Studying the Dielectric Properties of a Protein Solution by Computer Simulation

A new method to calculate broadband dielectric spectra of solvents from molecular dynamics simulations demonstrated with polarizable force fields

Simulating the dielectric spectra of solvents requires the nuanced definition of inter- and intra-molecular forces. Non-polarizable force fields, while thoroughly benchmarked for dielectric applications, do not capture all the spectral features of solvents, such as water. Conversely, polarizable force fields have been largely untested in the context of dielectric spectroscopy but include charge and dipole fluctuations that contribute to intermolecular interactions. We benchmark non-polarizable force fields and the polarizable force fields AMOEBA03 and HIPPO for liquid water and find that the polarizable force fields can capture all the experimentally observed spectral features with varying degrees of accuracy. However, the non-polarizable force fields miss at least one peak. To diagnose this deficiency, we decompose the liquid water spectra from polarizable force fields at multiple temperatures into static and induced dipole contributions and find that the peak originates from induced dipole contributions. Broadening our inquiry to other solvents parameterized with the AMOEBA09 force field, we demonstrate good agreement between the experimental and simulated dielectric spectra of methanol and formamide. To produce these spectra, we develop a new computational approach to calculate the dielectric spectrum via the fluctuation dissipation theorem. This method minimizes the error in both the low and high frequency portions of the spectrum, improving the overall accuracy of the simulated spectrum and broadening the computed frequency range.

Temperature-Dependent Dielectric Relaxation Measurements of (Betaine + Urea + Water) Deep Eutectic Solvent in Hz-GHz Frequency Window: Microscopic Insights into Constituent Contributions and Relaxation Mechanisms

A combined experimental and simulation study of dielectric relaxation (DR) of a deep eutectic solvent (DES) composed of betaine, urea, and water with the composition [Betaine:Urea:Water = 11.7:12:1 (weight ratio) and 9:18:5 (molar ratio)] was performed to explore and understand the interaction and dynamics of this system. Temperature-dependent (303 ≤ T/K ≤ 343) measurements were performed over 9 decades of frequency, combining three different measurement setups. Measured DR, comprising four distinct steps with relaxation times spreading over a few picoseconds to several nanoseconds, was found to agree well with simulations. The simulated total DR spectra, upon dissection into three self (intraspecies) and three cross (interspecies) interaction contributions, revealed that the betaine-betaine self-term dominated (∼65%) the relaxation, while the urea-urea and water-water interactions contributed only ∼7% and ∼1%, respectively. The cross-terms (betaine-urea, betaine-water, and urea-water) together accounted for <30% of the total DR. The slowest DR component with a time constant of ∼1-10 ns derived dominant contribution from betaine-betaine interactions, where betaine-water and urea-water interactions also contributed. The subnanosecond (0.1-0.6 ns) time scale originated from all interactions except betaine-water interaction. An extensive interaction of water with betaine and urea severely reduced the average number of water-water H-bonds (∼0.7) and heavily decreased the static dielectric constant of water in this DES (εs ∼ 2). Furthermore, simulated first rank collective single particle reorientational relaxations (C1(t)) and the structural H-bond fluctuation dynamics (CHB (t)) exhibited multiexponential kinetics with time scales that corresponded well with those found both in the simulated and measured DR.

Linear and Nonlinear Dielectric Response of Intrinsically Disordered Proteins

Linear and nonlinear dielectric responses of solutions of intrinsically disordered proteins (IDPs) were analyzed by combining molecular dynamics simulations with formal theories. A large increment of the linear dielectric function over that of the solvent is found and related to large dipole moments of IDPs. The nonlinear dielectric effect (NDE) of the IDP far exceeds that of the bulk electrolyte, offering a route to interrogate protein conformational and rotational statistics and dynamics. Conformational flexibility of the IDP makes the dipole moment statistics consistent with the gamma/log-normal distributions and contributes to the NDE through the dipole moment's non-Gaussian parameter. The intrinsic non-Gaussian parameter of the dipole moment combines with the protein osmotic compressibility in the nonlinear dielectric susceptibility when dipolar correlations are screened by the electrolyte. The NDE is dominated by dipolar correlations when electrolyte screening is reduced.

