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.     

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.     

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.     

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.     

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.     

Ab initio self-consistent field and potential-dependent partial equalization of orbital electronegativity calculations of hydration properties of N-acetyl-N'-methyl-alanineamide

Using a recently developed parallel computation algorithm, ab initio self-consistent field (SCF) calculations were carried out to estimate the relative hydration energies for 12 low-energy conformations of N-acetyl-N'-methyl-alanineamide. The requisite SCF calculations were carried out using 6-31G and 6-31G* basis sets, both in the absence and presence of a perturbing potential arising from a model solvent. The alpha R, alpha L, polyproline II (PII), and pi helical conformations were preferentially stabilized by the solvent potential, whereas conformations with intramolecular hydrogen-bonding C5 and C7 were preferred in the gas phase. Average vicinal nmr coupling constants (JNH-C alpha H), calculated using the total energies of the various solvated conformations, were consistent with observed coupling constants for this peptide in aqueous solution. Substantial alteration of the solute charge density occurred upon equilibration with the reaction field, as was exemplified in changes both in the molecular dipole moments and in atom-centered multipoles, when the molecule was transferred from a medium of low dielectric constant to one of high dielectric constant. In order to model these changes in charge density with an empirical scheme, we have implemented a novel monopolar representation of the solute charge density based on a potential-dependent form of partial equalization of orbital electronegativities (PDPEOE). In the atom-centered point charge PDPEOE representation, charge flows from one region of the solute to another in response to external fields. Hydration energies calculated using the PDPEOE representation are similar to those calculated by the SCF procedure. Also, the PDPEOE calculations yielded changes in molecular dipole moments upon solvation that agreed closely with the changes in the calculated ab initio SCF dipole moments.     

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.     

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.     

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.     

Charge calculations in molecular mechanics 6: the calculation of partial atomic charges in nucleic acid bases and the electrostatic contribution to DNA base pairing.

A previously described scheme for the direct calculation of the partial atomic charges in molecules (CHARGE2) is applied to the nucleic acid bases. It is shown that inclusion of the omega-technique for the calculation of HMO derived pi charges is of particular importance for these highly polar systems. The molecular dipole moments obtained for the resulting charges are in very good agreement with the observed values for a variety of substituted purine and pyrimidine bases. The partial atomic charges for cytosine, thymine, guanine and adenine (as the 1-methyl and 9-methyl forms) are given and compared with values calculated by a variety of molecular orbital and empirical schemes. All the schemes reproduce the same general trends, with the possible exception of those calculated by the Del Re method, though the charges given by Kollman are in general somewhat larger than the others. The electrostatic contribution to the Watson-Crick base pair interaction energies are calculated using these partial atomic charges. The electrostatic contributions obtained from the M.O. derived atomic charges are less than half the observed values, as are those obtained by the Gasteiger method. The electrostatic contributions calculated from the CHARGE2 atomic charges and those of Kollman are in reasonable agreement with the observed values. The influence of a distant-dependent dielectric constant is examined, but no clear pattern emerges.     

Photoabsorption of green and red fluorescent protein chromophore anions in vacuo

Photoabsorption properties of green and red fluorescent protein chromophore anions in vacuo were investigated theoretically, based on the experimental results in gas phase [Phys. Rev. Lett. 2001, 87, 228102; Phys. Rev. Lett. 2003, 90, 118103]. Their calculated transition energies in absorption with TD-DFT and ZINDO methods are directly compared to the experimental reports in gas phase, and the calculations with ZINDO method can correctly reproduce the absorption spectra. The orientation and strength of their transition dipole moments were revealed with transition density. We also showed the orientation and result of their intramolecular charge transfer with transition difference density. The calculated results show that with the increase of the extended conjugated system, the orientation of transition dipole moments and the orientation of charge transfer can be reversed. They are the linear responds with the external electric fields. These theoretical results reveal the insight understanding of the photoinduced dynamics of green and red fluorescent protein chromophore anions and cations in vacuo.     

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.     

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.     

