key: cord-0455860-ttief57a
authors: Reiser, Mario; Girelli, Anita; Ragulskaya, Anastasia; Das, Sudipta; Berkowicz, Sharon; Bin, Maddalena; Ladd-Parada, Marjorie; Filianina, Mariia; Poggemann, Hanna-Friederike; Begam, Nafisa; Akhundzadeh, Mohammad Sayed; Timmermann, Sonja; Randolph, Lisa; Chushkin, Yuriy; Seydel, Tilo; Boesenberg, Ulrike; Hallmann, Jorg; Moller, Johannes; Rodriguez-Fernandez, Angel; Rosca, Robert; Schaffer, Robert; Scholz, Markus; Shayduk, Roman; Zozulya, Alexey; Madsen, Anders; Schreiber, Frank; Zhang, Fajun; Perakis, Fivos; Gutt, Christian
title: Resolving molecular diffusion and aggregation of antibody proteins with megahertz X-ray free-electron laser pulses
date: 2022-02-22
journal: nan
DOI: nan
sha: 1bf14edc62739737f58b0f096135543a8c7f502b
doc_id: 455860
cord_uid: ttief57a

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 dose rates below $1.16,mathrm{kGymu s^{-1}}$ in a time window up to $10,mathrm{mu s}$, 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.

The European X-ray Free-Electron Laser Facility (EuXFEL) is the rst X-ray free electron laser (XFEL) generating ultrashort hard X-ray pulses with megahertz repetition rate. Megahertz X-ray photon correlation spectroscopy (MHz-XPCS) [1] [2] [3] makes use of this high repetition rate and the high degree of transverse coherence to measure di usive dynamics with (sub-) microsecond temporal resolution. In biological systems, typical di usion coe cients in dense cellular environments range from D 0 ≈ 0.1 to 10 nm 2 µs −1 [4] [5] [6] [7] [8] [9] which in turn requires to resolve time scales from τ ≈ 0.5 to 5 µs (see Fig. 1 ) in order to trace the complex many-body interactions between proteins and the solvent on molecular length scales. This window of length and time scales is not accessible by optical techniques such as dynamic light scattering, which measures longer length scales (micrometers), or neutron spectroscopy techniques such as neutron spin echo or inelastic neutron scattering, which measure on faster time scales of nanoseconds and below. Clearly, experimental techniques are needed to close this gap and measure collective dynamics on microsecond time scales and nanometer length scales. By analyzing uctuating X-ray speckle patterns, MHz-XPCS is potentially capable of closing this gap, as we demonstrate here, and enables us to gain information on equilibrium and out-ofequilibrium collective dynamics of protein solutions.

Protein dynamics in crowded environments are particularly relevant in the context of intra- * mario.reiser@fysik.su.se † f.perakis@fysik.su.se ‡ christian.gutt@uni-siegen.de cellular transport in the cytoplasm of eukaryotic cells [10] , phase transitions in biomolecular condensates [11] [12] [13] , aggregation phenomena [14, 15] and drug production [16] . In highly concentrated environments, the dynamics di er signi cantly from that of a dilute system, whereas the exact mechanisms that in uence the dynamics on di erent time scales are not yet fully understood [6, 7, 17] . It was found that in vivo dynamics in cells exhibit tremendously reduced di usion compared to in vitro measurements of diluted proteins in bu er solutions [18] [19] [20] [21] [22] [23] [24] [25] . It is believed that the level of slowing-down depends on the particular system and possibly additional crowding agents [6, 18, [26] [27] [28] . In addition to excluded volume e ects [29, 30] , there can be contributions from the local water dynamics of the hydration layer [31] , quinary interactions of proteins with other cytoplasmic constituents [18, 19, [32] [33] [34] [35] , and transient cluster formation [36] [37] [38] [39] [40] that in uence intracellular protein di usion. Also, the dynamics often exhibit anomalous behavior-i.e., non-Brownian and in particular subdi usive dynamics [26, 41, 42 ]-and so one cannot simply extrapolate the dynamics from the dilute regime. Clearly, new methods are needed to directly probe di usive dynamics in crowded biological solutions on (sub-) microsecond time scales and nanometer length scales to study these phenomena.

