Macromolecular crowding in biological media is an essential factor for cellular function. The interplay of intermolecular interactions at multiple time and length scales governs a fine-tuned system of reaction and transport processes, including particularly protein diffusion as a limiting or driving factor. Using quasielastic neutron backscattering, we probe the protein self-diffusion in crowded aqueous solutions of bovine serum albumin on nanosecond time and nanometer length scales employing the same protein as crowding agent. The measured diffusion coefficient DðφÞ strongly decreases with increasing protein volume fraction φ explored within 7% ≤ φ ≤ 30%. With an ellipsoidal protein model and an analytical framework involving colloid diffusion theory, we separate the rotational D r ðφÞ and translational D t ðφÞ contributions to DðφÞ. The resulting D t ðφÞ is described by short-time self-diffusion of effective spheres. Protein self-diffusion at biological volume fractions is found to be slowed down to 20% of the dilute limit solely due to hydrodynamic interactions. macromolecular crowding | quasi-elastic neutron scattering | globular proteins T he interior of biological cells is a medium with a macromolecular volume fraction of up to 40%. This crowding crucially affects reaction kinetics and equilibria in the cell (1, 2). Cellular function and structure thus cannot be understood without a systematic understanding of both phase behavior and transport processes in crowded media. Diffusion is the main transport process for systems at low Reynolds numbers, governing many dynamic processes in nature (3). From the perspective of a single tracer molecule, all other molecules act as obstacles. In vivo diffusion coefficients for globular proteins in living cells (4-7) are strongly decreased compared to the in vitro diffusion coefficient in dilute buffer solutions. Systematic measurements of the tracer diffusion of proteins dissolved in concentrated suspensions of crowding agents, i.e., other proteins or polymers, reveal a complex dependence of the slowing down on the combination of tracer molecule and crowding agent (8-10). Furthermore, macromolecular crowding is found to induce subdiffusive behavior in several cases (11,12), being suggested as a slower but more reliable diffusive search process inside the cell (13). This anomalous diffusion process has been found also in theory and simulations (12-15) suggesting a crossover from subdiffusive behavior at small times to diffusive behavior at larger times.Proteins are macromolecules generally with a nonspherical shape and a nonhomogeneous surface charge, showing specific interactions with ligands. Furthermore, proteins not only show global motions like translational and rotational diffusion but also internal and interdomain motions. Therefore, proteins pose a challenge to colloid theory (16,17). In a recent simulation study Ando and Skolnick (4) revealed that using an equivalent-sphere model for macromolecules is a reasonable approximation to describe diffusion. Moreover, ...

We report on a joint experimental-theoretical study of collective diffusion in, and static shear viscosity of solutions of bovine serum albumin (BSA) proteins, focusing on the dependence on protein and salt concentration. Data obtained from dynamic light scattering and rheometric measurements are compared to theoretical calculations based on an analytically treatable spheroid model of BSA with isotropic screened Coulomb plus hard-sphere interactions. The only input to the dynamics calculations is the static structure factor obtained from a consistent theoretical fit to a concentration series of small-angle X-ray scattering (SAXS) data. This fit is based on an integral equation scheme that combines high accuracy with low computational cost. All experimentally probed dynamic and static properties are reproduced theoretically with an at least semi-quantitative accuracy. For lower protein concentration and low salinity, both theory and experiment show a maximum in the reduced viscosity, caused by the electrostatic repulsion of proteins. The validity range of a generalized Stokes-Einstein (GSE) relation connecting viscosity, collective diffusion coefficient, and osmotic compressibility, proposed by Kholodenko and Douglas [PRE, 1995[PRE, , 51, 1081 is examined. Significant violation of the GSE relation is found, both in experimental data and in theoretical models, in semi-dilute systems at physiological salinity, and under low-salt conditions for arbitrary protein concentrations.

The dynamics of proteins in solution is a complex and hierarchical process, affected by the aqueous environment as well as temperature. We present a comprehensive study on nanosecond time and nanometer length scales below, at, and above the denaturation temperature Td. Our experimental data evidence dynamical processes in protein solutions on three distinct time scales. We suggest a consistent physical picture of hierarchical protein dynamics: (i) self-diffusion of the entire protein molecule is confirmed to agree with colloid theory for all temperatures where the protein is in its native conformational state. At higher temperatures T > Td, the self-diffusion is strongly obstructed by cross-linking or entanglement. (ii) The amplitude of backbone fluctuations grows with increasing T, and a transition in its dynamics is observed above Td. (iii) The number of mobile side-chains increases sharply at Td while their average dynamics exhibits only little variations. The combination of quasi-elastic neutron scattering and the presented analytical framework provides a detailed microscopic picture of the protein molecular dynamics in solution, thereby reflecting the changes of macroscopic properties such as cluster formation and gelation.

Abstract. Proteins in solution move subject to a complex superposition of global translational and rotational diffusion as well as internal relaxations covering a wide range of time scales. With the advent of new high-flux neutron spectrometers in combination with enhanced analysis frameworks it has become possible to separate these different contributions. We discuss new approaches to the analysis by presenting example spectra and fits from data recorded on the backscattering spectrometers IN16, IN16B, and BASIS on the same protein solution sample. We illustrate the separation of the rotational and translational diffusion contribution, the accurate treatment of the solvent contribution, and the extraction of information on internal fluctuations. We also exemplify the progress made in passing from second-to third-generation backscattering spectrometers.

The short-time self-diffusion D of the globular model protein bovine serum albumin in aqueous (D2O) solutions has been measured comprehensively as a function of the protein and trivalent salt (YCl3) concentration, noted cp and cs, respectively. We observe that D follows a universal master curve D(cs,cp) = D(cs = 0,cp) g(cs/cp), where D(cs = 0,cp) is the diffusion coefficient in the absence of salt and g(cs/cp) is a scalar function solely depending on the ratio of the salt and protein concentration. This observation is consistent with a universal scaling of the bonding probability in a picture of cluster formation of patchy particles. The finding corroborates the predictive power of the description of proteins as colloids with distinct attractive ion-activated surface patches.

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Cold‐neutron backscattering spectrometers are designed for inelastic neutron scattering experiments at a high energy resolution, where 0.5 µeV FWHM can routinely be achieved at the incident wavelength λ≃ 6.3 Å. The phase‐space transformation (PST) technique can be used to enhance the neutron flux at the sample position of such backscattering spectrometers at the expense of an acceptable increase of the beam divergence. Technically, the PST is achieved by a rotating disc carrying mosaic crystals on its circumference. Here a new analytical framework to describe the Bragg reflection of a divergent polychromatic beam from a moving mosaic crystal is discussed. Results obtained using this framework are compared with detailed Monte Carlo numerical simulations. The results presented here provide a deeper understanding of the PST and in particular of the optimum circumferential crystal speed of a PST device.