Potentiometric titration studies on globular proteins

A power series method was applied to solve the Poisson-Boltzmann equation for the spherical polyelectrolyte model and numerical calculation with an electronic computer was performed to obtain surface electric potential on rigid globular proteins. Deviation from the ideal linear relationship in Linderstrom-Lang's plot was found to become noticeable as the surface charge density and the radius of protein increases and ionic strength decreases. The calculated surface potential was compared with potentiometric titration data of several proteins whose radii have been analyzed. Assuming the radius of the counterions to be equal to about 1.0 Å, the data for phenolic groups in ribonuclease and for carboxyl groups in conalbumin were interpreted. Reversible intramolecular transformation was found for α-lactalbumin by comparing the present results with the potentiometric titration data for carboxyl groups. The molecular size of each protein was discussed.     

Small-angle X-ray scattering studies of Escherichia colil-asparaginase

Small angle X-ray scattering studies on Escherichia colil-asparaginase solutions show that the enzyme has a radius of gyration of 34.0 Å ± 0.5 Å at pH 7. The radius of gyration of the dissociated monomer is 16.0 Å ± 1.0 Å; it has the general shape of a prolate ellipsoid with an axial ratio of 1.4. A tetramer of four such ellipsoids arranged with 222 symmetry gives good agreement between measured and calculated radii of gyration if the distance between subunit centers is 43 Å. The tetramer dissociates on dilution below 1% and at pH values below 3.0. Acid-induced denaturation at pH 2.0 is irreversible in contrast to the reversible guanidine-HCl-induced denaturation.     

Surface pH controls purple-to-blue transition of bacteriorhodopsin. A theoretical model of purple membrane surface.

We have developed a surface model of purple membrane and applied it in an analysis of the purple-to-blue color change of bacteriorhodopsin which is induced by acidification or deionization. The model is based on dissociation and double layer theory and the known membrane structure. We calculated surface pH, ion concentrations, charge density, and potential as a function of bulk pH and concentration of mono- and divalent cations. At low salt concentrations, the surface pH is significantly lower than the bulk pH and it becomes independent of bulk pH in the deionized membrane suspension. Using an experimental acid titration curve for neutral, lipid-depleted membrane, we converted surface pH into absorption values. The calculated bacteriohodopsin color changes for acidification of purple, and titrations of deionized blue membrane with cations or base agree well with experimental results. No chemical binding is required to reproduce the experimental curves. Surface charge and potential changes in acid, base and cation titrations are calculated and their relation to the color change is discussed. Consistent with structural data, 10 primary phosphate and two basic surface groups per bacteriorhodopsin are sufficient to obtain good agreement between all calculated and experimental curves. The results provide a theoretical basis for our earlier conclusion that the purple-to-blue transition must be attributed to surface phenomena and not to cation binding at specific sites in the protein.     

Three-dimensional image reconstruction of straight flagella from a mutant Salmonella typhimurium.

The structure of the straight flagella from a mutant Salmonella typhimurium was studied by electron microscopy using digital image processing, including three-dimensional reconstruction, to an effective resolution of about 14 Å.Three-dimensional studies suggest that there are two sets of intersubunit bonds, i.e. intraprotofilament bonds along the (n = 11, l = 1) helix at a radius of about 55 Å and interprotofilament bonds along the (n = ?5, l = 7) helix at radii of about 10 to 15 Å and 50 Å, and along the (n = 6, l = 8) helix at a radius of about 45 Å and along the (n = 1, l = 15) helix at a radius of about 20 Å. There are four high density regions in a morphological subunit. These regions are situated at radii of about 15 Å, 40 Å, 70 Å and 80 Å. Variation was seen in the position of the high density regions at radii of about 15 Å and 40 Å among the ten models that were reconstituted individually. The regions at radii of 40 Å and 70 Å are the highest in density. The radial distance between these two regions is consistent with the 32 Å feature of a cylindrically averaged Patterson function calculated using equatorial data from X-ray diffraction pattern (Champness, 1968,1971).At the outer radii of the flagellum the shape of the morphological subunit roughly corresponded to that of the “chevron” described by O'Brien &; Bennett (1972), but there was no corresponding structure at the inner radii; the appearance of chevrons in that region might arise from the superposition of the two sides of the helical lattice.The biological significance of the “beaded” submolecular structure of flagellin and the presence of two sets of intersubunit bonds at the different radii is discussed with reference to the waveform and polymorphic behaviour of flagellar filaments.     

Aggregation of tyrocidine in aqueous solutions.

