Protein Boson Peak Originated from Hydration-Related Multiple Minima Energy Landscape

Principal Component Analysis and Related Methods for Investigating the Dynamics of Biological Macromolecules

Principal component analysis (PCA) is used to reduce the dimensionalities of high-dimensional datasets in a variety of research areas. For example, biological macromolecules, such as proteins, exhibit many degrees of freedom, allowing them to adopt intricate structures and exhibit complex functions by undergoing large conformational changes. Therefore, molecular simulations of and experiments on proteins generate a large number of structure variations in high-dimensional space. PCA and many PCA-related methods have been developed to extract key features from such structural data, and these approaches have been widely applied for over 30 years to elucidate macromolecular dynamics. This review mainly focuses on the methodological aspects of PCA and related methods and their applications for investigating protein dynamics.

Cancellation between auto- and mutual correlation contributions of protein/water dynamics in terahertz time-domain spectra

Terahertz time-domain spectra (THz-TDS) were investigated using the results of molecular dynamics (MD) simulations of Staphylococcal nuclease at two hydration states in the temperature range between 100 and 300 K. The temperature dependence of THz-TDS was found to differ significantly from that of the incoherent neutron scattering spectra (INSS) calculated from the same MD simulation results. We further examined contributions of the mutual and auto-correlations of the atomic fluctuations to THz-TDS and found that the negative value of the former contribution nearly canceled out the positive value of the latter, resulting in a monotonic increase of the reduced absorption cross section. Because of this cancellation, no distinct broad peak was observed in the absorption lineshape function of THz-TDS, whereas the protein boson peak was observed in INSS. The contribution of water molecules to THz-TDS was extremely large for the hydrated protein at temperatures above 200 K, in which large-amplitude motions of water were excited. The combination of THz-TDS, INSS and MD simulations has the potential to extract function-relevant protein dynamics occurring on the picosecond to nanosecond timescale.

Universality and Structural Implications of the Boson Peak in Proteins

The softness and rigidity of proteins are reflected in the structural dynamics, which are in turn affected by the environment. The characteristic low-frequency vibrational spectrum of a protein, known as boson peak, is an indication of the structural rigidity of the protein at a cryogenic temperature or dehydrated conditions. In this article, the effect of hydration, temperature, and pressure on the boson peak and volumetric properties of a globular protein are evaluated by using inelastic neutron scattering and molecular dynamics simulation. Hydration, pressurization, and cooling shift the boson peak position to higher energy and depress the peak intensity and decreases the protein and cavity volumes. We found the correlation between the boson peak and cavity volume in a protein. A decrease of cavity volume means the increase of rigidity, which is the origin of the boson peak shift. Boson peak is the universal property of a protein, which is rationalized by the correlation.

Dynamics of proteins in solution

The dynamics of proteins in solution includes a variety of processes, such as backbone and side-chain fluctuations, interdomain motions, as well as global rotational and translational (i.e. center of mass) diffusion. Since protein dynamics is related to protein function and essential transport processes, a detailed mechanistic understanding and monitoring of protein dynamics in solution is highly desirable. The hierarchical character of protein dynamics requires experimental tools addressing a broad range of time- and length scales. We discuss how different techniques contribute to a comprehensive picture of protein dynamics, and focus in particular on results from neutron spectroscopy. We outline the underlying principles and review available instrumentation as well as related analysis frameworks.

Cryo-Cooling Effect on DHFR Crystal Studied by Replica-Exchange Molecular Dynamics Simulations

Cryo-cooling is routinely performed before x-ray diffraction image collection to reduce the damage to crystals due to ionizing radiation. It has been suggested that although backbone structures are usually very similar between room temperature and cryo-temperature, cryo-cooling may hamper biologically relevant dynamics. In this study, the crystal of Escherichia coli dihydrofolate reductase is studied with replica-exchange molecular dynamics simulation, and the results are compared with the crystal structure determined at cryo-temperature and room temperature with the time-averaged ensemble method. Although temperature dependence of unit cell compaction and root mean-square fluctuation of Cα is found in accord with experiment, it is found that the protein structure at low temperature can be more heterogeneous than the ensemble of structures reported by using the time-averaged ensemble method, encouraging further development of the time-averaged ensemble method and indicating that data should be examined carefully to avoid overinterpretation of one average structure.

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.

Structure and collective dynamics of hydrated anti-freeze protein type III from 180 K to 298 K by X-ray diffraction and inelastic X-ray scattering

We investigated hydrated antifreeze protein type III (AFP III) powder with a hydration level h (=mass of water/mass of protein) of 0.4 in the temperature range between 180 K and 298 K using X-ray diffraction and inelastic X-ray scattering (IXS). The X-ray diffraction data showed smooth, largely monotonic changes between 180 K and 298 K without freezing water. Meanwhile, the collective dynamics observed by IXS showed a strong change in the sound velocity at 180 K, after being largely temperature independent at higher temperatures (298-220 K). We interpret this change in terms of the dynamic transition previously discussed using other probes including THz IR absorption spectroscopy and incoherent elastic and quasi-elastic neutron scattering. This finding suggests that the dynamic transition of hydrated proteins is observable on the subpicosecond time scale as well as nano- and pico-second scales, both in collective dynamics from IXS and single particle dynamics from neutron scattering. Moreover, it is most likely that the dynamic transition of hydrated AFP III is not directly correlated with its hydration structure.