Collective Spectroscopy of Solvation Phenomena: Conflicts, Challenges, and Opportunities

Different spectroscopy types reveal different aspects of molecular processes in soft matter. In particular, collective observables can provide insights into intermolecular correlations invisible to the more popular single-particle methods. In this perspective we feature the dielectric relaxation spectroscopy (DRS) with an emphasis on the proper interpretation of this complex observable aided by computational spectroscopy. While we focus on the history and recent advances of DRS in the fields of biomolecular hydration and nanoconfinement, the discussion transcends this particular field and provides a guide for how collective spectroscopy types supported by computational decomposition can be employed to further our understanding of soft matter phenomena.

Extraction of Dielectric Permittivity from Atomistic Molecular Dynamics Simulations and Microwave Measurements

The design of new biotechnology depends on the prediction and measurement of the electrical properties of biomolecules. The dielectric permittivity, in particular, is highly important for the design of microwave systems for diagnostics, yet this property is rarely explicitly targeted during the development of biomolecular force fields for molecular dynamics (MD) simulations. In order to explore the ability of existing force fields to reproduce the frequency-dependent permittivity, we carried out MD simulations of various aqueous solutions, including pure water, isopropyl alcohol, alanine, and the protein ubiquitin. The TIP3P, TIP4P, TIP4P/ε, and SWM4-NDP water models were used along with the CHARMM36m and Drude protein force fields. An experimental setup using a truncated coaxial line was created to measure the permittivity of the same solutions to check for measure-model agreement. We found that one of the nonpolarizable force fields (TIP4P/ε + CHARMM36m) and the polarizable force fields (SWM4-NDP + Drude) closely agree with experimental results. This demonstrates the strength of the tuned TIP4P/ε water model, as well as the physical validity of polarizable force fields in capturing dielectric permittivity. This represents an important step toward the predictive design of biosensors.

Protein Dielectrophoresis: A Tale of Two Clausius-Mossottis-Or Something Else?

Standard DEP theory, based on the Clausius-Mossotti (CM) factor derived from solving the boundary-value problem of macroscopic electrostatics, fails to describe the dielectrophoresis (DEP) data obtained for 22 different globular proteins over the past three decades. The calculated DEP force appears far too small to overcome the dispersive forces associated with Brownian motion. An empirical theory, employing the equivalent of a molecular version of the macroscopic CM-factor, predicts a protein's DEP response from the magnitude of the dielectric β-dispersion produced by its relaxing permanent dipole moment. A new theory, supported by molecular dynamics simulations, replaces the macroscopic boundary-value problem with calculation of the cross-correlation between the protein and water dipoles of its hydration shell. The empirical and formal theory predicts a positive DEP response for protein molecules up to MHz frequencies, a result consistently reported by electrode-based (eDEP) experiments. However, insulator-based (iDEP) experiments have reported negative DEP responses. This could result from crystallization or aggregation of the proteins (for which standard DEP theory predicts negative DEP) or the dominating influences of electrothermal and other electrokinetic (some non-linear) forces now being considered in iDEP theory.

Solvent-mediated forces in protein dielectrophoresis

DEP is an established method to manipulate micrometer-sized particles, but standard continuum theories predict only negligible effects for nanometer-sized proteins despite contrary experimental evidence. A theoretical description of protein DEP needs to consider details on the molecular scale. Previous work toward this goal addressed the role of orientational polarization of static protein dipole moments for dielectrophoretic effects, which successfully predicts the general magnitude of dielectrophoretic forces on proteins but does not readily explain negative DEP forces observed for proteins in some experiments. However, contributions to the protein chemical potential due to protein-water interactions have not yet been considered in this context. Here, we utilize atomistic molecular dynamics simulations to evaluate polarization-induced changes in the protein solvation free energy, which result in a solvent-mediated contribution to dielectrophoretic forces. We quantify solvent-mediated dielectrophoretic forces for two proteins and a small peptide in water, which follow expectations for protein-water dipole-dipole interactions. The magnitude of solvent-mediated dielectrophoretic forces exceeds predictions of nonmolecular continuum theories, but plays a minor role for the total dielectrophoretic force for the simulated proteins due to dominant contributions from the orientational polarization of their static protein dipoles. However, we extrapolate that solvent-mediated contributions to negative protein DEP forces will become increasingly relevant for multidomain proteins, complexes and aggregates with large protein-water interfaces, as well as for high electric field frequencies, which provides a potential mechanism for corresponding experimental observations of negative protein DEP.

