Inelastic X-ray Scattering Studies of the Short-Time Collective Vibrational Motions in Hydrated Lysozyme Powders and Their Possible Relation to Enzymatic Function

Intra-protein interacting collective modes in the terahertz frequency region

Understanding how proteins work requires a thorough understanding of their internal dynamics. Proteins support a wide range of motions, from the femtoseconds to seconds time scale, relevant to crucial biological functions. In this context, the term "protein collective dynamics" refers to the complex patterns of coordinated motions of numerous atoms throughout the protein in the sub-picosecond time scale (terahertz frequency region). It is hypothesized that these dynamics have a substantial impact on the regulation of functional dynamical mechanisms, including ligand binding and allosteric signalling, charge transport direction, and the regulation of thermodynamic and thermal transport properties. Using the theoretical framework of hydrodynamics, the collective dynamics of proteins had previously been described in a manner akin to that of simple liquids, i.e. in terms of a single acoustic-like excitation, related to intra-protein vibrational motions. Here, we employ an interacting-mode model to analyse the results from molecular dynamics simulations and we unveil that the vibrational landscape of proteins is populated by multiple acoustic-like and low-frequency optic-like modes, with mixed symmetry and interfering with each other. We propose an interpretation at the molecular level of the observed scenario that we relate to the side-chains and the hydrogen-bonded networks dynamics. The present insights provide a perspective for understanding the molecular mechanisms underlying the energy redistribution processes in the interior of proteins.

Experimental mapping of short-wavelength phonons in proteins

Phonons are quasi-particles, observed as lattice vibrations in periodic materials, that often dampen in the presence of structural perturbations. Nevertheless, phonon-like collective excitations exist in highly complex systems, such as proteins, although the origin of such collective motions has remained elusive. Here we present a picture of temperature and hydration dependence of collective excitations in green fluorescent protein (GFP) obtained by inelastic neutron scattering. Our results provide evidence that such excitations can be used as a measure of flexibility/softness and are possibly associated with the protein’s activity. Moreover, we show that the hydration water in GFP interferes with the phonon propagation pathway, enhancing the structural rigidity and stability of GFP.

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Quantum phenomena in biology have long fascinated people around the world

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This work presents a direct experimental observation of phonons, the quantum vibrations in a protein

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The collective excitations or phonons in proteins were detected by utilizing inelastic neutron scattering technique at Oak Ridge National Laboratory

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Our results illustrate the flexibility-activity relationship in proteins by mapping the temperature and hydration dependence of these collective excitations

Spatiotemporal mapping of mesoscopic liquid dynamics

The study of liquid dynamics at mesoscopic scales is still strewn with difficulty due to limitations in theory and experiment. Historically, significant attention has been given to the analysis of space-time correlation functions and their frequency-Fourier transforms at a few discrete wave numbers. The massive computing power afforded by modern high performance computing clusters and the advent of a wide-angle neutron spin-echo spectrometer, however, have unlocked a more intuitive and fruitful approach to this problem. Using molecular dynamics simulations, here we demonstrate the benefits of spatiotemporally mapping intermediate scattering functions on a dense grid of correlation times and wave numbers. Four model systems are investigated: a Lennard-Jones liquid, a coarse-grained bead-spring polymer, a molten sodium chloride, and a poly(ethylene oxide) melt. We show that the spatiotemporal mapping approach is particularly useful for elucidating the mesoscopic dynamics in these liquids, where several underlying mechanisms, such as molecular relaxations, hydrodynamic modes, and nonhydrodynamic excitations, are potentially at play. Compared to the traditional method, direct visualization of density space-time correlation functions on two-dimensional color maps permits appraisals of complicated dynamical behavior at mesoscales in a global manner. For example, the scaling relations between space and time for different types of molecular motions can be straightforwardly identified on these plots, without any model-dependent analysis. Additionally, we show how theoretical ideas regarding collective mesoscopic dynamics, such as the classical hydrodynamic theory, the convolution approximation, and a recently proposed phenomenological model, can be discussed in terms of the global features of spatiotemporal maps of intermediate scattering functions. The new perspective offered by the spatiotemporal mapping method should prove useful for the study of liquid dynamics in general.

