Effects of solvent damping on side chain and backbone contributions to the protein boson peak

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.

Ergodicity breaking of iron displacement in heme proteins

We present a model of the dynamical transition of atomic displacements in proteins. Increased mean-square displacement at higher temperatures is caused by the softening of the force constant for atomic/molecular displacements by electrostatic and van der Waals forces from the protein-water thermal bath. Displacement softening passes through a nonergodic dynamical transition when the relaxation time of the force-force correlation function enters, with increasing temperature, the instrumental observation window. Two crossover temperatures are identified. The lower crossover, presently connected to the glass transition, is related to the dynamical unfreezing of rotations of water molecules within nanodomains polarized by charged surface residues of the protein. The higher crossover temperature, usually assigned to the dynamical transition, marks the onset of water translations. All crossovers are ergodicity breaking transitions depending on the corresponding observation windows. Allowing stretched exponential relaxation of the protein-water thermal bath significantly improves the theory-experiment agreement when applied to solid protein samples studied by Mössbauer spectroscopy.

Investigating Structure and Dynamics of Proteins in Amorphous Phases Using Neutron Scattering

In order to increase shelf life and minimize aggregation during storage, many biotherapeutic drugs are formulated and stored as either frozen solutions or lyophilized powders. However, characterizing amorphous solids can be challenging with the commonly available set of biophysical measurements used for proteins in liquid solutions. Therefore, some questions remain regarding the structure of the active pharmaceutical ingredient during freezing and drying of the drug product and the molecular role of excipients. Neutron scattering is a powerful technique to study structure and dynamics of a variety of systems in both solid and liquid phases. Moreover, neutron scattering experiments can generally be correlated with theory and molecular simulations to analyze experimental data. In this article, we focus on the use of neutron techniques to address problems of biotechnological interest. We describe the use of small-angle neutron scattering to study the solution structure of biological molecules and the packing arrangement in amorphous phases, that is, frozen glasses and freeze-dried protein powders. In addition, we discuss the use of neutron spectroscopy to measure the dynamics of glassy systems at different time and length scales. Overall, we expect that the present article will guide and prompt the use of neutron scattering to provide unique insights on many of the outstanding questions in biotechnology.

THz frequency spectrum of protein-solvent interaction energy using a recurrence plot-based Wiener-Khinchin method

The dynamics of a protein and the water surrounding it are coupled via nonbonded energy interactions. This coupling can exhibit a complex, nonlinear, and nonstationary nature. The THz frequency spectrum for this interaction energy characterizes both the vibration spectrum of the water hydrogen bond network, and the frequency range of large amplitude modes of proteins. We use a Recurrence Plot based Wiener-Khinchin method RPWK to calculate this spectrum, and the results are compared to those determined using the classical auto-covariance-based Wiener-Khinchin method WK. The frequency spectra for the total nonbonded interaction energy extracted from molecular dynamics simulations between the β-Lactamase Inhibitory Protein BLIP, and water molecules within a 10 Å distance from the protein surface, are calculated at 150, 200, 250, and 310 K, respectively. Similar calculations are also performed for the nonbonded interaction energy between the residues 49ASP, 53TYR, and 142PHE in BLIP, with water molecules within 10 Å from each residue respectively at 150, 200, 250, and 310 K. A comparison of the results shows that RPWK performs better than WK, and is able to detect some frequency data points that WK fails to detect. This points to the importance of using methods capable of taking the complex nature of the protein-solvent energy landscape into consideration, and not to rely on standard linear methods. In general, RPWK can be a valuable addition to the analysis tools for protein molecular dynamics simulations. Proteins 2016; 84:1549-1557. © 2016 Wiley Periodicals, Inc.

Elasticity and Inverse Temperature Transition in Elastin

Elastin is a structural protein and biomaterial that provides elasticity and resilience to a range of tissues. This work provides insights into the elastic properties of elastin and its peculiar inverse temperature transition (ITT). These features are dependent on hydration of elastin and are driven by a similar mechanism of hydrophobic collapse to an entropically favorable state. Using neutron scattering, we quantify the changes in the geometry of molecular motions above and below the transition temperature, showing a reduction in the displacement of water-induced motions upon hydrophobic collapse at the ITT. We also measured the collective vibrations of elastin gels as a function of elongation, revealing no changes in the spectral features associated with local rigidity and secondary structure, in agreement with the entropic origin of elasticity.

Protein dynamics: from rattling in a cage to structural relaxation

We present an overview of protein dynamics based mostly on results of neutron scattering, dielectric relaxation spectroscopy and molecular dynamics simulations. We identify several major classes of protein motions on the time scale from faster than picoseconds to several microseconds, and discuss the coupling of these processes to solvent dynamics. Our analysis suggests that the microsecond backbone relaxation process might be the main structural relaxation of the protein that defines its glass transition temperature, while faster processes present some localized secondary relaxations. Based on the overview, we formulate a general picture of protein dynamics and discuss the challenges in this field.

