Retention of small charged impurities during ultrafiltration

Ultrafiltration is used to remove small impurities from a variety of processing streams. However, the clearance of small charged impurities may be inadequate due to electrostatic exclusion by the charged ultrafiltration membranes, an effect that has been largely unappreciated. Ultrafiltration experiments were performed to evaluate the transmission of several model impurities with different electrical charge through ultrafiltration membranes having different surface charge characteristics. Highly charged impurities are strongly rejected by charged cellulose and polyethersulfone membranes even though these solutes are much smaller than the membrane pore size. These effects could be eliminated by using high ionic strength solutions to shield the electrostatic interactions. The sieving data are in good agreement with model calculations based on the partitioning of charged spheres into charged cylindrical pores. Guidelines are developed for estimating conditions needed to obtain effective removal of small charged impurities through charged ultrafiltration membranes.     

Electron transfer between flavodoxin semiquinone and c-type cytochromes: correlations between electrostatically corrected rate constants, redox potentials, and surface topologies

We have measured the ionic strength dependence of the rate constants for electron transfer from the semiquinone of Clostridium pasteurianum flavodoxin to 12 c-type cytochromes and several inorganic oxidants using stopped-flow methodology. The experimental data were fit quite well by an electrostatic model that represents the interaction domains as parallel disks with a point charge equal to the charge within this region of the protein. The analysis provides an evaluation of the electrostatic interaction energy and the rate constant at infinite ionic strength (k affinity). The electrostatic charge on the oxidant within the interaction site can be obtained from the electrostatic energy, and for most of those reactants for which structures are available, the results are in good agreement with expectation. The k affinity values were found to correlate with redox potential differences, as expected from the theory of adiabatic (or nonadiabatic) outer-sphere electron-transfer reactions. Deviations from the theoretical curves are interpreted in terms of the influence of surface topology on reaction rate constants. In general, we find that electrostatic effects, steric influences, and redox potential all exert a much larger effect on reaction rate constants for the flavodoxin-cytochrome system than has been previously observed for free flavin-cytochrome interactions. The implications of this for determining biological specificity are discussed.     

The sliding-helix voltage sensor: mesoscale views of a robust structure–function relationship

The voltage sensor (VS) domain of voltage-gated ion channels underlies the electrical excitability of living cells. We simulate a mesoscale model of the VS domain to determine the functional consequences of some of its physical elements. Our mesoscale model is based on VS charges, linear dielectrics, and whole-body motion, applied to an S4 "sliding helix." The electrostatics under voltage-clamped boundary conditions are solved consistently using a boundary-element method. Based on electrostatic configurational energy, statistical-mechanical expectations of the experimentally observable relation between displaced charge and membrane voltage are predicted. Consequences of the model are investigated for variations of S4 configuration (α- and 3(10)-helical), countercharge alignment with S4 charges, protein polarizability, geometry of the gating canal, screening of S4 charges by the baths, and fixed charges located at the bath interfaces. The sliding-helix VS domain has an inherent electrostatic stability in the explored parameter space: countercharges present in the region of weak dielectric always retain an equivalent S4 charge in that region but allow sliding movements displacing 3-4 e (0). That movement is sensitive to small energy variations (<2?kT) along the path dependent on a number of electrostatic parameters tested in our simulations. These simulations show how the slope of the relation between displaced charge and voltage could be tuned in a channel.     

Development of an in vitro model of primate cervical goblet cells

Mucins, are densely packed in secretory granules of goblet cells. Upon exocytosis they undergo massive hydration that results in the formation of the mucus gel. Because the mucin polymer network is held together by tangles and low energy bonds, the rheological properties of this gel are mainly determined by the degree of postexocytotic hydration. Hydration in mucus is governed by a Donnan equilibrium as it is driven by electrostatic interaction among the polyionic charges of the mucins and other fixed polyions. Although, variations of charge density of the mucin polymer could be an efficient physiologic mechanism to control the rate of mucus hydration and rheology, this subject has not been investigated. In here we describe a primary tissue culture system of cervical goblet cells of the monkey uterus. This preparation allows to measure directly the kinetic of hydration of exocytosed mucins. Because the physicochemical parameters of the bathing medium can be effectively controlled, variations in the kinetic of mucins swelling upon exocytosis, can be used as a convenient indicator of fluctuations of charge density in secretory products. Since the cervical mucosa readily respond to endocrine influences, this preparation can provide a useful model to study the effect of hormones or other transmitters on polyionic charge density of secretory product.     

