Dielectric properties of hemoglobin and myoglobin. II. Dipole moment of sperm whale myoglobin

This paper is concerned with the molecular origin of the dipole moment of sperm whale myoglobin as it can be calculated from the dielectric dispersion at 1 Mcps on the basis of a mechanism of orientational polarization. It was possible to compare the dielectric increment of native myoglobin and its change during the reaction with bromo acetate with dipole moments calculated according to the known coordinates of the charged groups of the molecule. The agreement between the two shows that in myoglobin only the permanent dipole moment due to these charged groups is important, and that contributions from other possible sources remain within the limits of experimental error.     

The structure and dipole moment of globular proteins in solution and crystalline states: use of NMR and X-ray databases for the numerical calculation of dipole moment

The large dipole moment of globular proteins has been well known because of the detailed studies using dielectric relaxation and electro-optical methods. The search for the origin of these dipolemoments, however, must be based on the detailed knowledge on protein structure with atomic resolutions. At present, we have two sources of information on the structure of protein molecules: (1) x-ray databases obtained in crystalline state; (2) NMR databases obtained in solution state. While x-ray databases consist of only one model, NMR databases, because of the fluctuation of the protein folding in solution, consist of a number of models, thus enabling the computation of dipole moment repeated for all these models. The aim of this work, using these databases, is the detailed investigation on the interdependence between the structure and dipole moment of protein molecules. The dipole moment of protein molecules has roughly two components: one dipole moment is due to surface charges and the other, core dipole moment, is due to polar groups such as N--H and C==O bonds. The computation of surface charge dipole moment consists of two steps: (A) calculation of the pK shifts of charged groups for electrostatic interactions and (B) calculation of the dipole moment using the pK corrected for electrostatic shifts. The dipole moments of several proteins were computed using both NMR and x-ray databases. The dipole moments of these two sets of calculations are, with a few exceptions, in good agreement with one another and also with measured dipole moments.     

The apparently symmetrical hexagonal bilayer hemoglobin from Lumbricus terrestris has a large dipole moment

The giant approximately 3.6 MDa hexagonal bilayer hemoglobin (HBL Hb) from Lumbricus terrestris consists of 12 213-kDa dodecamers of four globin chains ([b + a + c]3[d]3) tethered to a central scaffold of approximately 36 non-globin, linker subunits L1-L4 (24-32 kDa). Three-dimensional reconstructions obtained by electron cryomicroscopy showed it to have a D6 point-group symmetry, with the two layers rotated approximately 16 degrees relative to each other. Measurement of the dielectric constants of the Hb and the dodecamer over the frequency range 5-100 kHz indicated relaxation frequencies occurring at 20-40 and 300 kHz, respectively, substantially lower than the 700-800 kHz in HbA. The dipole moments calculated using Oncley's equation were 17,300 +/- 2300 D and 1400 D for the Hb and dodecamer, respectively. The approximately threefold higher dipole moment of the dodecamer relative to HbA is consistent with an asymmetric shape in solution suggested by small-angle X-ray scattering. Although a two-term Debye equation and a prolate ellipsoid of revolution model provided a good fit to the experimental dielectric dispersion of the dodecamer, a three-term Debye equation based on an oblate ellipsoid of revolution model was required to fit the asymmetric dielectric dispersion curve of the Hb: the required additional term may represent either an induced dipole moment or a substructure which rotates independently of the main permanent dipole component of the Hb. The D6 point-group symmetry implies that the dipole moments of the dodecamers cancel out. Thus, in addition to a possible contribution from fluctuations of the proton distribution, the large dipole moment of the Hb may be due to an asymmetric distribution of the heterogeneous linker subunits.     

Electric polarization of polyelectrolyte and colloid media: dielectric versus electro-optic approach

The theories of dielectric dispersion and of electric birefringence as a representative of electro-optic methods are considered and it is shown that they both depend in a similar way simply on the real part of the complex electric polarizability of the macromolecules or the particles. The latter also contains the permanent dipole moment. Experimental data on dielectric dispersion, electric birefringence and electric light scattering of strongly elongated, rod-like poly(tetrafluoroethylene) particles are compared and an attempt is made to extend the dielectric dispersion curve to lower frequencies using electric birefringence and electric light scattering data. Further, the experimental data on dielectric dispersion, electric light scattering, electro-orientation and dipolophoresis for the more complicated Escherichia coli particles are compared. Again, the possibility to extend the 10 kHz-100 MHz dielectric dispersion curve down below 1 Hz by using electric light scattering data is examined. The good matching of the dielectric dispersion and electric light scattering frequency curves found in the overlapping frequency range (10 kHz-5 MHz) essentially enhances the chance that dielectric dispersion below 1 MHz is related to alpha dispersion and not to electrode polarization. Thus it is not only possible to obtain additional information on the mechanism of polarization at lower-frequency dielectric dispersion, but also to extend our knowledge about the effective dielectric properties of biological complex fluids to frequencies essentially below 1 MHz. This could be important for the understanding of the effect of low-frequency electromagnetic fields on living matter.     

