Resolving molecular diffusion and aggregation of antibody proteins with megahertz X-ray free-electron laser pulses

X-ray free-electron lasers (XFELs) with megahertz repetition rate can provide novel insights into structural dynamics of biological macromolecule solutions. However, very high dose rates can lead to beam-induced dynamics and structural changes due to radiation damage. Here, we probe the dynamics of dense antibody protein (Ig-PEG) solutions using megahertz X-ray photon correlation spectroscopy (MHz-XPCS) at the European XFEL. By varying the total dose and dose rate, we identify a regime for measuring the motion of proteins in their first coordination shell, quantify XFEL-induced effects such as driven motion, and map out the extent of agglomeration dynamics. The results indicate that for average dose rates below 1.06 kGy μs−1 in a time window up to 10 μs, it is possible to capture the protein dynamics before the onset of beam induced aggregation. We refer to this approach as correlation before aggregation and demonstrate that MHz-XPCS bridges an important spatio-temporal gap in measurement techniques for biological samples.


Coherence and Speckle Contrast
The experimental speckle contrast, β exp depends on nearly all experimental parameters such as pixel size speckle size, beam size, sample thickness, momentum transfer q, the transverse and longitudinal coherence properties of the X-rays, etc. β exp can be calculated as the product of the longitudinal contrast factor, β l , and the transverse contrast factor, β t : For XFELs, the model described in Hruszkewycz et al. [1] is often employed to estimate β l (q).
A detailed description of the mathematical formalism can be found in the supplementary material of [1]. Lehmkühler et al. [2] show that the speckle contrast at EuXFEL can be described by this model as well. β l is determined by the energy bandwidth, ∆E/E, which can be decreased by using a seeded beam or a monochromator. Both were not available for this experiment.
Instead, the pink SASE beam was used with an energy bandwidth of ∆E/E ≈ 2 × 10 −3 . For the transverse coherence factor, β t ≈ 0.5 was found for different XFELs including European XFEL [2][3][4][5]. Eventually, the following model was used to describe the data

Signal-to-Noise Ratio
Following the work of Falus et al. [6], the XPCS signal-to-noise ratio, R sn , can be calculated as where β is the speckle contrast, I is the intensity in numbers of photons per pixel, N p = 20 is the number of pulses or images used to calculate the first point of the correlation functions, N trains is the number of trains that are averaged, N pix = 7494 is the number of pixels in the q-bin where the correlation function is calculated. volume. The data have been rebinned along the abscissa and the error bars indicate the standard deviation within each bin. In addition, the total measurement time is indicated assuming that every pulse is used for the analysis. The measurement time obviously depends on both machine performance and filtering criteria applied during the experiment as not every train might be usable for the analysis, e.g., because of very low intensity. In Fig. 2, it is assumed that every train is used for the analysis. In our experiment about 20 % of the trains were discarded.
The visible fluctuations in R sn are probably related to fluctuating instrument parameters and varying machine performance.
The primary advantage of using a monochromatic beam is that it would allow for a larger beam size with similar contrast, hence yielding a lower photon density on the sample. This reduces the radiation damage to the sample and the amount of sample needed. It also increases the scattering volume and scattering intensity and thus strongly increases the signal-to-noise ratio [7].

Dose dependence of the Hydrodynamic Radius
We plot the normalized hydrodynamic radius R h as a function of dose in Fig. 4a and as a function of root mean squared displacement in Fig. 4b for comparison as in the main manuscript.
From fitting the data of the lowest and highest dose rate (dashed lines) with an exponential model we conclude that R h increases by a factor of two after (19.2 ± 1.0) kGy for a dose rate of 1.06 kGy µs −1 and after (32 ± 3) kGy for a dose rate of 4.75 kGy µs −1 . These values correspond to starting times of (18.1 ± 0.9) µs and (6.8 ± 0.6) µs, respectively.