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

Coupling between overall rotational diffusion and domain motions in proteins and its effect on dielectric spectra

In this work, we formulate a closed-form solution of the model of a semirigid molecule for the case of fluctuating and reorienting molecular electric dipole moment. We illustrate with numeric calculations the impact of protein domain motions on dielectric spectra using the example of the 128 kDa protein dimer of Enzyme I. We demonstrate that the most drastic effect occurs for situations when the characteristic time of protein domain dynamics is comparable to the time of overall molecular rotational diffusion. We suggest that protein domain motions could be a possible explanation for the high-frequency contribution that accompanies the major relaxation dispersion peak in the dielectric spectra of protein aqueous solutions. We propose that the presented computational methodology could be used for the simultaneous analysis of dielectric spectroscopy and nuclear magnetic resonance data. Proteins 2015; 83:1571-1581. © 2015 Wiley Periodicals, Inc.

Orientational alignment of amyloidogenic proteins in pre-aggregated solutions

In the present study we combine dielectric relaxation spectroscopy with generalized Born simulations to explore the role of orientational order for protein aggregation in solutions of bovine pancreatic insulin at various pH conditions. Under aggregation-prone conditions at low pH, insulin monomers prefer antiparallel dipole alignments, which are consistent with the orientation of the monomeric subunits in the dimer structure. This alignment is also true for two dimers, suggesting that already at moderate protein concentrations the species assemble in equilibrium clusters, in which the molecules adopt preferred orientations also found for the protomers of the corresponding oligomers.

Protein dielectrophoresis and the link to dielectric properties

There is a growing interest in protein dielectrophoresis (DEP) for biotechnological and pharmaceutical applications. However, the DEP behavior of proteins is still not well understood which is important for successful protein manipulation. In this paper, we elucidate the information gained in dielectric spectroscopy (DS) and electrochemical impedance spectroscopy (EIS) and how these techniques may be of importance for future protein DEP manipulation. EIS and DS can be used to determine the dielectric properties of proteins predicting their DEP behavior. Basic principles of EIS and DS are discussed and related to protein DEP through examples from previous studies. Challenges of performing DS measurements as well as potential designs to incorporate EIS and DS measurements in DEP experiments are also discussed.

The Design and Operation of Ultra-Sensitive and Tunable Radio-Frequency Interferometers

Dielectric spectroscopy (DS) is an important technique for scientific and technological investigations in various areas. DS sensitivity and operating frequency ranges are critical for many applications, including lab-on-chip development where sample volumes are small with a wide range of dynamic processes to probe. In this work, we present the design and operation considerations of radio-frequency (RF) interferometers that are based on power-dividers (PDs) and quadrature-hybrids (QHs). Such interferometers are proposed to address the sensitivity and frequency tuning challenges of current DS techniques. Verified algorithms together with mathematical models are presented to quantify material properties from scattering parameters for three common transmission line sensing structures, i.e., coplanar waveguides (CPWs), conductor-backed CPWs, and microstrip lines. A high-sensitivity and stable QH-based interferometer is demonstrated by measuring glucose-water solution at a concentration level that is ten times lower than some recent RF sensors while our sample volume is ~1 nL. Composition analysis of ternary mixture solutions are also demonstrated with a PD-based interferometer. Further work is needed to address issues like system automation, model improvement at high frequencies, and interferometer scaling.

Charge invariant protein-water relaxation in GB1 via ultrafast tryptophan fluorescence

The protein–water interface is a critical determinant of protein structure and function, yet the precise nature of dynamics in this complex system remains elusive. Tryptophan fluorescence has become the probe of choice for such dynamics on the picosecond time scale (especially via fluorescence “upconversion”). In the absence of ultrafast (“quasi-static”) quenching from nearby groups, the TDFSS (time-dependent fluorescence Stokes shift) for exposed Trp directly reports on dipolar relaxation near the interface (both water and polypeptide). The small protein GB1 contains a single Trp (W43) of this type, and its structure is refractory to pH above 3. Thus, it can be used to examine the dependence of dipolar relaxation upon charge reconfiguration with titration. Somewhat surprisingly, the dipolar dynamics in the 100 fs to 100 ps range were unchanged with pH, although nanosecond yield, rates, and access all changed. These results were rationalized with the help of molecular dynamics (including QM-MM) simulations that reveal a balancing, sometimes even countervailing influence of protein and water dipoles. Interestingly, these simulations also showed the dominant influence of water molecules which are associated with the protein interface for up to 30 ps yet free to rotate at approximately “bulk” water rates.

Dynamics of water molecules and sodium ions in solid hydrates of nucleotides

The dynamics of the co-ordinating water and metal cations in solid hydrates of nucleotide salts is explored with solid-state NMR spectroscopy and DFT calculations.