Radiation damage constitutes a major challenge for X-ray scattering experiments with protein solutions. Radiolysis of water and the fast distribution of the free radicals formed rapidly degrade the protein molecules. Hence, a typical upper limits of tolerable absorbed doses is estimated on the order of a few kilo Grays in these experiments with the exact value being strongly dependent on the chemical composition of the system [43] [44] [45] [46] . Protein aggregation is a signature of beam-induced damage in protein solutions visible via changes in the X-ray scattering form factor. Aggregation processes and the spread of free radicals are both driven by di usive dynamics and act on nano-and microsecond time scales [14, [47] [48] [49] . The study of such time-dependent dynamic processes in aqueous solutions of bio-molecules when illuminated with X-rays is of considerable relevance for understanding biological aspects of ionizing radiation. In addition, MHz-XFEL experiments deliver extremely high dose rates to the sample, on the order of several kilo Grays per microsecond, compared to experiments at synchrotron sources with typical dose rates of kilo Grays per second. The e ects of such high dose rates on structure and dynamics of protein solutions are still unknown.

Here, we report the rst MHz-XPCS experiment with radiation sensitive protein solutions at the Materials Imaging and Dynamics (MID) instrument [50] at EuXFEL. We investigate the dynamics in a concentrated bovine immunoglobulin (Ig) solution where 80 % of the Ig is constituted by IgG [51, 52] . Immunoglobulin is an abundant antibody protein that can be found, for instance, in the blood of animals and humans. Polyethylene glycol (PEG) is added to the solution as a depletant and induces attractive protein-protein interactions that-depending on concentration and temperature-can result in liquid-liquid phase separation (LLPS) [51, 52] .

This combination renders the Ig-PEG system an interesting candidate for the MHz-XPCS measurements in the context of both crowding dynamics in concentrated protein solutions and the formation of biomolecular condensates.

We employed X-ray pulses with repetition rates of 2.2 and 1.1 MHz corresponding to minimum delay times of 440 and 880 ns between two consecutive pulses, respectively. The X-ray pulses were delivered in trains of up to 200 pulses with a train frequency of 10 Hz (see Fig. 1 ). This time structure makes it possible to conduct MHz-XPCS measurements within a single train, while the time between subsequent trains is su ciently long to refresh the sample via translation.

The data presented here were acquired at the MID instrument in small-angle X-ray scattering (SAXS) geometry with a pink beam, i.e., using self-ampli ed spontaneous emission (SASE) without a monochromator, and a photon energy of 9 keV [50] . A sketch of the experimental setup is shown in Fig. 1 . The Adaptive Gain Integrating Pixel Detector (AGIPD) [53] was placed 7.46 m behind the sample with most of the sample-detector ight path being evacuated. The Ig-PEG solutions were lled into quartz capillaries with an outer diameter of 1.5 mm and a wall thickness of 20 µm. A Linkam scienti c instruments stage was used to control and stabilize the sample temperature at 298 K, which is above the binodal in the single phase regime of the Ig-PEG system [51, 52] . The X-ray beam was focused to a diameter of 10 µm (FWHM) using compound refractive lenses to increase the speckle contrast and the signal-to-noise (SNR) of the XPCS measurements [54] .

Tab. 1: Measurement parameters: D rate is the average dose rate, f FEL is the XFEL frequency, and τ min is the minimum XPCS delay time. The average number of incident photons per X-ray pulse (ph/pls) on the sample is denoted Φ c . N train is the number of pulse trains averaged in the analysis. Megahertz X-ray photon correlation spectroscopy (MHz-XPCS) measurements are performed by using trains of X-ray pulses, which illuminate the sample. The spacing between two pulses within a train is τ min and was varied between 440 and 880 ns where a train is delivered every 100 ms. By analyzing sequential X-ray scattering patterns measured with the adaptive gain integrated pixel detector (AGIPD), information about the dynamics of the sample can be obtained in the form of intensity auto-correlation functions calculated from uctuating speckle patterns.

and adjusted such that the samples were exposed to the lowest possible dose while keeping the scattered intensity high enough to reach a su cient SNR. For example, with an average pulse energy of 1.2 m J and 3925 µm CVD attenuator thickness 6.5 × 10 8 photons per X-ray pulse illuminate the sample. The incoming ux results in an average scattering signal of less than 10 −1 photons per pixel per image. In addition to the absolute dose also the average dose rate was varied, i.e., the absorbed dose per time, measured in kGy µs −1 .