Protein dielectrophoresis: Key dielectric parameters and evolving theory

Globular proteins exhibit dielectrophoresis (DEP) responses in experiments where the applied field gradient factor ∇E² appears far too small, according to standard DEP theory, to overcome dispersive forces associated with the thermal energy kT of disorder. To address this a DEP force equation is proposed that replaces a previous empirical relationship between the macroscopic and microscopic forms of the Clausius-Mossotti factor. This equation relates the DEP response of a protein directly to the dielectric increment δε⁺ and decrement δε^- that characterize its β-dispersion at radio frequencies, and also indirectly to its intrinsic dipole moment by way of providing a measure of the protein's effective volume. A parameter Γ_pw , taken as a measure of cross-correlated dipole interactions between the protein and its water molecules of hydration, is included in this equation. For 9 of the 12 proteins, for which an evaluation can presently be made, Γ_pw has a value of ≈4600 ± 120. These conclusions follow an analysis of the failure of macroscopic dielectric mixture (effective medium) theories to predict the dielectric properties of solvated proteins. The implication of a polarizability greatly exceeding the intrinsic value for a protein might reflect the formation of relaxor ferroelectric nanodomains in its hydration shell.

Dielectric spectroscopy and time dependent Stokes shift: two faces of the same coin?

Different types of spectroscopy capture different aspects of dynamics and different ranges of intermolecular contributions.

Fundamental limitations of the time-dependent Stokes shift for investigating protein hydration dynamics

In the TDSS measured in protein systems, large protein contributions fully obscure hydration dynamics.

Complex Dynamics of Water in Protein Confinement

This paper studies single-molecule and collective dynamics of water confined in protein powders by means of molecular dynamics simulations. The single-particle dynamics show a modest retardation compared to the bulk but become highly stretched in the powder, with the stretching exponent of ≃0.2. The collective dynamics of the total water dipole are affected by intermolecular correlations inside water and by cross-correlations between the water and the protein. The dielectric spectrum of water in the powder has two nearly equal-amplitude peaks: a Debye peak with ≃16 ps relaxation time and a highly stretched peak with the relaxation time of ≃13 ns and a stretching exponent of ≃0.12. The slower relaxation component is not seen in the single-molecule correlation functions and can be assigned to elastic protein motions displacing water in the powder. The loss spectrum of the intermediate scattering function reported by neutron-scattering experiments is also highly stretched, with the high-frequency wing scaling according to a power law. Translational dynamics can become much slower in the powder than in the bulk but are overshadowed by the rotational loss in the overall loss spectrum of neutron scattering.

Frequency Dependent Non- Thermal Effects of Oscillating Electric Fields in the Microwave Region on the Properties of a Solvated Lysozyme System: A Molecular Dynamics Study

The use of microwaves in every day's applications raises issues regarding the non thermal biological effects of microwaves. In this work we employ molecular dynamics simulations to advance further the dielectric studies of protein solutions in the case of lysozyme, taking into consideration possible frequency dependent changes in the structural and dynamic properties of the system upon application of electric field in the microwave region. The obtained dielectric spectra are identical with those derived in our previous work using the Fröhlich-Kirkwood approach in the framework of the linear response theory. Noticeable structural changes in the protein have been observed only at frequencies near its absorption maximum. Concerning Cα position fluctuations, different frequencies affected different regions of the protein sequence. Furthermore, the influence of the field on the kinetics of protein-water as well as on the water-water hydrogen bonds in the first hydration shell has been studied; an extension of the Luzar-Chandler kinetic model was deemed necessary for a better fit of the applied field results and for the estimation of more accurate hydrogen bond lifetime values.

