Dielectric Spectroscopy of Proteins as a Quantitative Experimental Test of Computational Models of Their Low-Frequency Harmonic Motions

Diffusion Coefficient of Intracrystalline Water in Intrinsic Hen Egg-White Lysozyme Crystals Determined by Confocal Raman Spectroscopy

Protein crystals composed of protein molecules are expected as a novel porous material. They have high porosity, and the knowledge of the diffusion of intracrystalline water is important. In this study, the diffusion coefficient of intracrystalline water in intrinsic hen egg-white lysozyme (HEWL) crystals was determined by a method that combines confocal Raman spectroscopy and air convection with controlled relative humidity. Similar to common porous materials, the drying process of the protein crystals includes three periods: constant-rate drying, falling-rate drying, and equilibrium state. During the falling-rate drying period, the drying rate depends on the diffusion of intracrystalline water in the protein crystal. The gradient of the water content was measured using confocal Raman spectroscopy. The diffusion coefficient of the intrinsic HEWL crystals was determined as 3.1 × 10^-7 cm²/s with a water content of 36.3 vol %. The estimated diffusion coefficients of the intrinsic HEWL crystals without cross-linking were in close agreement with those of the cross-linked protein crystals. This study is timely as the knowledge of the intrinsic diffusion coefficient is useful not only for understanding the mechanism of hydration of proteins but also in practical applications such as porous materials, drug binding, and cryoprotectant soaks.

Probing terahertz dynamics of multidomain protein in cell-like confinement

The development of meaningful descriptions of multidomain proteins exhibiting complex inter-domain dynamics modes is a key challenge for understanding their roles in molecular recognition and signalling processes. Here we developed a generally applicable approach for probing the low frequency collective hydration dynamics of multidomain proteins that uses terahertz spectroscopy of a protein molecule confined in a phospholipid reverse micelles environment (named Droplet THz). With the combination of normal mode analysis, we demonstrated the binding of calcium ions modulates the local inter-domain motion of the human coagulant factor VIII protein in a concentration-dependent manner. These findings highlight the Droplet THz as a valuable tool for dissecting the ultrafast dynamics of domain motion in the multidomain proteins and suggest a modulating mechanism of calcium ions on the structural flexibility and function of human coagulant proteins.

Probing Adaptation of Hydration and Protein Dynamics to Temperature

Protein dynamics is strongly influenced by the surrounding environment and physiological conditions. Here we employ broadband megahertz-to-terahertz spectroscopy to explore the dynamics of water and myoglobin protein on an extended time scale from femto- to nanosecond. The dielectric spectra reveal several relaxations corresponding to the orientational polarization mechanism, including the dynamics of loosely bound, tightly bound, and bulk water, as well as collective vibrational modes of protein in an aqueous environment. The dynamics of loosely bound and bulk water follow non-Arrhenius behavior; however, the dynamics of water molecules in the tightly bound layer obeys the Arrhenius-type relation. Combining molecular simulations and effective-medium approximation, we have determined the number of water molecules in the tightly bound hydration layer and studied the dynamics of protein as a function of temperature. The results provide the important impact of water on the biochemical functions of proteins.

The origin and impact of bound water around intrinsically disordered proteins

Proteins and water couple dynamically over a wide range of time scales. Motivated by their central role in protein function, protein-water dynamics and thermodynamics have been extensively studied for structured proteins, where correspondence to structural features has been made. However, properties controlling intrinsically disordered protein (IDP)-water dynamics are not yet known. We report results of megahertz-to-terahertz dielectric spectroscopy and molecular dynamics simulations of a group of IDPs with varying charge content along with structured proteins of similar size. Hydration water around IDPs is found to exhibit more heterogeneous rotational and translational dynamics compared with water around structured proteins of similar size, yielding on average more restricted dynamics around individual residues of IDPs, charged or neutral, compared with structured proteins. The on-average slower water dynamics is found to arise from excess tightly bound water in the first hydration layer, which is related to greater exposure to charged groups. The more tightly bound water to IDPs correlates with the smaller hydration shell found experimentally, and affects entropy associated with protein-water interactions, the contribution of which we estimate based on the dielectric measurements and simulations. Water-IDP dynamic coupling at terahertz frequencies is characterized by the dielectric measurements and simulations.