Energetics and self-assembly of amphipathic peptide pores in lipid membranes

We present a theoretical study of the energetics, equilibrium size, and size distribution of membrane pores composed of electrically charged amphipathic peptides. The peptides are modeled as cylinders (mimicking alpha-helices) carrying different amounts of charge, with the charge being uniformly distributed over a hydrophilic face, defined by the angle subtended by polar amino acid residues. The free energy of a pore of a given radius, R, and a given number of peptides, s, is expressed as a sum of the peptides' electrostatic charging energy (calculated using Poisson-Boltzmann theory), and the lipid-perturbation energy associated with the formation of a membrane rim (which we model as being semitoroidal) in the gap between neighboring peptides. A simple phenomenological model is used to calculate the membrane perturbation energy. The balance between the opposing forces (namely, the radial free energy derivatives) associated with the electrostatic free energy that favors large R, and the membrane perturbation term that favors small R, dictates the equilibrium properties of the pore. Systematic calculations are reported for circular pores composed of various numbers of peptides, carrying different amounts of charge (1-6 elementary, positive charges) and characterized by different polar angles. We find that the optimal R's, for all (except, possibly, very weakly) charged peptides conform to the "toroidal" pore model, whereby a membrane rim larger than approximately 1 nm intervenes between neighboring peptides. Only weakly charged peptides are likely to form "barrel-stave" pores where the peptides essentially touch one another. Treating pore formation as a two-dimensional self-assembly phenomenon, a simple statistical thermodynamic model is formulated and used to calculate pore size distributions. We find that the average pore size and size polydispersity increase with peptide charge and with the amphipathic polar angle. We also argue that the transition of peptides from the adsorbed to the inserted (membrane pore) state is cooperative and thus occurs rather abruptly upon a change in ambient conditions.     

Investigating protein-protein interaction surfaces using a reduced stereochemical and electrostatic model

A method of calculating the electrostatic potential energy between two molecules, using finite difference potential, is presented. A reduced charge set is used so that the interaction energy can be calculated as the two static molecules explore their full six-dimensional configurational space. The energies are contoured over surfaces fixed to each molecule with an interactive computer graphics program. For two crystal structures (trypsin-trypsin inhibitor and anti-lysozyme Fab-lysozyme), it is found that the complex corresponds to highly favourable interacting regions in the contour plots. These matches arise from a small number of protruding basic residues interacting with enhanced negative potential in each case. The redox pair cytochrome c peroxidase-cytochrome c exhibits an extensive favourably interacting surface within which a possible electron transfer complex may be defined by an increased electrostatic complementarity, but a decreased electrostatic energy. A possible substrate transfer configuration for the glycolytic enzyme pair glyceraldehyde phosphate dehydrogenase-phosphoglycerate kinase is presented.     

Spatial optimization of electrostatic interactions between the ionized groups in globular proteins

A model approach is suggested to estimate the degree of spatial optimization of the electrostatic interactions in protein molecules. The method is tested on a set of 44 globular proteins, representative of the available crystallographic data. The theoretical model is based on macroscopic computation of the contribution of charge–charge interactions to the electrostatic term of the free energy for the native proteins and for a big number of virtual structures with randomly distributed on protein surface charge consetellations (generated by a Monte-Carlo technique). The statistical probability of occurrence of random structures with electrostatic energies lower than the energy of the native protein is suggested as a criterion for spatial optimization of the electrostatic interactions. The results support the hypothesis that the folding process optimizes the stabilizing effect of electrostatic interactions, but to very different degree for different proteins. A parallel analysis of ion pairs shows that the optimization of the electrostatic term in globular proteins has increasingly gone in the direction of rejecting the repulsive short contacts between charges of equal sign than of creating of more salt bridges (in comparison with the statistically expected number of shortrange ion pairs in the simulated random structures). It is observed that the decrease in the spatial optimization of the electrostatic interactions is usually compensated for by an appearance of disulfide bridges in the covalent structure of the examined proteins. © 1994 Wiley-Liss, Inc.     

