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.     

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.     

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.     

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 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.     

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 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.     

Electric dipole moments of the fluorescent probes Prodan and Laurdan: experimental and theoretical evaluations

Several experimental and theoretical approaches can be used for a comprehensive understanding of solvent effects on the electronic structure of solutes. In this review, we revisit the influence of solvents on the electronic structure of the fluorescent probes Prodan and Laurdan, focusing on their electric dipole moments. These biologically used probes were synthesized to be sensitive to the environment polarity. However, their solvent-dependent electronic structures are still a matter of discussion in the literature. The absorption and emission spectra of Prodan and Laurdan in different solvents indicate that the two probes have very similar electronic structures in both the ground and excited states. Theoretical calculations confirm that their electronic ground states are very much alike. In this review, we discuss the electric dipole moments of the ground and excited states calculated using the widely applied Lippert–Mataga equation, using both spherical and spheroid prolate cavities for the solute. The dimensions of the cavity were found to be crucial for the calculated dipole moments. These values are compared to those obtained by quantum mechanics calculations, considering Prodan in vacuum, in a polarizable continuum solvent, and using a hybrid quantum mechanics–molecular mechanics methodology. Based on the theoretical approaches it is evident that the Prodan dipole moment can change even in the absence of solute–solvent-specific interactions, which is not taken into consideration with the experimental Lippert–Mataga method. Moreover, in water, for electric dipole moment calculations, it is fundamental to consider hydrogen-bonded molecules.     

Dipole moment analysis of membrane proteins suggests role in orientation in the membrane

The position independent dipole membrane proteins need to be oriented in the membrane in order to function as channels, transporters or recognition systems. Membrane proteins can be broadly classified as either predominantly alpha helical or beta barrel in nature. All the different types of thirteen beta barrel membrane proteins (2OMF, 2POR, 1PRN, 1PHO, 1IIV, 1AF6, 1AOT, 2MPR, 1OSM, 1QJ8, 1BXW, 2FCP and 1FEP) and six alpha helical membrane proteins (1BL8, 1MSL, 1QLB, 1AR1, 1PSS and 1QHJ) from the Protein Data Bank were analyzed. Dipole moment was calculated for both classes of proteins. In all the oligomers, the orientation of the dipole was found to be parallel to direction of insertion that is perpendicular to the possible membrane layer. Monomers do not show a similar orientation. In all the alpha helical oligomers, the dipole points from the intra-cellular to the extra-cellular side. In the oligomeric beta barrel proteins, the direction of the dipole is from the extra-cellular to the intra-cellular side, except for OmpF from E.coli, Omp36 from Klebsiella pneumonia and LamB from E.coli where the situation is reversed. However, the dipole moments of the monomeric proteins and the monomers of the oligomers themselves are not oriented parallel to the molecular axis and the insertion orientation, but they are almost parallel to the membrane surface. It is possible that the quaternary oligomeric association is necessary for the correct orientation in the membrane and this is aided by the dipole orientation. The electrostatic potential surface calculated with all atoms, which also do not show clear separation of charge surfaces. Calculations suggest that backbone structure and oligomer are sufficient for providing the dipole orientation.     

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.     

Contributions of dipole moments, quadrupole moments, and molecular polarizabilities to the anesthetic potency of fluorobenzenes

Previous studies have emphasized the role of molecular polarizability and electric moments, especially dipole and quadrupole moments, in binding of drugs to sites of action. A recent publication of ED50s that prevent response to a noxious stimulus for eight fluorobenzenes has made it possible to compare anesthetic potency with ab initio Hartree-Fock calculations of molecular polarizability as well as dipole and quadrupole moments. Fluorobenzenes provide a stringent test of the role of electric moments in anesthetic potency because individual dipole moments range from 0 to 2.84 debye (D) while the quadrupole moment of benzene is large and negative (-30 x 10(-40) C m(2)), that of hexafluorobenzene is large and positive (30 x 10(-40) C m(2)), and that of 1,3,5-trifluorobenzene is nearly zero. We found that anesthetic potency of fluorobenzenes was not affected by the presence of either dipole or quadrupole moments. This result is surprising because fluoroalkanes and fluorocycloalkanes are most potent when half fluorinated and are usually not anesthetics when perfluorinated. The results suggest that electrostatic interactions are not important for binding of fluorobenzenes at sites of anesthetic action and that these sites are different from those that bind conventional anesthetics.     

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.     

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.     

Electrostatics of hemoglobins from measurements of the electric dichroism and computer simulations.

