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 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.     

Electrostatics and electrodynamics of bacteriorhodopsin.

The stationary electric dichroism of bacteriorhodopsin is in qualitative, but not quantitative, agreement with the orientation function for disks having a permanent dipole directed perpendicular to the plane and an induced dipole in the plane. Fits of the orientation function to data measured at low field strengths demonstrate: an increase of the permanent dipole moment mu with the square of the disk radius r2, whereas the polarizability alpha increases with r4; the ionic strength dependence is small for mu and clearly stronger for alpha; the permanent dipole moment is 4x10(6) D at r = 0.5 micron. According to the risetime constants, the induced dipole does not saturate and increases to 4x10(8) D at 40 kV/cm and r = 0.5 micron. The data indicate that the permanent dipole is not of some interfacial character but is due to a real assymetry of the charge distribution. The experimental dipole moment per protein monomer is approximately 55 D, whereas calculations based on the structure of Grigorieff et al. (Grigorieff, N., T.A. Ceska, K.H. Downing, J.M. Baldwin, and R. Henderson. 1996. Electron-crystallographic refinement of the structure of bacteriorhodopsin. J. Mol. Biol. 259:393-421) provide a dipole moment of approximately 570 D. The difference is probably due to a nonsymmetric distribution of charged lipid residues. It is concluded that experimental dipole moments reflect the mu-potential at the plane of shear for rotational diffusion, in analogy to the sigma-potential used for translational diffusion. It is suggested that the permanent dipole of bacteriorhodopsin supports proton transport by attraction of protons inside and repulsion of protons outside of the cell. Dichroism rise curves at field strengths between E = 150 and 800 V/cm reveal an exponential component with time constants tau 3r in the range between 1 and 40 ms, which is not found in Brownian dynamics simulations on a disk structure using hydrodynamic and electric parameters characteristic of bacteriorhodopsin disks. The experimental data suggest that this process reflects a cooperative change of the bacteriorhodopsin structure, which is induced already at a remarkably low field strength of approximately 150 V/cm.     

The nature of protein dipole moments: experimental and calculated permanent dipole of alpha-chymotrypsin

The electric dichroism of alpha-chymotrypsin has been measured in buffers of various pH values and ion compositions. The stationary dichroism obtained as a function of the electric field strength is not compatible with an induced dipole mechanism and clearly shows that alpha-chymotrypsin is associated with a substantial permanent dipole moment. After correction for the internal directing electric field according to a sphere model, the dipole moment is 1.6 X 10(-27) C m at pH 8.3 (corresponding to 480 D). This value decreases with decreasing pH (to 1.2 X 10(-27) C m at pH 4.2), but is almost independent of the monovalent salt concentration in the range from 2 to 12 mM and of Mg2+ addition up to 1 mM. The assignment of the permanent dipole moment is confirmed by analysis of the dichroism rise curves. The dichroism decay time constants of (31 +/- 1) ns at 2 degrees C can be represented by a spherical model with a radius of 25-26 A, which is consistent with the known X-ray structure. The limiting linear dichroism is slightly dependent on the buffer composition and demonstrates subtle variations of the protein structure. As a complement to the experimental results, electric and hydrodynamic parameters of alpha-chymotrypsin have been calculated according to the known X-ray structure. Bead model simulations provide the center of diffusion, which is used to calculate dipole moments according to the equilibrium charge distribution evaluated from standard pK values.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

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 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.     

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.     

Electro-optical measurements on aqueous suspension of purple membrane from Halobacterium halobium

The permanent dipole moment, polarizability, and the retinal angle of Halobacterium halobium purple membranes were determined at different pH values. All of the parameters have a maximum between pH 5 and 6. There is a reversal in the direction of the permanent dipole moment near pH 5. The value of permanent dipole moment was determined to be 60 D/protein at pH 6.6, and the value obtained for polarizability was 3 X 10(-28) Fm2/membrane fragment. The retinal angle of all-trans retinal was 0.8 degrees smaller than that of the 13-cis conformation.     