Measurement and computation of the dipole moment of globular proteins III: Chymotrypsin

The dipole moments of alpha- and gamma-chymotrypsin are determined experimentally using the dielectric constant measuring method. The values thus obtained are compared with the results of the electric dichroism measurements for alpha-chymotrypsins by other investigators. The agreement is reasonably good, if not satisfactory. The cause of difference appears to be due to the difficulty of finding the correct internal field. The interaction between two neighboring dipoles is found to be a minor component of the local fields. Secondly, the dipole moment of alpha-chymotrypsin was computed using Protein Data Bases. The dipole moment of proteins consists of two major components, the moment due to fixed surface charges and the core moment due to polar chemical bonds. The method of calculation was described in detail in previous papers. The pK shifts of polar side chains were calculated using the methods of Tanford et al. and its modification by Warshel et al. The agreement between measured and calculated dipole moments is satisfactory.     

On the electric polarization of DNA

Dielectric dispersion of DNA was studied in the frequency range 100 Hz–100 kHz at four different temperatures (6–30°C). The dielectric increment ε₀–ε_∞ increased with the rise of temperature. The relaxation time, on the other hand, decreased. Both the increase in dielectric increment and the decrease in relaxation time could not be explained on the basis of the counterion polarization theory. Dipole moment was estimated from Kirkwood theory. It was found to decrease systematically with temperature. Even at 0°C there was a dipole moment of 10⁴D.     

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.     

Study of dielectric behavior of DNA in shear gradient

The dielectric behavior of the DNA molecule is investigated in the presence of mechanical force as well as the electrical field. In the present experiment, the direction of the electrical field is perpendicular to that of the mechanical force. The dipole moment of polar molecules manifest itself as dielectric increment at low frequencies or as the conductance increment at high frequencies. These two quantities are closely related to each other by Eq. (1) in the text. Because of the difficulty due to electrode polarization at low frequencies, no useful information was obtained by investigating the dielectric increment in the present system. Therefore, the effect of shear gradient was studied by measuring the conductance increment at high frequencies with various velocity gradients. The conductance increment decreased when the shear was applied perpendicular to the electrical field. The conductance change is converted into the unit of dielectric constant; it was found that the dielectric increment of DNA solution decreases by as much as 85 percent. From these observations, it is concluded that the direction of the dipole moment in DNA is longitudinal rather than transverse. The same experiment was repeated with the random coil DNA and no anisotropy in the dielectric increment was observed.     

Dielectric constant dependence of biological oxidation-reduction. 1. A model of polarity-dependent ferrocytochrome c oxidation

A theoretical model for the effect of the dielectric constant (c) of the solvent medium on ferrocytochrome c oxidation by ferricyanide is developed to account for the observed variations of the rate constant (k) of reactions in aqueous binary mixtures with alcohols (less than 5-10 mol% ethanol and propranolol). A correlation between k and c is found if ln k is expressed as a function of the Kirkwood parameter (c-1)(2c+1). The results of calculations indicate that the use of the 'overall dipole moment' of cytochrome c in oxidoreduction studies is likely to be unreliable. Instead, the decrease in k in alcohol/water mixtures is best explained--in conformity with Onsager's theory of the reaction field--by a polarity effect on the dipole moment of the cytochrome c heme upon diffusion of the polar solvent molecules into the low dielectric constant heme crevice.     

A theoretical study of the dielectric constant of protein

The dielectric properties of a protein molecule were investigated by calculating a 'local dielectric constant' with the aid of normal mode analysis. This local dielectric constant was calculated from the electronic polarization of atoms and the orientational polarization of local dipoles. The former was obtained from atomic polarizations of the whole atoms in a protein molecule. The latter was determined from the fluctuation-dissipation theorem. The degree of dipole fluctuation was calculated from the positional fluctuation of each atom obtained by the normal mode analysis. Assuming a minimum volume for a continuum model, the resulting local dielectric constants ranged from 1 to 20 inside the protein.     

