[en] Elastic and quasielastic neutron scattering experiments on complex systems are often difficult to interpret unambiguously directly using analytical dynamical models. In such cases computer simulations can be used to provide information at atomic detail. Here we report on the use of normal mode analysis (NMA) and molecular dynamics (MD) simulations of a small protein, bovine pancreatic trypsin inhibitor (BPTI) in vacuum and in various solvents. The simulations were performed over a range of temperatures (80-300 K). The vacuum simulation data are used to investigate neutron scattering properties. Effects are determined of instrumental energy resolution and of approximations commonly used to extract mean-square displacement data from elastic scattering experiments. Both the presence of a distribution of mean-square displacements in the protein and the use of the Gaussian approximation to the dynamic structure factor lead to quantified underestimation of the mean-square displacement obtained. Variation of the environment of the protein shows that the dry protein has higher fluctuations at lower temperatures than in the solvated protein, in agreement with recent experiments , that the dynamical transition is solvent-independent on short timescales (also in agreement with experiment ), and that at longer timescales it is strongly activated by water

[en] An understanding of low-frequency, collective protein dynamics at low temperatures can furnish valuable information on functional protein energy landscapes, on the origins of the protein glass transition and on protein-protein interactions. Here, molecular dynamics (MD) simulations and normal-mode analyses are performed on various models of crystalline myoglobin in order to characterize intra- and interprotein vibrations at 150 K. Principal component analysis of the MD trajectories indicates that the Boson peak, a broad peak in the dynamic structure factor centered at about 2-2.5 meV, originates from 102 collective, harmonic vibrations. An accurate description of the environment is found to be essential in reproducing the experimental Boson peak form and position. At lower energies other strong peaks are found in the calculated dynamic structure factor. Characterization of these peaks shows that they arise from harmonic vibrations of proteins relative to each other. These vibrations are likely to furnish valuable information on the physical nature of protein-protein interactions

[en] The dynamical origin of the x-ray diffuse scattering by crystals of a protein, Staphylococcal nuclease, is determined using molecular dynamics simulation. A smooth, nearly isotropic scattering shell at q=0.28 A ring ^-1 originates from equal contributions from correlations in nearest-neighbor water molecule dynamics and from internal protein motions, the latter consisting of α-helix pitch and inter-β-strand fluctuations. Superposed on the shell are intense, three-dimensional scattering features that originate from a very small number of slowly varying (>10 ns) collective motions. The individual three-dimensional features are assigned to specific collective motions in the protein, and some of these explicitly involve potentially functional active-site deformations

[en] Understanding the mechanism of proton pumping requires a detailed description of the energetics and sequence of events associated with the proton transfers, and of how proton transfer couples to conformational rearrangements of the protein. Here, we discuss our recent advances in using computer simulations to understand how bacteriorhodopsin pumps protons. We emphasize the importance of accurately describing the retinal geometry and the location of water molecules

[en] Molecular dynamics simulations of a crystalline protein, Staphylococcal nuclease, over the pressure range 1 bar to 15 kbar reveal a qualitative change in the internal protein motions at ≅4 kbar. This change involves the existence of two linear regimes in the mean-square displacement for internal protein motion, < u²>(P) with a twofold decrease in the slope for P>4 kbar. The major effect of pressure on the dynamics is a loss, with increasing pressure of large amplitude, collective protein modes below 2 THz effective frequency, accompanied by restriction of large-scale solvent translational motion

[en] Incoherent neutron scattering is widely used to probe picosecond-nanosecond time scale dynamics of molecular systems. In systems of spatially confined atoms the relatively high intensity of elastic incoherent neutron scattering is often used to obtain a first estimate of the dynamics present. For many complex systems, however, experimental elastic scattering is difficult to interpret unambiguously using analytical dynamical models that go beyond the determination of an average mean-square displacement. To circumvent this problem a description of the scattering is derived here that encompasses a variety of analytical models in a common framework. The framework describes the time-converged part of the dynamic structure factor [the elastic incoherent scattering function (EISF)] and lends itself to practical use by explicitly incorporating effects due to the finite energy resolution of the instrument used. The dependence of the elastic scattering on wave vector is examined, and it is shown how heterogeneity in the distribution of mean-square displacements can be related to deviations of the scattering from Gaussian behavior. In this case, a correction to fourth order in the scattering vector can be used to extract the variance of the distribution of mean-square displacements. The formalism is used in a discussion of measurements on dynamics accompanying the glass transition in molecular systems. By fitting to experimental data obtained on a protein solution the present methodology is used to show how the existence of a temperature-dependent relaxation frequency can lead to a transition in the measured mean-square displacement in the absence of an EISF change