Rigidity, secondary structure, and the universality of the boson peak in proteins

Complementary neutron- and light-scattering results on nine proteins and amino acids reveal the role of rigidity and secondary structure in determining the time- and lengthscales of low-frequency collective vibrational dynamics in proteins. These dynamics manifest in a spectral feature, known as the boson peak (BP), which is common to all disordered materials. We demonstrate that BP position scales systematically with structural motifs, reflecting local rigidity: disordered proteins appear softer than α-helical proteins; which are softer than β-sheet proteins. Our analysis also reveals a universal spectral shape of the BP in proteins and amino acid mixtures; superimposable on the shape observed in typical glasses. Uniformity in the underlying physical mechanism, independent of the specific chemical composition, connects the BP vibrations to nanometer-scale heterogeneities, providing an experimental benchmark for coarse-grained simulations, structure/rigidity relationships, and engineering of proteins for novel applications.

Painting biological low-frequency vibrational modes from small peptides to proteins

We use experiments and simulation to investigate the validity of different model systems used to study the low-frequency vibrations of proteins.

The glassy state of crambin and the THz time scale protein-solvent fluctuations possibly related to protein function

BACKGROUND

THz experiments have been used to characterize the picosecond time scale fluctuations taking place in the model, globular protein crambin.

RESULTS

Using both hydration and temperature as an experimental parameter, we have identified collective fluctuations (<= 200 cm(-1)) in the protein. Observation of the protein dynamics in the THz spectrum from both below and above the glass transition temperature (Tg) has provided unique insight into the microscopic interactions and modes that permit the solvent to effectively couple to the protein thermal fluctuations.

CONCLUSIONS

Our findings suggest that the solvent dynamics on the picosecond time scale not only contribute to protein flexibility but may also delineate the types of fluctuations that are able to form within the protein structure.

Dynamics and rigidity in an intrinsically disordered protein, β-casein

The emergence of intrinsically disordered proteins (IDPs) as a recognized structural class has forced the community to confront a new paradigm of structure, dynamics, and mechanical properties for proteins. We present novel data on the similarities and differences in the dynamics and nanomechanical properties of IDPs and other biomacromolecules on the picosecond time scale. An IDP, β-casein (CAS), has been studied in a calcium bound and unbound state using neutron and light scattering techniques. We show that CAS partially folds and stiffens upon calcium binding, but in the unfolded state, it is softer than folded proteins such as green fluorescence protein (GFP). We also see that some localized diffusive motions in CAS have a larger amplitude than in GFP at this time scale but are still smaller than those observed in tRNA. In spite of these differences, CAS dynamics are consistent with the classes of motions seen in folded protein on this time scale.

Coherent neutron scattering and collective dynamics in the protein, GFP

Collective dynamics are considered to be one of the major properties of soft materials, including biological macromolecules. We present coherent neutron scattering studies of the low-frequency vibrations, the so-called boson peak, in fully deuterated green fluorescent protein (GFP). Our analysis revealed unexpectedly low coherence of the atomic motions in GFP. This result implies a low amount of in-phase collective motion of the secondary structural units contributing to the boson peak vibrations and fast conformational fluctuations on the picosecond timescale. These observations are in contrast to earlier studies of polymers and glass-forming systems, and suggest that random or out-of-phase motions of the β-strands contribute greater than two-thirds of the intensity to the low-frequency vibrational spectra of GFP.

THz time scale structural rearrangements and binding modes in lysozyme-ligand interactions

Predicting the conformational changes in proteins that are relevant for substrate binding is an ongoing challenge in the aim of elucidating the functional states of proteins. The motions that are induced by protein-ligand interactions are governed by the protein global modes. Our measurements indicate that the detected changes in the global backbone motion of the enzyme upon binding reflect a shift from the large-scale collective dominant mode in the unbound state towards a functional twisting deformation that assists in closing the binding cleft. Correlated motion in lysozyme has been implicated in enzyme function in previous studies, but detailed characterization of the internal fluctuations that enable the protein to explore the ensemble of conformations that ultimately foster large-scale conformational change is yet unknown. For this reason, we use THz spectroscopy to investigate the picosecond time scale binding modes and collective structural rearrangements that take place in hen egg white lysozyme (HEWL) when bound by the inhibitor (NAG)3. These protein thermal motions correspond to fluctuations that have a role in both selecting and sampling from the available protein intrinsic conformations that communicate function. Hence, investigation of these fast, collective modes may provide knowledge about the mechanism leading to the preferred binding process in HEWL-(NAG)3. Specifically, in this work we find that the picosecond time scale hydrogen-bonding rearrangements taking place in the protein hydration shell with binding modify the packing density within the hydrophobic core on a local level. These localized, intramolecular contact variations within the protein core appear to facilitate the large cooperative movements within the interfacial region separating the α- and β- domain that mediate binding. The THz time-scale fluctuations identified in the protein-ligand system may also reveal a molecular mechanism for substrate recognition.