Dynamic structure factor of a lipid bilayer in the presence of a high electric field

The influence of a high average electric field (∼1 V/nm) in the hydrophobic interior of a bilayer lipid membrane on short-wavelength in-plane phononic motions of lipid chains is considered. The average electric field is assumed to be nearly constant on a picosecond time scale and a nanometer length scale. This field may be induced, for instance, by externally applied subnanosecond electric pulses or the membrane dipole potential. Using a generalized hydrodynamic approach, we derive a corresponding electrohydrodynamic model generalized to high wave numbers. In the considered approximation, all electric field effects are reduced only to a constant contribution to the generalized isothermal compressibility modulus. The corresponding dynamic structure factor for a lipid bilayer is derived. We show that due to polarization effects, the high field can critically impact the dynamics of longitudinal acousticlike modes at wave numbers near the major peak of the static structure factor. We estimate quantitatively that for typical lipid bilayers, transverse high electric fields can cause strong phonon energy softening, enhancement of phonon population, and formation of a gap in the dispersion of excitation frequency. The results obtained agree with simulations of the initiation of lipid bilayer electropores, suggesting that the proposed model reproduces the essential features of the field's impact on atomic density fluctuations. The proposed mechanism may have significant implications for the understanding of electroporation, passive molecular transport, and spontaneous pore formation in lipid bilayers.

Atomic Dynamics in Simple Liquid: de Gennes Narrowing Revisited

The de Gennes narrowing phenomenon is frequently observed by neutron or x-ray scattering measurements of the dynamics of complex systems, such as liquids, proteins, colloids, and polymers. The characteristic slowing down of dynamics in the vicinity of the maximum of the total scattering intensity is commonly attributed to enhanced cooperativity. In this Letter, we present an alternative view on its origin through the examination of the time-dependent pair correlation function, the van Hove correlation function, for a model liquid in two, three, and four dimensions. We find that the relaxation time increases monotonically with distance and the dependence on distance varies with dimension. We propose a heuristic explanation of this dependence based on a simple geometrical model. This finding sheds new light on the interpretation of the de Gennes narrowing phenomenon and the α-relaxation time.

Water is an active matrix of life for cell and molecular biology

Szent-Győrgi called water the "matrix of life" and claimed that there was no life without it. This statement is true, as far as we know, on our planet, but it is not clear whether it must hold throughout the cosmos. To evaluate that question requires a close consideration of the many varied and subtle roles that water plays in living cells-a consideration that must be free of both an assumed essentialism that gives water an almost mystical life-giving agency and a traditional tendency to see it as a merely passive solvent. Water is a participant in the "life of the cell," and here I describe some of the features of that active agency. Water's value for molecular biology comes from both the structural and dynamic characteristics of its status as a complex, structured liquid as well as its nature as a polar, protic, and amphoteric reagent. Any discussion of water as life's matrix must, however, begin with an acknowledgment that our understanding of it as both a liquid and a solvent is still incomplete.

LK peptide side chain dynamics at interfaces are independent of secondary structure

Real-time observation of the ultrafast motions of leucine side chains within model peptides at the water–air interface with representative folds – α-helix, 3₁₀-helix, β-strand – show that interfacial dynamics are mostly determined by surface interactions.

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.

Robust elastic network model: A general modeling for precise understanding of protein dynamics

In the study of protein dynamics relevant to functions, normal mode analysis based on elastic network models (ENMs) has become popular. These models are usually validated by comparing the calculated atomic fluctuation for a single protein in a vacuum to experimental temperature factors in the crystal packing state. Without reflecting the crystal packing effect, in addition, their arbitrary assignment of spring constants leads to inaccurate simulation results, yielding a low correlation of the B-factor. To overcome this limitation, we propose a robust elastic network model (RENM) that not only considers the crystalline effect by using symmetric constraint information but also uses lumped masses and specific spring constants based on the type of amino acids and chemical interactions, respectively. Simulation results with more than 500 protein structures verify qualitatively and quantitatively that one can obtain the better correlation of the B-factor by RENM without additional computational burden. Moreover, an optimal spring constant in physical units (dyne/cm) is quantitatively determined as a function of the temperature at 100 and 290K, which enables us to predict the atomic fluctuations and vibrational density of states (VDOS) without a fitting process. The additional investigation of 80 high-resolution crystal structures with anisotropic displacement parameters (ADPs) indicates that RENM could give a full description of vibrational characteristics of individual residues in proteins.

Hydration-dependent dynamic crossover phenomenon in protein hydration water

The characteristic relaxation time τ of protein hydration water exhibits a strong hydration level h dependence. The dynamic crossover is observed when h is higher than the monolayer hydration level hc=0.2-0.25 and becomes more visible as h increases. When h is lower than hc, τ only exhibits Arrhenius behavior in the measured temperature range. The activation energy of the Arrhenius behavior is insensitive to h, indicating a local-like motion. Moreover, the h dependence of the crossover temperature shows that the protein dynamic transition is not directly or solely induced by the dynamic crossover in the hydration water.