The formation of aggregates of tyrocidine B at 4°C and 20°C in aqueous solutions was studied by means of light scattering and fluorescent techniques. The apparent weight molecular weight of tyrocidine B aggregates was found to be 36,000 at 4°C and 28,800 at 20°C. Fluorescence titration experiments with dansyl-chloride resulted in an aggregational number of 31 (4°) and 28 (20°) indicating that one molecule of dye is bound per monomer of molecular weight 1,200. From a Scatchard plot apparent association constants of 1.22 × 10⁵ M (4°) and 0.95 × 10⁵ M (20°) were calculated. From the angular dependence of scattered intensity the radii of gyration were determined to be 60 Å and 58 Å, respectively.     

Light scattering during the hysteresis effect in poly(A)·2poly(U)

Light-scattering studies on buffered aqueous solutions of the triple-stranded polyribonucleic acid poly(A)·2poly(U) were carried out at neutral pH and during titration. At pH 7.1 and 22°C, a sample of commercially available polymer in 0.005M phosphate buffer gave a Zimm plot which yielded values for the weight-average molecular weight, M _w, of 874,000 ± 1800 g/mol, a root-mean-square radius, ρ of 930 ± 22 Å, and a second viral coefficient of 0.51 ± 0.05 × 10 ^?3 cm³g^?1 mol. The light-scattering data were also analyzed by serval linear and nonlinear least-squares programs which were devised to determine the model (e.g., rod, coil, or zigzag) which could best describe the shape of the molecule. It was found that a rodlike model, perhaps with a few bends, was in best overall agreement with the data. The assumption that the molecule is a thin rod leads to a value for the linear density of 206 g mol^?1 Å^?1 and a translation of 3.3 Å per residue. These values are also in close agreement with those expected for a triple-stranded, thin, base-stacked molecule. During titration from neutral pH with 0.1M HCl, the observed apparent molecular weight slowly increased until at about pH 3.5 a sudden, large increase (about 30-fold) occurred. The root-mean-square radius, on the other hand, after an initial small decrease (of about 25%), also exhibited a large increase (about 4-fold). Upon back titration with 0.1M NaOH, the molecular parameters did not retrace the original path, but instead exhibited hysteresis—the M _w and ρ _z are both larger on the basic branch than on the acid branch at a corresponding pH. A plot of long ρ _z against log(M _w) during the interval in which the high-moelcular-weight form was present (below pH 3.5 on the acid branch, and on the basic branch) gave a straight line with a slope of ?. This suggests that the aggregates were composed of some tens of rather open radom coils, presumably of poly(A)·poly(A), and that the hysteresis may be caused under conditions by the metastability of the entangled coils.     

Monte Carlo and Poisson–Boltzmann calculations of the fraction of counterions bound to DNA

The counterion density and the condensation region around DNA have been examined as functions of both ion size and added-salt concentration using Metropolis Monte Carlo (MC) and Poisson–Boltzmann (PB) methods. Two different definitions of the “bound” and “free” components of the electrolyte ion atmosphere were used to compare these approaches. First, calculation of the ion density in different spatial regions around the polyelectrolyte molecule indicates, in agreement with previous work, that the PB equation does not predict an invariance of the surface concentration of counterions as electrolyte is added to the system. Further, the PB equation underestimates the counterion concentration at the DNA surface, compared to the MC results, the difference being greatest in the grooves, where ionic concentrations are highest. If counterions within a fixed radius of the helical axis are considered to be bound, then the fraction of polyelectrolyte charge neutralized by counterions would be predicted to increase as the bulk electrolyte concentration increases. A second categorization—one in which monovalent cations in regions where the average electrostatic potential is ledd than ?kT are considered to be bound—provides an informative basis for comparison of MC and PB with each other and with counterion-condensation theory. By this criterion, PB calculations on the B from of DNA indicate that the amount of bound counterion charge per phosphate group is about .67 and is independent of salt concentration. A particularly provocative observatiob is that when this binding criterion is used, MC calculations quantitatively reproduce the bound fraction predicated by counterion-condensation theory for all-atom models of B-DNA and A-DNA as well as for charged cylindera of varying lineat charge densities. For example, for B-DNA and A-DNA, the fractions of phosphate groups neutralized by 2 Å hard sphere counterions are 0.768 and .817, respectively. For theoretical studies, the rediys enclosing the region in which the electrostatic potential is calculated studies, the radius enclosing the region in which the electrostatic potential is calculated to be less than ?kT is advocated s a more suitable binding or condensation radius that enclosing the fraction of counterions given by (1 – ξ^?1). A comparsion of radii calculated using both of these definitions is presented. © 1994 John Wiley & Sons, Inc.     

