No abstract

Elastic incoherent neutron scattering (EINS) data can be approximated with a Gaussian function of q in a low q region. However, in a higher q region the deviation from a Gaussian function becomes non-negligible. Protein dynamic properties can be derived from the analyses of the non-Gaussian behavior, which has been experimentally investigated. To evaluate the origins of the non-Gaussian behavior of protein dynamics, we conducted a molecular dynamics (MD) simulation of staphylococcal nuclease. Instead of the ordinary cumulant expansion, we decomposed the non-Gaussian terms into three components: (i) the component originating from the heterogeneity of the mean-square fluctuation, (ii) that from the anisotropy, and (iii) that from higher-order terms such as anharmonicity. The MD simulation revealed various dynamics for each atom. The atomic motions are classified into three types: (i) "harmonic," (ii) "anisotropic," and (iii) "anharmonic." However, each atom has a different degree of anisotropy. The contribution of the anisotropy to the total scattering function averages out due to these differences. Anharmonic motion is described as the jump among multiple minima. The jump distance and the probability of the residence at one site vary from atom to atom. Each anharmonic component oscillates between positive and negative values. Thus, the contribution of the anharmonicity to the total scattering is canceled due to the variations in the anharmonicity. Consequently, the non-Gaussian behavior of the total EINS from a protein can be analyzed by the dynamical heterogeneity.

A new two-step algorithm is developed for reconstructing the three-dimensional diffraction intensity of a globular biological macromolecule from many experimentally measured quantum-noise-limited two-dimensional X-ray laser diffraction patterns, each for an unknown orientation. The first step is classification of the two-dimensional patterns into groups according to the similarity of direction of the incident X-rays with respect to the molecule and an averaging within each group to reduce the noise. The second step is detection of common intersecting circles between the signal-enhanced two-dimensional patterns to identify their mutual location in the three-dimensional wavenumber space. The newly developed algorithm enables one to detect a signal for classification in noisy experimental photon-count data with as low as $0.1 photons per effective pixel. The wavenumber of such a limiting pixel determines the attainable structural resolution. From this fact, the resolution limit due to the quantum noise attainable by this new method of analysis as well as two important experimental parameters, the number of two-dimensional patterns to be measured (the load for the detector) and the number of pairs of two-dimensional patterns to be analysed (the load for the computer), are derived as a function of the incident X-ray intensity and quantities characterizing the target molecule.

Three-dimensional (3D) structures of biomolecules provide insight into their functions. Using X-ray free-electron laser (XFEL) scattering experiments, it was possible to observe biomolecules that are difficult to crystallize, under conditions that are similar to their natural environment. However, resolving 3D structure from XFEL data is not without its challenges. For example, strong beam intensity is required to obtain sufficient diffraction signal and the beam incidence angles to the molecule need to be estimated for diffraction patterns with significant noise. Therefore, it is important to quantitatively assess how the experimental conditions such as the amount of data and their quality affect the expected resolution of the resulting 3D models. In this study, as an example, the restoration of 3D structure of ribosome from two-dimensional diffraction patterns created by simulation is shown. Tests are performed using the diffraction patterns simulated for different beam intensities and using different numbers of these patterns. Guidelines for selecting parameters for slice-matching 3D reconstruction procedures are established. Also, the minimum requirements for XFEL experimental conditions to obtain diffraction patterns for reconstructing molecular structures to a high-resolution of a few nanometers are discussed.