Electric potential distributions around discrete charges in a dielectric membrane—electrolyte solution system

Within the framework of the linearized Debye-Hückel theory an exact solution of the problem of calculating the electric potential caused by discrete fixed charges located at arbitrary positions with respect to a dielectric membrane-solution interface is presented. It takes into account the existence of an electrolyte solution on both sides of the membrane. Asymmetric ionic conditions are allowed for. For some interesting typical cases of fixed charge locations and electrolyte ionic strengths electric potential distributions were calculated and discussed. It is shown that, if the fixed charges were at or in front of the membrane surface, the characteristic distance of the electric potential decay was comparable to the Debye-Hückel length. At the opposite membrane surface only very small electric potentials can be observed. If, however, the fixed charge was placed below the membrane surface the electric potential in lateral direction and towards the other membrane surface largely increased. This effect was very sensitive to the position of the fixed charge with respect to the membrane surface.     

Influence of cation binding on the electro-optically determined electric moments of purple membranes

Analysis of the elect ro-optically determined permanent dipole moment and electric polarizability of purple membrane fragments reveals the complex nature of the membrane electric moments.The problem to distinguish between the contribution of the membrane structural charges (charged groups of the polypeptide chain and polar lipid headarouos), bound cations and the electric double layer structure deserves particular attention not only because of its importance for electro-optics but also in respect to the relation of the membrane surface electric properties to the membarans transport function.The removal of divalent cations (Ca²⁺ and Mg²⁺) bound to purple membrane in the native state induces a cat ion-free species or purple membrane (deionized - blue membrane) with drastically changed spectroscopic properties and function. The preseent paper summarizes our study on the electric moments of blue membrane and their changes during the blue to purple transition. We intended to provide an insight into the possible regulation of this reversible transition (purple-to-blue and blue-to-purple) through changes of the asymmetric charge distribution and the importance of the asymmetric interfacial charge distribution for the proton transfer in purple membranes.The changes in the electric moments (permanent and induced dipole moments) of purple membrane fragments upon di- and trivalent cations binding to cation-depleted purple membranes were studied by electric light scattering (rotational electrokinetics) in d.c. and a.c. electric fields, and by electric pulses with reversing polarity, the results show a recovery of the membrane charge asymmetry (permanent dipole moment) though not of the induced dipole moment.     

Effects of electric fields on proton transport through water chains

Molecular dynamics simulations on quantum energy surfaces are carried out to study the effects of perturbing electric fields on proton transport (PT) in protonated water chains. As an idealized model of a hydrophobic cavity in the interior of a protein the water molecules are confined into a carbon nanotube (CNT). The water chain connects a hydrated hydronium ion (H3O+) at one end of the CNT and an imidazole molecule at the other end. Without perturbing electric fields PT from the hydronium proton donor to the imidazole acceptor occurs on a picosecond time scale. External perturbations to PT are created by electric fields of varying intensities, normal to the CNT axis, generated by a neutral pair of charges on the nanotube wall. For fields above approximately 0.5 VA, the hydronium ion is effectively trapped at the CNT center, and PT blocked. Fields of comparable strength are generated inside proteins by nearby polar/charged amino acids. At lower fields the system displays a rich dynamic behavior, where the excess charge shuttles back and forth along the water chain before reaching the acceptor group on the picosecond time scale. The effects of the perturbing field on the proton movement are analyzed in terms of structural and dynamic properties of the water chain. The implications of these observations on PT in biomolecular systems and its control by external perturbing fields are discussed.     

861 — Charge motion inside the bacteriorhodopsin molecule

The bacteriorhodopsin molecules in Halobacteria membranes pump protons after light absorption. During this action light energy is transduced into electrochemical energy. The importance of proton pumping in bioenergetics, prompted us to work out three different macroscopically oriented systems of bacteriorhodopsin molecules to study the molecular events of charge motion inside the molecules. The flash-excited absorption changes and electric signals were measured simultaneously. It has been established that the time constants of the absorption and electric signals (evoked as displacement currents of moving charges) are the same in the pH range of 4–8; the analysis of amplitudes of electric signals gives the distances of charge motion inside the protein; the first step of charge motion is faster than 30 ps; proton translocation needs water molecules to be present; the stoichiometry does not change with pH until pH 10.5; tyrosin modification blocks the pumping activity but modest protein digestion does not influence it in the pH range of 4–10.     