The evolution of the time-resolved SAXS signal as a function of dose and dose rate is analyzed by computing the azimuthally integrated intensity I(q, t) as a function of absolute momentum transfer, q = 4π/λ sin (2θ/2), where λ is the X-ray wavelength and 2θ is the scattering angle, We quantify the evolution of structural changes by calculating the Porod invariant

in the accessible q-range (q min = 0.1 nm −1 , q max = 0.6 nm −1 ) as a function of dose (see Fig. 2b ).

Q P (D) displays an initial plateau up to a maximum dose of 10 kGy after which it starts to decrease more than two percent from its initial value. At doses below 10 kGy, the protein structure seems una ected by the X-ray illumination-at least on the length scales probed here.

In this low-dose regime, we also extract the dose rate dependence of the Porod invariant by averaging the Q p (D) data for D < 10 kGy. The results are displayed in the inset in Fig. 2b demonstrating the absence of a dose rate dependence in the SAXS signal. This is in agreement with previous work reporting that the absolute absorbed dose is the main driver for radiation damage and dose rate e ects are only weak [46] . Megahertz X-ray photon correlation spectroscopy (MHz-XPCS)

The disordered protein solutions give rise to a speckle pattern in the far-eld when illuminated by coherent radiation. The dynamics can be studied by analyzing the speckle intensity uctuations that are related to the microscopic motion of the protein molecules. The intensity I p (q, t)

is measured at time t by pixel p within a concentric region of interest (ROI) of constant absolute momentum transfer. We utilized an XPCS adapted acquisition scheme in which the sample is continuously moving through the X-ray beam with 400 µm s −1 . The sample movement is negligible during an X-ray train ensuring illumination of the same sample spot on microsecond time scales. In between two trains the sample position o set is large enough to completely renew the sample volume, and thus to avoid accumulated damage. The low intensity scattering signal requires averaging correlation functions from many trains (between 2000 and 9000 see Table 1 ) to increase the SNR. Around 80 % of the acquired trains are used for the XPCS analysis while the rest are discarded after applying lters based on diagnostics such as extremely low intensity due to the SASE uctuations.

We compare measurements with average dose rates, D rate , from 1.16 to 5.20 kGy µs −1 . The in uence of dose and dose rate on the protein dynamics can be quanti ed with the help of two-time correlation functions (TTCs) [55, 56] which essentially represent the correlation coe cient between speckle images taken at times t 1 and t 2 at momentum transfer q:

Here, . . . p denotes an average over all pixels with the same absolute momentum transfer, q.

The data calibration and analysis work ow for MHz-XPCS with AGIPD is described in detail in Dallari et al. [3] . Time-resolved intra-train intensity auto-correlation functions, g 2 (q, τ ), are calculated by averaging sections of the TTCs as indicated by the white arrow in Fig. 3a . We label the g 2 (q, τ )

functions by its initial dose value at t 2 while noting that the dose increases further with each point of the correlation function. The correlation functions are modelled by a Kohlrausch-Williams-Watts (KWW) function:

where β(q) is the q-dependent speckle contrast [57] (β(q = 0.15 nm −1 ) ≈ 11 %) and α is the KWW exponent. Brownian di usion is characterized by a quadratic q-dependence of the relaxation rates Γ(q) = D 0 q 2 , where D 0 is the di usion coe cient, and simple exponential behavior (α = 1). KWW exponents smaller than one are typically observed in supercooled liquids, and gels and can indicate heterogeneous dynamics with a distribution of relaxation times [58] . A quadratic q-dependence and a q-independent KWW exponent are used to model the data. Fig. 3d shows that within the experimental accuracy this model describes the data well. Fig. 3c shows correlation functions for di erent dose rates for absolute doses below 5 kGy.

