Phasing of coherent femtosecond X-ray diffraction from size-varying nanocrystals.

The scattering between Bragg reflections from nanocrystals is used to aid solution of the phase problem. We describe a method for reconstructing the charge density of a typical molecule within a single unit cell, if sufficiently finely-sampled "snap-shot" diffraction data (as provided a free-electron X-ray laser) are available from many nanocrystals of different sizes lying in random orientations. By using information on the particle-size distribution within the patterns, this digital method succeeds, using all the data, without knowledge of the distribution of particle size or requiring atomic-resolution data.

Femtosecond protein nanocrystallography-data analysis methods.

X-ray diffraction patterns may be obtained from individual submicron protein nanocrystals using a femtosecond pulse from a free-electron X-ray laser. Many "single-shot" patterns are read out every second from a stream of nanocrystals lying in random orientations. The short pulse terminates before significant atomic (or electronic) motion commences, minimizing radiation damage. Simulated patterns for Photosystem I nanocrystals are used to develop a method for recovering structure factors from tens of thousands of snapshot patterns from nanocrystals varying in size, shape and orientation. We determine the number of shots needed for a required accuracy in structure factor measurement and resolution, and investigate the convergence of our Monte-Carlo integration method.

Expression, purification and crystallization of CTB-MPR, a candidate mucosal vaccine component against HIV-1.

CTB-MPR is a fusion protein between the B subunit of cholera toxin (CTB) and the membrane-proximal region of gp41 (MPR), the transmembrane envelope protein of Human immunodeficiency virus 1 (HIV-1), and has previously been shown to induce the production of anti-HIV-1 antibodies with antiviral functions. To further improve the design of this candidate vaccine, X-ray crystallography experiments were performed to obtain structural information about this fusion protein. Several variants of CTB-MPR were designed, constructed and recombinantly expressed in Escherichia coli. The first variant contained a flexible GPGP linker between CTB and MPR, and yielded crystals that diffracted to a resolution of 2.3 Å, but only the CTB region was detected in the electron-density map. A second variant, in which the CTB was directly attached to MPR, was shown to destabilize pentamer formation. A third construct containing a polyalanine linker between CTB and MPR proved to stabilize the pentameric form of the protein during purification. The purification procedure was shown to produce a homogeneously pure and monodisperse sample for crystallization. Initial crystallization experiments led to pseudo-crystals which were ordered in only two dimensions and were disordered in the third dimension. Nanocrystals obtained using the same precipitant showed promising X-ray diffraction to 5 Šresolution in femtosecond nanocrystallography experiments at the Linac Coherent Light Source at the SLAC National Accelerator Laboratory. The results demonstrate the utility of femtosecond X-ray crystallography to enable structural analysis based on nano/microcrystals of a protein for which no macroscopic crystals ordered in three dimensions have been observed before.

Signal, noise, and resolution in correlated fluctuations from snapshot small-angle x-ray scattering.

It has been suggested that the three-dimensional structure of one particle may be reconstructed using the scattering from many identical, randomly oriented copies ab initio, without modeling or a priori information. This may be possible if these particles are frozen in either space or time, so that the conventional two-dimensional small-angle x-ray scattering (SAXS) distribution contains fluctuations and is no longer isotropic. We consider the magnitude of the correlated fluctuation SAXS (CFSAXS) signal for typical x-ray free-electron laser (XFEL) beam conditions and compare this against the errors derived with the inclusion of Poisson photon counting statistics. The resulting signal-to-noise ratio (SNR) is found to rapidly approach a limit independent of the number of particles contributing to each diffraction pattern, so that the addition of more particles to a "single-particle-per-shot" experiment may be of little value, apart from reducing solvent background. When the scattering power is significantly less than one photon per particle per Shannon pixel, the SNR grows in proportion to incident flux. We provide simulations for protein molecules in support of these analytical results, and discuss the effects of solvent background scatter. We consider the SNR dependence on resolution and particle size, and discuss the application of the method to glasses and liquids, and the implications of more powerful XFELs, smaller focused beams, and higher pulse repetition rates for this approach. We find that an accurate CFSAXS measurement may be acquired to subnanometer resolution for protein molecules if a 9-keV beam containing 10(13) photons is focused to a ~100-nm spot diameter, provided that the effects of solvent background can be reduced sufficiently.

