Electric dichroism of DNA. Influence of the ionic environment on the electric polarizability

In order to test the diffuse ion atmosphere polarization model recently developed by us, the effects of ionic strength, titrating with Mg2+ and Co(NH3)3+6, and coion charge on the electric polarizability of short fragments of DNA are investigated. The results are consistent with the predictions of the theory and show that the diffuse ion atmosphere polarization contributes significantly to the overall orientation of DNA. At low ionic strengths, we attempt to separate the total dipole moment into two components: one that agrees well with the Debye-Hückel ion atmosphere calculations, while the other, presumably due to condensed counterion polarization, appears to be substantially independent of the ionic strength. At higher salt concentrations, however, a simple separation into dipole components is not possible, perhaps due to a significant coupling of ion flows between the diffuse atmosphere and the condensed counterion layer.     

Effect of a molecular dipole on the ionic strength dependence of a biomolecular rate constant. Identification of the site of reaction.

A theory is proposed for determining the location of a reaction site on a protein of known tertiary structure with an asymmetric charge distribution by an analysis of the effect of ionic strength on the rate of reaction of the protein with a small ion, using equations of Brønsted (J. N. Brønsted, 1922, Z. Phys, Chem. 102:169-207), Debye and Hückel (P. Debye and E. Hückel, 1923, Phys. Z. 24:185-206), and Kirkwood (J. G. Kirkwood, 1934, J. Chem. Phys. 2:351-361). The theory is based on the fact that the dipole moment of the transition complex differs from that of the protein, which will be reflected in the ionic strength dependence of the reaction. The location of the small ion with respect to the dipole axis of the protein can be calculated from this difference. For protein-protein reactions, an a priori assumption has to be made about the orientation of one of the reaction partners, since many different orientations of the reactants with respect to each other result in dipole moments of the same magnitude.     

Intracellular pH determination by a 31P-NMR technique. The second dissociation constant of phosphoric acid in a biological system

To evaluate the accuracy of pH determination by 31P-NMR, factors which influence the pK value of phosphate were appraised on the basis of the titration of 1 mM phosphate buffer solution. When the method is used for the determination of cytoplasmic pH, ionic strength is the major factor causing shifts of apparent pK (pK') value, and the magnitude of the shift can be predicted from the ionic strength calculated by means of the Debye-Hückel equation. Ions (Na+, K+, Mg2+, and Ca2+) and salivary protein affected the pK' value by 0.1 to 0.3 units in solution with a given ionic strength depending on the species of ion. The form of the titration curve varied with temperature. Based on these results, the value of 6.75 was obtained with the uncertainty of 0.12 for the intracellular pK' of frog muscle at 24 degrees C.     

Polarizability of the ionic cloud around a charged membrane sheet

The polarizability of the ionic cloud around a charged membrane sheet parallel to the surface is calculated. The membrane is modeled as an infinitely thin and long strip of width 2d'. The Poisson-Boltzmann equation is solved with an external electric field as a perturbation. The polarizability is given in closed integral form, with numerical results. At higher salt concentration the polarizability varies approximately as kappa(-3), where kappa is the Debye-Hückel constant. The given theoretical result can account for the a.c. electrodichroism of purple membrane suspensions.     

Analysis of excess Gibbs energy of electrolyte solutions: a new model for aqueous solutions

This paper presents an analysis of the excess Gibbs free energy of aqueous electrolytes. The analysis of experimental data leads to the conclusion that the equilibrium state for dilute univalent electrolytes in water involves an intercalation of water and ionic liquid crystal domains. Excess free energy of the solution is determined by the Madelung energy of hydrated ion-pair liquid crystals, and the energy associated with a shift in the structural equilibrium of water. The data that point to such a model include: molecular orbital-molecular dynamics applied to electrolyte water systems; Raman spectra; infrared spectra; magnetic resonance spectra of ions; the apparent density of water; and the excess free energy of electrolytes in aqueous solutions. Molecular orbital-molecular dynamics calculations of relatively large water clusters containing a molecule of sodium iodide show that the solvent separated ion pair exists in a substantial potential well compared to other possible structures. Raman spectra of univalent electrolyte solutions as a function of concentration can be quantitatively modeled using only the spectra of pure water and electrolyte solution at the concentration of the solvent separated ion pair. The other observations are consistent with the structures proposed from the Raman spectral study. The new model provides a satisfactory account of the fact that the excess free energy of dilute (<0.2 mol/l) solutions is generally more negative than anticipated on the basis of Debye-Hückel theory, and that the equilibrium evidence points to the same functional behavior at very low concentrations as is seen at 0.05 mol/l. We present a testable hypothesis that the excess free energy, and other thermodynamic properties of the solutions do not follow the Debye-Hückel limiting law. The tests of this hypothesis must involve only equilibrium measurements at concentrations between 0.05 and 0.0005 mol/l. This hypothesis concerning the structure of aqueous electrolyte solutions is not in conflict in any way with the Debye-Hückel-Onsager theory of electrical conductivity.     

