Relaxation dynamics of a protein solution investigated by dielectric spectroscopy

In the present work, we provide a dielectric study on two differently concentrated aqueous lysozyme solutions in the frequency range from 1MHz to 40GHz and for temperatures from 275 to 330K. We analyze the three dispersion regions, commonly found in protein solutions, usually termed β-, γ-, and δ-relaxations. The β-relaxation, occurring in the frequency range around 10MHz and the γ-relaxation around 20GHz (at room temperature) can be attributed to the rotation of the polar protein molecules in their aqueous medium and the reorientational motion of the free water molecules, respectively. The nature of the δ-relaxation, which is often ascribed to the motion of bound water molecules, is not yet fully understood. Here we provide data on the temperature dependence of the relaxation times and relaxation strengths of all three detected processes and on the dc conductivity arising from ionic charge transport. The temperature dependences of the β- and γ-relaxations are closely correlated. We found a significant temperature dependence of the dipole moment of the protein, indicating conformational changes. Moreover we find a breakdown of the Debye-Stokes-Einstein relation in this protein solution, i.e., the dc conductivity is not completely governed by the mobility of the solvent molecules. Instead it seems that the dc conductivity is closely connected to the hydration shell dynamics.     

Temperature-dependent dielectric properties of slightly hydrated horn keratin

With an aim to reveal the mechanism of protein-water interaction in a predominantly two phase model protein system this study investigates the frequency and temperature dependence of dielectric constant epsilon' and loss factor epsilon' in cow horn keratin in the frequency range 30 Hz to 3 MHz and temperature range 30-200 degrees C at two levels of hydration. These two levels of hydration were achieved by exposing the sample to air at 50% relative humidity (RH) at ambient temperature and by evacuating the sample for 72 h at 105 degrees C. A low frequency dispersion (LFD) and an intermediate frequency alpha-dispersion were the two main dielectric responses observed in the air-dried sample. The LFD and the high frequency arm of the alpha-dispersion followed the same fractional power law of frequency. Within the framework of percolation cluster model these dispersions, respectively have been attributed to percolation of protons between and within the clusters of hydrogen-bonded water molecules bound to polar or ionizable protein components. The alpha-dispersion peak, which results from intra-cluster charge percolation conformed to Cole-Cole modified Debye equation. Temperature dependence of the dielectric constant in the air-dried sample exhibited peaks at 120 and 155 degrees C which have been identified as temperatures of onset of release of water bound to polar protein components in the amorphous and crystalline regions, respectively. An overall rise in the permittivity was observed above 175 degrees C, which has been identified as the onset of chain melting in the crystalline region of the protein.     

Trifluoroethanol and binding to model membranes stabilize a predicted turn in a peptide corresponding to the first extracellular loop of the angiotensin II AT(1A) receptor

Deuterium oxide solutions of a triple-helical polysaccharide schizophyllan, undergoing an order-disorder transition centered around 17 degrees C, were studied by the time-domain reflectometry (TDR) to obtain dielectric dispersions in the solution and frozen states. In the solution state, the dispersion below the transition temperature is resolved in three dispersions (relaxation times at 0 degrees C) ascribed to side chain glucose residue (1; 102 ns), structured water (s; 2.0 ns) and bulk water (h), respectively, from low to high frequencies. Bulk water is divided into slow water (h2; 0.04 ns) and free or pure water (h1; 0.02 ns). Above the transition temperature structured water almost disappears and is compensated by slow water. Structured water is similar to bound water for proteins but different from it because of this transition behavior. Another dispersion (l) seen at the lowest frequency is assigned to the rotation of side-chain glucose residue coupled with hydrated water. Parts of this dispersion and structured water are suggested to constitute bound water. In the frozen state were observed a major dispersion (h; 0.14 ns) and a minor one (m; 28 ns), which were ascribed to considerably mobile and less mobile waters. They are similar to but not exactly the same as that for unfreezable water in bovine serum albumin solutions argued by Miura et al. (Biopolymers, 1995, Vol. 36, p. 9). Water is molded into different structures by the triple helix.     