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.     

Electrooptical measurements demonstrate a large permanent dipole moment associated with acetylcholinesterase.

Acetylcholinesterase (AChE) from krait (Bungarus fasciatus) venom is a soluble, nonamphiphilic monomer of 72 kDa. This snake venom AChE has been analyzed by measurements of the stationary and the transient electric dichroism at different field strengths. The stationary values of the dichroism are consistent with the orientation function for permanent dipoles and are not consistent with the orientation function for induced dipoles. The permanent dipole moment obtained by least-squares fits for a buffer containing 5 mM MES is 1000 D, after correction for the internal directing field, assuming a spherical shape of the protein. The dipole moment decreases with increasing buffer concentration to 880 D at 10 mM MES and 770 D at 20 mM MES. The dichroism decay time constant is 90 ns (+/- 10%) which is clearly larger than the value expected from the size/shape of the protein and indicates contributions from sugar residues attached to the protein. The dichroism rise times observed at low field strengths are larger than the decay times and, thus, support the assignment of a permanent dipole moment, although it has not been possible to approach the limit where the energy of the dipole in the electric field is sufficiently low compared to kT. The experimental value of the permanent dipole moment is similar to that calculated for a model structure of Bungarus fasciatus AChE, which has been constructed from its amino and acid sequence, in analogy to the crystal structure of AChE from Torpedo californica.     

Deconvolution can be used in electrooptic studies to correct for non-ideal electric excitation pulses only when the electric dipole moment of the studied molecules is predominantly induced

The electric field pulses used for most measurements of transient electrooptic properties such as birefringence and dichroism, are rectangular and assumed to be ideal, but in practice do all such pulses have non-zero rise and fall times. Claims have been made that this non-ideality may be taken into account by employing standard deconvolution techniques. We find that this approach yields exact results in the zero electric field limit when the electric dipole moment of the studied macromolecules is predominantly induced. However, for finite electric field strengths and/or macromolecules with partly or fully permanent electric dipole moments, we find that the deconvolution method yields erroneous estimates of the electrooptic relaxation times. When the decay time of the electric pulse and the electrooptic decay time are equal, and the system is operated in the Kerr domain, this systematic error for macromolecules with purely permanent electric dipole moment equals 37%. In a research field where the uncertainty of the reported relaxation times normally is assumed to be only a few percent this is an error that may seriously mislead unsuspecting users. We find that this systematic error can readily be avoided by employing standard numerical integration of a set of coupled first-order differential equations instead of the standard deconvolution techniques.     

Solution conformation of brazzein by H nuclear magnetic resonance: resonance assignment and secondary structure

Brazzein is a sweet-tasting protein isolated from the fruit of the West African plant Pentadiplandra brazzeana Baillon. It is the smallest and the most water-soluble sweet protein discovered so far, it is also highly thermostable. The proton NMR study of brazzein at 600 MHz (pH 3.5, 300K) is presented. Complete sequence specific assignment of the individual backbone and sidechain proton resonances were achieved using through-bond and through-space connectivities obtained from standard two-dimensional NMR techniques. The secondary structure of brazzein contains one -helix (residues 21–29), one short 3₁₀-helix (residues 14–17), two strands of antiparallel β-sheet (residues 34–39, 44–50) and probably a third strand (residues 5–7) near the N-terminus.     

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.     

Temperature-dependent van der Waals forces

Biological systems can experience a strong van der Waals interaction involving electromagnetic fluctuations at the low frequency limit. In lipid-water mixtures the free energy of this interaction is proportional to temperature, primarily involves an entropy change, and has qualitative features of a “hydrophobic bond.” Protein-protein attraction in dilute solution is due as much to low frequency proton fluctuation (Kirkwood-Shumaker forces) and permanent dipole forces as to high frequency (infrared and UV) van der Waals intreactions. These conclusions are described in terms of numerical calculations via the Lifshitz theory of van der Waals forces.     

