.

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Justification for neglecting the elastic scattering from a water layer 81 The analysis performed in this work has excluded the diffraction signal due to the elastic scattering from the water layer around 82 the sample, in order to better observe the effects of radiation damage and inelastic scattering on the diffraction signal. Figure S5   83 shows that, in practice, the elastic scattering signal from the water layer dominates, and increasingly so for thicker layers -as 84 one would expect from considering the increasing number of atoms (scatterers) in thicker water layer(s). One could also expect 85 that this signal may be reasonably removed in two limiting cases. The first is the case of a relatively thin layer of water, which