What Can Really Be Learned from Dielectric Spectroscopy of Protein Solutions? A Case Study of Ribonuclease A

Nanogap dielectric spectroscopy for aptamer-based protein detection

Among the various label-free methods for monitoring biomolecular interactions, capacitive sensors stand out due to their simple instrumentation and compatibility with multiplex formats. However, electrode polarization due to ion gradient formation and noise from solution conductance limited early dielectric spectroscopic measurements to high frequencies only, which in turn limited their sensitivity to biomolecular interactions, as the applied excitation signals were too fast for the charged macromolecules to respond. To minimize electrode polarization effects, capacitive sensors with 20 nm electrode separation were fabricated using silicon dioxide sacrificial layer techniques. The nanoscale separation of the capacitive electrodes in the sensor results in an enhanced overlapping of electrical double layers, and apparently a more ordered "ice-like" water structure. Such effects in turn reduce low frequency contributions from bulk sample resistance and from electrode polarization, and thus markedly enhance sensitivity toward biomolecular interactions. Using these nanogap capacitive sensors, highly sensitive, label-free aptamer-based detection of protein molecules is achieved.

Structure of the alanine hydration shell as probed by NMR chemical shifts and indirect spin-spin coupling

The structure of the alanine hydration shell was modeled by Carr-Parinello molecular dynamics (CPMD) to explain subtle differences in NMR chemical shifts and indirect spin-spin coupling constants of the neutral (zwitterionic), cationic, and anionic forms of this amino acid. In comparison with classical molecular dynamics (MD), the quantum mechanical CPMD approach revealed a more structured solvent and significant differences in the radial and angular distributions of the water molecules around the solute. In particular, the solvent was predicted to be organized around the uncharged COOH and NH(2) residues to a similar degree as that for the charged ones. This was not the case with MD. For snapshot CPMD configurations, the NMR parameters were computed by density functional theory (DFT) and averaged. Obtained values were significantly closer to experimental parameters known for (15)N and (13)C isotopically labeled alanine than those calculated by the conventional implicit dielectric solvent model. The NMR results also quantitatively reflect a superiority of the CPMD over the MD explicit solvent treatment. A further improvement of the computed spin-spin coupling constants could be achieved by taking into account vibrational averaging beyond the harmonic approximation. Differently positioned water molecules in the clusters cause an unexpectedly large scattering of the NMR parameters. About 10-15 dynamics snapshots were required for a satisfactory convergence of the shifts and couplings. The NMR chemical shift was found to be much more sensitive to the molecular hydration than the coupling. The results thus indicate a large potential of the NMR spectroscopy and quantum simulations to probe not only the structure of molecules but also their interactions with the environment.

Site-dependent excited-state dynamics of a fluorescent probe bound to avidin and streptavidin

The excited-state dynamics of biotin-spacer-Lucifer-Yellow (LY) constructs bound to avidin (Avi) and streptavidin (Sav) was investigated using femtosecond spectroscopy. Two different locations in the proteins, identified by molecular dynamics simulations of Sav, namely the entrance of the binding pocket and the protein surface, were probed by varying the length of the spacer. A reduction of the excited-state lifetime, stronger in Sav than in Avi, was observed with the long spacer construct. Transient absorption measurements show that this effect originates from an electron transfer quenching of LY, most probably by a nearby tryptophan residue. The local environment of the LY chromophore could be probed by measuring the time-dependent polarisation anisotropy and Stokes shift of the fluorescence. Substantial differences in both dynamics were observed. The fluorescence anisotropy decays analysed by using the wobbling-in-a-cone model reveal a much more constrained environment of the chromophore with the short spacer. Moreover, the dynamic Stokes shift is multiphasic in all cases, with a approximately 1 ps component that can be ascribed to diffusive motion of bulk-like water molecules, and with slower components with time constants varying not only with the spacer, but with the protein as well. These slow components, which depend strongly on the local environment of the probe, are ascribed to the motion of the hydration layer coupled to the conformational dynamics of the protein.

Myoglobin and Apomyoglobin in their Native, Molten Globule and Acid-Denaturated States. A Dielectric Relaxation Study

The acid-induced unfolding of myoglobin and its haem-free derivative apo-myoglobin is studied by broadband dielectric relaxation spectroscopy at pH values near 5, 4 and 2, which reflect the transition N → MG → UA from the native state (N) via a molten globule state (MG) to an acid-unfolded state (UA). Spectral changes are singled out by considering difference spectra for the transitions N → MG and N → UA. A pronounced increase of the amplitude of the tumbling motion of holo-myoglobin and apo-myoglobin in the sequence N → MG→ UA reflects the increase of their electrical dipole moments by progressive unfolding. A distinct high-frequency shoulder of the tumbling mode indicates an enhanced internal protein dynamics in the unfolded states. The calculated Stokes radii confirm a compact nature of the MG state and a large increase in size of the UA state relative to the native state. In the native state the Stokes radii deduced from the dielectric spectra agree fairly well with those deduced from dynamic light scattering. In the MG state, and particularly in the UA state, the Stokes radii determined by light scattering are markedly larger than those determined by dielectric relaxation. The difference is attributed to aggregation of the unfolded species, which affects dynamic light scattering more than dielectric relaxation. In the high-frequency regime, the dielectric spectra indicate that unfolding enhances the number of water molecules showing bulk-like dynamics, but the effect is rather weak.