Dielectric properties of proteins from simulation: the effects of solvent, ligands, pH, and temperature

We have used a standard Fr?hlich-Kirkwood dipole moment fluctuation model to calculate the static dielectric permittivity, epsilon(0), for four different proteins, each of which was simulated under at least two different conditions of pH, temperature, solvation, or ligand binding. For the range of proteins and conditions studied, we calculate values for epsilon(0) between 15 and 40. Our results show, in agreement with prior work, that the behavior of charged residues is the primary determinant of the effective permittivity. Furthermore, only environmental changes that alter the properties of charged residues exert a significant effect on epsilon. In contrast, buried water molecules or ligands have little or no effect on protein dielectric properties.     

Conformational substates of myoglobin detected by extrinsic dynamic fluorescence studies

The extent of conformational substates of two apomyoglobins, i.e., sperm whale and tuna apomyoglobin, was investigated by examining the fluorescence decay in the frequency domain of the extrinsic fluorophore TNS [6-(p-toluidino)-2-naphthalenesulfonic acid] bound to the heme binding site. Data analysis was performed in terms of a continuous, unimodal lifetime distribution having a Lorentzian shape. The results were compared with those for the free fluorophore in an isotropic nonviscous solvent. The incorporation of TNS into the protein matrix resulted in a broadening of the lifetime distribution due to the microenvironmental heterogeneity generated by structural fluctuations. The larger width of lifetime distribution observed for TNS bound to tuna apomyoglobin was related to a more extended conformational space accessible to the fluorophore in this protein compared to sperm whale myoglobin. A temperature increase from 15 to 40 degrees C produced a further broadening of the lifetime distributions of TNS bound to both proteins. This result can be explained by assuming the existence of conformational substates at high energy content or separated by high energy barriers, which are not populated at low temperature. The overall picture emerging from the reported data is that the lifetime distributions of TNS bound to apomyoglobins are determined largely by the number of conformational substates accessible to the protein matrix and, to a lesser extent, by the interconversion rates among these states.     

A measure of conformational entropy change during thermal protein unfolding using neutron spectroscopy

Thermal unfolding of proteins at high temperatures is caused by a strong increase of the entropy change which lowers Gibbs free energy change of the unfolding transition (DeltaG(unf) = DeltaH - TDeltaS). The main contributions to entropy are the conformational entropy of the polypeptide chain itself and ordering of water molecules around hydrophobic side chains of the protein. To elucidate the role of conformational entropy upon thermal unfolding in more detail, conformational dynamics in the time regime of picoseconds was investigated with neutron spectroscopy. Confined internal structural fluctuations were analyzed for alpha-amylase in the folded and the unfolded state as a function of temperature. A strong difference in structural fluctuations between the folded and the unfolded state was observed at 30 degrees C, which increased even more with rising temperatures. A simple analytical model was used to quantify the differences of the conformational space explored by the observed protein dynamics for the folded and unfolded state. Conformational entropy changes, calculated on the basis of the applied model, show a significant increase upon heating. In contrast to indirect estimates, which proposed a temperature independent conformational entropy change, the measurements presented here, demonstrated that the conformational entropy change increases with rising temperature and therefore contributes to thermal unfolding.     

Combining conformational flexibility and continuum electrostatics for calculating pK(a)s in proteins

Protein stability and function relies on residues being in their appropriate ionization states at physiological pH. In situ residue pK(a)s also provides a sensitive measure of the local protein environment. Multiconformation continuum electrostatics (MCCE) combines continuum electrostatics and molecular mechanics force fields in Monte Carlo sampling to simultaneously calculate side chain ionization and conformation. The response of protein to charges is incorporated both in the protein dielectric constant (epsilon(prot)) of four and by explicit conformational changes. The pK(a) of 166 residues in 12 proteins was determined. The root mean square error is 0.83 pH units, and >90% have errors of <1 pH units whereas only 3% have errors >2 pH units. Similar results are found with crystal and solution structures, showing that the method's explicit conformational sampling reduces sensitivity to the initial structure. The outcome also changes little with protein dielectric constant (epsilon(prot) 4-20). Multiconformation continuum electrostatics titrations show coupling of conformational flexibility and changes in ionization state. Examples are provided where ionizable side chain position (protein G), Asn orientation (lysozyme), His tautomer distribution (RNase A), and phosphate ion binding (RNase A and H) change with pH. Disallowing these motions changes the calculated pK(a).     

