Coherent diffraction of a single virus particle: the impact of a water layer on the available orientational information.

Coherent diffractive imaging using x-ray free-electron lasers (XFELs) may provide a unique opportunity for high-resolution structural analysis of single particles sprayed from an aqueous solution into the laser beam. As a result, diffraction images are measured from randomly oriented objects covered by a water layer. We analyze theoretically how the thickness of the covering water layer influences the structural and orientational information contained in the recorded diffraction images. This study has implications for planned experiments on single-particle imaging with XFELs.

Observation of structural anisotropy and the onset of liquidlike motion during the nonthermal melting of InSb.

The melting dynamics of laser excited InSb have been studied with femtosecond x-ray diffraction. These measurements observe the delayed onset of diffusive atomic motion, signaling the appearance of liquidlike dynamics. They also demonstrate that the root-mean-squared displacement in the [111] direction increases faster than in the [110] direction after the first 500 fs. This structural anisotropy indicates that the initially generated fluid differs significantly from the equilibrium liquid.

Clocking femtosecond X rays.

Linear-accelerator-based sources will revolutionize ultrafast x-ray science due to their unprecedented brightness and short pulse duration. However, time-resolved studies at the resolution of the x-ray pulse duration are hampered by the inability to precisely synchronize an external laser to the accelerator. At the Sub-Picosecond Pulse Source at the Stanford Linear-Accelerator Center we solved this problem by measuring the arrival time of each high energy electron bunch with electro-optic sampling. This measurement indirectly determined the arrival time of each x-ray pulse relative to an external pump laser pulse with a time resolution of better than 60 fs rms.

Atomic-scale visualization of inertial dynamics.

The motion of atoms on interatomic potential energy surfaces is fundamental to the dynamics of liquids and solids. An accelerator-based source of femtosecond x-ray pulses allowed us to follow directly atomic displacements on an optically modified energy landscape, leading eventually to the transition from crystalline solid to disordered liquid. We show that, to first order in time, the dynamics are inertial, and we place constraints on the shape and curvature of the transition-state potential energy surface. Our measurements point toward analogies between this nonequilibrium phase transition and the short-time dynamics intrinsic to equilibrium liquids.

Potential for biomolecular imaging with femtosecond X-ray pulses.

Sample damage by X-rays and other radiation limits the resolution of structural studies on non-repetitive and non-reproducible structures such as individual biomolecules or cells. Cooling can slow sample deterioration, but cannot eliminate damage-induced sample movement during the time needed for conventional measurements. Analyses of the dynamics of damage formation suggest that the conventional damage barrier (about 200 X-ray photons per A2 with X-rays of 12 keV energy or 1 A wavelength) may be extended at very high dose rates and very short exposure times. Here we have used computer simulations to investigate the structural information that can be recovered from the scattering of intense femtosecond X-ray pulses by single protein molecules and small assemblies. Estimations of radiation damage as a function of photon energy, pulse length, integrated pulse intensity and sample size show that experiments using very high X-ray dose rates and ultrashort exposures may provide useful structural information before radiation damage destroys the sample. We predict that such ultrashort, high-intensity X-ray pulses from free-electron lasers that are currently under development, in combination with container-free sample handling methods based on spraying techniques, will provide a new approach to structural determinations with X-rays.

The solution conformations of amino acids from molecular dynamics simulations of Gly-X-Gly peptides: comparison with NMR parameters.

The conformations that amino acids can adopt in the random coil state are of fundamental interest in the context of protein folding research and studies of protein-peptide interactions. To date, no detailed quantitative data from experimental studies have been reported; only nuclear magnetic resonance parameters such as chemical shifts and J coupling constants have been reported. These experimental nuclear magnetic resonance data represent averages over multiple conformations, and hence they do not provide unique structural information. I have performed relatively long (2.5 ns) molecular dynamics simulations of Gly-X-Gly tripeptides, surrounded by explicit water molecules, where X represents eight different amino acids with long side chains. From the trajectories one can calculate time averaged backbone chemical shifts and 3J(NH alpha) coupling constants and compare these with experimental data. These calculated quantities are quite close to the experimental values for most amino acids, suggesting that these simulations are a good model for the random coil state of the tripeptides. On the basis of my simulations I predict 3J(alphabeta) coupling constants and present dihedral distributions for the phi, psi, as well as chi1 and chi2 angles. Finally, I present correlation plots for these dihedral angles.

