Fluorescence energy transfer in one dimension: Frequency-domain fluorescence study of DNA–fluorophore complexes

The theory for the salt dependence of the free energy, entropy, and enthalpy of a polyelectrolyte in the PB (PB) model is extended to treat the nonspecific salt dependence of polyelectrolyte–ligand binding reactions. The salt dependence of the binding constant (K) is given by the difference in osmotic pressure terms between the react ants and the products. For simple 1-1 salts it is shown that this treatment is equivalent to the general preferential interaction model for the salt dependence of binding [C. Anderson and M. Record (1993) Journal of Physical Chemistry, Vol. 97, pp. 7116–7126]. The salt dependence, entropy, and enthalpy are compared for the PB model and one specific form of the preferential interaction coefficient model that uses counterion condensation/limiting law (LL) behavior. The PB and LL models are applied to three ligand–polyelectrolyte systems with the same net ligand charge: a model sphere–cylinder binding reaction, a drug–DNA binding reaction, and a protein–DNA binding reaction. For the small ligands both the PB and limiting law models give (ln K vs. In [salt]) slopes close in magnitude to the net ligand charge. However, the enthalpy/entropy breakdown of the salt dependence is quite different. In the PB model there are considerable contributions from electrostatic enthalpy and dielectric (water reorientation) entropy, compared to the predominant ion cratic (release) entropy in the limiting law model. The relative contributions of these three terms in the PB model depends on the ligand: for the protein, ion release entropy is the smallest contribution to the salt dependence of binding. The effect of three approximations made in the LL model is examined: These approximations are (1) the ligand behaves ideally, (2) the preferential interaction coefficient of the polyelectrolyte is unchanged upon ligand binding, and (3) the polyelectrolyte preferential interaction coefficient is given by the limiting law/counterion-condensation value. Analysis of the PB model shows that assumptions 2 and 3 break down at finite salt concentrations. For the small ligands the effects on the slope cancel, however, giving net slopes that are similar in the PB and LL models, but with a different entropy/enthalpy breakdown. For the protein ligand the errors from assumptions 2 and 3 in the LL model do not cancel. In addition, the ligand no longer behaves ideally due to its complex structure and charge distribution. Thus for the protein the slope is no longer related simply to the net ligand charge, and the PB model gives a much larger slope than the LL model. Additionally, in the PB model most of the salt dependence of the protein binding comes from the change in ligand activity, i.e. from nonspecific anion effects, in contrast to the small ligand case. While the absolute binding is sensitive to polyelectrolyte length, little length effect is seen on the salt dependence for the small ligands at 0.1M salt, and for lengths > 60 Å. Almost no DNA length dependenceis seen in the salt dependence of the protein binding, since this is determined primarily by the protein, not the DNA. © 1995 John Wiley & Sons, Inc.     

Alamethicin channel conductance modified by lipid charge

The membrane surface charge modifies the conductance of ion channels by changing the electric potential and redistributing the ionic composition in their vicinity. We have studied the effects of lipid charge on the conductance of a multi-state channel formed in planar lipid bilayers by the peptide antibiotic alamethicin. The channel conductance was measured in two lipids: in a neutral dioleoylphosphatidylethanolamine (DOPE) and a negatively charged dioleoylphosphatidylserine (DOPS). The charge state of DOPS was manipulated by the pH of the membrane-bathing solution. We find that at high salt concentrations (e.g., 2 M NaCl) the effect of the lipid charge is below the accuracy of our measurements. However, when the salt concentration in the membrane-bathing solution is decreased, the surface charge manifests itself as an increase in the conductance of the first two channel levels that correspond to the smallest conductive alamethicin aggregates. Our analysis shows that both the salt and pH dependence of the surface charge effect can be rationalized within the nonlinear Poisson-Boltzmann approach. Given channel conductance in neutral lipids, we use different procedures to account for the surface charge (e.g., introduce averaging over the channel aperture and take into account Na+ adsorption to DOPS heads), but only one adjustable parameter: an effective distance from the nearest lipid charge to the channel mouth center. We show that this distance varies by 0.3-0.4 nm upon channel transition from the minimal conducting aggregate (level L0) to the next larger one (level L1). This conclusion is in accord with a simple geometrical model of alamethicin aggregation.     