Modeling implicit reorganization in continuum descriptions of protein-protein interactions

The determination of free energies that govern protein-protein recognition is essential for a detailed molecular understanding of biological specificity. Continuum models of macromolecular interactions, in which the solvent is treated by an implicit representation and the proteins are treated semi-microscopically, are computationally tractable for estimating free energies, yet many questions remain concerning their accuracy. This article reports a continuum analysis of the free-energy changes underlying the binding of 31 interfacial alanine substitutions of two complexes of the antihen egg white lysozyme (HEL) antibody D1.3 bound with HEL or the antibody E5.2. Two implicit schemes for modeling the effects of protein and solvent relaxation were examined, in which the protein environment was treated as either homogeneous with a "protein dielectric constant" of epsilon(p) = 4 or inhomogeneous, with epsilon(p) = 4 for neutral residues and epsilon(p) = 25 for ionized residues. The results showed that the nonuniform dielectric model reproduced the experimental differences better, with an average absolute error of +/-1.1 kcal/mol, compared with +/-1.4 kcal/mol for the uniform model. More importantly, the error for charged residues in the nonuniform model is +/-0.8 kcal/mol and is nearly half of that corresponding to the uniform model. Several substitutions were clearly problematic in determining qualitative trends and probably required explicit structural reorganization at the protein-protein interface.     

Optimization of solvation models for predicting the structure of surface loops in proteins

A novel procedure for optimizing the atomic solvation parameters (ASPs) sigma(i) developed recently for cyclic peptides is extended to surface loops in proteins. The loop is free to move, whereas the protein template is held fixed in its X-ray structure. The energy is E(tot) = E(FF)(epsilon = nr) + summation operator sigma(i)A(i), where E(FF)(epsilon = nr) is the force-field energy of the loop-loop and loop-template interactions, epsilon = nr is a distance-dependent dielectric constant, and n is an additional parameter to be optimized. A(i) is the solvent-accessible surface area of atom i. The optimal sigma(i) and n are those for which the loop structure with the global minimum of E(tot)(n, sigma(i)) becomes the experimental X-ray structure. Thus, the ASPs depend on the force field and are optimized in the protein environment, unlike commonly used ASPs such as those of Wesson and Eisenberg (Protein Sci 1992;1:227-235). The latter are based on the free energy of transfer of small molecules from the gas phase to water and have been traditionally combined with various force fields without further calibration. We found that for loops the all-atom AMBER force field performed better than OPLS and CHARMM22. Two sets of ASPs [based on AMBER (n = 2)], optimized independently for loops 64-71 and 89-97 of ribonuclease A, were similar and thus enabled the definition of a best-fit set. All these ASPs were negative (hydrophilic), including those for carbon. Very good (i.e., small) root-mean-square-deviation values from the X-ray loop structure were obtained with the three sets of ASPs, suggesting that the best-fit set would be transferable to loops in other proteins as well. The structure of loop 13-24 is relatively stretched and was insensitive to the effect of the ASPs.     

Protein-bound water molecule counting by resolution of (1)H spin-lattice relaxation mechanisms