Hemoglobins from normal human cells, from sickle cells, and from horse were investigated by electrooptical methods in their oxy and deoxy forms. The reduced linear dichroism measured as a function of the electric field strength demonstrates the existence of permanent dipole moments in the range of 250-400 Debye units. The reduced limiting dichroism is relatively small (< or = 0.1); it is negative for hemoglobin from sickle cells and positive for the hemoglobins from normal human cells and from horse. The dichroism decay time constants are in the range from about 55 to 90 ns. Calculations of the electrooptical data from available crystal structures are given according to models of various complexity, including Monte Carlo simulations of proton fluctuations with energies evaluated by a finite difference Poisson-Boltzmann procedure. The experimental dipole moments are shown to be consistent with the results of the calculations. In the case of human deoxyhemoglobin, the root mean square dipole is higher than the mean dipole by a factor of about 4.5, indicating a particularly large relative contribution due to proton fluctuations. The ratio of the root mean square dipole to the mean dipole is much smaller (approximately 1.1 to approximately 1.5) for the other hemoglobin molecules. The calculations demonstrate that the dichroism decay time constants are not simply determined by the size/shape of the proteins, but are strongly influenced by the orientation of the dipole vector with respect to the axis of maximal absorbance. The comparison of experimental and calculated electrooptical data provides a useful test for the accuracy of electrostatic calculations and/or for the equivalence of structures in crystals and in solutions.     

Helix packing moments reveal diversity and conservation in membrane protein structure

Helical membrane proteins are more tightly packed and the packing interactions are more diverse than those found in helical soluble proteins. Based on a linear correlation between amino acid packing values and interhelical propensity, we propose the concept of a helix packing moment to predict the orientation of helices in helical membrane proteins and membrane protein complexes. We show that the helix packing moment correlates with the helix interfaces of helix dimers of single pass membrane proteins of known structure. Helix packing moments are also shown to help identify the packing interfaces in membrane proteins with multiple transmembrane helices, where a single helix can have multiple contact surfaces. Analyses are described on class A G protein-coupled receptors (GPCRs) with seven transmembrane helices. We show that the helix packing moments are conserved across the class A family of GPCRs and correspond to key structural contacts in rhodopsin. These contacts are distinct from the highly conserved signature motifs of GPCRs and have not previously been recognized. The specific amino acid types involved in these contacts, however, are not necessarily conserved between subfamilies of GPCRs, indicating that the same protein architecture can be supported by a diverse set of interactions. In GPCRs, as well as membrane channels and transporters, amino acid residues with small side-chains (Gly, Ala, Ser, Cys) allow tight helix packing by mediating strong van der Waals interactions between helices. Closely packed helices, in turn, facilitate interhelical hydrogen bonding of both weakly polar (Ser, Thr, Cys) and strongly polar (Asn, Gln, Glu, Asp, His, Arg, Lys) amino acid residues. We propose the use of the helix packing moment as a complementary tool to the helical hydrophobic moment in the analysis of transmembrane sequences.     

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.     

Correlation between substituent constants and hyperpolarizabilities for di-substituted trans-azobenzenes

Nonlinear optical properties of a series of disubstituted trans-azobenzenes were studied. The structures were fully optimized by B3LYP/6-31+G* and both static polarizabilities and hyperpolarizabilities were then calculated by the derivative method. In order to show the relationships between dipole moments, (hyper)polarizabilities and the structures, three kinds of substituent constants were applied to correlate with both ground state dipole moment and hyperpolarizabilities. Both physical properties have a satisfactory correlation with substituent constants Σσ_+/? and bond length alternation. Overall, the electronic excitation contribution to the hyperpolarizabilities is rationalized in terms of the two-level model.     

A model for the calculation of the dielectric dispersion and the dipole moment of globular proteins in solution

We describe a new procedure whereby the magnitude of the dielectric dispersion of a solution of globular protein molecules can be calculated. The protein molecule is considered to have spherical symmetry and the charged residues are thought to be situated in a medium whose dielectric constant increases continuously as a function of the distance from the centre of mass. The dipole moment of the protein in the solution is made up of two parts: the intrinsic dipole moment due to the charge distribution of the protein and the dipole moment due to polarization of the medium and the ionic cloud. When the model is applied to solutions of cytochrome c it is found that polarization of the medium results in a decrease in the dielectric dispersion amplitude. The mean square dipole moment calculated with the help of this method indicates that the fluctuation of the configurations cannot be responsible for the large dispersion in the megahertz region.