Long-range DNA-water interactions

DNA functions only in aqueous environments and adopts different conformations depending on the hydration level. The dynamics of hydration water and hydrated DNA leads to rotating and oscillating dipoles that, in turn, give rise to a strong megahertz to terahertz absorption. Investigating the impact of hydration on DNA dynamics and the spectral features of water molecules influenced by DNA, however, is extremely challenging because of the strong absorption of water in the megahertz to terahertz frequency range. In response, we have employed a high-precision megahertz to terahertz dielectric spectrometer, assisted by molecular dynamics simulations, to investigate the dynamics of water molecules within the hydration shells of DNA as well as the collective vibrational motions of hydrated DNA, which are vital to DNA conformation and functionality. Our results reveal that the dynamics of water molecules in a DNA solution is heterogeneous, exhibiting a hierarchy of four distinct relaxation times ranging from ∼8 ps to 1 ns, and the hydration structure of a DNA chain can extend to as far as ∼18 Å from its surface. The low-frequency collective vibrational modes of hydrated DNA have been identified and found to be sensitive to environmental conditions including temperature and hydration level. The results reveal critical information on hydrated DNA dynamics and DNA-water interfaces, which impact the biochemical functions and reactivity of DNA.

Functional-State Dependence of Picosecond Protein Dynamics

We examine temperature-dependent picosecond dynamics of two benchmarking proteins lysozyme and cytochrome c using temperature-dependent terahertz permittivity measurements. We find that a double Arrhenius temperature dependence with activation energies E₁ ∼ 0.1 kJ/mol and E₂ ∼ 10 kJ/mol fits the folded and ligand-free state response. The higher activation energy is consistent with the so-called protein dynamical transition associated with beta relaxations at the solvent-protein interface. The lower activation energy is consistent with correlated structural motions. When the structure is removed by denaturing, the lower-activation-energy process is no longer present. Additionally, the lower-activation-energy process is diminished with ligand binding but not for changes in the internal oxidation state. We suggest that the lower-energy activation process is associated with collective structural motions that are no longer accessible with denaturing or binding.

Solvent dynamics play a decisive role in the complex formation of biologically relevant redox proteins

Electron transfer processes between proteins are vital in many biological systems. Yet, the role of the solvent in influencing these redox reactions remains largely unknown. In this study, terahertz-time domain spectroscopy (THz-TDS) is used to probe the collective hydration dynamics of flavoenzyme ferredoxin-NADP+-reductase (FNR), electron transfer protein ferredoxin-1 (PetF), and the transient complex that results from their interaction. Results reveal changes in the sub-picosecond hydration dynamics that are dependent upon the surface electrostatic properties of the individual proteins and the transient complex. Retarded solvent dynamics of 8-9 ps are observed for FNR, PetF, and the FNR:PetF transient complex. Binding of the FNR:PetF complex to the substrate NADP+ results in bulk-like solvent dynamics of 7 ps, showing that formation of the ternary complex is entropically favored. Our THz measurements reveal that the electrostatic interaction of the protein surface with water results in charge sensitive changes in the solvent dynamics. Complex formation between the positively charged FNR:NADP+ pre-complex and the negatively charged PetF is not only entropically favored, but in addition the solvent reorganization into more bulk-like water assists the molecular recognition process. The change in hydration dynamics observed here suggests that the interaction with the solvent plays a significant role in mediating electron transfer processes between proteins.

Recent progress in the science of complex coacervation

Complex coacervation is an associative, liquid-liquid phase separation that can occur in solutions of oppositely-charged macromolecular species, such as proteins, polymers, and colloids. This process results in a coacervate phase, which is a dense mix of the oppositely-charged components, and a supernatant phase, which is primarily devoid of these same species. First observed almost a century ago, coacervates have since found relevance in a wide range of applications; they are used in personal care and food products, cutting edge biotechnology, and as a motif for materials design and self-assembly. There has recently been a renaissance in our understanding of this important class of material phenomena, bringing the science of coacervation to the forefront of polymer and colloid science, biophysics, and industrial materials design. In this review, we describe the emergence of a number of these new research directions, specifically in the context of polymer-polymer complex coacervates, which are inspired by a number of key physical and chemical insights and driven by a diverse range of experimental, theoretical, and computational approaches.