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.

Secondary structure and rigidity in model proteins

There is tremendous interest in understanding the role that secondary structure plays in the rigidity and dynamics of proteins. In this work we analyze nanomechanical properties of proteins chosen to represent different secondary structures: α-helices (myoglobin and bovine serum albumin), β-barrels (green fluorescent protein), and α + β + loop structures (lysozyme). Our experimental results show that in these model proteins, the β motif is a stiffer structural unit than the α-helix in both dry and hydrated states. This difference appears not only in the rigidity of the protein, but also in the amplitude of fast picosecond fluctuations. Moreover, we show that for these examples the secondary structure correlates with the temperature- and hydration-induced changes in the protein dynamics and rigidity. Analysis also suggests a connection between the length of the secondary structure (α-helices) and the low-frequency vibrational mode, the so-called boson peak. The presented results suggest an intimate connection of dynamics and rigidity with the protein secondary structure.

Elastic and conformational softness of a globular protein

Flexibility, or softness, is crucial for protein function and consists of a conformational component, involving jumps between potential wells, and an elastic component, involving fluctuations within the wells. Combining molecular dynamics simulation with incoherent neutron scattering and light scattering measurements on green fluorescent protein, we reveal a relationship between the intrawell fluctuations and elastic moduli of the protein. This finding leads to a simple means of experimentally separating the conformational from the elastic atomic displacements.

Dynamics of protein and its hydration water: neutron scattering studies on fully deuterated GFP

We present a detailed analysis of the picosecond-to-nanosecond motions of green fluorescent protein (GFP) and its hydration water using neutron scattering spectroscopy and hydrogen/deuterium contrast. The analysis reveals that hydration water suppresses protein motions at lower temperatures (<~ 200 K), and facilitates protein dynamics at high temperatures. Experimental data demonstrate that the hydration water is harmonic at temperatures <~ 180-190 K and is not affected by the proteins' methyl group rotations. The dynamics of the hydration water exhibits changes at ~ 180-190 K that we ascribe to the glass transition in the hydrated protein. Our results confirm significant differences in the dynamics of protein and its hydration water at high temperatures: on the picosecond-to-nanosecond timescale, the hydration water exhibits diffusive dynamics, while the protein motions are localized to <~3 Å. The diffusion of the GFP hydration water is similar to the behavior of hydration water previously observed for other proteins. Comparison with other globular proteins (e.g., lysozyme) reveals that on the timescale of 1 ns and at equivalent hydration level, GFP dynamics (mean-square displacements and quasielastic intensity) are of much smaller amplitude. Moreover, the suppression of the protein dynamics by the hydration water at low temperatures appears to be stronger in GFP than in other globular proteins. We ascribe this observation to the barrellike structure of GFP.

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.

Coupled relaxations at the protein-water interface in the picosecond time scale

The spectral behaviour of a protein and its hydration water has been investigated through neutron scattering. The availability of both hydrogenated and perdeuterated samples of maltose-binding protein (MBP) allowed us to directly measure with great accuracy the signal from the protein and the hydration water alone. Both the spectra of the MBP and its hydration water show two distinct relaxations, a behaviour that is reminiscent of glassy systems. The two components have been described using a phenomenological model that includes two Cole-Davidson functions. In MBP and its hydration water, the two relaxations take place with similar average characteristic times of approximately 10 and 0.2 ps. The common time scales of these relaxations suggest that they may be a preferential route to couple the dynamics of the water hydrogen-bond network around the protein surface with that of protein fluctuations.

Fingerprints of amorphous icelike behavior in the vibrational density of states of protein hydration water

The low-frequency modes of protein hydration water are investigated by inelastic neutron scattering. Experiments on both protonated and fully deuterated maltose binding protein samples allow us to unambiguously single out the contribution from water. The low-energy vibrational density of states of hydration water at 100 K is similar to the density of states of high- and low-density amorphous ice, and quite different from that of simple forms of crystalline ice. This result can be related to the picture of hydration water mass density depending on the protein surface curvature, which supports its glassy behavior.

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.