Does a dry protein undergo a glass transition?

Bovine serum albumin (BSA) with extremely low hydration level 0.04, which is usually defined as dry, has been investigated in the temperature range between 200 and 340 K by incoherent inelastic neutron scattering using the neutron time-of-flight spectrometer FOCUS (PSI, Switzerland). Anomalous temperature behavior has been revealed for relaxational and low-frequency vibrational dynamics of BSA in the vicinity of 250 K. The mean-square atomic displacement has been shown to exhibit a change in the slope of temperature dependence near the same temperature. The presented results point out that the glass-like transition occurs in the dry protein.

Redox-promoting protein motions in rubredoxin

Proteins are dynamic objects, constantly undergoing conformational fluctuations, yet the linkage between internal protein motion and function is widely debated. This study reports on the characterization of temperature-activated collective and individual atomic motions of oxidized rubredoxin, a small 53 residue protein from thermophilic Pyrococcus furiosus (RdPf). Computational modeling allows detailed investigations of protein motions as a function of temperature, and neutron scattering experiments are used to compare to computational results. Just above the dynamical transition temperature which marks the onset of significant anharmonic motions of the protein, the computational simulations show both a significant reorientation of the average electrostatic force experienced by the coordinated Fe(3+) ion and a dramatic rise in its strength. At higher temperatures, additional anharmonic modes become activated and dominate the electrostatic fluctuations experienced by the ion. At 360 K, close to the optimal growth temperature of P. furiosus, simulations show that three anharmonic modes including motions of two conserved residues located at the protein active site (Ile7 and Ile40) give rise to the majority of the electrostatic fluctuations experienced by the Fe(3+) ion. The motions of these residues undergo displacements which may facilitate solvent access to the ion.

Effect of solvation-related interaction on the low-temperature dynamics of proteins

The effect of solvation-related interaction on the low-temperature dynamics of proteins is studied by taking into account the desolvation barriers in the interactions of native contacts. It is found out that about the folding transition temperature, the protein folds in a cooperative manner, and the water molecules are expelled from the hydrophobic core at the final stage in the folding process. At low temperature, however, the protein would generally be trapped in many metastable conformations with some water molecules frozen inside the protein. The desolvation takes an important role in these processes. The number of frozen water molecules and that of frozen states of proteins are further analyzed with the methods based on principal component analysis (PCA) and the clustering of conformations. It is found out that both the numbers of frozen water molecules and the frozen states of the protein increase quickly below a certain temperature. Especially, the number of frozen states of the protein increases exponentially following the decrease in the temperature, which resembles the basic features of glassy dynamics. Interestingly, it is observed that the freezing of water molecules and that of protein conformations happen at almost the same temperature. This suggests that the solvation-related interaction performs an important role for the low-temperature dynamics of the model protein.

Hydration affects both harmonic and anharmonic nature of protein dynamics

To understand the effect of hydration on protein dynamics, inelastic neutron-scattering experiments were performed on staphylococcal nuclease samples at differing hydration levels: dehydrated, partially hydrated, and hydrated. At cryogenic temperatures, hydration affected the collective motions with energies lower than 5 meV, whereas the high-energy localized motions were independent of hydration. The prominent change was a shift of boson peak toward higher energy by hydration, suggesting a hardening of harmonic potential at local minima on the energy landscape. The 240 K transition was observed only for the hydrated protein. Significant quasielastic scattering at 300 K was observed only for the hydrated sample, indicating that the origin of the transition is the motion activated by hydration water. The neutron-scattering profile of the partially hydrated sample was quite similar to that of the hydrated sample at 100 K and 200 K, whereas it was close to the dehydrated sample at 300 K, indicating that partial hydration is sufficient to affect the harmonic nature of protein dynamics, and that there is a threshold hydration level to activate anharmonic motions. Thus, hydration water controls both harmonic and anharmonic protein dynamics by differing means.

Hydration effect on low-frequency protein dynamics observed in simulated neutron scattering spectra

Hydration effects on protein dynamics were investigated by comparing the frequency dependence of the calculated neutron scattering spectra between full and minimal hydration states at temperatures between 100 and 300 K. The protein boson peak is observed in the frequency range 1–4 meV at 100 K in both states. The peak frequency in the minimal hydration state shifts to lower than that in the full hydration state. Protein motions with a frequency higher than 4 meV were shown to undergo almost harmonic motion in both states at all temperatures simulated, whereas those with a frequency lower than 1 meV dominate the total fluctuations above 220 K and contribute to the origin of the glass-like transition. At 300 K, the boson peak becomes buried in the quasielastic contributions in the full hydration state but is still observed in the minimal hydration state. The boson peak is observed when protein dynamics are trapped within a local minimum of its energy surface. Protein motions, which contribute to the boson peak, are distributed throughout the whole protein. The fine structure of the dynamics structure factor is expected to be detected by the experiment if a high resolution instrument (<∼20 μeV) is developed in the near future.

Low-Temperature Protein Dynamics: A Simulation Analysis of Interprotein Vibrations and the Boson Peak at 150 K

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 approximately 2-2.5 meV, originates from approximately 10(2) 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.