Comparing Fig. 3b and Fig. 3c reveals that the e ect of the total dose on the correlation functions is di erent from the e ect of the dose rate. Fig. 3c indicates that the dynamics become faster with dose rate as the correlation functions shift to shorter time scales while the overall lineshape appears to change only slightly. This is di erent from the behavior observed with increasing total dose in Fig. 3b where the shape of the correlation functions drastically changes from a simple exponential decay at low doses to a highly stretched (α < 1) and almost logarithmic decay at higher dose values. We account for these changing KWW exponents by computing the average relaxation rate [59, 60] 

Using these average relaxation rates one pair of parameters (D 0 , α) is calculated per dose and dose rate, where D 0 = Γ (q)/q 2 . The results are displayed in Fig. 4 .

The di usion coe cients in Fig. 4a reveal a pronounced dose and dose rate dependence as already indicated by the correlation functions in Fig. 3 and are higher than expected for the base temperature of T 0 = 298 K. Therefore, we denote D 0 reported here is as an e ective di usion coe cient discussed in more detail in the following section. The numbers obtained reveal that the correlation functions exhibit a simple exponential shape (α=1) for low doses while they are increasingly stretched above 10 kGy, which approximately coincides with the dose value where a decrease in D 0 becomes apparent (Fig. 4a) . The simultaneous decrease of D 0 and the KWW exponent for high doses points towards beam-induced aggregation of the proteins (cf. Fig. 2 ), which results in slower di usion and increasingly stretched exponential behavior.

Our results indicate that static and dynamic properties are in uenced in di erent ways by the intense X-ray pulses of the XFEL. MHz-SAXS reveals that the static scattering signal-within the accessible q-window-is preserved below an absorbed dose of 10 kGy. This threshold value is independent of the applied dose rate (Fig. 2b inset) . These ndings are in good agreement with previous synchrotron results from both solution scattering [43, 46, 61] and crystallogra-phy experiments [62] which point towards no or only extremely weak dose rate dependence of static scattering signals from protein samples and typical critical dose values of protein solutions in the range of a few kGy. It is noteworthy that the extremely high dose rates and microsecond time scales probed with an XFEL yield similar threshold values (≈ 10 kGy) as the orders of magnitude lower dose rates used at a synchrotron (≈ 1 kGy s −1 [52] ).

Generally, radiation damage in aqueous protein solutions is mainly attributed to the diffusion and successive reaction of proteins with radicals produced by radiolysis, such as OH -.

Radiolysis itself involves a variety of di erent time and length scales where the radicals are not uniformly generated in the solvent, but distributed initially in nanoscale traces which broaden and di use into the bulk on timescales of hundreds of nanoseconds to microseconds during the chemical stage [63] . The primary yield of OHradicals is high, with 2.5 OHper 100 eV absorbed after one microsecond [64] , leading to an average of 0.3 OHradicals per Ig protein molecule needed to induce measurable changes to the SAXS signal (see Fig. 2 Furthermore, it is interesting to examine the dynamics at dose values below the static damage threshold of 10 kGy obtained from the MHz-SAXS analysis. The di usion constants are almost independent of the dose for a given dose rate. However, D 0 displays a pronounced rate dependence and increases by almost a factor of four between the lowest and the highest dose rate (Fig. 4a) . Illuminating a sample with highly intense X-ray pulses can lead to a temperature increase. Based on the X-ray beam size of 10 µm, we estimate that the generated heat dissipates with a time constant of 470 µs (see Methods section below), which is much longer than the measurement window covered by a g 2 -function here (20 µs). Thus, the illuminated sample volume does not cool down noticeably during a measurement and the maximum accumulated heat only depends on the uence per pulse and the number of pulses illuminating the same sample volume. We further hypothesize that the intense MHz XFEL pulses create a non-equilibrium state triggering processes on the sub-microsecond time scale. One example of such processes is the spatial homogenization of the aforementioned radiolysis products. The typical rates of secondary products such as OHradicals are on the order of microseconds [65, 66] . Thus, on sub-microsecond time scales, the XFEL pulses simultaneously produce and probe a spatially inhomogeneous local distribution of the radiolysis products. The resulting chemical gradients, molecular repulsion due to dose rate dependent protein charging, and possibly changes of the ionic strength of the solution could contribute to the observed enhanced di usive motion. Clearly, more systematic data and additional work by theory and simulation is needed to understand this XFEL driven motion.