Terahertz Dynamics in Human Cells and Their Chromatin

The terahertz dynamics of human cells of the U937 line and their chromatin has been investigated by high-resolution inelastic X-ray scattering. To highlight its dynamical features in situ, nuclear DNA has been stained by uranyl-acetate salt. The general behavior of the collective dynamics of the whole cell is quite similar to that of bulk water, with a nearly wavevector-independent branch located at about 5 meV and a propagating mode with a linear trend corresponding to a speed of sound of 2900 ± 100 m/s. We provide the first experimental evidence for the existence of two branches also in the dispersion curves of chromatin. The high-energy mode displays an acoustic-like behavior with a sound velocity similar to unstained cells, but in this case the branch likely originates from the superposition of intramolecular DNA optic modes. A low-energy optic-like branch, distinctive of the chromatin moiety, is found at about 2.5 meV.

One role of hydration water in proteins: key to the "softening" of short time intraprotein collective vibrations of a specific length scale

High resolution inelastic X-ray scattering (IXS) experiments show that the "phonon energy softening" and "phonon population enhancement" observed in a hydrated native protein when increasing the temperature from 200 K to physiological temperature are not directly related to the protein structure. Such phenomena were also observed in a denatured sample without a defined tertiary structure and with a limited residual secondary structure. However, in a dry sample, such "softening" is strongly suppressed. These facts suggest that the above-mentioned protein "softening" phenomenon is water-induced. In addition, increasing the hydration level can also induce "phonon energy softening" at room temperature, but not at 200 K. This change may be due to a qualitative difference in the dynamics of hydration water at 200 K and at room temperature.

On the Coupling between the Collective Dynamics of Proteins and Their Hydration Water

Picosecond time scale dynamics of hydrated proteins has been connected with the onset of biological activity as it coincides with solvent-solute hydrogen bond rearrangements and amino acid rotational relaxation time scales. The presence and fluctuations of protein hydration water (PHW) largely influence protein motions that are believed to be slaved to those of the solvent, yet to date, how protein and hydration water dynamics are coupled remains unclear. Here, we provide a significant advance in characterizing this coupling; we present the first full study of both the longitudinal and transverse coherent collective motions in a protein-solvent system. The data show unexpectedly the presence in the water dynamics of collective modes belonging to the protein. The properties of these modes, in particular, their propagation velocities and amplitudes, indicate a strengthening of the interactions and a higher rigidity of the network of solvent molecules close to the protein surface. Accordingly, the present study presents the most compelling and clear evidence of a very strong dynamical coupling between a protein and its hydration water, previously suggested by studies using various experimental techniques.

Protein electron transfer: Dynamics and statistics

Electron transfer between redox proteins participating in energy chains of biology is required to proceed with high energetic efficiency, minimizing losses of redox energy to heat. Within the standard models of electron transfer, this requirement, combined with the need for unidirectional (preferably activationless) transitions, is translated into the need to minimize the reorganization energy of electron transfer. This design program is, however, unrealistic for proteins whose active sites are typically positioned close to the polar and flexible protein-water interface to allow inter-protein electron tunneling. The high flexibility of the interfacial region makes both the hydration water and the surface protein layer act as highly polar solvents. The reorganization energy, as measured by fluctuations, is not minimized, but rather maximized in this region. Natural systems in fact utilize the broad breadth of interfacial electrostatic fluctuations, but in the ways not anticipated by the standard models based on equilibrium thermodynamics. The combination of the broad spectrum of static fluctuations with their dispersive dynamics offers the mechanism of dynamical freezing (ergodicity breaking) of subsets of nuclear modes on the time of reaction/residence of the electron at a redox cofactor. The separation of time-scales of nuclear modes coupled to electron transfer allows dynamical freezing. In particular, the separation between the relaxation time of electro-elastic fluctuations of the interface and the time of conformational transitions of the protein caused by changing redox state results in dynamical freezing of the latter for sufficiently fast electron transfer. The observable consequence of this dynamical freezing is significantly different reorganization energies describing the curvature at the bottom of electron-transfer free energy surfaces (large) and the distance between their minima (Stokes shift, small). The ratio of the two reorganization energies establishes the parameter by which the energetic efficiency of protein electron transfer is increased relative to the standard expectations, thus minimizing losses of energy to heat. Energetically efficient electron transfer occurs in a chain of conformationally quenched cofactors and is characterized by flattened free energy surfaces, reminiscent of the flat and rugged landscape at the stability basin of a folded protein.