Discrete charge effects on the Donnan potential and surface potential of a soft particle

The Donnan potential and surface potential of soft particles (i.e., polyelectrolyte-coated hard particles) in an electrolyte solution play an essential role in their electric behaviors. These potentials are usually derived via a continuum model in which fixed charges inside the surface layer are distributed with a continuous charge density. In this paper, for a plate-like soft particle consisting of a cubic lattice of fixed point charges, on the basis of the linearized Poisson–Boltzmann equation, we derive expressions for the electric potential distribution in the regions inside and outside the surface layer. This expression is given in terms of a sum of the screened Coulomb potentials produced by the point charges within the surface layer. We show that the deviation of the results of the discrete charge model from those of the continuous charge model becomes significant as the ratio of the lattice spacing to the Debye length becomes large.     

Towards a quantum chemical software package utilizing transferable fragments as molecular building blocks

Computer programs have been developed or are under development for the IBM personal computer that enable their users to get information on atomic charges, electrostatic potentials, conformational and other properties of molecular systems containing H, C, N, O, F, Si, P, S, or Cl atoms. The zero-order wavefunction is constructed of strictly localized molecular orbitals with fixed atomic orbital coefficients. The wave function can be refined by optimizing these coefficients, i.e., considering inductive effects via a coupled set of 2 × 2 secular equations within the CNDO /2 approximation. Delocalization and exchange effects are accounted for by expanding the wavefunction on a basis of the aforementioned strictly localized orbitals, instead of conventional atomic orbitals, and solving the corresponding SCF equations. Our method has been applied to the study of large systems. We calculated the electrostatic field of the complex of β-trypsin and basic pancreatic trypsin inhibitor and it has been found that strong field regions more or less coincide with hydration sites. A further potential application of protein electrostatic fields is in NMR spectroscopy. We found a linear correlation between C^αH or backbone NH proton chemical shifts and the protein field at the site of the corresponding proton. At last, we propose a simple method to mimic the bulk around atomic clusters modeling crystalline and amorphous silicon. Based on this method we found a linear correlation between atomic net charges and bond angle distortions in silicon clusters with 35 atoms.     

On the nature of liquid junction and membrane potentials

Whenever a spatially inhomogeneous electrolyte, composed of ions with different mobilities, is allowed to diffuse, charge separation and an electric potential difference is created. Such potential differences across very thin membranes (e.g. biomembranes) are often interpreted using the steady state Goldman equation, which is usually derived by assuming a spatially constant electric field. Through the fundamental Poisson equation of electrostatics, this implies the absence of free charge density that must provide the source of any such field. A similarly paradoxical situation is encountered for thick membranes (e.g. in ion-selective electrodes) for which the diffusion potential is normally interpreted using the Henderson equation. Standard derivations of the Henderson equation appeal to local electroneutrality, which is also incompatible with sources of electric fields, as these require separated charges. We analyse self-consistent solutions of the Nernst-Planck-Poisson equations for a 1 : 1-univalent electrolyte to show that the Goldman and Henderson steady-state membrane potentials are artefacts of extraneous charges created in the reservoirs of electrolyte solution on either side of the membrane, due to the unphysical nature of the usual (Dirichlet) boundary conditions assumed to apply at the membrane-electrolyte interfaces. We also show, with the aid of numerical simulations, that a transient electric potential difference develops in any confined, but initially non-uniform, electrolyte solution. This potential difference ultimately decays to zero in the real steady state of the electrolyte, which corresponds to thermodynamic equilibrium. We explain the surprising fact that such transient potential differences are well described by the Henderson equation by using a computer algebra system to extend previous steady-state singular perturbation theories to the time-dependent case. Our work therefore accounts for the success of the Henderson equation in analysing experimental liquid-junction potentials.     