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.

Thickness of the hydration layer of a protein from molecular dynamics simulation

Water molecules around a protein exhibit slow dynamics with respect to that of pure bulk water. One important issue in protein hydration is the thickness of the hydration layer (i.e., the distance from the protein surface up to which the water dynamics is influenced by the protein). Estimation of thickness is crucial to understand better the properties of "biological water" and the role that it plays in guiding the protein's function. We have performed an atomistic molecular dynamics simulation of an aqueous solution of the protein villin headpiece subdomain or HP-36 to estimate the thickness of its hydration water. In particular, several dynamical properties of water around different segments (three alpha-helices) of the protein have been calculated by varying the thickness of the hydration layers. It is found that in general the influence of the helices on water properties extends beyond the first hydration layer. However, the heterogeneous nature of water among the first hydration layers of the three helices diminishes as the thickness is increased. It indicates that, for a small protein such as HP-36, the thickness of "biological water" is uniform for different segments of the protein.

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.

Correlation between the Dynamics of Hydrogen Bonds and the Local Density Reorganization in the Protein Hydration Layer

An atomistic molecular dynamics simulation of the protein villin headpiece subdomain or HP-36 has been carried out with explicit water to explore the microscopic inhomogeneity of local density reorganization of the hydration layers of the three alpha-helical segments of the protein. The density reorganization of the hydration layer of helix-3 is found to occur faster than that for the hydration layers of the other two helices. It is noticed that such inhomogeneous density reorganization at the surface of different secondary structures exhibits excellent correlation with the microscopic dynamics of hydrogen bonds between the protein residues and the hydration water. Further, it is observed that the reorientation of water molecules involved in the formation and breaking of protein-water or water-water hydrogen bonds plays an important role in determining the dynamics of local density of the hydration layer. The faster density reorganization of the hydration layer of helix-3 is also consistent with the functionality of HP-36, as helix-3 contains several active site residues.

Single particle and collective hydration dynamics for hydrophobic and hydrophilic peptides

We have conducted extensive molecular dynamics simulations to study the single particle and collective dynamics of water in solutions of N-acetyl-glycine-methylamide, a model hydrophilic protein backbone, and N-acetyl-leucine-methylamide, a model (amphiphilic) hydrophobic peptide, as a function of peptide concentration. Various analytical models commonly used in the analysis of incoherent quasielastic neutron scattering (QENS), are tested against the translational and rotational intermediate scattering function, the mean square displacement of the water molecule center of mass, and fits to the second-order rotational correlation function of water evaluated directly from the simulation data. We find that while the agreement between the model-free analysis and analytical QENS models is quantitatively poor, the qualitative feature of dynamical heterogeneity due to caging is captured well by all approaches. The center of mass collective and single particle intermediate scattering functions of water calculated for these peptide solutions show that the crossover from collective to single particle-dominated motions occurs at a higher value of Q for high concentration solutions relative to low concentration because of the greater restriction in movement of water molecules due to confinement. Finally, we have shown that at the same level of confinement of the two peptides, the aqueous amphiphilic amino acid solution shows the strongest deviation between single particle and collective dynamics relative to the hydrophilic amino acid, indicating that chemical heterogeneity induces even greater spatial heterogeneity in the water dynamics.

Approximate Values for Force Constant and Wave Number Associated with a Low-Frequency Concerted Motion in Proteins Can Be Evaluated by a Comparison of X-ray Structures

Low-frequency internal motions in protein molecules play a key role in biological functions. A direct relationship between low-frequency motions and enzymatic activity has been suggested for bovine pancreatic ribonuclease (RNase A). The flexibility-function relationship in this enzyme has been attributed to a subtle and concerted breathing motion of the beta-sheet regions occurring upon substrate binding and release. Here, we calculate an approximate value for the force constant and the wave number of the low-frequency beta-sheet breathing motion of RNase A, by using the Boltzmann hypothesis on a set of data derived from a simple conventional structural superimposition of an unusual large number of X-ray structures available for the protein. The results agree with previous observations and with theoretical predictions on the basis of normal-mode analysis. To the best of our knowledge, this is the first example in which the wave number and the force constant of a low-frequency concerted motion in a protein are directly derived from X-ray structures.