Towards a complete characterization of the δ-dispersion in dielectric spectroscopy of protein–water systems

The δ-process in dielectric spectroscopy of protein–water systems is computationally analyzed in great detail, in relation to other experiments.

Impact of secondary structure and hydration water on the dielectric spectrum of poly-alanine and possible relation to the debate on slaved versus slaving water

Using extensive molecular dynamics simulations of a single eight-residue alanine polypeptide in explicit water, we investigate the influence of α-helix formation on the dielectric spectrum. For this, we project long equilibrium trajectories into folded and unfolded states and thereby obtain dielectric spectra representative for disordered as well α-helical conformations without the need to change any other system parameter such as pH or temperature. The absorption spectrum in the α-helical state exhibits a feature in the sub-GHz range that is significantly stronger than in the unfolded state. As we show by an additional decomposition into peptide and water contributions, this slow dielectric mode, the relaxation time of which matches the independently determined peptide rotational relaxation time, is mostly caused by peptide polarization correlations, but also contains considerable contributions from peptide-water correlations. In contrast, the peptide spectral contribution shows no features in the GHz range where bulk water absorbs, not even in the peptide-water correlation part, we conclude that hydration water around Ala8 is more influenced by peptide polarization relaxation effects than the other way around. A further decomposition into water-self and water-collective polarization correlations shows that the dielectric response of hydration water is, in contrast to electrolyte solutions, retarded and that this retardation is mostly due to collective effects, the self relaxation of hydration water molecules is only slightly slowed down compared to bulk water. We find the dynamic peptide-water polarization cross correlations to be rather long-ranged and to extend more than one nanometer away from the peptide-water interface into the water hydration shell, in qualitative agreement with previous simulation studies and recent THz absorption experiments.

A Study of Dielectric Properties of Proteinuria between 0.2 GHz and 50 GHz

This paper investigates the dielectric properties of urine in normal subjects and subjects with chronic kidney disease (CKD) at microwave frequency of between 0.2 GHz and 50 GHz. The measurements were conducted using an open-ended coaxial probe at room temperature (25°C), at 30°C and at human body temperature (37°C). There were statistically significant differences in the dielectric properties of the CKD subjects compared to those of the normal subjects. Statistically significant differences in dielectric properties were observed across the temperatures for normal subjects and CKD subjects. Pearson correlation test showed the significant correlation between proteinuria and dielectric properties. The experimental data closely matched the single-pole Debye model. The relaxation dispersion and relaxation time increased with the proteinuria level, while decreasing with the temperature. As for static conductivity, it increased with proteinuria level and temperature.

Tuning direct current streaming dielectrophoresis of proteins

Dielectrophoresis (DEP) of biomolecules has large potential to serve as a novel selectivity parameter for bioanalytical methods such as (pre)concentration, fractionation, and separation. However, in contrast to well-characterized biological cells and (nano)particles, the mechanism of protein DEP is poorly understood, limiting bioanalytical applications for proteins. Here, we demonstrate a detailed investigation of factors influencing DEP of diagnostically relevant immunoglobulin G (IgG) molecules using insulator-based DEP (iDEP) under DC conditions. We found that the pH range in which concentration of IgG due to streaming iDEP occurs without aggregate formation matches the pH range suitable for immunoreactions. Numerical simulations of the electrokinetic factors pertaining to DEP streaming in this range further suggested that the protein charge and electroosmotic flow significantly influence iDEP streaming. These predictions are in accordance with the experimentally observed pH-dependent iDEP streaming profiles as well as the determined IgG molecular properties. Moreover, we observed a transition in the streaming behavior caused by a change from positive to negative DEP induced through micelle formation for the first time experimentally, which is in excellent qualitative agreement with numerical simulations. Our study thus relates molecular immunoglobulin properties to observed iDEP, which will be useful for the future development of protein (pre)concentration or separation methods based on DEP.

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.