Water proton spin-lattice relaxation is studied in dilute solutions of bovine serum albumin as a function of magnetic field strength, oxygen concentration, and solvent deuteration. In contrast to previous studies conducted at high protein concentrations, the observed relaxation dispersion is accurately Lorentzian with an effective correlation time of 41 +/- 3 ns when measured at low proton and low protein concentrations to minimize protein aggregation. Elimination of oxygen flattens the relaxation dispersion profile above the rotational inflection frequency, nearly eliminating the high field tail previously attributed to a distribution of exchange times for either whole water molecules or individual protons at the protein-water interface. The small high-field dispersion that remains is attributed to motion of the bound water molecules on the protein or to internal protein motions on a time scale of order one ns. Measurements as a function of isotope composition permit separation of intramolecular and intermolecular relaxation contributions. The magnitude of the intramolecular proton-proton relaxation rate constant is interpreted in terms of 25 +/- 4 water molecules that are bound rigidly to the protein for a time long compared with the rotational correlation time of 42 ns. This number of bound water molecules neglects the possibility of local motions of the water in the binding site; inclusion of these effects may increase the number of bound water molecules by 50%.     

Water in keratin. Piezoelectric, dielectric, and elastic experiments.

To investigate actions of water in keratin, the piezoelectric, dielectric, and elastic constants are measured at 10 Hz, at temperatures between -160 and 150 degrees C, and at various hydration levels. From changes in the piezoelectric, dielectric, and dynamic mechanical parameters with moisture content (m.c.), we have identified three regimes (I, II, and III) in the hydration of water for keratin. At high hydration (21% m.c.) around 0 degree C, the piezoelectric constants for keratin steeply decrease with increasing temperature. This may be attributed to interfacial polarization which is strongly related to self-associated water molecules (particularly regime III water) just around crystalline helical regions which can exhibit the stress-induced, i.e., piezoelectric, polarization and may be attributed to electrode polarization induced by the increase of mobile ions in the amorphous matrix region, some of which would be released from their trapped states just around the piezoelectric phase by the regime III water. With increasing hydration, the elastic constants for keratin are found to increase below -70 degrees C and decrease above -70 degrees C. This suggests a viscoelastic transition of the keratin structure due to bound water (regime II water). The piezoelectric, dielectric, and elastic loss peaks are found at around -120 degrees C for hydrated keratin, believed to be due to tightly bound water (regime I water), which acts only to stiffen the keratin structure. The adsorption regions of water in keratin are discussed by a piezoelectric two-phase model, which consists of piezoelectric and nonpiezoelectric phases. It is proposed that water molecule would at least adsorb in the nonpiezoelectric phase.     

Dielectric dispersion in aqueous solutions of oxyhaemoglobin and carboxyhaemoglobin

The relative permittivity and conductivity of aqueous solutions of oxyhaemoglobin and carboxyhaemoglobin were measured over the frequency range 150kHz-100MHz. To minimize errors of measurement the investigations were carried out with three different samples of each type of haemoglobin, independent apparatus being used in two different laboratories. The dielectric increment and relaxation time were calculated at each of several temperatures from the results. These lead to a dipole moment of 400 Debyes and an activation enthalpy of 17.6+/-1.4kJ.mol(-1), both of which were found to be independent of temperature to within experimental error over the range 3-35 degrees C. The value of the dipole moment shows that the distribution of charge throughout the haemoglobin molecule is nearly symmetrical with respect to the centre of charge. The magnitude of the activation enthalpy is similar to that of the viscosity of water, in accord with the common observation that dielectric relaxation and viscosity are related phenomena. No significant differences are found between the dielectric parameters of oxyhaemoglobin and carboxyhaemoglobin. Combining the results with those obtained from X-ray diffraction of the solid a hydration value of 0.45g of water/g of protein is suggested, subject to the limitations of the model used. Finally, the results indicate the presence of a subsidiary dispersion, which could be attributed to the above quantity of bound water having a static permittivity of about 100 and a relaxation frequency in the region 100-200MHz.     