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.     

Electric birefringence studies of rabbit skeletal tropomyosin

The electric birefringence of rabbit skeletal tropomyosin and its nonpolymerizable derivative was studied as a function of protein concentration, pulse length, and electric field strength. Analyses of the zero field birefringence decay curves show that nonpolymerizable tropomyosin, which has had on average six C-terminal residues removed, and tropomyosin are both well approximated by rigid cylinders in solution at low salt concentrations at 20°C. The measured relaxation times for the monomers of polymerizable and nonpolymerizable tropomyosin are 1.5 ± 0.4 μs and 1.30 ± 0.2 μs, respectively, in good agreement with the values calculated from the known dimensions. For tropomyosin the electrical pulse induces the formation of linear dimers. Orientation occurs primarily by a permanent dipole mechanism. Permanent and induced dipole moments were calculated from reversing field experiments and from the saturation of the birefringence. Removal of the six C-terminal residues decreases the measured permanent dipole moment by 9.5%, from 6300 to 5700 Debyes, which is in good agreement with the 7% decrease calculated for permanent dipole contributions arising from the peptide dipoles and from the asymmetric distribution of the formal charges. This change is due primarily to the removal of Asp 280.     

Polarized absorption spectra of green fluorescent protein single crystals: transition dipole moment directions

Polarized absorption spectra of orthorhombic crystals of wild-type green fluorescent protein (GFP) were measured between 350 and 520 nm to obtain information on the directions of the electronic transition dipole moments ((-->)m) of the chromophore relative to the molecular axes. The transition dipole moment orientation is a basic spectroscopic parameter of relevance to biologists when interpreting F?rster-type fluorescence resonance energy transfer data and for comparing absorbance and fluorescence spectra of GFP with quantum chemical calculations. Maximal extinction was obtained throughout the spectrum when the polarization direction of the electric vector of incident light was parallel to the c-axis of the crystal. The transition dipole moments were assumed to be parallel to the plane of the chromophore. With this assumption and the measured dichroic ratios in the crystals, the transition dipole moments associated with the neutral (lambda(max) = 398 nm) and anionic (lambda(max) = 478 nm) forms of the chromophore were found to subtend angles of approximately 26 degrees and 13 degrees (counterclockwise), respectively, with the vector that joins the phenolic and imidazolinone oxygen atoms of the chromophore.     

Anisotropic electric properties of purple membrane and their change during the photoreaction cycle

Purple membrane suspension shows two different orientations in electric fields of different frequencies. The orientation at low frequencies (less than or equal to approximately 10 Hz), with the membrane surface perpendicular to the electric field, is due to permanent dipole moment of the membrane and the orientation at high frequencies (greater than or equal to approximately 100 Hz), with the surface parallel to the electric field, is due to induced dipole moment. By quantitative analysis of these orientations, we determined the permanent dipole moment and the polarizability. Both values varied according to the membrane size: the permanent dipole moment ranged from 500 kD to 10 MD and was proportional to the square of the diameter of the membrane. The polarizability ranged from 1 X 10(-13) to 1 X 10(-11)cm3 and was proportional to the third to fourth power of the diameter. Because the permanent dipole moment was proportional to the area of the membrane, we could determine permanent dipole moment per bacteriorhodopsin. By determining the actual membrane size under electron microscopy, we got 98 D/bacteriorhodopsin. We also concluded that the direction of the permanent dipole moment was from the cytoplasmic to the extracellular side. These values, however, were strongly dependent on the ionic strength in the medium, suggesting a screening effect due to counter ions near the membrane surface. We evaluated the screening effect and showed about a four-charge difference between the two sides of the purple membrane. Under illumination, we found that the permanent dipole moment decreased from 98 to 63 D/bacteriorhodopsin. From the best-oriented sample, we also concluded that the angle of retinal against the axis normal to the membrane surface was greater than 68.6 degrees.