[en] The role of methyl groups in the onset of low-temperature anharmonic dynamics in a crystalline protein at low temperature is investigated using atomistic molecular dynamics (MD) simulation. Anharmonicity appears at 150 ∼ K, far below the much-studied solvent-activated dynamical transition at ∼ 220 K. A significant fraction of methyl groups exhibit nanosecond time scale rotational jump diffusion at 150 K. The splitting and shift in peak position of both the librational band (around 100 cm^-1) and the torsional band (around 270?300 cm^-1) also differ significantly among methyl groups, depending on the local environment. The simulation results provide no evidence for a correlation between methyl dynamics and solvent exposure, consistent with the hydration-independence of the low-temperature anharmonic dynamics observed in neutron scattering experiments. The calculated proton mean-square fluctuation and methyl NMR order parameters show a systematic nonlinear dependence on the rotational barrier which can be described using model functions. The methyl groups that exhibit many rotational excitations are located near xenon cavities, suggesting that cavities in proteins act as activation centers of anharmonic dynamics. The dynamic heterogeneity and the environmental sensitivity of motional parameters and low-frequency spectral bands of CH3 groups found here suggest that methyl dynamics may be used as a probe to investigate the relation between low-energy structural fluctuations and packing defects in proteins

[en] In the light-driven bacteriorhodopsin proton pump, the first proton transfer step is from the retinal Schiff base to a nearby carboxylate group. The mechanism of this transfer step is highly controversial, in particular whether a direct proton jump is allowed. Here, we review the structural and energetic determinants of the direct proton transfer path computed by using a combined quantum mechanical/molecular mechanical approach. Both protein flexibility and electrostatic interactions play an important role in shaping the proton transfer energy profile. Detailed analysis of the energetics of putative transitions in the first half of the photocycle focuses on two elements that determine the likelihood that a given configuration of the active site is populated during the proton-pumping cycle. First, the rate-limiting barrier for proton transfer must be consistent with the kinetics of the photocycle. Second, the active-site configuration must be compatible with a productive overall pumping cycle

[en] The change of protein vibrations on ligand binding is of functional and thermodynamic importance. Here, this process is characterized using a simple analytical 'ball-and-spring' model and all-atom normal-mode analysis (NMA) of the binding of the cancer drug, methotrexate (MTX) to its target, dihydrofolate reductase (DHFR). The analytical model predicts that the coupling between protein vibrations and ligand external motion generates entropy-rich, low-frequency vibrations in the complex. This is consistent with the atomistic NMA which reveals vibrational softening in forming the DHFR-MTX complex, a result also in qualitative agreement with neutron-scattering experiments. Energy minimization of the atomistic bound-state (B) structure while gradually decreasing the ligand interaction to zero allows the generation of a hypothetical 'intermediate' (I) state, without the ligand force field but with a structure similar to that of B. In going from I to B, it is found that the vibrational entropies of both the protein and MTX decrease while the complex structure becomes enthalpically stabilized. However, the relatively weak DHFR:MTX interaction energy results in the net entropy gain arising from coupling between the protein and MTX external motion being larger than the loss of vibrational entropy on complex formation. This, together with the I structure being more flexible than the unbound structure, results in the observed vibrational softening on ligand binding.

[en] Molecular dynamics simulation and normal mode analysis are used to calculate the vibrational density of states of dihydrofolate reductase complexed with nicotinamide adenine dinucleotide phosphate at 120 K and the results are compared with the experimental spectrum derived from inelastic neutron scattering. The simulation results indicate that the experimental spectrum arises from an average over proteins trapped in different conformations with structural differences mainly in the loop regions, and that these conformations have significantly different low-frequency (<20 cm-1) spectra. Thus, the experimentally measured spectrum is an average over the vibrational modes of different protein conformations and is thus inhomogeneously broadened. The implications of this broadening for future neutron scattering experiments and ligand binding calculations are discussed