The question arises why the faster dynamics at higher dose rates do not lead to a dose rate dependent aggregation visible in the SAXS signal. We address this question by employing the Stokes-Einstein relation and estimating the temporal evolution of the relative changes to the

where D 0 (0) and R h (0) represent the respective values at the minimum dose in Fig. 4 . The increase of this ratio serves as an indicator for protein aggregation. Fig. 6 shows that aggregation sets in earlier and develops faster for higher dose rates. For a dose rate of 1.16 kGy µs −1 , R h (t)/R h (0) has doubled after 16 µs and already after 8 µs for 5.21 kGy µs −1 . Using the measured di usion coefcients D 0 , we further calculate the time dependent root mean square displacement (RMSD) ∆x 2 (t) = √ 6D 0 t of the proteins and plot R h (t)/R h (0) as a function of RMSD (see Fig. 6b ). The data for the di erent dose rates collapse onto a single master curve (red line) indicating that the onset of aggregation depends mainly on the RMSD the protein molecules. Higher dose rate induce faster movement of the proteins, and thus the RMSD necessary for aggregation is reached earlier. Fig. 6b also reveals that aggregation sets in after a RMSD of about 10 nm and the space a single protein can explore in the crowded solution before that happens is indicated by a the red dashed circle. This area is quite large considering that the sample is a densely packed solution of 250 mg ml −1 , where the mean free path l between two molecules is typically smaller than their radius. We estimate l = 1/(nπ(2R h ) 2 ) = 2.6 nm from the number density n and the molecular radius R h = 5.5 nm of an Ig molecule which in turn implies an average number of contacts between proteins on the order of N = ∆x 2 (t) /l 2 ≈ 14 before aggregation sets in.

Our analysis indicates that aggregation is not strictly translational di usion limited, but multiple contacts are necessary to attach two protein molecules to each other and form aggregates.

This may hint towards the importance of speci c interaction sites driving the aggregation process [67] . In addition, we note that unfolding processes which increase the protein propensity to aggregate do also occur on time scales of microseconds [68] . Thus, the observed initial period of constant R h points towards a minimum incubation time on the order of 10 µs before the proteins locally unfold or a time needed for rotational motion of molecules in order to allow activated sites to form local bonds. This incubation time and the minimum RMSD of 10 nm de ne a window where dynamics can be measured in a correlation before aggregation scheme similar to di raction before destruction [69] given the dose rate is below 1.16 kGy µs −1 (see Fig. 5b ). Additional data with more dose rates could allow to develop new methods to estimate the di usion coe cients at zero dose rate [70] . Such an approach would allow for applying moderate doses and dose rates in MHz-XPCS experiments, which would increase the SNR and reduce the overall measurement time and sample consumption. Furthermore, the onset of phase transitions in biomolecular condensates could be investigated which occur on microsecond time scales [52, 58, 71] , but are hard to repeat thousands of times. Finally, we note that the SNR in future XPCS experiments can be signi cantly enhanced by making use of the self-seeding schemes which provide a much larger longitudinal coherence length and, thus, increases the speckle contrast. Further technical improvements such as MHz detectors with smaller pixel size are needed to improve the SNR even further which allows extending the accessible q-range and lower the dose rate needed. Summarizing, we demonstrated that MHz-XPCS is a unique tool for measuring dynamics of biological macromolecules in solution on molecular length scales and on the time scales relevant for di usive motion in cells. Importantly, our results indicate that for dose rates below 1.16 kGy µs −1 , allows to study equilibrium dynamics within the rst coordination shell of the molecules. Higher XFEL dose rates drive the dynamics and lead to increasing di usion coecients and aggregation which sets in after a time window of 10 µs. We refer to this approach as correlation before aggregation which allows to capture protein dynamics in solution before the manifestation of X-ray induced e ects, similar to the di raction before destruction approach used in protein crystallography. Additional experiments and simulations are needed to fully understand the underlying physics of the involved processes. Understanding the observed dose rate dependence of the di usion process involves accurate knowledge of a number of yet unknown factors, such as the role of the interaction potentials, concentration, solvent chemical composition, and size and masses of the proteins. Resolving these properties and the role of radiolysis processes and their products in this context will determine the best data acquisition strategies for measuring the unperturbed dynamic properties.