Molecular dynamics simulations of Leu-enkephalin in water and DMSO.

The structure of Leu-enkephalin (L-Enk) and Met-enkephalin (M-Enk) have frequently been studied, in particular by nuclear magnetic resonance spectroscopy. After more than 20 years of research, it was concluded that enkephalins have no preferred structure in aqueous solution, but that they may have in other solvents. We have performed molecular dynamics simulations of zwitterionic L-Enk in water, and zwitterionic as well as neutral L-Enk dimethyl sulfoxide (DMSO). In water the peptide is very flexible, although there seems to be a preference for compact conformations. In DMSO, the peptide forms a clear salt bridge in the zwitterionic form, but has no preferred conformation in the neutral form. This difference in conformation may provide an explanation for measurements in DMSO in which multiple conformations were found to exist. In this paper we introduce a new formulation for a dihedral angle autocorrelation function, and apply it to study side-chain dynamics in L-Enk. We find that the side-chain dynamics of the large Tyr and Phe residues cannot be adequately sampled in 2.0-ns simulations, while this does seem to be possible for the smaller Leu side chain.

Molecular modeling of the RNA binding N-terminal part of cowpea chlorotic mottle virus coat protein in solution with phosphate ions.

The RNA-binding N-terminal arm of the coat protein of cowpea chlorotic mottle virus has been studied with five molecular dynamics simulations of 2.0 ns each. This 25-residue peptide (pep25) is highly charged: it contains six Arg and three Lys residues. An alpha-helical fraction of the sequence is stabilized in vitro by salts. The interaction of monophosphate (Pi) ions with pep25 was studied, and it was found that only two Pi ions are bound to pep25 on average, but water-mediated interactions between pep25 and Pi, which provide electrostatic screening for intrapeptide interactions, are abundant. Shielding by the Pi ions of repulsive electrostatic interactions between Arg sidechains increases the alpha-helicity of pep25. A hydrogen bond at the N-terminal end of the alpha-helix renders extension of the alpha-helix in the N-terminal direction impossible, in agreement with evidence from nuclear magnetic resonance experiments.

Molecular dynamics simulations of peptides from BPTI: a closer look at amide-aromatic interactions.

Molecular dynamics (MD) simulations of short peptides in water were performed to establish whether it is possible to reproduce experimental data from chemical shift measurements by nuclear magnetic resonance spectroscopy. Three different tetrapeptides were studied. The first, YTGP (Tyr-Thr-Gly-Pro), shows an electrostatic interaction between the aromatic ring of Tyr and the backbone amide hydrogen atom of Gly. The second, YTAP (Tyr-Thr-Ala-Pro), cannot make such an interaction because of steric hindrance of the Ala side chain and hence does not show a well-defined conformation. The third, FTGP (Phe-Thr-Gly-Pro), is shown to alternate between two different conformations. It is demonstrated that small differences in chemical shift, corresponding to these slightly different conformations, can be quantitatively modeled in MD simulations when using the proper force-field parameters and water model Explicit inclusion of hydrogen atoms o the aromatic rings is essential for a proper description of electrostatic interactions, but the choice of the water model is equally important. We found that a combination of the SPC/E water model and a revised GROMOS87 force field gives close agreement with experiment, while the same and other force fields in combination with SPC or TIP3P water did not reproduce the NMR data at all. Simulations of a longer peptide from bovine pancreatic trypsin inhibitor, containing the YTGP sequence, did show the interaction between the aromatic ring and the amide hydrogen, but not as pronounced as the simulations of shorter periods.

Bending of the calmodulin central helix: a theoretical study.

The crystal structure of calcium-calmodulin (CaM) reveals a protein with a typical dumbbell structure. Various spectroscopic studies have suggested that the central linker region of CaM, which is alpha-helical in the crystal structure, is flexible in solution. In particular, NMR studies have indicated the presence of a flexible backbone between residues Lys 77 and Asp 80. This flexibility is related directly to the function of the protein because it enables the N- and C-terminal domains of the protein to move toward each other and bind to the CaM-binding domain of a target protein. We have investigated the flexibility of the CaM central helix by a variety of computational techniques: molecular dynamics (MD) simulations, normal mode analysis (NMA), and essential dynamics (ED) analysis. Our MD results reproduce the experimentally determined location of the bend in a simulation of only the CaM central helix, indicating that the bending point is an intrinsic property of the alpha-helix, for which the remainder of the protein is not important. Interestingly, the modes found by the ED analysis of the MD trajectory are very similar to the lowest frequency modes from the NM analysis and to modes found by an ED analysis of different structures in a set of NMR structures. Electrostatic interactions involving residues Arg 74 and Asp 80 seem to be important for these bending motions and unfolding, which is in line with pH-dependent NMR and CD studies.