Electrostatic interaction between ion-penetrable membranes in a salt-free medium

A set of coupled equations is given which determines the distributions of the electric potential and counterions in a system of two interacting identical ion-penetrable membranes of thickness d at separation h immersed in a salt-free medium containing only counterions. The solution to these coupled equations also gives the electrostatic repulsive force between the membranes. It is shown that the interaction force remains finite at h-->0, unlike the case of the interaction between two planar charged surfaces (d-->0), and that the interaction force becomes independent of the membrane fixed charge and membrane thickness d at very large h. Finally, an approximate single transcendental equation giving the solution to the coupled equations is derived.     

Electrostatic properties and macroscopic electrodiffusion in OmpF porin and mutants

The bacterial porin OmpF found in the outer membrane of E. coli is a wide channel, characterized by its poor selectivity and almost no ion specificity. It has an asymmetric structure, with relatively large entrances and a narrow constriction. By applying continuum electrostatic methods we determine the ionization states of titratable amino acid residues in the protein and calculate self-consistently the electric potential 3-D distribution within the channel. The average electrostatic properties are then represented by an effective fixed charge distribution along the pore which is the input for a macroscopic electrodiffusion model. The theoretical predictions agree with measurements performed under different salt gradients and pH. The sensitivity of reversal potential and conductance to the direction of the salt gradient and the solution pH is captured by the model. The theory is also able to explain the influence of the lipid membrane charge. The same methodology is satisfactorily applied to some OmpF mutants involving slight structural changes but a large number of net charges. The correlation found between atomic structure and ionic selectivity shows that the transport characteristics of wide channels like OmpF and its mutants are mainly regulated by the collective action of a large number of residues, rather than by the specific interactions of residues at particular locations.     

Donnan equilibrium of ionic drugs in pH-dependent fixed charge membranes: theoretical modeling

We have studied theoretically the partition equilibrium of a cationic drug between an electrolyte solution and a membrane with pH-dependent fixed charges using an extended Donnan formalism. The aqueous solution within the fixed charge membrane is assumed to be in equilibrium with an external aqueous solution containing six ionic species: the cationic drug (DH(+)), the salt cations (Na(+) and Ca(2+)), the salt anion (Cl(-)), and the hydrogen and hydroxide ions. In addition to these mobile species, the membrane solution may also contain four fixed species attached to the membrane chains: strongly acid sulfonic groups (SO(3)(-)), weakly acid carboxylic groups in dissociated (COO(-)) and neutral (COOH) forms, and positively charged groups (COO...Ca(+)) resulting from Ca(2+) binding to dissociated weakly acid groups. The ionization state of the weak electrolyte groups attached to the membrane chains is analyzed as a function of the local pH, salt concentration, and drug concentration in the membrane solution, and particular attention is paid to the effects of the Ca(2+) binding to the negatively charged membrane fixed groups. The lipophilicity of the drug is simulated by the chemical partition coefficient between the membrane and external solutions giving the tendency of the drug to enter the membrane solution due to hydrophobic interactions. Comparison of the theoretical results with available experimental data allows us to explain qualitatively the effects that the pH, salt concentration, drug concentration, membrane fixed charge concentration, and Ca(2+) binding exert on the ionic drug equilibrium. The role of the interfacial (Donnan) electric potential difference between the membrane and the external solutions on this ionic drug equilibrium is emphasized throughout the paper.     

Suspended particles surrounded by an inhomogeneously charged permeable membrane. Solution of the Poisson-Boltzmann equation by means of the network method

The Poisson-Boltzmann equation is numerically solved for a suspended spherical particle surrounded by a permeable membrane that contains an inhomogeneous distribution of fixed charges. The calculations are carried out using the network simulation method, which makes it possible to solve the problem in the most general case, extending previous results (J.P. Hsu, Y.C. Kuo, J. Membrane Sci. 108 (1995) 107). Approximate analytical expressions for the counterion concentration and the electric potential in the membrane are also presented, together with criteria that determine their ranges of validity. The limiting case of a distribution of fixed charges in the membrane that reduces to a surface charge is also analyzed. It is shown that the solution for this case, considering a vanishingly small radius of the core, reduces to a superposition of solutions corresponding to a charged impermeable particle suspended in an electrolyte solution and to a cavity filled with a charged electrolyte solution.     