Dielectric spectroscopy in the GHz region on fully hydrated zwitterionic amino acids

The complex dielectric permittivity of eight different amino acids in water solutions was determined in the frequency range from 0.2 to 20 GHz at room temperature, trying to span the whole range of solubility in each case. Two relaxations were observed at room temperature in this frequency range, which can be mainly assigned to the rotation of amino acids in the aqueous environment, and the reorientational motion of water molecules, respectively. Although the amino acids have a charged (zwitterionic) nature with huge dipole moments, the tendency towards dipolar alignment seems to be very weak, over the investigated concentration ranges. For these small bio-molecules, water screens solute-solute interactions and amino acids remain typically as isolated hydrated monomers. The dielectric results were used to estimate the number of water molecules restrained by each solute molecule. Finally, the comparison between the amino acid relaxation times made it possible to discuss the relationship between rotational dynamics and the structure and hydrodynamic coupling of the amino acid studied.

A new view of the bacterial cytosol environment

The cytosol is the major environment in all bacterial cells. The true physical and dynamical nature of the cytosol solution is not fully understood and here a modeling approach is applied. Using recent and detailed data on metabolite concentrations, we have created a molecular mechanical model of the prokaryotic cytosol environment of Escherichia coli, containing proteins, metabolites and monatomic ions. We use 200 ns molecular dynamics simulations to compute diffusion rates, the extent of contact between molecules and dielectric constants. Large metabolites spend ∼80% of their time in contact with other molecules while small metabolites vary with some only spending 20% of time in contact. Large non-covalently interacting metabolite structures mediated by hydrogen-bonds, ionic and π stacking interactions are common and often associate with proteins. Mg²⁺ ions were prominent in NIMS and almost absent free in solution. Κ⁺ is generally not involved in NIMSs and populates the solvent fairly uniformly, hence its important role as an osmolyte. In simulations containing ubiquitin, to represent a protein component, metabolite diffusion was reduced owing to long lasting protein-metabolite interactions. Hence, it is likely that with larger proteins metabolites would diffuse even more slowly. The dielectric constant of these simulations was found to differ from that of pure water only through a large contribution from ubiquitin as metabolite and monatomic ion effects cancel. These findings suggest regions of influence specific to particular proteins affecting metabolite diffusion and electrostatics. Also some proteins may have a higher propensity for associations with metabolites owing to their larger electrostatic fields. We hope that future studies may be able to accurately predict how binding interactions differ in the cytosol relative to dilute aqueous solution.

The cytosol is the major cellular environment housing the majority of cellular activity. Although the cytosol is an aqueous environment, it contains high concentrations of ions, metabolites, and proteins, making it very different from dilute aqueous solution, which is frequently used for in vitro biochemistry. Recent advances in metabolomics have provided detailed concentration data for metabolites in E.coli. We used this information to construct accurate atomistic models of the cytosol solution. We find that, unlike the situation in dilute solutions, most metabolites spend the majority of their time in contact with other metabolites, or in contact with proteins. Furthermore, we find large non-covalently interacting metabolite structures are common and often associated with proteins. The presence of proteins reduced metabolite diffusion owing to long lasting correlations of motion. The dielectric constant of these simulations was found to differ from that of pure water only through a large contribution from proteins as metabolite and monatomic ion effects largely cancel. These findings suggest specific protein spheres of influence affecting metabolite diffusion and the electrostatic environment.

Hydration water dynamics near biological interfaces

We performed classical molecular dynamics simulations using both fixed-charge and polarizable water and protein force fields to contrast the hydration dynamics near hydrophilic and amphiphilic peptides as a function of temperature. The high peptide concentrations we use serve as a model for the surface of folded proteins where hydration layers around each residue overlap significantly. Through simulation we determine that there are notable differences in the water dynamics analyzed from the outer and inner hydration layer regions of the amphiphilic peptide solution that explains the experimentally observed presence of two translational relaxations, while the hydrophilic peptide solution shows only a single non-Arrhenius translational process with no distinction between hydration layers. Given that water dynamics for the amphiphilic peptide system reproduces all known rotational and translational hydration dynamical anomalies exhibited by hydration water near protein surfaces, our analysis provides strong evidence that dynamical signatures near biological interfaces arises because of frustration in the hydration dynamics induced by chemical heterogeneity, as opposed to just topological roughness, of the protein surface.