Water Structure and Properties at Hydrophilic and Hydrophobic Surfaces

The properties of water on both molecular and macroscopic surfaces critically influence a wide range of physical behaviors, with applications spanning from membrane science to catalysis to protein engineering. Yet, our current understanding of water interfacing molecular and material surfaces is incomplete, in part because measurement of water structure and molecular-scale properties challenges even the most advanced experimental characterization techniques and computational approaches. This review highlights progress in the ongoing development of tools working to answer fundamental questions on the principles that govern the interactions between water and surfaces. One outstanding and critical question is what universal molecular signatures capture the hydrophobicity of different surfaces in an operationally meaningful way, since traditional macroscopic hydrophobicity measures like contact angles fail to capture even basic properties of molecular or extended surfaces with any heterogeneity at the nanometer length scale. Resolving this grand challenge will require close interactions between state-of-the-art experiments, simulations, and theory, spanning research groups and using agreed-upon model systems, to synthesize an integrated knowledge of solvation water structure, dynamics, and thermodynamics.

Near-field THz micropolarimetry

We introduce a method for rapid determination of anisotropic terahertz absorption with sub micron resolution and high spectral integrity in the terahertz range. The method is ideal for microscopic and environmentally sensitive materials such as 2-D materials and protein crystals where the anisotropic absorption is critical to understanding underlying physics. We introduce the idea of using an iso-response relationship between the THz polarization and electro optic probe polarization to enable stationary sample polarization measurements covering a full 2π polarization dependence measurement.

Heterogeneity of water structure and dynamics at the protein-water interface

In this molecular dynamics simulation study, we analyze the local structural and dynamic properties of water hydrating the protein ubiquitin on a spatial grid with 1 Å resolution. This allows for insights into the spatial distribution of water number densities, molecular orientations, translations, and rotations as a function of distance from the protein surface. Water molecule orientations follow a heterogeneous distribution with preferred local orientations of water dipoles and O-H bond vectors up to 10-15 Å distances from the protein, while local variations of the water number density converge to homogeneous bulk-like values within less than 8 Å. Interestingly, we find that the long-ranged orientational structure of water does not impact either the translational or rotational dynamics of water. Instead, heterogeneous distributions of local dynamical parameters and averaged dynamical retardation factors are only found close to the protein surface and follow a distance dependence comparable to heterogeneities in the local water number density. This study shows that the formation of nanodomains of preferred water orientations far from the protein does not significantly impact dynamical processes probed as a non-local average in most experiments.

High-Precision Megahertz-to-Terahertz Dielectric Spectroscopy of Protein Collective Motions and Hydration Dynamics

The low-frequency collective vibrational modes in proteins as well as the protein-water interface have been suggested as dominant factors controlling the efficiency of biochemical reactions and biological energy transport. It is thus crucial to uncover the mystery of the hydration structure and dynamics as well as their coupling to collective motions of proteins in aqueous solutions. Here, we report dielectric properties of aqueous bovine serum albumin protein solutions as a model system using an extremely sensitive dielectric spectrometer with frequencies spanning from megahertz to terahertz. The dielectric relaxation spectra reveal several polarization mechanisms at the molecular level with different time constants and dielectric strengths, reflecting the complexity of protein-water interactions. Combining the effective-medium approximation and molecular dynamics simulations, we have determined collective vibrational modes at terahertz frequencies and the number of water molecules in the tightly bound and loosely bound hydration layers. High-precision measurements of the number of hydration water molecules indicate that the dynamical influence of proteins extends beyond the first solvation layer, to around 7 Å distance from the protein surface, with the largest slowdown arising from water molecules directly hydrogen-bonded to the protein. Our results reveal critical information of protein dynamics and protein-water interfaces, which determine biochemical functions and reactivity of proteins.

