Calculation and measurement of the dipole moment of small proteins: Use of protein data base

The dipole moments of small protein molecules were determined experimentally in order to validate the calculated dipole moments by previous investigators. We found that the agreements are satisfactory for some proteins. There are, however, many proteins for which the agreement is less than satisfactory. In order to find the cause of the disagreement, the dipole moments of these proteins were recalculated using the Brookhaven Protein Data Bank. We calculated the dipole moment due to fixed surface charges and the bond moments of all the carbonyl groups in main chain and side chains. The calculation consists of the mean moments and their mean square fluctuations. In addition, we investigated the effect of electrostatic interactions between charged sites for several proteins. These results show that incorporation of the interactions does not affect substantially the calculated dipole moments. The rms fluctuation of the dipole moment is found to be small but not negligible. In conclusion, recalculated dipole moments are in good agreement with the observed values. © 1993 John Wiley & Sons, Inc.     

Computation of the dipole moments of proteins.

A simple and computationally feasible procedure for the calculation of net charges and dipole moments of proteins at arbitrary pH and salt conditions is described. The method is intended to provide data that may be compared to the results of transient electric dichroism experiments on protein solutions. The procedure consists of three major steps: (i) calculation of self energies and interaction energies for ionizable groups in the protein by using the finite-difference Poisson-Boltzmann method, (ii) determination of the position of the center of diffusion (to which the calculated dipole moment refers) and the extinction coefficient tensor for the protein, and (iii) generation of the equilibrium distribution of protonation states of the protein by a Monte Carlo procedure, from which mean and root-mean-square dipole moments and optical anisotropies are calculated. The procedure is applied to 12 proteins. It is shown that it gives hydrodynamic and electrical parameters for proteins in good agreement with experimental data.     

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.     

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.     

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.     

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.     

The dipole moment of the electron carrier adrenodoxin is not critical for redox partner interaction and electron transfer

Dipole moments of proteins arise from helical dipoles, hydrogen bond networks and charged groups at the protein surface. High protein dipole moments were suggested to contribute to the electrostatic steering between redox partners in electron transport chains of respiration, photosynthesis and steroid biosynthesis, although so far experimental evidence for this hypothesis was missing. In order to probe this assumption, we changed the dipole moment of the electron transfer protein adrenodoxin and investigated the influence of this on protein-protein interactions and electron transfer. In bovine adrenodoxin, the [2Fe-2S] ferredoxin of the adrenal glands, a dipole moment of 803 Debye was calculated for a full-length adrenodoxin model based on the Adx(4-108) and the wild type adrenodoxin crystal structures. Large distances and asymmetric distribution of the charged residues in the molecule mainly determine the observed high value. In order to analyse the influence of the resulting inhomogeneous electric field on the biological function of this electron carrier the molecular dipole moment was systematically changed. Five recombinant adrenodoxin mutants with successively reduced dipole moment (from 600 to 200 Debye) were analysed for their redox properties, their binding affinities to the redox partner proteins and for their function during electron transfer-dependent steroid hydroxylation. None of the mutants, not even the quadruple mutant K6E/K22Q/K24Q/K98E with a dipole moment reduced by about 70% showed significant changes in the protein function as compared with the unmodified adrenodoxin demonstrating that neither the formation of the transient complex nor the biological activity of the electron transfer chain of the endocrine glands was affected. This is the first experimental evidence that the high dipole moment observed in electron transfer proteins is not involved in electrostatic steering among the proteins in the redox chain.     

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.     

The dipole moment of membrane proteins: potassium channel protein and beta-subunit.