Molecular dynamics simulations of N-terminal peptides from a nucleotide binding protein.

Molecular dynamics (MD) simulations of N-terminal peptides from lactate dehydrogenase (LDH) with increasing length and individual secondary structure elements were used to study their stability in relation to folding. Ten simulations of 1-2 ns of different peptides in water starting from the coordinates of the crystal structure were performed. The stability of the peptides was compared qualitatively by analyzing the root mean square deviation (RMSD) from the crystal structure, radius of gyration, secondary and tertiary structure, and solvent accessible surface area. In agreement with earlier MD studies, relatively short (< 15 amino acids) peptides containing individual secondary structure elements were generally found to be unstable; the hydrophobic alpha 1-helix of the nucleotide binding fold displayed a significantly higher stability, however. Our simulations further showed that the first beta alpha beta supersecondary unit of the characteristic dinucleotide binding fold (Rossmann fold) of LDH is somewhat more stable than other units of similar length and that the alpha 2-helix, which unfolds by itself, is stabilized by binding to this unit. This finding suggests that the first beta alpha beta unit could function as an N-terminal folding nucleus, upon which the remainder of the polypeptide chain can be assembled. Indeed, simulations with longer units (beta-alpha-beta-alpha and beta-alpha-beta-alpha beta-beta) showed that all structural elements of these units are rather stable. The outcome of our studies is in line with suggestions that folding of the N-terminal portion of LDH in vivo can be a cotranslational process that takes place during the ribosomal peptide synthesis.

Phosphorylation-induced torsion-angle strain in the active center of HPr, detected by NMR and restrained molecular dynamics refinement.

The structure of the phosphorylated form of the histidine-containing phosphocarrier protein HPr from Escherichia coli has been solved by NMR and compared with that of unphosphorylated HPr. The structural changes that occur upon phosphorylation of His 15, monitored by changes in NOE patterns, 3JNHH alpha-coupling constants, and chemical shifts, are limited to the region around the phosphorylation site. The His15 backbone torsion angles become strained upon phosphorylation. The release of this strain during the phosphoryl-transfer to Enzyme II facilitates the transport of carbohydrates across the membrane. From an X-ray study of Streptococcus faecalis HPr (Jia Z, Vandonselaar M, Quail JW, Delbaere LTJ, 1993, Nature 361:94-97), it was proposed that the observed torsion-angle strain at residue 16 in unphosphorylated S. faecalis HPr has a role to play in the protein's phosphocarrier function. The model predicts that this strain is released upon phosphorylation. Our observations on E. coli HPr in solution, which shows strain only after phosphorylation, and the fact that all other HPrs studied thus far in their unphosphorylated forms show no strain either, led us to investigate the possibility that the crystal environment causes the strain in S. faecalis HPr. A 1-ns molecular dynamics simulation of S. faecalis HPr, under conditions that mimic the crystal environment, confirms the observations from the X-ray study, including the torsion-angle strain at residue 16. The strain disappeared, however, when S. faecalis HPr was simulated in a water environment, resulting in an active site configuration virtually the same as that observed in all other unphosphorylated HPrs. This indicates that the torsion-angle strain at Ala 16 in S. faecalis HPr is a result of crystal contacts or conditions and does not play a role in the phosphorylation-dephosphorylation cycle.

Determination of proton transfer rate constants using Ab initio, molecular dynamics and density matrix evolution calculations.

In this work we give an overview of the methodologies required to compute the rate of proton transfer in hydrogen bonded systems in solution. Using ab initio or density functional methods we determine proton potentials of a truncated system as a function of proton-donor proton-acceptor distance as well as nonbonding parameters. By classical molecular dynamics we evaluate a swarm of proton potentials with the proton fixed in the reactant well. The rate of proton transfer is calculated perturbatively using the Density Matrix Evolution (DME) method, going beyond the Born Oppenheimer approximation. The method is illustrated by two examples: hydrogen malonate and the active center of HIV-1 protease.