Further studies on the origins of asymmetric charge partitioning in protein homodimers

Dissociation of gas-phase protonated protein dimers into their constituent monomers can result in either symmetric or asymmetric charge partitioning. Dissociation of alpha-lactalbumin homodimers with 15+ charges results in a symmetric, but broad, distribution of protein monomers with charge states centered around 8+/7+. In contrast, dissociation of the 15+ heterodimer consisting of one molecule in the oxidized form and one in the reduced form results in highly asymmetric charge partitioning in which the reduced species carries away predominantly 11+ charges, and the oxidized molecule carries away 4+ charges. This result cannot be adequately explained by differential charging occurring either in solution or in the electrospray process, but appears to be best explained by the reduced species unfolding upon activation in the gas phase with subsequent separation and proton transfer to the unfolding species in the dissociation complex to minimize Coulomb repulsion. For dimers of cytochrome c formed directly from solution, the 17+ charge state undergoes symmetric charge partitioning whereas dissociation of the 13+ is asymmetric. Reduction of the charge state of dimers with 17+ charges to 13+ via gas-phase proton transfer and subsequent dissociation of the mass selected 13+ ions results in a symmetric charge partitioning. This result clearly shows that the structure of the dimer ions with 13+ charges depends on the method of ion formation and that the structural difference is responsible for the symmetric versus asymmetric charge partitioning observed. This indicates that the asymmetry observed when these ions are formed directly from solution must come about due either to differences in the monomer conformations in the dimer that exist in solution or that occur during the electrospray ionization process. These results provide additional evidence for the origin of charge asymmetry that occurs in the dissociation of multiply charged protein complexes and indicate that some solution-phase information can be obtained from these gas-phase dissociation experiments.     

Properties of atoms in molecules

The electronic charges and the positions of the centers of these charges have been calculated for the atoms of a number of second- and third-row heteronuclear diatomic molecules. For both the oxygen and the fluorine atoms, the charge associated with one of these atoms can be correlated, within a series of molecules containing that atom, with both the orbital energy of the atom's 1s electrons and also with the difference in electronegativities of the atoms that comprise the molecule. The centers of electronic charge are outside of the internuclear regions, except for the positive atoms in the more ionic molecules and in HF.     

Decharging of globular proteins and protein complexes in electrospray

Electrospray ionization mass spectrometry (ESI-MS) is a valuable tool in structural biology for investigating globular proteins and their biomolecular interactions. During the electrospray ionization process, proteins become desolvated and multiply charged, which may influence their structure. Reducing the net charge obtained during the electrospray process may be relevant for studying globular proteins. In this report we demonstrate the effect of a series of inorganic and organic gas-phase bases on the number of charges that proteins and protein complexes attain. Solution additives with very strong gas-phase basicities (GB) were identified among the so-called "proton sponges". The gas-phase proton affinities (PA) of the compounds that were added to the aqueous protein solutions ranged from 700 to 1050 kJ mol(-1). Circular dichroism studies showed that in these solutions the proteins retain their globular structures. The size of the proteins investigated ranged from the 14.3 kDa lysozyme up to the 800 kDa tetradecameric chaperone complex GroEL. Decharging of the proteins in the electrospray process by up to 60 % could be achieved by adding the most basic compounds rather than the more commonly used ammonium acetate additive. This decharging process probably results from proton competition events between the multiply protonated protein ions and the basic additives just prior to the final desolvation. We hypothesize that such globular protein species, which attain relatively few charges during the ionization event, obtain a gas-phase structure that more closely resembles their solution-phase structure. Thus, these basic additives can be useful in the study of the biologically relevant properties of globular proteins by using mass spectrometry.     