Specific and non-specific protein association in solution: computation of solvent effects and prediction of first-encounter modes for efficient configurational bias Monte Carlo simulations

Weak and ultraweak protein-protein association play a role in molecular recognition and can drive spontaneous self-assembly and aggregation. Such interactions are difficult to detect experimentally, and are a challenge to the force field and sampling technique. A method is proposed to identify low-population protein-protein binding modes in aqueous solution. The method is designed to identify preferential first-encounter complexes from which the final complex(es) at equilibrium evolve. A continuum model is used to represent the effects of the solvent, which accounts for short- and long-range effects of water exclusion and for liquid-structure forces at protein/liquid interfaces. These effects control the behavior of proteins in close proximity and are optimized on the basis of binding enthalpy data and simulations. An algorithm is described to construct a biasing function for self-adaptive configurational-bias Monte Carlo of a set of interacting proteins. The function allows mixing large and local changes in the spatial distribution of proteins, thereby enhancing sampling of relevant microstates. The method is applied to three binary systems. Generalization to multiprotein complexes is discussed.

Quantitative cw Overhauser effect dynamic nuclear polarization for the analysis of local water dynamics

Liquid state Overhauser effect Dynamic Nuclear Polarization (ODNP) has experienced a recent resurgence of interest. The ODNP technique described here relies on the double resonance of electron spin resonance (ESR) at the most common, i.e. X-band (∼10GHz), frequency and ¹H nuclear magnetic resonance (NMR) at ∼15 MHz. It requires only a standard continuous wave (cw) ESR spectrometer with an NMR probe inserted or built into an X-band cavity. We focus on reviewing a new and powerful manifestation of ODNP as a high frequency NMR relaxometry tool that probes dipolar cross relaxation between the electron spins and the ¹H nuclear spins at X-band frequencies. This technique selectively measures the translational mobility of water within a volume extending 0.5-1.5 nm outward from a nitroxide radical spin probe that is attached to a targeted site of a macromolecule. It allows one to study the dynamics of water that hydrates or permeates the surface or interior of proteins, polymers, and lipid membrane vesicles. We begin by reviewing the recent advances that have helped develop ODNP into a tool for mapping the dynamic landscape of hydration water with sub-nanometer locality. In order to bind this work coherently together and to place it in the context of the extensive body of research in the field of NMR relaxometry, we then rephrase the analytical model and extend the description of the ODNP-derived NMR signal enhancements. This extended model highlights several aspects of ODNP data analysis, including the importance of considering all possible effects of microwave sample heating, the need to consider the error associated with various relaxation rates, and the unique ability of ODNP to probe the electron-¹H cross-relaxation process, which is uniquely sensitive to fast (tens of ps) dynamical processes. By implementing the relevant corrections in a stepwise fashion, this paper draws a consensus result from previous ODNP procedures and then shows how such data can be further corrected to yield clear and reproducible saturation of the NMR hyperpolarization process. Finally, drawing on these results, we broadly survey the previous ODNP dynamics literature. We find that the vast number of published, empirical hydration dynamics data can be reproducibly classified into regimes of surface, interfacial, vs. buried water dynamics.

Protein dielectrophoresis: advances, challenges, and applications

Protein dielectrophoresis (DEP) has the potential to play an important role as a manipulation, fractionation, preconcentration, and separation method in bioanalysis and as manipulation tool for nanotechnological applications. The first demonstrations of protein DEP have been reported almost 20 years ago. Since then various experimental realizations to manipulate proteins by DEP as well as more targeted applications employing protein DEP have been demonstrated. This review summarizes the experimental studies in the field of protein DEP trapping and focusing as well as specific applications in separation, molecular patterning, on bioprobes and biosensors. While a comprehensive theoretical model describing protein DEP is still lacking we also attempt to provide an overview of the factors influencing protein DEP and relate to currently available theoretical models. We further point out the variations in experimental conditions used in the past to study the somewhat 20 proteins as well as the implications of protein molecular structure to the DEP response.

Hydration-state change of horse heart cytochrome c corresponding to trifluoroacetic-acid-induced unfolding