Medium reorganization energy and enzymatic reaction activation energy

Reorganization and activation energies for charge transfer reactions occurring inside a dielectric sphere have been calculated by solving the problem of polar medium reorganization within and outside a dielectric sphere placed in another infinite dielectric. The dielectric sphere is assumed to simulate a protein globule, i.e. an enzyme molecule. It has been shown that for some reaction types the activation energy tends to decrease as the globule radius increases and that for each of the reaction types considered there is an optimal globule radius an increase of which does not bring about any tangible activation energy reduction. The calculated optimal radii for different processes are in good agreement with the increasing molecular sizes in the series: ribonuclease less than or equal to lysozyme less than serine proteinases approximately equal to cysteine proteinases less than NAD-dependent dehydrogenases. The calculated radii are usually about 1.5 to 1.7 times (and molecular masses about 4-5 times) smaller than the experimental ones. The reasons for this discrepancy are discussed and it has been suggested that the approximate nature of the treatment of a protein globule as a structureless dielectric is the main reason. It is shown that charge transfer at an acute angle to the globule surface is the optimum process. For endoergonic reaction stages it is the net charge transfer towards the periphery and for exoergonic ones that in the reverse direction which are advantageous. These conclusions are consistent with the data about the structure of the above-mentioned enzymes.     

Electrical and hydrodynamical properties of polypeptides in solution. I. Poly(L-glutamic acid) in methanol-water mixtures

The electric birefringence of poly(L -glutamic acid) (PLGA) in methanol–water mixtures has been measured by the use of the rectangular pulse technique at 25°C. The permanent dipole moment, the anisotropy of electrical polarizability, and the optical anisotropy factor of PLGA in solution were obtained from the dependence of the steady-state birefringence on the electric field strength. Further, the mean length of PLGA in solution was calculated by a parameter method developed for analyzing the decay curve of electric birefringence. The permanent dipole moment per unit length obtained from these studies was 2.9₆, 2.4₈, 2.3₀, 2.6₆ D/Å in pure methanol, 10, 30, and 50 vol-% water, respectively. The increase of water content caused the decrease of the mean length and broadened the length distribution of PLGA. These results are discussed in relation to the viscosity and the electrical conductivity of PLGA solutions.     

Electrostatic properties of cells estimated by absorption and fluorescence spectroscopy

A colloid titration method was used to determine the surface charge of cells of a human colon adenocarcinoma cell line WiDr; 6.2±0.8×10⁸ charges per cell were found. The apparent surface charge density was calculated using the cell surface area estimated by a Coulter counter. Alternatively, the lower limit of the cell surface area was estimated by visible microscopy. The same procedure was applied for human skin fibroblasts, resulting in the value 9.4±1.1×10⁸ charges per cell. This is significantly higher (p<0.05) than that of WiDr cells, presumably because of the different size of the cells. According to the estimations using the Coulter counter, the median diameter was higher in the case of skin fibroblasts. Fluorimetric titration of the fluorescent probe U-6 was used to estimate the interfacial potential of the WiDr cells. A shift of the titration curve of the U-6 probe toward higher pH values compared to that in pure buffer solutions was found in the presence of the WiDr cells. From the displacement of the midpoints of the titration curves, the interfacial potential of the WiDr cells was found to be about−35.8 mV. Incubation of the cells at two different pH values (7.4 and 6.8) did not result in any significant modification of the electrostatic properties of the cells under the experimental conditions of the present study. Electron microscopy revealed a distinct difference in the surface morphology of the WiDr cells compared to human skin fibroblasts. Numerous microvilli present on the surface of WiDr cells indicated marked uncertainties in cell surface area estimations. This gives large uncertainties in the real surface charge densities of cells.     

Structure and mechanism of action of riboflavin-binding protein: Small-angle X-ray scattering,sedimentation, and circular dichroism studies on the holo- and apoproteins