The influence of electrostatic forces on the structure and dynamics of molecular ionic liquids

The vast majority of molecular dynamics simulations are based on nonpolarizable force fields with fixed partial charges for all atoms. The traditional way to obtain these charges are quantum-mechanical calculations performed prior to simulation. Unfortunately, the set of the partial charges heavily relies on the method and the basis set used. Therefore, investigations of the influence of charge variation on simulation data are necessary in order to validate various charge sets. This paper elucidates the consequences of different charge sets on the structure and dynamics of the ionic liquid: 1-ethyl-3-methyl-imidazolium dicyanoamide. The structural features seem to be more or less independent of the partial charge set pointing to a dominance of shape force as modeled by Lennard-Jones parameters. This can be seen in the radial distribution and orientational correlation functions. The role of electrostatic forces comes in when studying dynamical properties. Here, significant deviations between different charge sets can be observed. Overall, dynamics seems to be governed by viscosity. In fact, all dynamical parameters presented in this work can be converted from one charge set to another by viscosity scaling.     

Estimates of the intramembrane field through the harmonics of capacitive current in inhomogeneous bilayer lipid membranes

Intramembrane field gives information about localisation of fixed charges or dipoles inside the lipid bilayer. There is systematic discrepancy between field estimates made by various methods. The possible reason of this discrepancy can be attributed to the misinterpretation of the data in the frames of the methods used. It stands for the method that is based on the compensation of the 2nd harmonic of capacitive current generated due to electrostriction phenomenon if sine voltage is applied to the bilayer. The theoretical grounds of the method mentioned are oversimplified because membrane heterogeneity has not been taken into consideration. The purpose of the work is the analysis of the generation of harmonics of capacitive current in inhomogeneous bilayer if intramembrane charges are located at different depth. The results of the study enable one to determine the position of intramembrane charges. The theoretical methods are used. The bilayer electrostriction induced by the electric field in the presence of intramembrane charges is computed. The intramembrane field depends upon localisation of the charges inside the bilayer like a sine curve; it goes to zero if the charges are located in the centre of the membrane. The charge discreteness affects the value of the compensation voltage due to nonlinearity of the bilayer deformations close to the charge. The probable appendices of outcomes are discussed for problems of intramembrane dye localisation and ion transport in the channel of sodium/potassium ATPase.     

A generalization of the charge equilibration method for nonmetallic materials

Assigning effective atomic charges that properly reproduce the electrostatic fields of molecules is a crucial step in the construction of accurate interatomic potentials. We propose a new approach to calculate these charges, which as previous approaches are, is based on the idea of charge equilibration. However, we only allow charge to flow between covalently bonded neighbors by using the concept of so-called split charges. The semiempirical fit parameters in our approach do not only reflect atomic properties (electronegativity and atomic hardness) but also bond-dependent properties. The new method contains two popular but hitherto disjunct approaches as limiting cases. We apply our methodology to a set of molecules containing the elements silicon, carbon, oxygen, and hydrogen. Effective charges derived from electrostatic potential surfaces can be predicted more than twice as accurately as with previous works, at the expense of one additional fit parameter per bond type controlling the polarizability between two bonded atoms. Additional bond-type parameters can be introduced, but barely improve the results. An increase in accuracy of only 30% over existing techniques is achieved when predicting Mulliken charges. However, this could be improved with additional bond-type parameters.     

Charge carrier field emission determines the number of charges on native state proteins in electrospray ionization

Although multiple charging in electrospray ionization (ESI) is essential to protein mass spectrometry, the underlying mechanism of multiple charging has not been explicated. Here, we present a new theory to describe ESI of native-state proteins and predict the number of excess charges on proteins in ESI. The theory proposes that proteins are ionized as charged residues in ESI, as they retain residual excess charges after solvent evaporation and do not desorb from charged ESI droplets. However, their charge state is not determined by the Rayleigh limit of a droplet of similar size to the protein; rather, their final charge state is determined by the electric field-induced emission of small charged solute ions and clusters from protein-containing ESI droplets. This theory predicts that the number of charges on a protein in ESI should be directly proportional to the square of the gas-phase protein diameter and to E*, the critical electric field strength at which ion emission from droplets occurs. This critical field strength is determined by the properties of the excess charge carriers (i.e., the solute) in droplets. Charge-state measurements of native-state proteins with molecular masses in the 5-76 kDa range in ammonium acetate and triethylammonium bicarbonate are in excellent agreement with theoretical predictions and strongly support the mechanism of protein ESI proposed here.