We investigate the hydration state of horse-heart cytochrome c (hh cyt c) in the unfolding process induced by trifluoroacetic acid (TFA). The conformation of hh cyt c changes from the native (N) state (2.9 < pH < 6.0) to the acid-unfolded (U(A)) state (1.7 < pH < 2.0) to the acid-induced molten globule (A) state (pH ∼1.2). Hydration properties of hh cyt c during this process are measured at 20°C by high-resolution dielectric relaxation (DR) spectroscopy, UV-vis absorbance, and circular dichroism spectroscopy. Constrained water of hh cyt c is observed at every pH as an ∼5-GHz Debye component (DC) (DR time, τ(D) ∼30 ps) and its DR amplitude (DRA) is increased by 77% upon N-to-U(A) transition, when pH changes from 6.0 to 2.0. Even in the N state, the DRA of the constrained-water component is found to be increased by 22% with decreasing pH from 6.0 to 2.9, suggesting an increase in the accessible surface area of native hh cyt c. Moreover, hypermobile water around native hh cyt c is detected at pH 6.0 as a 19-GHz DC (τ(D) ∼ 8.4 ps <τ(DW) = 9.4 ps), but is not found at other pH values. The DRA signal of constrained water is found to return to the pH 2.9 (N-state) level upon U(A)-to-A transition. Fast-response water (slightly slower than bulk) around A-state hh cyt c is detected at pH 1.2, and this suggests some accumulation of TFA(-) ions around the peptide chain. Thus, this high-resolution DR spectroscopy study reveals that hh cyt c exhibits significant hydration-state change in the TFA-unfolding process.

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

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

Dielectric spectroscopy study on ionic liquid microemulsion composed of water, TX-100, and BmimPF6

We report here a broadband dielectric spectroscopy study on an ionic liquid microemulsion (ILM) composed of water, Triton X-100 (TX-100), and 1-butyl-3-methylimidazolium hexafluorophosphate (bmimPF(6)). It is found that the phase behavior of this ILM can be easily identified by its dielectric response. The dielectric behavior of the ILM in the GHz range is consistent with that of TX-100∕water mixtures with comparable water-to-TX-100 weight ratio. It consists of the relaxations due to ethylene oxide (EO) unit relaxation, hydration water dynamics, and∕or free water dynamics. The water content dependence of the EO unit relaxation suggests that this relaxation involves dynamics of hydration water molecules. In the IL-in-water microemulsion phase, it is found that bmimPF(6) molecules are preferentially dissolved in water when their concentration in water is lower than the solubility. An additional dielectric relaxation that is absent in the TX-100∕water mixtures is observed in the frequency range of 10(7)-10(8) Hz for this ILM. This low-frequency relaxation is found closely related to the bmimPF(6) molecule and could be attributed to the hopping of its cations∕anions between the anionic∕cationic sites.

Quantitation of pH-induced aggregation in binary protein mixtures by dielectric spectroscopy

This paper presents a quantitative approach for measuring pH-controlled protein aggregation using dielectric spectroscopy. The technique is demonstrated through two aggregation experiments, the first between β-lactoglobulin (β-Lg) and hen lysozyme (HENL) and the second between bovine serum albumin (BSA) and HENL. In both experiments, the formation of aggregates is strongly dependent on the solution pH and is clearly indicated by a decrease in the measured permittivity when the second protein is added. A quantifiable lower-bound on the ratio of proteins involved in the aggregation process is obtained from the permittivity spectra. Lower-bound aggregation ratios of 83 % for β-Lg/HENL at pH 6.0 and 48 % for BSA/HENL at pH 9.2 were consistent with turbidity measurements made on the same solutions.

Self-consistent treatment of the local dielectric permittivity and electrostatic potential in solution for polarizable macromolecular force fields

A self-consistent method is presented for the calculation of the local dielectric permittivity and electrostatic potential generated by a solute of arbitrary shape and charge distribution in a polar and polarizable liquid. The structure and dynamics behavior of the liquid at the solute/liquid interface determine the spatial variations of the density and the dielectric response. Emphasis here is on the treatment of the interface. The method is an extension of conventional methods used in continuum protein electrostatics, and can be used to estimate changes in the static dielectric response of the liquid as it adapts to charge redistribution within the solute. This is most relevant in the context of polarizable force fields, during electron structure optimization in quantum chemical calculations, or upon charge transfer. The method is computationally efficient and well suited for code parallelization, and can be used for on-the-fly calculations of the local permittivity in dynamics simulations of systems with large and heterogeneous charge distributions, such as proteins, nucleic acids, and polyelectrolytes. Numerical calculation of the system free energy is discussed for the general case of a liquid with field-dependent dielectric response.

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.

Dielectric spectroscopy of molecular interactions based on the avidin-biotin complex

Dielectric spectroscopy is used to probe the electrical properties of biomolecules dissolved in liquids. A 40 μl cell is constructed out of acrylic with polished, stainless steel electrodes. Experiments are performed on avidin and biotin-labeled BSA, showing characteristics of aggregation. Experiments with avidin and biotin demonstrate shifts in dielectric relaxation of the avidin associated with changes in the dipole moment and size of the molecule due to biotin binding. These shifts are analyzed in the context of biomolecular changes. These experiments demonstrate the utility of impedance spectroscopy to detect changes due to small molecules binding to proteins.