Universal features of water dynamics in solutions of hydrophilic polymers, biopolymers, and small glass-forming materials

A systematic investigation by dielectric spectroscopy of 18 different water-rich mixtures with very different hydrophilic substances shows universal features for the water dynamics. The temperature dependence of the relaxation times exhibits a crossover from non-Arrhenius to Arrhenius behavior at the T(g) range of the mixtures. Furthermore, the temperature dependence of the relaxation times presents a universal behavior both above and below the crossover temperature. We also show that these features suggest that the observed crossover is associated with the emergence of confinement effects.

Simulation studies of the protein-water interface. II. Properties at the mesoscopic resolution

We report molecular dynamics (MD) simulations of three protein-water systems (ubiquitin, apo-calbindin D(9K), and the C-terminal SH2 domain of phospholipase C-gamma1), from which we compute the dielectric properties of the solutions. Since two of the proteins studied have a net charge, we develop the necessary theory to account for the presence of charged species in a form suitable for computer simulations. In order to ensure convergence of the time correlation functions needed for the analysis, the minimum length of the MD simulations was 20 ns. The system sizes (box length, number of waters) were chosen so that the resulting protein concentrations are comparable to experimental conditions. A dielectric component analysis was carried out to analyze the contributions from protein and water to the frequency-dependent dielectric susceptibility chi(omega) of the solutions. Additionally, an even finer decomposition into protein, two solvation shells, and the remaining water (bulk water) was carried out. The results of these dielectric decompositions were used to study protein solvation at mesoscopic resolution, i.e., in terms of protein, first and second solvation layers, and bulk water. This study, therefore, complements the structural and dynamical analyses at molecular resolution that are presented in the companion paper. The dielectric component contributions from the second shell and bulk water are very similar in all three systems. We find that the proteins influence the dielectric properties of water even beyond the second solvation shell, in agreement with what was observed for the mean residence times of water molecules in protein solutions. By contrast, the protein contributions, as well as the contributions of the first solvation shell, are system specific. Most importantly, the protein and the first water shell around ubiquitin and apo-calbindin are anticorrelated, whereas the first water shell around the SH2 domain is positively correlated.

A molecular dynamics study of the dielectric properties of aqueous solutions of alanine and alanine dipeptide

Molecular dynamics simulations were used to compute the frequency-dependent dielectric susceptibility of aqueous solutions of alanine and alanine dipeptide. We studied four alanine solutions, ranging in concentration from 0.13-0.55 mol/liter, and two solutions of alanine dipeptide (0.13 and 0.27 mol/liter). In accord with experiment we find a strong dielectric increment for both solutes, whose molecular origin is shown to be the zwitterionic nature of the solutes. The dynamic properties were analyzed based on a dielectric component analysis into solute, a first hydration shell, and all remaining (bulk) waters. The results of this three component decomposition were interpreted directly, as well as by uniting the solute and hydration shell component to a "suprasolute" component. In both approaches three contributions to the frequency-dependent dielectric properties can be discerned. The quantitatively largest and fastest component arises from bulk water [i.e., water not influenced by the solute(s)]. The interaction between waters surrounding the solute(s) (the hydration shell) and bulk water molecules leads to a relaxation process occurring on an intermediate time scale. The slowest relaxation process originates from the solute(s) and the interaction of the solute(s) with the first hydration shell and bulk water. The primary importance of the hydration shell is the exchange of shell and bulk waters; the self-contribution from bound water molecules is comparatively small. While in the alanine solutions the solute-water cross-terms are more important than the solute self-term, the solute contribution is larger in the dipeptide solutions. In the latter systems a much clearer separation of time scales between water and alanine dipeptide related properties is observed. The similarities and differences of the dielectric properties of the amino acid/peptide solutions studied in this work and of solutions of mono- and disaccharides and of the protein ubiquitin are discussed.