Electrical properties of hydrated collagen. I. Dielectric properties

The effect of water on the low-frequency (10²-10⁵ H_z) complex permittivitv of native, sold-state collagen has been investigated experimentally. Measurements at ambient temperature show that dry collagen exhibits essentially no frequency or temperature dependence. As water is absorbed, both dielectric constant and loss factor increase simultaneously and rise sharply upward at a hydration level which may be associated with the completion of the primary absorption layer as determined from independent water absorption studies. The behaviour is qualitatively identical to that observed for other proteins and related materials. Temperature-dependent measurements made under vacuum conditions in the range ?196°C to +100°C are characteristic of the dielectric properties of the water in the sample. Dehydration produced by successive temperature recycling to the maximum temperature effectively eliminates any temperature or frequency dependence. A maximum in the temperature-dependent curves is found at about +40°C and is explained as the superposition of two processes: (1) the transition of water molecules from bound to free states, and (2) the difffusion of water molecules out of the system. The dielectric constant of dry collagen, after desorption at ambient temperature, is about 4.5. Desorption at elevated temperatures reduced the room temperature value to about 2.3 and the liquid nitrogen temperature value to a number indistinguishable from the optical value of n² = 2.16.     

Calculation of the spectrum of dielectric losses in the protein-water system

The spectrum of dielectric losses in the frequency range up to microwaves for haemoglobin solution (Hb) in water was calculated. For humidified Hb the concentration relationships of epsilon components having a break of curve with water concentration exceeding some critical value were also determined. For three water fractions in the solution to be calculated the model of confined rotators was applied. The fractions of ice-like water, H2O molecules with weak H-bonds and protein-bound water were investigated. The protein molecules considered as a rigid rotator were calculated in terms of the extended diffusion model. A qualitative agreement with the experimental data was obtained. A possibility is shown of establishing relations between the Debye times in the dispersion regions beta, delta, gamma and the model parameters. The latter characterize the microscopic motion of polar molecules during the correlation time of the rotator angular velocity.     

The thermodynamics of protein-protein recognition as characterized by a combination of volumetric and calorimetric techniques: the binding of turkey ovomucoid third domain to alpha-chymotrypsin

We have used ultrasonic velocimetry, high-precision densimetry, and fluorescence spectroscopy, in conjunction with isothermal titration and differential scanning calorimetry, to characterize the binding of turkey ovomucoid third domain (OMTKY3) to alpha-chymotrypsin. We report the changes in volume and adiabatic compressibility that accompany the association of these proteins at 25 degrees C and pH 4.5. In addition, we report the changes in free energy, enthalpy, entropy, and heat capacity upon the binding of OMTKY3 to alpha-chymotrypsin over a temperature range of 20-40 degrees C. Our volume and compressibility data, in conjunction with X-ray crytsallographic data on the OMTKY3-alpha-chymotrypsin complex, suggest that 454(+/-22) water molecules are released to the bulk state upon the binding of OMTKY3 to alpha-chymotrypsin. Furthermore, these volumetric data suggest that the intrinsic compressibility of the two proteins decreases by 7%. At each temperature studied, OMTKY3 association with alpha-chymotrypsin is entropy driven with a large, unfavorable enthalpy contribution. The observed entropy of the binding reflects interplay between two very large favorable and unfavorable terms. The favorable term reflects an increase in the hydrational entropy resulting from release to the bulk of 454 water molecules. The unfavorable term is related to a decrease in the configurational entropy and, consequently, a decrease in the conformational dynamics of the two proteins. In general, we discuss the relationship between macroscopic and microscopic properties, in particular, identifying and quantifying the role of hydration in determining the thermodynamics of protein recognition as reflected in volumetric and calorimetric parameters.     

The effect of protein relaxation on charge-charge interactions and dielectric constants of proteins.