Increased bandwidth for dielectric spectroscopy of proteins through electrode surface preparation

Dielectric spectroscopy measurements of liquids are often limited by electrode polarization. The influence of surface polishing and deposition of the conducting polymer polypyrrole/polystyrenesulfonate (PPy/PSS) on the polarization impedance is investigated. A quantitative description of the electrode polarization contribution to the real-valued permittivity spectrum is derived. This description explains the origin of the ω(-const). (const.>1) dependency commonly observed in permittivity measurements. Electrode surface roughness is correlated with both the magnitude and phase of the constant phase element. Generally, rougher electrodes have better performance, and an order of magnitude bandwidth improvement is achieved using PPy/PSS electrodes.

Note: electrode polarization of Galinstan electrodes for liquid impedance spectroscopy

Electrode polarization is a significant obstacle in the impedance measurements of ionic liquids. An atomically smooth electrode surface could potentially reduce unwanted impedance contributions from electrode polarization. Liquid metal electrodes were formed by adhering Galinstan to acrylic plates in a parallel-plate capacitor arrangement. Electrode polarization was compared to a similar cell with stainless steel electrodes. The impedance of salt and protein solutions (β-lactoglobulin) was measured from 40 Hz to 110 MHz. Because of oxide layer formation, the performance of the Galinstan electrode is significantly different than the theoretical ideal.

Broadband RF impedance spectroscopy in micromachined microfluidic channels

Impedance spectroscopy in the radio frequency range from 100 MHz to 20 GHz can reveal the dielectric relaxations of biological and chemical solutions. S-parameters for a coplanar waveguide are derived. To perform these measurements, a coplanar waveguide device was fabricated on a conventional FR-4 substrate for fluid interrogation. The microfluidic channel was formed by milling conventional waveguides and laser-cutting channels in the dielectric substrate. Measurements using this device were performed on standards: deionized water, isopropyl alcohol, and air. These measurements were compared to those taken with a conventional dielectric probe. The results demonstrate the ability of the fabricated device to extract varying transmission parameters due to changing sample properties.

Temperature-stable parallel-plate dielectric cell for broadband liquid impedance measurements

A liquid impedance cell for broadband impedance measurements up to 110 MHz is presented. The design incorporates temperature control and minimizes parasitic capacitance and inductance. The cell is simple to fabricate and uses chemically resistant materials, stainless steel, and Teflon. This dielectric cell can be used in a variety of liquid measurements, particularly those related to impedance measurements of biological objects in solution. Temperature control is illustrated in measurements of the permittivity of deionized water from 5 to 55  °C. Numerical fitting procedures employed on the relaxation curves indicate good agreement with previous studies on beta-lactoglobulin and hen lysozyme. Titration capability is demonstrated through dielectric titration of hen lysozyme and beta-lactoglobulin.

Dynamics of biological macromolecules: not a simple slaving by hydration water

We studied the dynamics of hydrated tRNA using neutron and dielectric spectroscopy techniques. A comparison of our results with earlier data reveals that the dynamics of hydrated tRNA is slower and varies more strongly with temperature than the dynamics of hydrated proteins. At the same time, tRNA appears to have faster dynamics than DNA. We demonstrate that a similar difference appears in the dynamics of hydration water for these biomolecules. The results and analysis contradict the traditional view of slaved dynamics, which assumes that the dynamics of biological macromolecules just follows the dynamics of hydration water. Our results demonstrate that the dynamics of biological macromolecules and their hydration water depends strongly on the chemical and three-dimensional structures of the biomolecules. We conclude that the whole concept of slaving dynamics should be reconsidered, and that the mutual influence of biomolecules and their hydration water must be taken into account.

Broadband depolarized light scattering study of diluted protein aqueous solutions

A broadband depolarized light scattering (DLS) study is performed on diluted lysozyme aqueous solutions as a function of temperature and concentration. The dynamical susceptibility, obtained in a wide spectral range (0.6-36000 GHz) through the coupled use of interferometric and dispersive devices, is interpreted and compared with neutron scattering and Raman-induced optical Kerr-effect literature data, thus giving a general picture of relaxation phenomena. We show that the proposed approach represents a suitable tool for investigating the hydration dynamics of protein-water solutions. A detailed analysis of the quasi-elastic scattering region evidences the existence of two distinct relaxational processes at picosecond time scales. The fast process (fractions of picosecond) is attributed to bulk water dynamics, while the slow one (few picoseconds) is attributed to dynamical rearrangements of water molecules strongly influenced by the protein (hydration water). The retardation effect here estimated of about 6-7 can be regarded as a direct measure of the increased protein-water and water-water hydrogen bond stability of the water molecules within the protein hydration shell. Interestingly, a similar effect was previously observed on small hydrophilic sugar molecules. Moreover, backbone and side chains torsional motions of the protein in the 600-5300 GHz frequency range are found to be insensitive to thermal variations and to eventual changes occurring in the premelting zone.