Dielectric Response of Imidazolium-Based Room-Temperature Ionic Liquids

We have used microwave dielectric relaxation spectroscopy to study the picosecond dynamics of five low-viscosity, highly conductive room temperature ionic liquids based on 1-alkyl-3-methylimidazolium cations paired with the bis((trifluoromethyl)sulfonyl)imide anion. Up to 20 GHz the dielectric response is bimodal. The longest relaxation component at the time scale of several 100 ps reveals strongly nonexponential dynamics and correlates with the viscosity in a manner consistent with hydrodynamic predictions for the diffusive reorientation of dipolar ions. Methyl substitution at the C2 position destroys this correlation. The time constants of the weak second process at the 20 ps time scale are practically the same for each salt. This intermediate process seems to correlate with similar modes in optical Kerr effect spectra, but its physical origin is unclear. The missing high-frequency portion of the spectra indicates relaxation beyond the upper cutoff frequency of 20 GHz, presumably due to subpicosecond translational and librational displacements of ions in the cage of their counterions. There is no evidence for orientational relaxation of long-lived ion pairs.

Dielectric Characterization of a Nanofiltration Membrane in Electrolyte Solutions: Its Double-Layer Structure and Ion Permeation

Dielectric spectroscopy (DS) was applied to a nanofiltration (NF) membrane to detect its double-layer structure and ion permeation. Dielectric measurements were carried out on the systems composed of the NF membrane NTR7450 and dilute solutions of eight electrolytes, LiCl, NaCl, KCl, NH(4)Cl, MgCl(2), CaCl(2), BaCl(2), and CuCl(2). Two relaxations were observed in the frequency range from 40 Hz to 4 MHz for each system. On the basis of characteristics of the dielectric spectra and the Maxwell-Wagner interfacial polarization theory, the low-frequency relaxation was attributed to inhomogeneity of the membrane structure itself, whereas the high-frequency relaxation was attributed to interfacial polarization between the membrane and the solution. A multiphase dielectric model previously developed by one of the authors and co-workers was adopted to present systems to analyze the dielectric spectra, and electric parameters, i.e., capacitance and conductance, of the two layers composing the membrane were obtained. The electric properties estimated for the two layers were different and changed with the environment in a different manner. Further analyses suggest that the two layers had a different separation mechanism due to their difference in materials, looseness, and fixed charge content. The fixed charge density of one layer was estimated, and the ion permeation difficulties in both layers was compared. This research revealed that DS was by far an effective method to obtain detailed electric parameters about the inner multilayer structure of the NF membrane and to elucidate separation mechanisms of each layer.

Structure and dynamics of water at the interface with phospholipid bilayers

We have performed two molecular-dynamics simulations to study the structural and dynamical properties of water at the interface with phospholipid bilayers. In one of the simulations the bilayer contained neutral phospholipid molecules, dioleoylphosphatidylcholine (DOPC); in the second simulation the bilayer contained charged lipid molecules, dioleoylphosphatidylserine (DOPS). From the density profile of water we observe that water next to the DOPS bilayer is more perturbed as compared to water near the DOPC bilayer. Using an energetic criterion for the determination of hydrogen bonding we find that water molecules create strong hydrogen bonds with the headgroups of the phospholipid molecules. Due to the presence of these bonds and also due to the confinement of water, the translational and orientational dynamics of water at the interface are slowed down. The degree of slowing down of the dynamics depends upon the location of water molecules near a lipid headgroup.

How Polar Are Ionic Liquids? Determination of the Static Dielectric Constant of an Imidazolium-based Ionic Liquid by Microwave Dielectric Spectroscopy

In a pilot study of the dielectric constant of room-temperature ionic liquids, we use dielectric spectroscopy in the megahertz/gigahertz regime to determine the complex dielectric function of five 1-alkyl-3-methylimidazolium salts, from which the static dielectric constant epsilon is obtained by zero-frequency extrapolation. The results classify the salts as moderately polar solvents. The observed epsilon-values at 298.15 K fall between 15.2 and 8.8, and epsilon decreases with increasing chain length of the alkyl residue of the cation. The anion sequence is trifluoromethylsulfonate > tetrafluoroborate approximately tetrafluorophosphate. The results indicate markedly lower polarities than found by spectroscopy with polarity-sensitive solvatochromic dyes.

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.

A phenomenological model of dynamical arrest of electron transfer in solvents in the glass-transition region

A phenomenological model of electron transfer reactions in solvents undergoing glass transition is discussed. The reaction constant cuts off slow polarization modes from the spectrum of nuclear thermal motions active on the observation time scale. The arrest of nuclear solvation in turn affects the reaction activation barrier making it dependent on the rate. The resultant rate constant is sought from a self-consistent equation. The model describes well the sharp change in the solvent Stokes shift of optical lines in the glass-transition region. It is also applied to describe the temperature dependence of primary charge separation and reduction of primary pair in photosynthetic reaction centers. The model shows that a weak dependence of the primary charge separation rate on temperature can be explained by dynamical arrest of nuclear solvation on the picosecond time scale of electron transfer. For reduction of primary pair by cytochrome, the model yields a sharp turnover of the reaction kinetics at the transition temperature when nuclear solvation freezes in.