Calculation of chromophore excited state energy shifts in response to molecular dynamics of pigment-protein complexes

The absorption and energy transfer properties of photosynthetic pigments are strongly influenced by their local environment or “site.” Local electrostatic fields vary in time with protein and chromophore molecular movement and thus transiently influence the excited state transition properties of individual chromophores. Site-specific information is experimentally inaccessible in many light-harvesting pigment–proteins due to multiple chromophores with overlapping spectra. Full quantum mechanical calculations of each chromophores excited state properties are too computationally demanding to efficiently calculate the changing excitation energies along a molecular dynamics trajectory in a pigment–protein complex. A simplified calculation of electrostatic interactions with each chromophores ground to excited state transition, the so-called charge density coupling (CDC) for site energy, CDC, has previously been developed to address this problem. We compared CDC to more rigorous quantum chemical calculations to determine its accuracy in computing excited state energy shifts and their fluctuations within a molecular dynamics simulation of the bacteriochlorophyll containing light-harvesting Fenna–Mathews–Olson (FMO) protein. In most cases CDC calculations differed from quantum mechanical (QM) calculations in predicting both excited state energy and its fluctuations. The discrepancies arose from the inability of CDC to account for the differing effects of charge on ground and excited state electron orbitals. Results of our study show that QM calculations are indispensible for site energy computations and the quantification of contributions from different parts of the system to the overall site energy shift. We suggest an extension of QM/MM methodology of site energy shift calculations capable of accounting for long-range electrostatic potential contributions from the whole system, including solvent and ions.     

Computed pore potentials of the nicotinic acetylcholine receptor

Electrostatic surface potentials in the vestibule of the nicotinic acetylcholine receptor (nAChR) were computed from structural models using the University of Houston Brownian Dynamics program to determine their effect on ion conduction and ionic selectivity. To further determine whether computed potentials accurately reflect the electrostatic environment of the channel, the potentials were used to predict the rate constants for diffusion-enhanced fluorescence energy transfer; the calculated energy transfer rates are directly comparable with those determined experimentally (see companion article by Meltzer et al. in this issue). To include any effects on the local potentials by the bound acceptor fluorophore crystal violet, its binding site was first localized within the pore by fluorescence energy transfer measurements from dansyl-C6-choline bound to the agonist sites and also by simulations of binding using Autodock. To compare the computed potentials with those determined experimentally, we used the predicted energy transfer rates from Tb3+ chelates of varying charge to calculate an expected potential using the Boltzmann relationship. This expected potential (from -20 to -40 mV) overestimates the values determined experimentally (from -10 to -25 mV) by two- to fourfold at similar conditions of ionic strength. Although the results indicate a basic discrepancy between experimental and computed surface potentials, both methods demonstrate that the vestibular potential has a relatively small effect on conduction and selectivity.     

The role of structural reorganization in charge carrier transfer in a DNA molecule

The model proposed for hole transfer in DNA molecules with different configurations allows for the changes in the reorganization energy during charge transfer in a nucleotide strand with variations in the degree of orbital overlap in neighboring nucleotide pairs in different molecular sequences. The rate of hole transfer occurring in a DNA molecule through the superexchange and hopping transfer mechanisms is limited by the vibrational relaxation of the geometry of the nucleotide bases, as well as by the dynamics of solvent molecules. The rate of charge transfer in the DNA molecule depends on the height of the potential barrier between the donor fragment and the molecular bridge and on the positional arrangement of nucleobase pairs and their number in the molecular bridge. Inclusion of the interstrand charge transfer, which is characterized by a small degree of orbital overlap in the nucleobases of the opposite strands, does not affect the total charge transfer in the DNA molecule. An increase of the number of parallel components (processes) in the hopping mechanism entails an increase in the rate of charge transfer in the double helix.     

Microscopic theory of the dielectric properties of proteins.

This paper investigates the microscopic mechanisms of charge screening in proteins. The screening of an arbitrary perturbing charge density by a protein and its surrounding solution is characterized by a generalized susceptibility, which is approximately given by the mean dipole-dipole correlation matrix of the system. This susceptibility is a microscopic quantity; the sum of its matrix elements gives the macroscopic susceptibility of continuum electrostatics. When screening of a single perturbing point charge is considered, this susceptibility reduces to a scalar quantity, dependent on position within the protein. The contribution of the positional degrees of freedom of the protein atoms can be estimated from molecular dynamics simulations. This contribution gives rise to large spatial variations of the susceptibility, whose significance for protein function is discussed. The model is applied to the small alpha helix deca-alanine, and to the electron-transfer protein cytochrome c. The results agree qualitatively with previous normal mode calculations. The importance, and the large spatial variations, of charge screening by deca-alanine suggest that dielectric screening may play a role in the binding of charged ligands by helices. In cytochrome c, the dielectric susceptibility in response to a point charge is at a minimum in the central heme region, resulting in a lowering of the reorganization free energy for charge transfer to and from the heme.     