Structure-factor analysis of femtosecond microdiffraction patterns from protein nanocrystals.

A complete set of structure factors has been extracted from hundreds of thousands of femtosecond single-shot X-ray microdiffraction patterns taken from randomly oriented nanocrystals. The method of Monte Carlo integration over crystallite size and orientation was applied to experimental data from Photosystem I nanocrystals. This arrives at structure factors from many partial reflections without prior knowledge of the particle-size distribution. The data were collected at the Linac Coherent Light Source (the first hard-X-ray laser user facility), to which was fitted a hydrated protein nanocrystal injector jet, according to the method of serial crystallography. The data are single 'still' diffraction snapshots, each from a different nanocrystal with sizes ranging between 100 nm and 2 µm, so the angular width of Bragg peaks was dominated by crystal-size effects. These results were compared with single-crystal data recorded from large crystals of Photosystem I at the Advanced Light Source and the quality of the data was found to be similar. The implications for improving the efficiency of data collection by allowing the use of very small crystals, for radiation-damage reduction and for time-resolved diffraction studies at room temperature are discussed.

Quantum Monte Carlo calculations of symmetric nuclear matter.

We present an accurate numerical study of the equation of state of nuclear matter based on realistic nucleon-nucleon interactions by means of auxiliary field diffusion Monte Carlo (AFDMC) calculations. The AFDMC method samples the spin and isospin degrees of freedom allowing for quantum simulations of large nucleonic systems and represents an important step forward towards a quantitative understanding of problems in nuclear structure and astrophysics.

1S0 Superfluid phase transition in neutron matter with realistic nuclear potentials and modern many-body theories.

The 1S0 pairing in neutron matter is studied using realistic two- and three-nucleon interactions. The auxiliary field diffusion Monte Carlo method and correlated basis function theory are employed to get quantitative and reliable estimates of the gap. The two methods are in good agreement up to the maximum gap density and both point to a slight reduction with respect to the standard BCS value. In fact, the maximum gap is about 2.5 MeV at kF approximately 0.8 fm(-1) in BCS and 2.2-2.4 MeV at kF approximately 0.6 fm(-1)in correlated matter. In general, the computed medium polarization effects are much smaller than those previously estimated within all theories. Truncations of Argonne to simpler forms give the same gaps in BCS, provided the truncated potentials have been refitted to the same data set. The three-nucleon interaction provides an additional increase of the gap of about 0.35 MeV.

HF dimer in small helium clusters: interchange-tunneling dynamics in a quantum environment.

We present diffusion quantum Monte Carlo calculations of the interchange tunneling splitting of (4)He(n)(HF)(2) clusters, n = 1-10. The tunneling splitting decreases rapidly for n = 1-4 clusters, and much more slowly for n>4. The decrease calculated for (4)He(n)(HF)(2) represents 74% of the reduction in the tunneling splitting measured recently for HF dimer in nanodroplets of more than 2000 He atoms. The first four He atoms quench the interchange tunneling very efficiently by virtue of occupying the equatorial ring which encircles the C(2h) transition state of the tunneling pathway.

Structure, rotational dynamics, and superfluidity of small OCS-doped He clusters.

The structural and dynamical properties of carbonyl sulfide (OCS) molecules solvated in helium clusters are studied using reptation quantum Monte Carlo, for cluster sizes n=3-20 He atoms. Computer simulations allow us to establish a relation between the rotational spectrum of the solvated molecule and the structure of the He solvent, and of both with the onset of superfluidity. Our results agree with a recent spectroscopic study of this system and provide a more complex and detailed microscopic picture of this system than inferred from experiments.