Time-Domain THz Spectroscopy Reveals Coupled Protein-Hydration Dielectric Response in Solutions of Native and Fibrils of Human Lysozyme

Here we reveal details of the interaction between human lysozyme proteins, both native and fibrils, and their water environment by intense terahertz time domain spectroscopy. With the aid of a rigorous dielectric model, we determine the amplitude and phase of the oscillating dipole induced by the THz field in the volume containing the protein and its hydration water. At low concentrations, the amplitude of this induced dipolar response decreases with increasing concentration. Beyond a certain threshold, marking the onset of the interactions between the extended hydration shells, the amplitude remains fixed but the phase of the induced dipolar response, which is initially in phase with the applied THz field, begins to change. The changes observed in the THz response reveal protein-protein interactions mediated by extended hydration layers, which may control fibril formation and may have an important role in chemical recognition phenomena.

Fingerprints of Conformational States of Human Hsp70 at Sub-THz Frequencies

Large multidomain proteins occur in different conformational states to function. Detection and monitoring of these different structural states are of crucial interest for understanding the mechanics of proteins. Using computational methods, we show that different protein conformational states of the two-domain 70 kDa human Heat-shock protein (hHsp70), with similar vibrational density of states, lead to remarkably different far-IR spectra at acoustical frequencies (ν < 300 GHz). We found that the slow damped motions of the positively charged residues of hHsp70 contribute the most to collective IR active modes at low frequencies (ν < 300 GHz). We predicted that different structural states and functional modes of large proteins, such as hHsp70, might be detected in the sub-THz frequency range by single-molecule spectroscopy similar to the recent extraordinary acoustic Raman spectroscopy (Wheaton S.; Nat. Photonics2015, 9, 68-72).

Theoretical Insights into Sub-Terahertz Acoustic Vibrations of Proteins Measured in Single-Molecule Experiments

Proteins are an important class of nanobioparticles with acoustical modes in the sub-THz frequency range. There is considerable interest to measure and establish the role of these acoustical vibrations for biological function. So far, the technique providing the most detailed information about the acoustical modes of proteins is the very recent Extraordinary Acoustic Raman (EAR) spectroscopy. In this technique, proteins are trapped in nanoholes and excited by two optical lasers of slightly different wavelengths producing an electric field at low frequency (<100 GHz). We demonstrate that the acoustical modes of proteins studied by EAR spectroscopy are both infrared- and Raman-active modes, and we provided interpretation of the spectroscopic fingerprints measured at the single-molecule level. A combination of the present calculations with techniques based on the excitation of a single nanobioparticle by an electric field, such as EAR spectroscopy, should provide a wealth of information on the role of molecular dynamics for biological function.

Theory of Acoustic Raman Modes in Proteins

We present a theoretical analysis that associates the resonances of extraordinary acoustic Raman (EAR) spectroscopy [Wheaton et al., Nat. Photonics 9, 68 (2015)] with the collective modes of proteins. The theory uses the anisotropic elastic network model to find the protein acoustic modes, and calculates Raman intensity by treating the protein as a polarizable ellipsoid. Reasonable agreement is found between EAR spectra and our theory. Protein acoustic modes have been extensively studied theoretically to assess the role they play in protein function; this result suggests EAR spectroscopy as a new experimental tool for studies of protein acoustic modes.

Equation to Line the Borders of the Folding-Unfolding Transition Diagram of Lysozyme

It is important for the formulators of biopharmaceuticals to predict the folding-unfolding transition of proteins. This enables them to process proteins under predetermined conditions, without denaturation. Depending on the apparent denaturation temperature (Tm) of lysozyme, we have derived an equation describing its folding-unfolding transition diagram. According to the water content and temperature, this diagram was divided into three different areas, namely, the area of the water-folded lysozyme phase, the area of the water-folded lysozyme phase and the bulk water phase, and the area of the denatured lysozyme phase. The water content controlled the appearance and intensity of the Raman band at ∼1787 cm(-1) when lysozyme powders were thermally denatured at temperatures higher than Tm.

Salt effects on the picosecond dynamics of lysozyme hydration water investigated by terahertz time-domain spectroscopy and an insight into the Hofmeister series for protein stability and solubility

The addition of salts into protein aqueous solutions causes changes in protein solubility and stability, the ability of which is known to be ordered in the Hofmeister series.