The mechanism of ion channel opening is one of the most fascinating problems in membrane biology. Based on phenomenological studies, early researchers suggested that the elementary process of ion channel opening may be the intramembrane charge movement or the orientation of dipolar proteins in the channel. In spite of the far reaching significance of these hypotheses, it has not been possible to formulate a comprehensive molecular theory for the mechanism of channel opening. This is because of the lack of the detailed knowledge on the structure of channel proteins. In recent years, however, the research on the structure of channel proteins made marked advances and, at present, we are beginning to have sufficient information on the structure of some of the channel proteins, e.g. potassium-channel protein and beta-subunits. With these new information, we are now ready to have another look at the old hypothesis, in particular, the dipole moment of channel proteins being the voltage sensor for the opening and closing of ion channels. In this paper, the dipole moments of potassium channel protein and beta-subunit, are calculated using X-ray diffraction data. A large dipole moment was found for beta-subunits while the dipole moment of K-channel protein was found to be considerably smaller than that of beta-subunits. These calculations were conducted as a preliminary study of the comprehensive research on the dipolar structure of channel proteins in excitable membranes, above all, sodium channel proteins.     

Dipole moment, enthalpy, and entropy changes of Hodgkin-Huxley type kinetic units.

Dipole moment, enthalpy, and entropy changes were calculated for hypothetical structural units which control the opening and closing of ionic channels in axon membranes. The changes of these thermodynamic functions were calculated both for activation (transition to intermediate complex) and for the structural transformation as a whole. The calculations are based on the experimentally determined Q10 values and the empirical formulae for the rate constants (alpha's and beta's) as functions of membrane potentials in Hodgkin-Huxley type models. From the calculated thermodynamic functions we suggest that the specific structural units of the axon membranes are probably of macromolecular (possible protein-like) dimensions with large dipole moments (hundreds of debyes). The calculated dipole moment changes of a single structural unit indicate that in many cases these dipole moments saturate at strong depolarizations or hyperpolarizations. The transitions in structural units show substantial activation enthalpies and entropies but the net enthalpy and entropy changes are practically negligible for the transition as a whole, i.e. the structural units presumably undergo displacements. While the calculated dipole moment changes associated with structural transformations in Loligo and Myxicola show similar potential dependencies, those for Rana usually show a different behavior. The relevance of the dipole moment changes to gating currents is discussed.     

The dipole moments of membrane proteins: potassium channel proteins. II. T1 assembly. Search for the voltage sensor

The dipole moments of potassium channel protein (Kcsa) and beta-subunits were discussed in the previous paper of this series [Takashima, Biophys. Chem. 94 (2001) 209-218]. While the dipole moment of beta-subunits was found to be very large, the dipole moment of Kcsa turned out to be somewhat smaller than beta-subunits. As the continuation of this work, the discussion of the present paper is focussed on the dipole moment of T1 assembly, another component of the K-channel. As discussed later, the calculation using the X-ray crystallographic data by MacKinnon et al., revealed an astoundingly large dipole moment for T1 assembly. The dipole moment of T1 assembly combined with the likewise large dipole moment of beta-subunits amounts to a sufficient value to play an essential role as a voltage sensor of potassium channel.     

Molecular dynamics of sickle and normal hemoglobins

Molecular dynamics (MD) simulations have been carried out for 62.5 ps on crystal structures of deoxy sickle cell hemoglobin (HbS) and normal deoxy hemoglobin (HbA) using the CHARMM MD algorithm, with a time step of 0.001 ps. In the trajectory analysis of the 12.5–62.5 (50 ps) simulation, oscillations of the radius of gyration and solvent-accessible surface area were calculated. HbS exhibited a general contraction during the simulation, while HbA exhibited a nearly constant size. The average deviations of simulated structures from the starting structures were found to be 1.8 Å for HbA and 2.3 Å for HbS. The average rms amplitudes of atomic motions (atomic flexibility) were about 0.7 Å for HbA and about 1.0 Å for HbS. The amplitudes of backbone motion correlate well with temperature factors derived from x-ray crystallography. A comparison of flexibility between the α- and β-chains in both HbA and HbS indicates that the β-chains generally exhibited greater flexibility than the α-chains, and that the HbS β-chains exhibit greater flexibility in the N-terminal and D- and F-helix regions than do those of HbA. The average amplitude of backbone torsional oscillations was about 9°, a value comparable with that of other simulations, with enhanced torsional oscillation occurring primarily at the ends of helices or in loop regions between helices. Comparison of atomic flexibility and torsional oscillation results suggests that the increased β-chain flexibility results from relatively concerted motions of secondary structure elements. The increased flexibility may play an important role in HbS polymerization. Time course analysis of conformational energy of association, hydrogen bonding and hydrophobic bonding (as calculated from solvent accessibility) shows that all three of these factors contribute to the stability of subunit association for both hemoglobins. © 1993 John Wiley & Sons, Inc.     