Electrostatic steering at acetylcholine binding sites

The electrostatic environments near the acetylcholine binding sites on the nicotinic acetylcholine receptor (nAChR) and acetylcholinesterase were measured by diffusion-enhanced fluorescence energy transfer (DEFET) to determine the influence of long-range electrostatic interactions on ligand binding kinetics and net binding energy. Changes in DEFET from variously charged Tb3+ -chelates revealed net potentials of -20 mV at the nAChR agonist sites and -14 mV at the entrance to the AChE active site, in physiological ionic strength conditions. The potential at the alphadelta-binding site of the nAChR was determined independently in the presence of d-tubocurarine to be -14 mV; the calculated potential at the alphagamma-site was approximately threefold stronger than at the alphadelta-site. By determining the local potential in increasing ionic strength, Debye-Hückel theory predicted that the potentials near the nAChR agonist binding sites are constituted by one to three charges in close proximity to the binding site. Examination of the binding kinetics of the fluorescent acetylcholine analog dansyl-C6-choline at ionic strengths from 12.5 to 400 mM revealed a twofold decrease in association rate. Debye-Hückel analysis of the kinetics revealed a similar charge distribution as seen by changes in the potentials. To determine whether the experimentally determined potentials are reflected by continuum electrostatics calculations, solutions to the nonlinear Poisson-Boltzmann equation were used to compute the potentials expected from DEFET measurements from high-resolution models of the nAChR and AChE. These calculations are in good agreement with the DEFET measurements for AChE and for the alphagamma-site of the nAChR. We conclude that long-range electrostatic interactions contribute -0.3 and -1 kcal/mol to the binding energy at the nAChR alphadelta- and alphagamma-sites due to an increase in association rates.     

On the theory of action potential propagation in plant cells

The distribution of an electric field in plant cells and zooblasts has been investigated during propagation of the action potential. The behavior of ions in the cytoplasm and in the extracellular fluid has been described with the equations of electric charge motion in electrolytes. It has been shown that the action potential causes an electric potential change not only in the depth of the cytoplasm but also in the extracellular area far from the lipid bilayer. The biomembrane resistance has been expressed by physical parameters of a cell, such as ionic diffusion coefficient in fluid, Debye-Hückel radius, dielectric constant etc. The presence of breaks in the action potential diagrams has been explained as a result of insufficient resolving power of the measuring devices at the instant the sodium ion channels of the bilayer open.     

Electrostatic dependence of the thrombin-thrombomodulin interaction

The rate constants for the binding interaction between thrombin and a fully active fragment of its anticoagulant cofactor, thrombomodulin, have been determined by surface plasmon resonance. At physiological ionic strength, the k(a) was 6.7x10(6) M(-1) s(-1 )and the dissociation rate constant was 0.033 s(-1). These extremely fast association and dissociation rates resulted in an overall binding equilibrium constant of 4.9 nM, which is similar to previously reported values. Changing the ionic strength from 100 mM to 250 mM NaCl caused a tenfold decrease in the association rate while the dissociation rate did not change significantly. A similar effect was observed with tetramethylammonium chloride. A Debye-Hückel plot of the data had a slope of -6 and an intercept at 0 ionic strength of 10(9) M(-1) s(-1). The same slope and intercept were obtained for data that was collected in the presence of glycerol to slow the association rates. These results show that the thrombin-TM456 interaction is extremely rapid and nearly completely electrostatically steered. An association model is presented in which TM456 approaches thrombin along the direction of the thrombin molecular dipole.     

Cytochrome b2, an electron carrier between flavocytochrome b2 and cytochrome c. Rapid kinetic characterization of the electron-transfer parameters with ionic-strength-dependence.