Riboflavin-binding protein, a transport protein occurring in egg whites, binds riboflavin tightly at pH values above 4.5 but releases it readily at pH values below 4.0. Structural aspects of this biologically important binding were studied by several methods. Analysis of sedimentation equilibrium data gave an average molecular weight of 32,500 ± 1000 for all forms of the protein and showed the absence of changes in quaternary structure when riboflavin was bound at neutral pH or released at pH 3.7. Sedimentation velocity showed no change in tertiary structure on binding at pH 7.0 but revealed a significant change in sedimentation constant at pH 3.7. While circular dichroism showed no appreciable change in secondary structure, it gave evidence of a marked change in the aromatic region at the lower pH. Small-angle X-ray scattering, going from the holoprotein at neutral pH to the apoprotein at low pH, showed a small but significant increase in radius of gyration (19.8 ± 0.2 vs 20.6 ± 0.1 Å) with slightly decreased anisotropy and with substantial increases in molecular volume (55,600 ± 530 vs 66,500 ± 240 ų), surface (11,840 ± 120 vs 13,470 ± 140 Å), and hydration (0.27 ± 0.01 vs 0.38 ± 0.01 g H₂O/g dry protein). Hydration values were obtained from small-angle X-ray scattering in two different ways for comparison with those calculated from sedimentation coefficients by way of frictional coefficients (derived from two different dimensionless ratios based independently on the structural small-angle X-ray scattering data). For either form of the protein, the surface calculated from an ellipsoidal model could account for only about 62% of the surface found experimentally. The excess surface was ascribed to topographic features of the molecule. Relative changes in this new parameter, together with the circular dichroism data and the known association of riboflavin binding with aromatic residues, suggested the opening of an aromatic-rich cleft concomitant with the release of riboflavin as a consequence of lowered pH.     

On the quaternary structure of native rabbit muscle phosphofructokinase.

Small angle X-ray scattering measurements on solutions of native rabbit muscle phosphofructokinase (EC 2.7.1.11; ATP; D-fructose-6-phosphate 1 phosphotransferase) show that the dimer has a radius of gyration of 32.5 Å and a molecular weight of 160,000, and that the biologically active tetramer has a radius of gyration of 51.5 Å and a molecular weight of 320.000. A possible model was calculated from scattering curves of the dimer and tetramer suggesting two hollow cylinders with cell dimensions for the dimer of a height of 78.0 Å and a long half axis of 38.0 Å, and for the tetramer of a height of 155.0 Å and an outer radius of 35.0 Å. The tetramer is formed along the 78.0 Å axis of the dimer by means of an end-to-end aggregation. The overall particle dimensions of the protomer of molecular weight 80,000 is calculated to be 35.0 × 30.0 × 55.0 Å, assuming an elliptical molecule. The distance between the centers of the two dimeric units within the tetramer is 104.5 ± 1.5 Å.     

Small-angle x-ray scattering by poly-L-alanine solutions

The radius of gyration and “persistence length” of poly-L -alanine, calculated from small-angle x-ray scattering data, have values of 56 Å and 44 Å, respectively, in dichloroacetic acid, and 78 Å and ～30 Å in a 1:1 v/v mixture of trifluoroacetic acid and trifluoroethanol. This can be interpreted to mean that poly-L -alanine exists in a relatively rigid, predominantly α-helical conformation in dichloroacetic acid and in an extended, more flexible form in the mixed solvent system.     

Swelling of brome mosaic virus as studied by intensity fluctuation spectroscopy.

The swelling of brome mosaic virus induced by pH and temperature has been investigated with intensity fluctuation spectroscopy. A special light-scattering cell was designed which permits titrations within the cell in which Stokes radii, pH and temperature are measured simultaneously. Freshly prepared viruses in the presence of EDTA at 20 °C show a partially irreversible swelling in a first titration cycle (pH 5.8 to 7.2 to 5.8): the viruses do not recontract completely to the original compact form. All further titration cycles lead to a closed hysteresis with respect to the Stokes radii. These are stable in the swelling branch (obtained when adding base) of the titration cycle, but metastable in the contraction branch (i.e. when adding acid). In the latter, the Stokes radii relax to the values observed in the swelling branch within a few hours. If MgCl₂ is present, fresh viruses have slightly bigger radii than with EDTA, and the initial titration cycle is closed. It exhibits a similarly pronounced hysteresis with a metastable contraction branch as in the abscence of divalent cations. However, further titrations do not exhibit significant hysteresis. An irreversible swelling of the viruses can be induced in the absence of Mg²⁺ by raising the temperature from 5 ° to 35 °C at a constant pH value. In the presence of MgCl₂, Stokes radii are not affected by temperature.     

Ring-current effects in the nmr of nucleic acids: A graphical approach

The spatial dependence of the ring-current magnetic anisotropy of nucleic acid bases is presented in a series of graphs in cylindrical coordinates. The curves may be used to calculate the ring-current shift at a point in a cylinder of radius 10Å extending 8 Å above and below each ring of the base. These distance effects are found to influence considerably the predicted chemical shifts of nucleic acid protons, particularly in RNA duplexes. The contribution of polarization (electric field) effects and the diamagnetic anisotropy of individual atoms (local Δ_χ) are briefly discussed.     