Barrier to rotation and conformation of the -NR2 group in cytosine and its derivatives. Part II. Experimental and theoretical dipole moments of methylated cytosines.

The dipole moments of several cytosine, methylaminocytosine and dime-thylaminocytosine derivatives with and without an ortho methyl group were determined experimentally in dioxane and benzene. Calculations of total energies and dipole moments were performed by the CNDO/2 and INDO methods for sp2 and sp3 hybridization of exocyclic nitrogen for different values of rotational angle phiC-N. Comparison of the experimental dipole moments with those calculated for the energy minima suggests that the conformation of the dimethylamino group is not planar and differs from that found in cytosine. 1,5,7-Trimethylcytosine, with the dipole moment of 7 Deby units, was considered to be the model compound which closely reproduces the dipole moment of cytosine.     

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.     

Influence of p<Emphasis Type="Italic">K</Emphasis><Subscript>a</Subscript> Shifts on the Calculated Dipole Moments of Proteins

The protein dipole moment is a low-resolution parameter that characterizes the second-order charge organization of a biomolecule. Theoretical approaches to calculate protein dipole moments rely on pK _a values, which are either computed individually for each ionizable residue or obtained from model compounds. The influence of pK _a shifts are evaluated first by comparing calculated and measured dipole moments of β-lactoglobulin. Second, calculations are made on a dataset of 66 proteins from the Protein Data Bank, and average differences are determined between dipole moments calculated with model pK _as, pK _as derived using a Poisson–Boltzmann approach, and empirically-calculated pK _as. Dipole moment predictions that neglect pK _a shifts are consistently larger than predictions in which they are included. The importance of pK _a shifts are observed to vary with protein size, internal permittivity, and solution pH.     

Dipole moment of alamethicin as related to voltage-dependent conductance in lipid bilayers.

The dipole moment of alamethicin, which produces voltage-dependent conductance in lipid-bilayer membranes, was measured in mixed solvents of ethanol and dioxane. The value of the dipole moment was found to increase from 40 to 75 DU (Debye units), as the concentration of ethanol increased from 0 (pure dioxane) to 40%. The relaxation frequency of alamethicin also changes from 10 to 40 MHz, depending upon the concentration of ethanol in mixed solvents. The length of alamethicin was calculated by using the relaxation time and was found to range from approximately 40 to 20 A. The dipole moment was independently calculated from voltage-dependent conductance and compared with the measured value. The calculated value was found to be larger than the value of direct measurements, indicating that several alamethicin molecules are required to form a conducting pore and that their dipole moments are oriented parallel to each other.     

Nitric oxide reduces sickle hemoglobin polymerization: potential role of nitric oxide-induced charge alteration in depolymerization