The oxidation-reduction properties of free cytochrome b2 isolated by controlled proteolysis from flavocytochrome b2, i.e. the flavodehydrogenase-bound cytochrome b2, were investigated by using stopped-flow spectrophotometry. The rapid kinetics of the reduction of cytochrome b2 by flavocytochrome b2 in the presence of L-lactate are reported. The self-exchange rate constant between reduced cytochrome b2 bound to the flavodehydrogenase and free cytochrome b2 was determined to be 10(5) M-1 X S-1 at 5 degrees C, I 0.2 and pH 7.0. The specific electron-transfer reaction between reduced cytochrome b2 and cytochrome c was also studied, giving an apparent second-order rate constant of 10(7) M-1 X S-1 at 5 degrees C, I 0.2 and pH 7.0. This electron-exchange rate is slightly modulated by ionic strength, following the Debye-Hückel relationship with a charge factor Z1Z2 = -1.9. Comparison of these data with those for the reduction of cytochrome c by flavodehydrogenase-bound cytochrome b2 [Capeillère-Blandin (1982) Eur. J. Biochem. 128, 533-542] leads to the conclusion that the intramolecular electron exchange between haem b2 and haem c within the reaction complex occurs at a rate very similar to that determined experimentally in presence of the flavodehydrogenase domain. The low reaction rate observed with free cytochrome b2 is ascribed to the low stability of the reaction complex formed between free cytochrome b2 and cytochrome c.     

Polyelectrolyte hysteresis interpreted as singularities in the Poisson--Boltzmann description.

Certain hysteresis-like activities in polyelectrolyte behavior are demonstrated to be explainable as due to singularities in the Harris-Rice solution of the Poi sson-Boltzmann equation for the polyelectrolyte subcompartment of the polyelectrolyte-solution system. On the other hand, other activities, e.g. osmotic effects and ion exchanges, are a function of the total system and explainable by Manning's and Oosawa's theories. It is suggested that the occurrence of hysteresis-like activities indicates the validity of the Debye-Hückel approximation, at least for that particular occurrence.     

Effect of Ion Streaming on Diffusion of Dust Grains in Dissipative System

The presence of strong electric fields in the sheath region of laboratory complex plasma induces an ion drift and perturbs the field around dust grains. The downstream focusing of ions leads to the formation of oscillatory kind of attractive wake potential which superimpose with the normal Debye-Hückel (DH) potential. The structural properties of complex plasma and diffusion coefficient of dust grains in the presence of such a wake potential have been investigated using Langevin dynamics simulation in the subsonic regime of ion flow. The study reveals that the diffusion of dust grains is strongly affected by the ion flow, so that the diffusion changes its character in the wake potential to the DH potential dominant regimes. The dependence of the diffusion coefficient on the parameters, such as the neutral pressure, dust grain size, ion flow velocity, and Coulomb coupling parameter, have been calculated for the subsonic regime by using the Green-Kubo expression, which is based on the integrated velocity autocorrelation function. It is found that the diffusion and the structural property of the system is intimately connected with the interaction potential and significantly get affected in the presence of ion flow in the subsonic regime.     

Donnan potential and surface potential of a charged membrane.

A model is presented for the electrical potential distribution across a charged biological membrane that is in equilibrium with an electrolyte solution. We assume that a membrane has charged surface layers of thickness d on both surfaces of the membrane, where the fixed charges are distributed at a uniform density N within the layers, and that these charged layers are permeable to electrolyte ions. This model unites two different concepts, that is, the Donnan potential and the surface potential (or the Gouy-Chapman double-layer potential). Namely, the present model leads to the Donnan potential when d much greater than 1/k' (k' is the Debye-Hückel parameter of the surface charge layer) and to the surface potential as d----0, keeping the product Nd constant. The potential distribution depends significantly on the thickness d of the surface charge layer when d less than or approximately equal to 1/k'.     

COVOL: an interactive program for evaluating second virial coefficients from the triaxial shape or dimensions of rigid macromolecules

An interactive program is described for calculating the second virial coefficient contribution to the thermodynamic nonideality of solutions of rigid macromolecules based on their triaxial dimensions. The FORTRAN-77 program, available in precompiled form for the PC, is based on theory for the covolume of triaxial ellipsoid particles [Rallison, J. M., and S.E Harding. (1985). J. Colloid Interface Sci. 103:284-289]. This covolume has the potential to provide a magnitude for the second virial coefficient of macromolecules bearing no net charge. Allowance for a charge-charge contribution is made via an expression based on Debye-Hückel theory and uniform distribution of the net charge over the surface of a sphere with dimensions governed by the Stokes radius of the macromolecule. Ovalbumin, ribonuclease A, and hemoglobin are used as model systems to illustrate application of the COVOL routine.     