Theoretical calculations on an acetic acid, 5-methylimidazole, methanol hydrogen bond network: a model charge relay system

The CNDO/2 MO SCF method is used to calculate canonical form stabilities, proton potential energy curves, charge redistributions, and hydrogen bond strengths in a model charge relay system. The model system consists of methanol, 5-methylimidazole and acetic acid. The carboxylate group is observed to (i) increase the negative charge on the methanol oxygen, (ii) increase the methanol-imidazole hydrogen bond strength and (iii) reduce the proton transfer energies. Consideration of an extended model system indicates that solvation of the model system further reduces the proton transfer energies. These results are consistant with the proposed role of the buried aspartate group in activating the reactive serine oxygen in the serine proteinase enzymes.     

Calculation of the total electrostatic energy of a macromolecular system: solvation energies, binding energies, and conformational analysis

In this report we describe an accurate numerical method for calculating the total electrostatic energy of molecules of arbitrary shape and charge distribution, accounting for both Coulombic and solvent polarization terms. In addition to the solvation energies of individual molecules, the method can be used to calculate the electrostatic energy associated with conformational changes in proteins as well as changes in solvation energy that accompany the binding of charged substrates. The validity of the method is examined by calculating the hydration energies of acetate, methyl ammonium, ammonium, and methanol. The method is then used to study the relationship between the depth of a charge within a protein and its interaction with the solvent. Calculations of the relative electrostatic energies of crystal and misfolded conformations of Themiste dyscritum hemerythrin and the VL domain of an antibody are also presented. The results indicate that electrostatic charge-solvent interactions strongly favor the crystal structures. More generally, it is found that charge-solvent interactions, which are frequently neglected in protein structure analysis, can make large contributions to the total energy of a macromolecular system.     

Role of the adenylate system and glycolytic flux in the control of protein synthesis in isolated rat lung cells

(1) Glucose stimulates the incorporation of amino acids into protein in lung cells isolated by digestion of the lung stroma with collagenase. This effect reflects mainly an increase in protein synthesis since no effect of glucose had been found to the uptake of amino acid precursors and, although glucose decreases the rate of intracellular proteolysis by 15%, this effect cannot account for the increased incorporation of radioactivity into proteins. Furthermore, glucose did not induce any significant change in the intracellular content of valine. (2) For glucose to act on protein synthesis, it must be glycolyzed since its stereoisomer, L-glucose, which is not metabolized by lung cells, has no effect. (3) The mechanism of glucose action does not seem to be related simply to variations of cellular ATP content or energy charge. The following arguments seem to support this conclusion: (i) glucose does not bring about significant variations in the concentration of reactants of the adenylate system; (ii) the increase in protein synthesis induced by glucose in energy-depleted cells correlates with a rise in ATP content and energy charge; however, adenosine, which increases ATP levels in a form quantitatively similar to glucose, is unable to affect protein synthesis: (iii) glucose also accelerates the incorporation of amino acids into proteins in adenosine-treated lung cells in which the ATP concentration was almost double that of the control and the energy charge was considerably elevated, ruling out the possibility that a rise in the steady-state concentration of ATP and/or energy charge alone could be responsible for the acceleration of protein synthesis. (4) It can be concluded that the effect of glucose in increasing protein synthesis in lung cells is dependent on some signal arising from its breakdown and not to variations in the concentration of reactants or energy charge of the adenylate system.     

Electrostatic potential and Born energy of charged molecules interacting with phospholipid membranes: calculation via 3-D numerical solution of the full Poisson equation.