Determination of Protein Surface Hydration by Systematic Charge Mutations

Protein surface hydration is critical to its structural stability, flexibility, dynamics, and function. Recent observations of surface solvation on picosecond time scales have evoked debate on the origin of such relatively slow motions, from hydration water or protein charged side chains, especially with molecular dynamics simulations. Here we used a unique nuclease with a single tryptophan as a local probe and systematically mutated three neighboring charged residues to differentiate the contributions from hydration water and charged side chains. By various mutations of one, two, and all three charged residues, we observed slight increases in the total tryptophan Stokes shifts with fewer neighboring charged residue(s) and found insensitivity of charged side chains to the relaxation patterns. The dynamics is correlated with hydration water relaxation with the slowest time in a dense charged environment and the fastest time at a hydrophobic site. On such picosecond time scales, the protein surface motion is restricted. The total Stokes shifts are dominantly from hydration water relaxation and the slow dynamics is from water-driven relaxation, coupled to local protein fluctuations.

New terahertz dielectric spectroscopy for the study of aqueous solutions

We present the development of a high precision, tunable far-infrared (terahertz) frequency-domain dielectric spectrometer for studying the dynamics of biomolecules in aqueous solutions in the gigahertz-to-terahertz frequency. As an important benchmark system, we report on the measurements of the absorption and refractive index for liquid water in the frequency range from 5 GHz to 1.12 THz (0.17-37.36 cm(-1) or 0.268-60 mm). The system provides a coherent radiation source with power up to 20 mW in the gigahertz-to-terahertz region. The dynamic range of our instrument reaches 10(12) and the system achieves a spectral resolution of less than 100 Hz. The temperature of samples can be controlled precisely with error bars of ±0.02 °C from 0 °C to 90 °C. Given these attributes, our spectrometer provides unique capabilities for the accurate measurement of even very strongly absorbing materials such as aqueous solutions.

Calculation of the infrared spectra of proteins

The CHARMM22 force field with associated partial charges is used to calculate the infrared spectra of a number of small proteins and some larger biothreat proteins. The calculated high-frequency region, from about 2,500 to 3,500 cm(-1), is dominated by stretching modes of hydrogen bonded to other atoms, and is very similar in all proteins. There is a peak at 3,430 cm(-1) whose intensity is predicted by these calculations to be a direct measure of arginine content. The calculated low-frequency THz region, up to 300 cm(-1), is also very similar in all the proteins and just reflects the vibrational density of states in agreement with experimental results. Calculations show that the intermediate-frequency region between 500 and 1,200 cm(-1) shows the greatest difference between individual proteins and is also the least affected by water absorption. However, to match experimental measurements in the amide region, it was necessary to reduce the hydrogen partial charges.

Dynamics of the stratification process in drying colloidal dispersions studied by terahertz time-domain spectroscopy

We present an optical study that reveals the bulk dynamics of the stratification process in drying colloidal dispersions. Terahertz time-domain spectroscopy has been used to measure in situ solventborne and waterborne paint layers as a function of drying time. The dynamic behavior of the dry top layer and wet bottom layer thickness, as well as the bulk thickness, reflect the principal processes of the established drying mechanism. In addition, the results demonstrate stratification only when the drying process is in the evaporation controlled regime, whereas the coating is shown to remain a single layer for diffusion controlled drying.

Sub-THz specific relaxation times of hydrogen bond oscillations in E.coli thioredoxin. Molecular dynamics and statistical analysis