On the dielectrically observable consequences of the diffusional motions of lipids and proteins in membranes

A system consisting of any array of cylindrical, polytopic membrane proteins (or protein complexes) possessed of a permanent dipole moment and immersed in a closed, spherical phospholipid bilayer sheet is considered. It is assumed that rotation of the protein (complex) in a plane normal to the membrane, if occurring, is restricted by viscous drag alone. Lateral diffusion is assumed either to be free and random or to be partially constrained by barriers of an unspecified nature. The dielectric relaxation times calculated for membrane protein rotation in a suspension of vesicles of the above type are much longer than those observed with globular proteins in aqueous solution, and fall in the mid-to-high audio frequency range. If the long range lateral diffusion of (charged) membrane protein complexes is essentially unrestricted, as in the "fluid mosaic" membrane model, dielectric relaxation times for lateral motions will lie, except in the case of the very smallest vesicles, in the sub-audio (ELF) range. If, in contrast, the lateral diffusion of membrane protein complexes is partially restricted by "barriers" or "long-range" interactions (of unspecified nature), significant dielectric dispersions may be expected in both audio- and radio-frequency ranges, the critical (characteristic) frequencies depending upon the average distance moved before a barrier is encountered. Similar analyses are given for rotational and translational motions of phospholipids. At very low frequencies, a dispersion due to vesicle orientation might in principle also be observed; the dielectrically observable extent of this rotation will depend, inter alia, upon the charge mobility and disposition of the membrane protein complexes, as well as, of course, on the viscosity of the aqueous phase. The role of electroosmotic interactions between double layer ions (and water dipoles) and proteins raised above the membrane surface is considered. In some cases, it seems likely that such interactions serve to raise the dielectric increment, relative to that which might otherwise have been expected, of dispersions due to protein motions in membranes. Depending upon the tortuosity of the ion-relaxation pathways, such a relaxation mechanism might lead to almost any characteristic frequency, and, even in the absence of protein/lipid motions, would cause dielectric spectra to be much broader than one might expect from a simple, macroscopic treatment.     

Dielectric relaxation and orientation of DNA molecules

A conductivity dispersion has been measured at very low frequencies (VLF) on several concentrated DNA solutions. By measuring simultaneously their electric birefringence decay, it is shown that the dielectric relaxation (which is related to the conductivity dispersion) is due to the molecular orientation. Different polarization mechanisms are discussed. It is concluded that the DNA polarizability measured in the VLF range can only be explained by the orientation of a permanent ionic dipole. It is suggested that such permanent dipoles could be caused by small differences in the ionic composition between the two molecular “ends;” the difference could either be stable (asymmetrical localization of protein impurities for instance) or transient (fluctuating dipoles explained by the Kirkwood-Schumaker theory).     

The possible formation of nano-clusters of succinic acid and maleic acid in tetrahydrofuran due to incomplete solvation

In continuation of our work on the conformational analysis of succinic acid (SA) and maleic acid (MA) in different solvents, we present here the experimental dielectric and IR and also the ab initio Hartree–Fock calculations of the two dicarboxylic acids in tetrahydrofuran (THF). The dielectric measurements are carried out at microwave X-band frequency of 9.7 GHz and the calculations are performed at STO-3G and 6-31G(d) basis sets. The dielectric data and the dipole moment determined experimentally are compared with the dipole moment determined from the conformal analysis. It is seen that the dielectric properties of SA/MA in THF are much different from that of SA/MA in 1-4, dioxane (1-4D) that we had reported previously. The IR spectra of SA–THF system is also reported here. The present study indicates the possible formation of nano-clusters of SA/MA in THF due to incomplete solvation by THF.     

Use of protein database for the computation of the dipole moments of normal and abnormal hemoglobins.

Previously, we discussed the calculation of the dipole moments of small proteins using the three-dimensional protein data-base. Our results demonstrate that the calculated dipole moments are in acceptable agreement with measured values. We, however, noted the difficulty of the calculation with larger proteins, in particular those consisting of several subunits. Hemoglobin (Hb) is a protein having a molecular weight of 64,000 that consists of four subunits, a typical case where the computation was found to be difficult. To circumvent the difficulties, we calculated the dipole moment of each subunit separately. The dipole moment of the whole protein was calculated by the vectorial summation of subunit moments. With this method, the calculated net dipole moment is in good agreement with the experimental value. Our calculation shows that the dipole moment vectors of subunits are, by and large, antiparallel in tetramers causing partial cancellation of the net dipole moment. In addition to normal HbA, the dipole moment of abnormal HbS was calculated using an approximate computational technique. Because of the loss of two negative changes as a result of the replacement of glutamic acid with valine in beta-chains, the dipole moment of HbS was found, experimentally and theoretically, to be significantly smaller than that of HbA.     