Understanding the physicochemical basis of the interaction of molecules with lipid bilayers is fundamental to membrane biology. In this study, a new, three-dimensional numerical solution of the full Poisson equation including local dielectric variation is developed using finite difference techniques in order to model electrostatic interactions of charged molecules with a non-uniform dielectric. This solution is used to describe the electric field and electrostatic potential profile of a charged molecule interacting with a phospholipid bilayer in a manner consistent with the known composition and structure of the membrane. Furthermore, the Born interaction energy is then calculated by appropriate integration of the electric field over whole space. Numerical computations indicate that the electrostatic potential profile surrounding a charge molecule and its resultant Born interaction energy are a function of molecular position within the membrane and change most significantly within the polar region of the bilayer. The maximum interaction energy is observed when the charge is placed at the center of the hydrophobic core of the membrane and is strongly dependent on the size of the charge and on the thickness of the hydrocarbon core of the bilayer. The numerical results of this continuum model are compared with various analytical approximations for the Born energy including models established for discontinuous slab dielectrics. The calculated energies agree with the well-known Born analytical expression only when the charge is located near the center of a hydrocarbon core of greater than 60 A in thickness. The Born-image model shows excellent agreement with the numerical results only when modified to include an appropriate effective thickness of the low dielectric region. In addition, a newly derived approximation which considers the local mean dielectric provides a simple and continuous solution that also agrees well with the numerical results.     

Differential electrostatic stabilization of A-, B-, and Z-forms of DNA

The static accessibility discrete charge algorithm for protein charge interactions is extended to the case of linear polyelectrolytes. In this model, the effective dielectric value between surface charge sites depends predominantly on the solvent ionic strength and the solvent accessibilities of the charge sites. This treatment accounts for the phenomena of specific ion binding in the context of a general electrostatic effect [Matthew and Richards (1982) Biochemistry 21 , 4989]. Specific ion sites are determined by locating areas of high electrostatic potential at the solvent interface of the macromolecule. At a given ionic strength the calculated potential at a site is taken to describe a binding constant and therefore the ion site occupancy. For a 20-base-pair fragment of B-DNA, net charge of ?40, 16 ion sites are indicated in the minor groove. The partial occupancy of each site increases from 0.2 to 0.5 as the ionic strength is increased from 0.01 to 0.50. Over the same range of ionic strength, the electrostatic free energy of this charge array is calculated to change from +0.6 to ?0.05 kcal/bp. Parallel behavior is predicted for A- and Z-DNA charge geometries. The most stable configuration, based on electrostatic criteria, at high ionic strength (I = 0.1–0.5) is that of Z-DNA. In this range, the ratio of “bound” sodium to phosphate is predicted to be less than 0.4.     

A Novel Hypothesis About Mechanisms Affecting Conduction Velocity of Central Myelinated Fibers

The hypothesis that gap junctions are implicated in facilitating axonal conduction has not yet been experimentally demonstrated at the electrophysiological level. We found that block of gap junctions with oleammide slows down axonal conduction velocity in the hippocampal Schaffer collaterals, a central myelinated pathway. Moreover, we explored the possibility that support by the oligodendrocyte to the axon involves energy metabolism, a hypothesis that has been recently proposed by some of us. In agreement with this hypothesis, we found that the effect of oleammide was reversed by pretreatment with creatine, a compound that is known to increase the energy charge of the tissue. Moreover, conduction velocity was also slowed down by anoxia, a treatment that obviously decreases the energy charge of the tissue, and by ouabain, a compound that blocks plasma membrane Na/K-ATPase, the main user of ATP in the brain. We hypothesize that block of gap junctions slows down conduction velocity in central myelinated pathways because oligodendrocytes synthesize ATP and transfer it to the axon through gap junctions.     

The medium reorganization energy for the charge transfer reactions in proteins

A low static dielectric permittivity of proteins causes the low reorganization energies for the charge transfer reactions inside them. This reorganization energy does not depend on the pre-existing intraprotein electric field. The charge transferred inside the protein interacts with its aqueous surroundings; for many globular proteins, the effect of this surroundings on the reorganization energy is comparable with the effect of reorganization of the protein itself while for the charge transfer in the middle of membrane the aqueous phase plays a minor role. Reorganization energy depends strongly on the system considered, and hence there is no sense to speak on the "protein reorganization energy" as some permanent characteristic parameter. We employed a simple algorithm for calculation of the medium reorganization energy using the numerical solution of the Poisson-Boltzmann equation. Namely, the reaction field energy was computed in two versions - all media having optical dielectric permittivity, and all the media with the static one; the difference of these two quantities gives the reorganization energy. We have calculated reorganization energies for electron transfer in cytochrome c, various ammine-ruthenated cytochromes c, azurin, ferredoxin, cytochrome c oxidase, complex of methylamine dehydrogenase with amicyanin, and for proton transfer in α-chymotrypsin. It is shown that calculation of the medium reorganization energy can be a useful tool in analysis of the mechanisms of the charge transfer reactions in proteins.