The sample preparation followed a procedure provided by the literature [51] . The experimental phase diagram of this system has been established in our previous work [51] .

The "parent solution" was equilibrated for about 24 h at 294 K and then brie y centrifuged, resulting in a clear dense and a dilute phase, separated by a sharp meniscus. The parent solution composition was immunoglobulin 200 mg/mL, PEG 12% w/v and NaCl 150 mM. The dense liquid phase was used for XPCS measurements with a concentration of roughly 250 mg mL −1 .

In order to quantify the amount of energy absorbed by a certain sample mass, we calculate the dose, D(t), absorbed by the sample in the course of the time t:

where A = 0.85 denotes the sample absorption estimated based on the chemical formula of IgG [52] , E c = 9 keV the photon energy, Φ c the photons ux, and d s = 1.5 mm the sample thickness. φ = 0.22 is the Ig volume fraction, ρ = 1.35 g cm −3 the Ig mass density, and z = 10 µm is the beam size. The dose is measured in Gray (1 Gy = 1 J kg −1 ).

Emergence of Anomalous Dynamics in Soft Matter Probed at the European XFEL

Microsecond Hydrodynamic Interactions in Dense Colloidal Dispersions Probed at the European XFEL

Analysis Strategies for MHz XPCS at the European XFEL

Calculation of Hydrodynamic Properties of Globular Proteins from Their Atomic-Level Structure

Coarse-Grained Molecular Simulation of Di usion and Reaction Kinetics in a Crowded Virtual Cytoplasm

Dynamics of Proteins in Solution

Protein Self-Di usion in Crowded Solutions

Dynamic Cluster Formation Determines Viscosity and Di usion in Dense Protein Solutions

Protein Short-Time Di usion in a Naturally Crowded Environment

Proteins and Antibodies in Serum, Plasma, and Whole Blood-Size Characterization Using Asymmetrical Flow Field-Flow Fractionation (AF4)

Weak Shape Anisotropy Leads to a Nonmonotonic Contribution to Crowding, Impacting Protein Dynamics under Physiologically Relevant Conditions

Dramatic In uence of Patchy Attractions on Short-Time Protein Diffusion under Crowded Conditions

Protein Translation inside Synthetic Membraneless Organelles

Determination of Protein Aggregation with Di erential Mobility Analysis: Application to IgG Antibody

Prevention of Thermally Induced Aggregation of IgG Antibodies by Noncovalent Interaction with Poly(Acrylate) Derivatives

A Colloid Approach to Self-Assembling Antibodies

Molecular Flexibility of Antibodies Preserved Even in the Dense Phase after Macroscopic Phase Separation

E ects of Proteins on Protein Di usion

Translational and Rotational Di usion of a Small Globular Protein under Crowded Conditions

Nuclear Magnetic Resonance of Rotational Mobility of Mouse Hemoglobin Labeled with (2-13C)Histidine

19F NMR Measurements of the Rotational Mobility of Proteins in Vivo

Crowding and Hydrodynamic Interactions Likely Dominate in Vivo Macromolecular Motion

Di usion of Injected Macromolecules within the Cytoplasm of Living Cells

Translational Diffusion of Globular Proteins in the Cytoplasm of Cultured Muscle Cells

Solute and Macromolecule Di usion in Cellular Aqueous Compartments

Anomalous Di usion of Proteins Due to Molecular Crowding

Tracer Di usion of Globular Proteins in Concentrated Protein Solutions

Crowding E ects on Di usion in Solutions and Cells

Macromolecular Crowding: Biochemical, Biophysical, and Physiological Consequences

Do Macromolecular Crowding Agents Exert Only an Excluded Volume E ect? A Protein Solvation Study