Coupling between lysozyme and glycerol dynamics: Microscopic insights from molecular-dynamics simulations

We explore possible molecular mechanisms behind the coupling of protein and solvent dynamics using atomistic molecular-dynamics simulations. For this purpose, we analyze the model protein lysozyme in glycerol, a well-known protein-preserving agent. We find that the dynamics of the hydrogen bond network between the solvent molecules in the first shell and the surface residues of the protein controls the structural relaxation (dynamics) of the whole protein. Specifically, we find a power-law relationship between the relaxation time of the aforementioned hydrogen bond network and the structural relaxation time of the protein obtained from the incoherent intermediate scattering function. We demonstrate that the relationship between the dynamics of the hydrogen bonds and the dynamics of the protein appears also in the dynamic transition temperature of the protein. A study of the dynamics of glycerol as a function of the distance from the surface of the protein indicates that the viscosity seen by the protein is not the one of the bulk solvent. The presence of the protein suppresses the dynamics of the surrounding solvent. This implies that the protein sees an effective viscosity higher than the one of the bulk solvent. We also found significant differences in the dynamics of surface and core residues of the protein. The former is found to follow the dynamics of the solvent more closely than the latter. These results allowed us to propose a molecular mechanism for the coupling of the solvent-protein dynamics.

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

The boson peak is a broad peak found in the low-frequency region of inelastic neutron and Raman scattering spectra in many glassy materials, including biopolymers below approximately 200 K. Here, we give a novel insight into the origins of the protein boson peak, which may also be valid for materials other than proteins. Molecular simulation reveals that the structured water molecules around a protein molecule increase the number of local minima in the protein energy landscape, which plays a key role in the origin of the boson peak. The peak appears when the protein dynamics are trapped within a local energy minimum at cryogenic temperatures. This trapping causes very low frequency collective motions to shift to higher frequencies. We demonstrate that the characteristic frequency of such systems shifts higher as the temperature decreases also in model one-dimensional energy surfaces with multiple minima.

Protein and solvent dynamics: How strongly are they coupled?

Analysis of Raman and neutron scattering spectra of lysozyme demonstrates that the protein dynamics follow the dynamics of the solvents glycerol and trehalose over the entire temperature range measured 100-350 K. The protein's fast conformational fluctuations and low-frequency vibrations and their temperature variations are very sensitive to behavior of the solvents. Our results give insight into previous counterintuitive observations that protein relaxation is stronger in solid trehalose than in liquid glycerol. They also provide insight into the effectiveness of glycerol as a biological cryopreservant.

Single-particle and collective dynamics of protein hydration water: a molecular dynamics study

We present an analysis based on molecular dynamics simulations of water single particle and collective density fluctuations in a protein crystal at 150 and 300 K. For the collective dynamics, the calculations predict the existence of two sound modes. The first one around 35 meV is highly dispersive and the second one around 9 meV is weakly dispersive in the k range studied here (0.5<k<4.2 A(-1)). We provide evidence that the boson peak around 4 meV in the single particle spectra arises from translational motion, is present in the coherent spectra, and is distinct from the two sound modes.

Vibrational dynamics of myoglobin determined by the phonon-assisted Mössbauer effect

The phonon-assisted Mössbauer effect is used to determine the partial phonon density of states of the iron within the active center of deoxymyoglobin, carboxymyoglobin, and dry and wet metmyoglobin between 40 and 300 K. Between 0 and 1 meV the iron density of states increases quadratically with the energy, as in a Debye solid. Mean sound velocities are extracted from this slope. Between 1 and 3 meV a nearly quadratic "Debye-like" increase follows due to the similar strength of intermolecular and intramolecular forces. Above 3 meV, optical vibrations are characteristic for the iron-ligand conformation. The overall mean square displacements of the heme iron atom obtained from the density of states agree well with the values of Mössbauer absorption experiments below 180 K. In the physiological temperature regime the data confirm the existence of harmonic vibrations in addition to the protein specific dynamics measured by Mössbauer absorption. In the Debye energy regime the mean square displacement of the iron is in agreement with that of the hydrogens measured by incoherent neutron scattering demonstrating the global character of these modes. At higher energies the vibration of the heavy iron atom at 33 meV in metmyoglobin is as large as that of the lightweight hydrogens at that energy. A freeze dried, rehydrated (h=0.38 g H2O/g protein) metmyoglobin sample shows an excess of states above the Debye law between 1 and 3 meV, similar to neutron scattering experiments. The room temperature density of states below 3 meV exhibit an increase of the density compared to the low temperature data, which can be interpreted as mode softening.

Role of protein-water hydrogen bond dynamics in the protein dynamical transition

The role of water in protein dynamics has been investigated using molecular dynamics simulations of crystals and a dehydrated powder. On the 100 ps time scale, the anharmonic and diffusive motions involved in the protein structural relaxation are correlated with the protein-water hydrogen bond dynamics. The complete structural relaxation of the protein requires relaxation of the hydrogen bond network via solvent translational displacement. Inhibiting the solvent translational mobility, and therefore the protein-water hydrogen bond dynamics, has an effect on the protein relaxation similar to dehydration.