The effect of the reorganization of the protein polar groups on charge-charge interaction and the corresponding effective dielectric constant (epsilon(eff)) is examined by the semimicroscopic version of the Protein Dipole Langevin Dipoles (PDLD/S) method within the framework of the Linear Response Approximation (LRA). This is done by evaluating the interactions between ionized residues in the reaction center of Rhodobacter sphaeroides, while taking into account the protein reorganization energy. It is found that an explicit consideration of the protein relaxation leads to a significant increase in epsilon(eff) and that semimicroscopic models that do not take this relaxation into account force one to use a large value for the so-called "protein dielectric constant," epsilon(p), of the Poisson-Boltzmann model or for the corresponding epsilon(in) in the PDLD/S model. An additional increase in epsilon(eff) is expected from the reorganization of ionized residues and from changes in the degree of water penetration. This finding provides further support for the idea that epsilon(in) (or epsilon(p)) represents contributions that are not considered explicitly. The present study also provides a systematic illustration of the nature of epsilon(eff), supporting our previously reported view that charge-charge interactions correspond to a large value of this "dielectric constant," even in protein interiors. It is also pointed out that epsilon(eff) for the interaction between ionizable groups in proteins is very different from the effective dielectric constant, epsilon'(eff), that determines the free energy of ion pairs in proteins (epsilon'(eff) reflects the effect of preoriented protein dipoles). Finally, the problems associated with the search for a general epsilon(in) are discussed. It is clarified that the epsilon(in) that reproduces the effect of protein relaxation on charge-charge interaction is not equal to the epsilon(in) that reproduces the corresponding effect upon formation of individual charges. This reflects fundamental inconsistencies in attempts to cast microscopic concepts in a macroscopic model. Thus one should either use a large epsilon(in) for charge-charge interactions and a small epsilon(in) for charge-dipole interactions or consider the protein relaxation microscopically.     

Microwave dielectric measurements of erythrocyte suspensions.

Complex dielectric constants of human erythrocyte suspensions over a frequency range from 45 MHz to 26.5 GHz and a temperature range from 5 to 40 degrees C have been determined with the open-ended coaxial probe technique using an automated vector network analyzer (HP 8510). The spectra show two separate major dispersions (beta and gamma) and a much smaller dispersion between them. The two major dispersions are analyzed with a dispersion equation containing two Cole-Cole functions by means of a complex nonlinear least squares technique. The parameters of the equation at different temperatures have been determined. The low frequency behavior of the spectra suggests that the dielectric constant of the cell membrane increases when the temperature is above 35 degrees C. The real part of the dielectric constant at approximately 3.4 GHz remains almost constant when the temperature changes. The dispersion shifts with temperature in the manner of a thermally activated process, and the thermal activation enthalpies for the beta- and gamma-dispersions are 9.87 +/- 0.42 kcal/mol and 4.80 +/- 0.06 kcal/mol, respectively.     

Characterization of the ethenoadenosine diphosphate binding site of myosin subfragment 1. Energetics of the equilibrium between two states of nucleotide.S1 and vanadate-induced global conformation changes detected by energy transfer

The fluorescence decay of 1,N6-ethenoadenosine diphosphate (epsilon ADP) bound to myosin subfragment 1 (S1) was studied as a function of temperature. The decay was biexponential, and the two lifetimes were quenched relative to the single lifetime of free epsilon ADP. The temperature dependence of the fractional intensities of the decay components showed two states of the S1.epsilon ADP complex. At pH 7.5 in 30 mM TES, 60 mM KCl, and 3 mM MgCl2, the equilibrium constant for the conversion of the low-temperature state (S1L.epsilon ADP) to the high-temperature state (S1H.epsilon ADP) was 40 at physiological temperatures, and delta H degrees = 13 kcal.mol-1 and delta S degrees = 49 cal.deg-1.mol-1. At 10 degrees C the equilibrium constant of S1 for epsilon ADP was 5, indicating that S1H.epsilon ADP was the dominant state, and that for the vanadate complex epsilon ADP.Vi was 0.7, suggesting that in S1.epsilon ADP.Vi the dominant state of the S1-nucleotide complex was converted from S1H.epsilon ADP to S1L.epsilon ADP. The single rotational correlation time of bound epsilon ADP at 10 degrees C decreased from 107 ns in S1.epsilon ADP to 74 ns in S1+.epsilon ADP.Vi. Conversion of the binary complex to the ternary vanadate complex resulted in a 3-A decrease in the energy transfer distance between bound epsilon ADP and N-[4-(dimethylamino)-3,5-dinitrophenyl]maleimide attached to SH1 and a decrease of the average distance between bound epsilon ADP and bound Co2+ from 12.6 to 8.3 A.(ABSTRACT TRUNCATED AT 250 WORDS)