Molecular view of water dynamics near model peptides

Incoherent quasi-elastic neutron scattering (QENS) has been used to measure the dynamics of water molecules in solutions of a model protein backbone, N-acetyl-glycine-methylamide (NAGMA), as a function of concentration, for comparison with results for water dynamics in aqueous solutions of the N-acetyl-leucine-methylamide (NALMA) hydrophobic peptide at comparable concentrations. From the analysis of the elastic incoherent structure factor, we find significant fractions of elastic intensity at high and low concentrations for both solutes, which corresponds to a greater population of protons with rotational time scales outside the experimental resolution (>13 ps). The higher-concentration solutions show a component of the elastic fraction that we propose is due to water motions that are strongly coupled to the solute motions, while for low-concentration solutions an additional component is activated due to dynamic coupling between inner and outer hydration layers. An important difference between the solute types at the highest concentration studied is found from stretched exponential fits to their experimental intermediate scattering functions, showing more pronounced anomalous diffusion signatures for NALMA, including a smaller stretched exponent beta and a longer structural relaxation time tau than those found for NAGMA. The more normal water diffusion exhibited near the hydrophilic NAGMA provides experimental support for an explanation of the origin of the anomalous diffusion behavior of NALMA as arising from frustrated interactions between water molecules when a chemical interface is formed upon addition of a hydrophobic side chain, inducing spatial heterogeneity in the hydration dynamics in the two types of regions of the NALMA peptide. We place our QENS measurements on model biological solutes in the context of other spectroscopic techniques and provide both confirming as well as complementary dynamic information that attempts to give a unifying molecular view of hydration dynamics signatures near peptides and proteins.

Water Structures of Differing Order and Mobility in Aqueous Solutions of Schizophyllan, a Triple-Helical Polysaccharide as Revealed by Dielectric Dispersion Measurements

Dielectric dispersion measurements were made on aqueous solutions of a triple-helical polysaccharide schizophyllan over a wide concentration range 10-50 wt % at -45 to +30 degrees C. In the solution state, three different water structures with the different relaxation times tau were found, namely, bound water (taul), structured water (taus), and loosely structured water (tauls) in addition to free water (tauP). Structured water is less mobile and loosely structured water is nearly as mobile as free water, but bound water with taul is much less mobile, thus taul >> taus >> tauls greater, similar tauP. The order-disorder transition accompanies the conversion between structured water and loosely structured water. However, the species with taus remains even in the disordered state and constitutes part of bound water in the entire temperature range. In the frozen state, in addition to bulk water formed by partial melting, two mobile species existed, which were assigned to liquidlike bound water and found to be a continuation of bound water in the solution state. These relaxation time data are discussed in connection with the entropy levels of the four structures deduced from heat capacity data (cf. Yoshiba, K.; et al. Biomacromolecules 2003, 4, 1348-1356).

Protein hydration dynamics in solution: a critical survey

The properties of water in biological systems have been studied for well over a century by a wide range of physical techniques, but progress has been slow and erratic. Protein hydration--the perturbation of water structure and dynamics by the protein surface--has been a particularly rich source of controversy and confusion. Our aim here is to critically examine central concepts in the description of protein hydration, and to assess the experimental basis for the current view of protein hydration, with the focus on dynamic aspects. Recent oxygen-17 magnetic relaxation dispersion (MRD) experiments have shown that the vast majority of water molecules in the protein hydration layer suffer a mere twofold dynamic retardation compared with bulk water. The high mobility of hydration water ensures that all thermally activated processes at the protein-water interface, such as binding, recognition and catalysis, can proceed at high rates. The MRD-derived picture of a highly mobile hydration layer is consistent with recent molecular dynamics simulations, but is incompatible with results deduced from intermolecular nuclear Overhauser effect spectroscopy, dielectric relaxation and fluorescence spectroscopy. It is also inconsistent with the common view of hydration effects on protein hydrodynamics. Here, we show how these discrepancies can be resolved.