Influence of pH and ionic strength on the steric mass-action model parameters around the isoelectric point of protein

The ion-exchange equilibrium and the dependence of the parameters in the steric mass-action (SMA) model on salt concentration and buffer pH around the isoelectric point of protein were studied. Bovine serum albumin (BSA, isoelectric point = 5.4) was used as a model protein and DEAE Sepharose FF as an ion exchanger. Finite batch adsorption experiments and isocratic elution chromatography were performed for the determination of the model parameters (i.e., characteristic charge, equilibrium constant, and steric factor). The results showed that pH had significant effects on the parameters. With an increase of pH from 4.5 to 6.5, the characteristic charge increased from 0.9 to 3.0 and leveled off as a plateau at pH above 5.5. The charge groups in the contact region of protein surface were considered to play a crucial role on the characteristic charge. The decrease of pH and increase of salt concentration lowered the absolute value of the zeta potential of the protein surface and led to a decrease of the equilibrium constant. The steric factor remained unchanged at about 31 at pH 5.5 and 6.0 and increased to 44.5 at pH 5.0 and 96.8 at pH 4.5, mainly as a result of the lower adsorption capacity of BSA at pH <5.5. Furthermore, the increase of the molecular volume of BSA at pH 4.5 would be an additional reason for the increase of the steric factor. Taking into account the effect of the pH and salt concentration on these parameters, the SMA model described the ion exchange equilibrium of protein more accurately.     

Specific ion effects: why the properties of lysozyme in salt solutions follow a Hofmeister series

Protein solubility in aqueous solutions depends in a complicated and not well understood way on pH, salt type, and salt concentration. Why for instance does the use of two different monovalent salts, potassium thiocyanate and potassium chloride, produce such different results? One important and previously neglected source of ion specificity is the ionic dispersion potential that acts between each ion and the protein. This attractive potential is found to be much stronger for SCN(-) than it is for Cl(-). We present model calculations, performed within a modified ion-specific double-layer theory, that demonstrate the large effect of including these ionic dispersion potentials. The results are consistent with experiments performed on hen egg-white lysozymes and on neutral black lipid membranes. The calculated surface pH and net lysozyme charge depend strongly on the choice of anion. We demonstrate that the lysozyme net charge is larger, and the corresponding Debye length shorter, in a thiocyanate salt solution than in a chloride salt solution. Recent experiments have suggested that pK(a) values of histidines depend on salt concentration and on ionic species. We finally demonstrate that once ionic dispersion potentials are included in the theory these results can quantitatively be reinterpreted in terms of a highly specific surface pH (and a salt-independent pK(a)).     

Repulsion between Oppositely Charged Planar Macroions

The repulsive interaction between oppositely charged macroions is investigated using Grand Canonical Monte Carlo simulations of an unrestricted primitive model, including the effect of inhomogeneous surface charge and its density, the depth of surface charge, the cation size, and the dielectric permittivity of solvent and macroions, and their contrast. The origin of the repulsion is a combination of osmotic pressure and ionic screening resulting from excess salt between the macroions. The excess charge over-reduces the electrostatic attraction between macroions and raises the entropic repulsion. The magnitude of the repulsion increases when the dielectric constant of the solvent is lowered (below that of water) and/or the surface charge density is increased, in good agreement with experiment. Smaller size of surface charge and the cation, their discreteness and mobility are other factors that enhance the repulsion and charge inversion phenomenons.     