The electric dipole moment of DNA-binding HU protein calculated by the use of NMR database

Electric birefringence measurements indicated the presence of a large permanent dipole moment in HU protein–DNA complex. In order to substantiate this observation, numerical computation of the dipole moment of HU protein homodimer was carried out by using NMR protein databases. The dipole moments of globular proteins have hitherto been calculated with X-ray databases and NMR data have never been used before. The advantages of NMR databases are: (a) NMR data are obtained, unlike X-ray databases, using protein solutions. Accordingly, this method eliminates the bothersome question as to the possible alteration of the protein structure due to the transition from the crystalline state to the solution state. This question is particularly important for proteins such as HU protein which has considerable internal flexibility’s; (b) the three dimensional coordinates of hydrogen atoms in protein molecules can be determined with a sufficient resolution and this enables the N–H as well as C=O bond moments to be calculated. Since the NMR database of HU protein from Bacillus stearothermophilus consists of 25 models, the surface charge as well as the core dipole moments were computed for each of these structures. The results of these calculations show that the net permanent dipole moments of HU protein homodimer is approximately 500–530 D (1 D=3.33×10⁻³⁰ Cm) at pH 7.5 and 600–630 D at the isoelectric point (pH 10.5). These permanent dipole moments are unusually large for a small protein of the size of 19.5 kDa. Nevertheless, the result of numerical calculations is compatible with the electro-optical observation, confirming a very large dipole moment in this protein.     

Linear dichroism of bimolecular chlorophyll-lipid membranes. The role of anisotropy and dispersion

Polarised absorption and reflection spectra of chlorophyll-containing bimolecular lipid membranes were obtained in the spectral range of 590–710 nm. The spectra were analysed using the formalism of the complex dielectric tensor which characterizes the optical anisotropy of the membrane and the light absorption therein.The maxima of the absorption spectra recorded at a 45° angle of incidence are located at 665 and 670 nm for light in which the electric vector is oriented parallel and perpendicular, respectively, to the plane of incidence. The analysis of these spectra shows that the spectral shift is wholly due to the dispersion of the real part of the dielectric tensor.The angle between the dipole transition moment in the red and the normal to the membrane was estimated to be 42.3–45.3°.On the basis of these results, a model absorption spectrum, simulating the dichroic properties of oriented chloroplasts, was calculated for a system of parallel membranes.Some of the possible artifacts introduced into the dichroic spectra of chloroplasts due to anisotropy and dispersion are discussed.     

The electric dipole moment of rhodopsin solubilized in Triton X-100.

The electric dipole moment of solubilized rhodopsin was determined with dielectric dispersion measurements. Rhodopsin was extracted from disc membranes of cattle rod outer segments with the nonionic detergent Triton X-100. The dipole moment of rhodopsin at its isoionic point in the detergent micelle is 720 D (150 charge-A). This value is comparable to dipole moments of nonmembrane proteins, especially those which tend to aggregate or polymerize. Flash irradiation of the rhodopsin results in an increase in the dipole moment of about 25 D (5 charge-A). The light-induced increase in dipole moment appears to be composed of two parts--a faster component related to a change in the number of protons bound by rhodopsin and a slower component apparently independent of the change in proton binding.     

Determination of the dipole moments of RNAse SA wild type and a basic mutant

In this study, we report the effects of acidic to basic residue point mutations (5K) on the dipole moment of RNAse SA at different pHs. Dipole moments were determined by measuring solution capacitance of the wild type (WT) and the 5K mutant with an impedance analyzer. The dipole moments were then (1) compared with theoretically calculated dipole moments, (2) analyzed to determine the effect of the point mutations, and (3) analyzed for their contribution to overall protein-protein interactions (PPI) in solution as quantitated by experimentally derived second virial coefficients. We determined that experimental and calculated dipoles were in reasonable agreement. Differences are likely due to local motions of residue side chains, which are not accounted for by the calculated dipole. We observed that the proteins' dipole moments increase as the pH is shifted further from their isoelectric points and that the wild-type dipole moments were greater than those of the 5K. This is likely due to an increase in the proportion of one charge (either negative or positive) relative to the other. A greater charge disparity corresponded to a larger dipole moment. Finally, the larger dipole moments of the WT resulted in greater attractive overall PPI for that protein as compared to the 5K.     

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.     

Ab initio and dielectric studies of succinic acid and maleic acid in 1,4-dioxane

In a continuing effort to understand the hydrogen bond through the study of dielectric and computational conformal studies of dilute solutions, succinic acid and maleic acid are studied in solutions of 1,4-dioxane solvent. Dielectric studies give an account of the net dipole moment of the system under study, which is then compared with the values obtained from conformal analysis. The dielectric measurements were made at 303 K at a frequency of 9.83 GHz using a X-band microwave test bench in order to determine the relaxation times and the dipole moments. The static dielectric permittivity and the high frequency dielectric permittivity were measured using a LCR meter and an Abbe's refractometer, respectively. The results are inspected in comparison with the dipole moment results of ab initio calculations of some of the conformers in gas phase and in liquid phase. Gaussian-03 software package with 6–31G(d) basis set optimisation was used for this purpose. Onsager's reaction field model is used to study the solvation of the dicarboxylic acids in 1,4-dioxane. The results are interpreted in terms of the intermolecular and intramolecular hydrogen bond interactions in the dilute systems.