Theoretical evaluation of dielectric absorption of microwave energy at the scale of nucleic acids

A theoretical model is proposed for the evaluation of dielectric properties of the cell nucleus between 0.3 and 3 GHz, as a function of its nucleic acids (NA) concentration (CNA). It is based on literature data on dielectric properties of DNA solutions and nucleoplasm. In skeletal muscle cells, the specific absorption rate (SAR) ratio between nucleoplasm and cytoplasm is found to be larger than one for CNA above 30 mg/ml. A nearly linear relationship is found between CNA and this nucleocytoplasmic SAR ratio. Considering the nanoscale of the layer of condensed counterions and bound water molecules at the NA-solution interface, the power absorption per unit volume is evaluated at this precise location. It is found to be between one and two orders of magnitude above that in muscle tissue as a whole. Under realistic microwave (MW) exposure conditions, however, these SAR inhomogeneities do not generate any significant thermal gradient at the scale considered here. Nevertheless, the question arises of a possible biological relevance of nonnegligible and preferential heat production at the location of the cell nucleus and of the NA molecules.

Anomalous dielectric relaxation of water molecules at the surface of an aqueous micelle

Dielectric relaxation of aqueous solutions of micelles, proteins, and many complex systems shows an anomalous dispersion at frequencies intermediate between those corresponding to the rotational motion of bulk water and that of the organized assembly or macromolecule. The precise origin of this anomalous dispersion is not well-understood. In this work we employ large scale atomistic molecular dynamics simulations to investigate the dielectric relaxation (DR) of water molecules in an aqueous micellar solution of cesium pentadecafluorooctanoate. The simulations clearly show the presence of a slow component in the moment-moment time correlation function [PhiMW(t)] of water molecules, with a time constant of about 40 ps, in contrast to only 9 ps for bulk water. Interestingly, the orientational time correlation function [Cmu(t)] of individual water molecules at the surface exhibits a component with a time constant of about 19 ps. We show that these two time constants can be related by the well-known micro-macrorelations of statistical mechanics. In addition, the reorientation of surface water molecules exhibits a very slow component that decays with a time constant of about 500 ps. An analysis of hydrogen bond lifetime and of the rotational relaxation in the coordinate frame fixed on the micellar body seems to suggest that the 500 ps component owes its origin to the existence of an extended hydrogen bond network of water molecules at the surface. However, this ultraslow component is not found in the total moment-moment time correlation function of water molecules in the solution. The slow DR of hydration water is found to be well correlated with the slow solvation dynamics of cesium ions at the water-micelle interface.

Dynamics of bound and free water in an aqueous micellar solution: analysis of the lifetime and vibrational frequencies of hydrogen bonds at a complex interface

In order to understand the nature and dynamics of interfacial water molecules on the surface of complex systems, large scale, fully atomistic molecular dynamics simulations of an aqueous micelle of cesium perfluorooctanoate (CsPFO) surfactant molecules have been carried out. The lifetime and the intermolecular vibrational frequencies of the hydrogen bonds that the water molecules form with the hydrophilic, polar head groups (PHG) of the surfactants are calculated. Our earlier classification [S. Balasubramanian et al., Curr. Sci. 84, 428 (2003); e-print cond-mat/0212097] of the interfacial water molecules, based on structural and energetic considerations, into bound and free types is further validated by their dynamics. Lifetime correlation functions of the water-surfactant hydrogen bonds show the long-lived nature of the bound water species. Surprisingly, the water molecules that are singly hydrogen bonded to the surfactants have a longer lifetime than those that form two such hydrogen bonds. The free water molecules that do not form any such hydrogen bonds behave similarly to bulk water in their reorientational dynamics. A few water molecules that form two such hydrogen bonds are orientationally locked in for durations of the order of a few hundreds of picoseconds; that is, much longer than their average lifetime. The intermolecular vibrational frequencies of these interfacial water molecules have been studied from the power spectra of their velocity autocorrelation function. We find a significant blue shift in the librational band of the interfacial water molecules, apart from a similar shift in the near neighbor bending modes, relative to water molecules in bulk. These blue shifts suggest an increase in rigidity in the structure around interfacial water molecules. This is in good agreement with recent incoherent, inelastic neutron scattering data on macromolecular solutions [S. Ruffle et al., J. Am. Chem. Soc. 124, 565 (2002)]. The results of the present simulations appear to be rather general and should be relevant to the understanding of the dynamics of water near any hydrophilic surface.