Nicotinic acetylcholine receptor channel electrostatics determined by diffusion-enhanced luminescence energy transfer

The electrostatic potentials within the pore of the nicotinic acetylcholine receptor (nAChR) were determined using lanthanide-based diffusion-enhanced fluorescence energy transfer experiments. Freely diffusing Tb3+ -chelates of varying charge constituted a set of energy transfer donors to the acceptor, crystal violet, a noncompetitive antagonist of the nAChR. Energy transfer from a neutral Tb3+ -chelate to nAChR-bound crystal violet was reduced 95% relative to the energy transfer to free crystal violet. This result indicated that crystal violet was strongly shielded from solvent when bound to the nAChR. Comparison of energy transfer from positively and negatively charged chelates indicate negative electrostatic potentials of -25 mV in the channel, measured in low ionic strength, and -10 mV measured in physiological ionic strength. Debye-Hückel analyses of potentials determined at various ionic strengths were consistent with 1-2 negative charges within 8 A of the crystal violet binding site. To complement the energy transfer experiments, the influence of pH and ionic strength on the binding of [3H]phencyclidine were determined. The ionic strength dependence of binding affinity was consistent with -3.3 charges within 8 A of the binding site, according to Debye-Hückel analysis. The pH dependence of binding had an apparent pKa of 7.2, a value indicative of a potential near -170 mV if the titratable residues are constituted of aspartates and glutamates. It is concluded that long-range potentials are small and likely contribute little to selectivity or conductance whereas close interactions are more likely to contribute to electrostatic stabilization of ions and binding of noncompetitive antagonists within the channel.     

Electrostatic interactions of fluorescein dyes with proteins

The interactions of a number of halogen derivatives of fluorescein with human carbonylhaemoglobin and human serum albumin have been studied. The binding affinities of these proteins were compared with the charge properties of the dyes. The charge properties, determined from titration curves. Hückel molecular orbital (HMO) calculations and the equilibria established between polar and non-polar phase testify to an important role of dipole moments of the halogen derivatives in their interactions with proteins.     

Quantitative analysis of the binding of melittin to planar lipid bilayers allowing for the discrete-charge effect

The interaction of melittin with lecithin bilayers was studied using the resulting surface potentials at the bilayer/water interfaces to monitor the association. Melittin added to the aqueous phase binds strongly to the interface but remains localized on that side of the bilayer to which it is added. The analysis of the binding curves reveals the inadequacy of the Gouy-Chapman theory for the fixed-charge surface potential in describing the electrostatic potential experienced by the adsorbed molecules. Calculations based on the Stern equation, modified for a discrete charge distribution, give a good fit to the experimental data. The thermodynamic analysis revealed different binding energies, Δ$\text{G}$°, at 10 and 100 mM ionic strength (?7.85 and ?8.26 kcal/mol, respectively). Binding saturates at an area of 650 Ų per melittin molecule. A change in the surface dipole potential corresponding to ?1.1 debye/?_a ($\text{?}{}_{\mathrm{a}}\text{= dielectric constant of the adsorption region}$) had to be postulated. The Debye-Hückel length for a charge bound to the membrane/solution interface was found to be about one-third smaller than in bulk solution.     

Membrane potential and Donnan potential

The Nernst-Planck-Poisson equations for the potential profile across a membrane are exactly solved without recourse to the assumption of constant field within the membrane. It is assumed that the membrane core of thickness dc is covered by a surface layer of thickness ds in which the membrane-fixed charges are distributed at a uniform density N. The membrane boundary potentials as well as the diffusion potentials contribute to the membrane potential. It is shown that for ds greater or similar 1/k, k being the Debye-Hückel parameter, the potential in the membrane surface layer except in the region very near the membrane/solution boundary is effectively equal to the Donnan potential and that its contribution to the membrane potential becomes dominant as N increases. For low N, on the other hand, the membrane potential arises mostly from the diffusion potential.     

A physical model of nerve axon—I. Ionic distribution,potential profile,and resting potential

A theory which is based on a set of assumptions different from those of the sodium theory is developed. Here the mobile ions are considered to be distributed at Donnan equilibrium and the axoplasm is regarded as an analog of a cation-exchanger. Following the spirit of the Debye-Hückel theory, some important features of the ionic distribution and electrical potential of the nerve fiber have been calculated. The results appear to be in better agreement with the experimental observations than the Goldman-Hodgkin-Katz equation. A summary of this work has been reported in the 1974 March meeting of the American Physical Society and the 1976 annual meeting of the Biophysical Society.