Glycocalyx electrostatic potential profile analysis: ion, pH, steric, and charge effects

The Poisson-Boltzmann equation is modified to consider charge ionogenicity, steric exclusion, and charge distribution in order to describe the perimembranous electrostatic potential profile in a manner consistent with the known morphology and biochemical composition of the cell's glycocalyx. Exact numerical and approximate analytical solutions are given for various charge distributions and for an extended form of the Donnan potential model. The interrelated effects of ionic conditions, bulk pH, ion binding, local dielectric, steric volume exclusion, and charge distribution on the local potential, pH, and charge density within the glycocalyx are examined. Local charge-induced, potential-mediated pH reductions cause glycocalyx charge neutralization. Under certain conditions, local potentials may be insensitive to ionic strength or may decrease in spite of increasing charge density. The volume exclusion of the glycocalyx reduces the local ion concentration, thereby increasing the local potential. With neutral lipid membranes, the Donnan and surface potential agree if the glycocalyx charge distribution is both uniform and several times thicker than the Debye length (approximately 20 A in thickness under physiological conditions). Model limitations in terms of application to microdomains or protein endo- and ectodomains are discussed.     

Probing the effect of electric field in 9,10-dimethoxy-2,6-bis(2-p-tolylethynyl)anthracene molecular nanowire using quantum chemical and charge density analysis

The effect of electric field (EF) in a newly designed molecular nanowire 9,10-dimethoxy-2,6-bis(2-p-tolylethynyl)anthracene has been analysed theoretically from the structural and electronic charge transport properties using quantum chemical and charge density calculations. The applied EF (0–0.36 VÅ^? 1) alters the molecular conformation, charge density distribution, electrostatic properties and the electronic energy levels of the molecule. Furthermore, the applied EF decreases the highest occupied molecular orbital–lowest unoccupied molecular orbital gap significantly from 1.775 to 0.258 eV and it also induces polarisation in the molecule, which leads to increase the dipole moment of the molecule. The electrostatic potential for various levels of applied EF reveals the charge-accumulated regions of the molecule. The I–V characteristics of the molecule have been studied against various applied fields using Landauer formalism.     

Optical properties of GaAs nanocrystals: influence of an electric field

A study of the electronic and optical properties of the hydrogen-terminated GaAs nanocrystals Ga₆₈As₆₈H₉₆ and Ga₉₂As₈₀H₁₀₈ is presented. In this study, their dielectric functions, refractive indices, and absorption coefficients were calculated using density functional theory (DFT). The influence of a uniform external electric field on the optical properties of the nanocrystals was also explored. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) for each nanocrystal were studied in the absence and the presence of the uniform external electric field. Our results indicate that the HOMO–LUMO gap decreases with increasing electric field strength. The calculated density of states revealed that the main reason for this shrinking gap is an increase in the delocalization of the gallium π-orbitals under the influence of an increasing external electric field. The permanent dipole moment and the polarizability of the nanocrystals under the induced electric field increased with increasing nanocrystal radius. The induced electric field caused a noticeable redshift in the absorption peaks. The electric field also increased the absorption intensity, particularly when the field strength was >0.25 V/Å.

Potentiometric titration of polyelectrolytes having stiff backbones

The potentiometric titration curves of carboxymethylcellulose, which has a relatively stiff backbone, and also of poly(D -glutamic acid) in the helical region are compared with the theoretical curves calculated assuming that the polyions are rods and have smeared charges on their surfaces. For carboxymethylcellulose good agreement is observed when its charge density is high, whereas as the charge density decreases the calculated curves deviate from the observed ones. The main reason for the disagreement at low charge densities may be attributed to the flexibility of the polymer backbone. For helical poly(D -glutamic acid) satisfactory agreement between calculated and observed curves is found if a radius thicker than the realistic radius is employed. The reason for the excessively large radius may be attributed to the inapplicability of the smeared charge model.     

On the Implementation of Friedman Boundary Conditions in Liquid Water Simulations

Abstract

We have applied the image approximation to the reaction field as suggested by H.L. Friedman [Mol. Phys., 29, 1533 (1975)] by investigating appropriate cavity sizes and system parameters for use in molecular simulations. The energy of and the structure around a central simple point charge (SPC) water molecule in a dielectric cavity was found to be in good agreement with the properties of a liquid sample. To confine the water molecules within the cavity, we introduced a short-range repulsion between a real charge and its image as the Lennard-Jones repulsive potential between oxygen atoms of the SPC potential. For a system of 65 water molecules a cavity radius of 10.45 Å is appropriate; this radius is altered to 12.00 Å for a cavity surrounding 113 molecules. The effect of the boundary is restricted to the outer-most water layer which is in contact with the dielectric continuum.