Molecular and statistical modeling of reduction peak potential and lipophilicity of platinum(IV) complexes

We report the results of the quantitative structure–property relationship analysis of 31 Pt(IV) complexes, for three of which the synthesis is reported for the first time. The X-ray structural analysis of one complex of the series was performed to demonstrate that the PM6 semiempirical method satisfactorily reproduces key features of the geometry of the complexes investigated. Molecular properties extracted from such calculations were then used to construct models of experimental data such as electrochemical peak potentials (evaluated by cyclic voltammetry) and the octanol–water partition coefficient (evaluated by a reversed-phase high performance liquid chromatography method), which are key aspects in the design of such Pt(IV) complexes as potential anticancer prodrugs. Statistically accurate models for both properties were found using combinations of surface areas, orbital energies, dipole moments, and atomic partial charges. These models could form the basis of virtual screening of potential drug molecules, allowing the prediction of properties, closely related to the antiproliferative activity of Pt(IV) complexes, directly from calculated data.     

Electrostatic and steric control of electron self-exchange in cytochromes c, c551, and b5.

The ionic strength dependence of the electron self-exchange rate constants of cytochromes c, c551, and b5 has been analyzed in terms of a monopole-dipole formalism (van Leeuwen, J.W. 1983. Biochim. Biophys. Acta. 743:408-421). The dipole moments of the reduced and oxidized forms of Ps. aeruginosa cytochrome c551 are 190 and 210 D, respectively (calculated from the crystal structure). The projections of these on the vector from the center of mass through the exposed heme edge are 120 and 150 D. For cytochrome b5, the dipole moments calculated from the crystal structure are 500 and 460 D for the reduced and oxidized protein; the projections of these dipole moments through the exposed heme edge are -330 and -280 D. A fit of the ionic strength dependence of the electron self-exchange rate constants gives -280 (reduced) and -250 (oxidized) D for the center of mass to heme edge vector. The self-exchange rate constants extrapolated to infinite ionic strength of cytochrome c, c551, and b5 are 5.1 x 10(5), 2 x 10(7), and 3.7 x 10(5) M-1 s-1, respectively. The extension of the monopole-dipole approach to other cytochrome-cytochrome electron transfer reactions is discussed. The control of electron transfer by the size and shape of the protein is investigated using a model which accounts for the distance of the heme from each of the surface atoms of the protein. These calculations indicate that the difference between the electrostatically corrected self-exchange rate constants of cytochromes c and c551 is due only in part to the different sizes and heme exposures of the two proteins.     

Ab initio calculations of molecular properties of low–lying electronic states of 2–cyclopenten–1–one – link with biological activity

Geometries, vibrational frequencies, vertical and adiabatic excitation energies, dipole moments and dipole polarizabilities of the ground and the three lowest electronic excited states, S(1)(n, π (*)), T(1)(n, π (*)), and T(2)(π, π (*)) of the 2-cyclopenten-1-one molecule (2CP) were calculated at the CCSD and CCSD(T) levels of approximation. Our results indicate that two triplets T(1)(n, π (*)) and T(2)(π, π (*)) are lying very close each to other, while the singlet S(1)(n, π (*)) is well above them. There are dramatic changes in dipole moments for (n, π (*)) excited states in respect to the ground state. On the other hand the T(2)(π, π (*)) state has a similar dipole moment as the ground state. These changes can be interpreted within the MO picture using electrostatic potential maps and changes in model IR spectra. Our CCSD(T) dipole moment data for the ground state and almost isoenergetic triplets T(1)(n, π (*)) and T(2)(π, π (*)) are 1.469?a.u., 0.551?a.u., and 1.124?a.u., respectively. Dipole polarizabilities of investigated excited states are much less affected by electron excitations than dipole moments. These are the first dipole moment and polarizability data of 2CP in the literature. The changes of molecular properties upon excitation to S(1)(n, π (*)) and T(1)(n, π (*)) correlate with the experimental data on the biological activity of 2CP related to the α, β-unsaturated carbonyl group.     

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.