Hydrogen bonds (H-bonds) in biological macromolecules are important for the molecular structure and functions. Since interactions via hydrogen bonds are weaker than covalent bonds, it can be expected that atomic movements involving H-bonds have low frequency vibrational modes. Sub-Terahertz (sub-THz) vibrational spectroscopy that combines measurements with molecular dynamics (MD) computational prediction has been demonstrated as a promising approach for biological molecule characterization. Multiple resonance absorption lines have been reported. The knowledge of relaxation times of atomic oscillations is critical for the successful application of THz spectroscopy for hydrogen bond characterization. The purpose of this work is to use atomic oscillations in the 0.35-0.7 THz range, found from molecular dynamic (MD) simulations of E.coli thioredoxin (2TRX), to study relaxation dynamics of two intra-molecular H-bonds, OH-N and OH-C. Two different complimentary techniques are used in this study, one is the analysis of the statistical distribution of relaxation time and dissipation factor values relevant to low frequency oscillations, and the second is the analysis of the autocorrelation function of low frequency quasi-periodic movements. By studying hydrogen bond atomic displacements, it was found that the atoms are involved in a number of collective oscillations, which are characterized by different relaxation time scales ranging from 2-3 ps to more than 150 ps. The existence of long lasting relaxation processes opens the possibility to directly observe and study H-bond vibrational modes in sub-THz absorption spectra of bio-molecules if measured with an appropriate spectral resolution. The results of measurements using a recently developed frequency domain spectroscopic sensor with a spectral resolution of 1 GHz confirm the MD analysis.

Biopharmaceutical liquid formulation: a review of the science of protein stability and solubility in aqueous environments

Formulation scientists employed in the biopharmaceutical industry face the challenge of creating liquid aqueous formulations for proteins that never had evolutionary pressure to be exceptionally stable or soluble. Yet commercial products usually need a shelf life of 2 years to be economically viable. The research done in this field is dominated by physical chemists who have developed theories like preferential interaction, preferential hydration and excluded volume to explain the mechanisms for the interaction between salt, small organic molecules and proteins. This review aims to translate the research findings on protein stability and solubility produced by the physical chemists and make it accessible to formulation scientists working within the biopharmaceutical industry.

Crowding induced collective hydration of biological macromolecules over extended distances

Ultrafast two-dimensional infrared (2D-IR) spectroscopy reveals picosecond protein and hydration dynamics of crowded hen egg white lysozyme (HEWL) labeled with a metal-carbonyl vibrational probe covalently attached to a solvent accessible His residue. HEWL is systematically crowded alternatively with polyethylene glycol (PEG) or excess lysozyme in order to distinguish the chemically inert polymer from the complex electrostatic profile of the protein crowder. The results are threefold: (1) A sharp dynamical jamming-like transition is observed in the picosecond protein and hydration dynamics that is attributed to an independent-to-collective hydration transition induced by macromolecular crowding that slows the hydration dynamics up to an order of magnitude relative to bulk water. (2) The interprotein distance at which the transition occurs suggests collective hydration of proteins over distances of 30-40 Å. (3) Comparing the crowding effects of PEG400 to our previously reported experiments using glycerol exposes fundamental differences between small and macromolecular crowding agents.

On the theory of dielectric spectroscopy of protein solutions

We present a theory of the dielectric response of solutions containing large solutes, of the nanometer size, in a molecular solvent. It combines the molecular dipole moment of the solute with the polarization of a large subensemble of solvent molecules at the solute-solvent interface. The goal of the theory is two-fold: (i) to formulate the problem of the dielectric response avoiding the reliance on the cavity-field susceptibility of dielectric theories and (ii) to separate the non-additive polarization of the interface, jointly produced by the external field of the laboratory experiment and the solute, from specific solute-solvent interactions contributing to the dielectric signal. The theory is applied to experimentally reported frequency-dependent dielectric spectra of lysozyme in solution. The analysis of the data in the broad range of frequencies up to 700 GHz shows that the cavity-field susceptibility, critical for the theory formulation, is consistent with the prediction of Maxwell's electrostatics in the frequency range of 10-200 GHz, but deviates from it outside this range. In particular, it becomes much smaller than the Maxwell result, and shifts to negative values, at small frequencies. The latter observation implies a dia-electric response, or negative dielectrophoresis, of hydrated lysozyme. It also implies that the effective protein dipole recorded by dielectric spectroscopy is much smaller than the value calculated from the protein's charge distribution. We suggest an empirical equation that describes both the increment of the static dielectric constant and the decrement of the Debye water peak with increasing protein concentration. It gives fair agreement with broad-band dispersion and loss spectra of protein solutions, but misses the δ-dispersion region.