We previously demonstrated that inhaling nitric oxide (NO) increases the oxygen affinity of sickle red blood cells (RBCs) in patients with sickle cell disease (SCD). Our recent studies found that NO lowered the P₅₀ values of sickle hemoglobin (HbS) hemolysates but did not increase methemoglobin (metHb) levels, supporting the role of NO, but not metHb, in the oxygen affinity of HbS. Here we examine the mechanism by which NO increases HbS oxygen affinity. Because anti-sickling agents increase sickle RBC oxygen affinity, we first determined whether NO exhibits anti-sickling properties. The viscosity of HbS hemolysates, measured by falling ball assays, increased upon deoxygenation; NO treatment reduced the increment. Multiphoton microscopic analyses showed smaller HbS polymers in deoxygenated sickle RBCs and HbS hemolysates exposed to NO. These results suggest that NO inhibits HbS polymer formation and has anti-sickling properties. Furthermore, we found that HbS treated with NO exhibits an isoelectric point similar to that of HbA, suggesting that NO alters the electric charge of HbS. NO–HbS adducts had the same elution time as HbA upon high performance liquid chromatography analysis. This study demonstrates that NO may disrupt HbS polymers by abolishing the excess positive charge of HbS, resulting in increased oxygen affinity.     

Cation Modulation of Hemoglobin Interaction with Sodium <Emphasis Type="Italic">n</Emphasis>-Dodecyl Sulfate (SDS). II: Calcium Modulation at pH 5.0

We investigate the conformational differences between HbA and HbS in the presence and absence of Ca(2+) concentrations (0-40 μM) akin to those within the erythrocyte cytoplasm and the membrane mimetic and native structure disrupting environments of the Plasmodium parasite food vacuole at pH 5.0. The experiments were monitored by UV-Vis spectrophotometery in the range of 250-650 nm. Our results suggest that the HbS, on interacting with both the membrane mimic and 40 μM Ca(2+), undergoes an "expansion" akin to the burst phase of proteins accompanied by tyrosine exposure while that of the HbA occurred with tryptophan exposure. Our results suggest conformational flexibility in the HbS unlike in the HbA. Besides, the spectral results also suggest that the HbS complexes with the Ca(2+) in its immediate environment without strain (due to its inherent conformational flexibility), unlike the HbA, thus appropriating the cation from its vicinity. The implications of these results are discussed in the light of possible mechanisms employed by the HbS to resist protease digestion or at least slow down the kinetics of the protease activities and on how these same factors can predispose the homozygous HbS individuals to sickling and consequent vaso-occlusive crisis.     

The electric potential field around cytochrome c and the effect of ionic strength on reaction rates of horse cytochrome c.

1. The electric potential fields around tuna ferri- and ferrocytochrome c were calculated assuming that (i) all of the lysines and arginines are protonated, (ii) all of the glutamic and aspartic acids and the terminal carboxylic acid are dissociated, and (iii) the haem has a net charge of +1e in the oxidized form. 2. Near the haem crevice high values for the potential (greater than +2.5 kT/e) are found. Consequently, electron transfer via the haem edge is favored if the oxidant or reductant is negatively charged. 3. The inhomogeneous distribution of charges leads to a dipole moment of 244 and 238 debye for oxidized and reduced tuna cytochrome c, respectively. Horse cytochrome c has dipole moments of 303 (oxidized) and 286 (reduced) debye. 4. A line through the positive and negative charge centres, the dipole axis, crosses the tuna cytochrome c surface at Ala 83 (positive part) and Lys 99 (negative part). The direction of the dipole axis of horse cytochrome c is very similar. Since the centre of the domain on the cytochrome c surface, which is involved in the binding to cytochrome c oxidase, is found at the beta-carbon of the Phe 82 in horse cytochrome c (Ferguson-Miller, S., Brautigan, D.L. and Margoliash, E. (1978) J. Biol. Chem. 253, 149--159) it is suggested that the direction of the dipole is of physiological importance. 5. The activity coefficients of horse ferri- and ferrocytochrome c were calculated as a function of ionic strength using a formula derived by Kirkwood (Kirkwood, J.G. (1934) J. Chem. Phys. 2, 351--361). 6. Due to the high net charge at pH 7.5 the influence of the dipole moments of horse ferri- and ferrocytochrome c on the respective activity coefficients can be neglected at I less than or equal to 50 mM. 7. Using the Br?nsted relation the effect of ionic strength on reaction rates of horse cytochrome c was calculated. Good agreement is found between theory and experimental results reported in the literature.