Simulation evidence for experimentally detectable low-temperature vibrational inhomogeneity in a globular protein

Far infrared spectroscopy of hydrogen bonding collective motions in complex molecular systems

Far infrared spectroscopy as a tool for the study of inter and intramolecular interactions in complex molecular structures.

On the relationship between low-frequency normal modes and the large-scale conformational changes of proteins

Normal mode analysis is a computational technique that allows to study the dynamics of biological macromolecules. It was first applied to small protein cases, more than thirty years ago. The interest in this technique then raised when it was realized that it can provide insights about the large-scale conformational changes a protein can experience, for instance upon ligand binding. As it was also realized that studying highly simplified protein models can provide similar insights, meaning that this kind of analysis can be both quick and simple to handle, several applications were proposed, in the context of various structural biology techniques. This review focuses on these applications, as well as on how the functional relevance of the lowest-frequency modes of proteins was established.

Conformational heterogeneity and low-frequency vibrational modes of proteins

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.

Neutron frequency windows and the protein dynamical transition

Proteins undergo an apparent dynamical transition on temperature variation that has been correlated with the onset of function. The transition in the mean-square displacement, , that is observed using a spectrometer or computer simulation, depends on the relationship between the timescales of the relaxation processes activated and the timescale accessible to the instrument or simulation. Models are described of two extreme situations---an "equilibrium" model, in which the long-time dynamics changes with temperature and all motions are resolved by the instrument used; and a "frequency window" model, in which there is no change in the long-time dynamics but as the temperature increases, the relaxation frequencies move into the instrumental range. Here we demonstrate that the latter, frequency-window model can describe the temperature and timescale dependences of both the intermediate neutron scattering function and derived from molecular dynamics simulations of a small protein in a cryosolution. The frequency-window model also describes the energy-resolution and temperature-dependences of obtained from experimental neutron scattering on glutamate dehydrogenase in the same solvent. Although equilibrium effects should also contribute to dynamical transitions in proteins, the present results suggests that frequency-window effects can play a role in the simulations and experiments examined. Finally, misquotations of previous findings are discussed in the context of solvent activation of protein dynamics and the possible relationship of this to activity.

Energy resolution and dynamical heterogeneity effects on elastic incoherent neutron scattering from molecular systems

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.

Temperature dependence of protein dynamics: computer simulation analysis of neutron scattering properties

The temperature dependence of the internal dynamics of an isolated protein, bovine pancreatic trypsin inhibitor, is examined using normal mode analysis and molecular dynamics (MD) simulation. It is found that the protein exhibits marked anharmonic dynamics at temperatures of approximately 100-120 K, as evidenced by departure of the MD-derived average mean square displacement from that of the harmonic model. This activation of anharmonic dynamics is at lower temperatures than previously detected in proteins and is found in the absence of solvent molecules. The simulation data are also used to investigate neutron scattering properties. The 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.

Solvent dependence of dynamic transitions in protein solutions

A transition as a function of increasing temperature from harmonic to anharmonic dynamics has been observed in globular proteins by using spectroscopic, scattering, and computer simulation techniques. We present here results of a dynamic neutron scattering analysis of the solvent dependence of the picosecond-time scale dynamic transition behavior of solutions of a simple single-subunit enzyme, xylanase. The protein is examined in powder form, in D(2)O, and in four two-component perdeuterated single-phase cryosolvents in which it is active and stable. The scattering profiles of the mixed solvent systems in the absence of protein are also determined. The general features of the dynamic transition behavior of the protein solutions follow those of the solvents. The dynamic transition in all of the mixed cryosolvent-protein systems is much more gradual than in pure D(2)O, consistent with a distribution of energy barriers. The differences between the dynamic behaviors of the various cryosolvent protein solutions themselves are remarkably small. The results are consistent with a picture in which the picosecond-time scale atomic dynamics respond strongly to melting of pure water solvent but are relatively invariant in cryosolvents of differing compositions and melting points.

Tertiary and quaternary conformational changes in aspartate transcarbamylase: a normal mode study

Aspartate transcarbamylase (ATCase) initiates the pyrimidine biosynthetic pathway in Escherichia coli. Binding of aspartate to this allosteric enzyme induces a cooperative transition between the tensed (T) and relaxed (R) states of the enzyme which involves large quaternary and tertiary rearrangements. The mechanisms of the transmission of the regulatory signal to the active site (60 A away) and that of the cooperative transition are not known in detail, although a large number of single, double, and triple site-specific mutants and chimeric forms of ATCase have been obtained and kinetically characterized. A previous analysis of the very low-frequency normal modes of both the T and R state structures of ATCase identified some of the large-amplitude motions mediating the intertrimer elongation and rotation that occur during the cooperative transition (Thomas et al., J. Mol. Biol. 257:1070-1087, 1996; Thomas et al., J. Mol. Biol. 261:490-506, 1996). As a complement to that study, the deformation of the quaternary and tertiary structure of ATCase by normal modes below 5 cm(-1) is investigated in this article. The ability of the modes to reproduce the domain motions occurring during the transition is analyzed, with special attention to the interdomain closure in the catalytic chain, which has been shown to be critical for homotropic cooperativity. The calculations show a coupling between the quaternary motions and more localized motions involving specific residues. The particular dynamic behavior of these residues is examined in the light of biochemical results to obtain insights into their role in the transmission of the allosteric signal.

Analysis of domain motions by approximate normal mode calculations

The identification of dynamical domains in proteins and the description of the low-frequency domain motions are one of the important applications of numerical simulation techniques. The application of these techniques to large proteins requires a substantial computational effort and therefore cannot be performed routinely, if at all. This article shows how physically motivated approximations permit the calculation of low-frequency normal modes in a few minutes on standard desktop computers. The technique is based on the observation that the low-frequency modes, which describe domain motions, are independent of force field details and can be obtained with simplified mechanical models. These models also provide a useful measure for rigidity in proteins, allowing the identification of quasi-rigid domains. The methods are validated by application to three well-studied proteins, crambin, lysozyme, and ATCase. In addition to being useful techniques for studying domain motions, the success of the approximations provides new insight into the relevance of normal mode calculations and the nature of the potential energy surface of proteins.