Protein Crowding A ects Hydration Structure and Dynamics

A Cell Is More than the Sum of Its (Dilute) Parts: A Brief History of Quinary Structure

Molecular Evolution, Intracellular Organization, and the Quinary Structure of Proteins

Biomolecular Interactions Modulate Macromolecular Structure and Dynamics in Atomistic Model of a Bacterial Cytoplasm

Variable Interactions between Protein Crowders and Biomolecular Solutes Are Important in Understanding Cellular Crowding

Cluster-Driven Dynamical Arrest in Concentrated Lysozyme Solutions

Equilibrium Clusters in Concentrated Lysozyme Protein Solutions

Formation of the Dynamic Clusters in Concentrated Lysozyme Protein Solutions

Lysozyme Protein Solution with an Intermediate Range Order Structure

Slow-Down in Di usion in Crowded Protein Solutions Correlates with Transient Cluster Formation

Anomalous Subdi usion Is a Measure for Cytoplasmic Crowding in Living Cells

Sampling the Cell with Anomalous Di usion-The Discovery of Slowness

Breaking the Radiation Damage Limit with Cryo-SAXS

Quantifying Radiation Damage in Biomolecular Small-Angle X-ray Scattering

Radiation Damage to Biological Macromolecules: Further Insights

Radiation Damage to a Protein Solution, Detected by Synchrotron X-ray Small-Angle Scattering: Dose-Related Considerations and Suppression by Cryoprotectants

Photon-In/Photon-Out X-ray Free-Electron Laser Studies of Radiolysis

Generation and Propagation of Radical Reactions on Proteins

Solvation Structure of Hydroxyl Radical by Car-Parrinello Molecular Dynamics

Materials Imaging and Dynamics (MID) Instrument at the European X-ray Free-Electron Laser Facility

E ective Interactions and Colloidal Stability of Bovine γ-Globulin in Solution

Microscopic Dynamics of Liquid-Liquid Phase Separation and Domain Coarsening in a Protein Solution Revealed by X-Ray Photon Correlation Spectroscopy

The Adaptive Gain Integrating Pixel Detector at the European XFEL

Optimizing the Signal-to-Noise Ratio for X-ray Photon Correlation Spectroscopy

Using Coherence to Measure Two-Time Correlation Functions

Time-Resolved Correlation: A New Tool for Studying Temporally Heterogeneous Dynamics

High Contrast X-ray Speckle from Atomic-Scale Order in Liquids and Glasses

Kinetics of Network Formation and Heterogeneous Dynamics of an Egg White Gel Revealed by Coherent X-Ray Scattering

Wave-Vector Dependence of the Dynamics in Supercooled Metallic Liquids

Entanglement-Controlled Subdi usion of Nanoparticles within Concentrated Polymer Solutions

Reaction Mechanisms in the Radiolysis of Peptides, Polypeptides, and Proteins

Observation of Decreased Radiation Damage at Higher Dose Rates in Room Temperature Protein Crystallography

Applications of the Spur Di usion Model to the Radiation Chemistry of Aqueous Solutions

Application and Theory of Petri Nets

Generation Mechanism of Hydroxyl Radical Species and Its Lifetime Prediction during the Plasma-Initiated Ultraviolet (UV)

Quantitative Estimation of Track Segment Yields of Water Radiolysis Species under Heavy Ions around Bragg Peak Energies Using Geant4-DNA

Kinetics of Protein-Protein Association Explained by Brownian Dynamics Computer Simulation

The Protein Folding 'Speed Limit'

Di raction before Destruction

Deciphering the Intrinsic Dynamics from the Beam-Induced Atomic Motions in Oxide Glasses

Interplay between Kinetics and Dynamics of Liquid-Liquid Phase Separation in a Protein Solution Revealed by Coherent X-ray Spectroscopy

We acknowledge the European XFEL in Schenefeld, Germany, for provision of X-ray free electron laser beamtime at Scienti c Instrument MID (Materials Imaging and Dynamics) and would like to thank the sta for their assistance. We acknowledge DESY ( 

pandemic. The manuscript was written by MR, FP and CG with input from all authors.

The authors declare no competing interests.