Evaluation of differences between dual salt‐pH gradient elution and mono gradient elution using a thermodynamic model: Simultaneous separation of six monoclonal antibody charge and size variants on preparative‐scale ion exchange chromatographic resin

The efficiencies of mono gradient elution and dual salt‐pH gradient elution for separation of six mAb charge and size variants on a preparative‐scale ion exchange chromatographic resin are compared in this study. Results showed that opposite dual salt‐pH gradient elution with increasing pH gradient and simultaneously decreasing salt gradient is best suited for the separation of these mAb charge and size variants on Eshmuno^® CPX. Besides giving high binding capacity, this type of opposite dual salt‐pH gradient also provides better resolved mAb variant peaks and lower conductivity in the elution pools compared to single pH or salt gradients. To have a mechanistic understanding of the differences in mAb variants retention behaviors of mono pH gradient, parallel dual salt‐pH gradient, and opposite dual salt‐pH gradient, a linear gradient elution model was used. After determining the model parameters using the linear gradient elution model, 2D plots were used to show the pH and salt dependencies of the reciprocals of distribution coefficient, equilibrium constant, and effective ionic capacity of the mAb variants in these gradient elution systems. Comparison of the 2D plots indicated that the advantage of opposite dual salt‐pH gradient system with increasing pH gradient and simultaneously decreasing salt gradient is the noncontinuous increased acceleration of protein migration. Furthermore, the fitted model parameters can be used for the prediction and optimization of mAb variants separation in dual salt‐pH gradient and step elution. © 2018 American Institute of Chemical Engineers Biotechnol. Prog., 34:973–986, 2018     

The influence of salt on the aggregation state of spectrin from bovine ertythrocyte membranes

Sedimentation velocity and gel filtration experiments have been performed with bovine spectrin over a wide range of neutral salt concentrations. Increasing salt concentrations tend to increase both the sedimentation coefficient of spectrin and the elution volume of the protein from 4% agarose columns. No conformation change can be detected by means of optical rotation measurements as the salt concentration is raised. The results are incompatible with the hypothesis that salt causes the aggregation of spectrin, but are consistent with the existence of marked charge effects operative at low salt concentrations. In support of the charge effect hypothesis, acidic groups have been detected on the agarose gels, and ion-exclusion behaviour on the column has been observed with other proteins of similar size.     

Interactions of macromolecules with salt ions: an electrostatic theory for the Hofmeister effect

Salting-out of proteins was discovered in the nineteenth century and is widely used for protein separation and crystallization. It is generally believed that salting-out occurs because at high concentrations salts and the protein compete for solvation water. Debye and Kirkwood suggested ideas for explaining salting-out (Debeye and MacAulay, Physik Z; 1925;131:22-29; Kirkwood, In: Proteins, amino acids and peptides as ions and dipolar ions. New York: Reinhold; 1943. p 586-622). However, a quantitative theory has not been developed, and such a theory is presented here. It is built on Kirkwood's idea that a salt ion has a repulsive interaction with an image charge inside a low dielectric cavity. Explicit treatment is given for the effect of other salt ions on the interaction between a salt ion and its image charge. When combined with the Debye-Hückel effect of salts on the solvation energy of protein charges (i.e., salting-in), the characteristic curve of protein solubility versus salt concentration is obtained. The theory yields a direct link between the salting-out effect and surface tension and is able to provide rationalizations for the effects of salt on the folding stability of several proteins.     

Structure and interactions of aggrecans: statistical thermodynamic approach

Weak polyelectrolytes tethered to cylindrical surfaces are investigated using a molecular theory. These polymers form a model system to describe the properties of aggrecan molecules, which is one of the main components of cartilage. We have studied the structural and thermodynamical properties of two interacting aggrecans with a molecular density functional theory that incorporates the acid-base equilibrium as well as the molecular properties: including conformations, size, shape, and charge distribution of all molecular species. The effect of acidity and salt concentration on the behavior is explored in detail. The repulsive interactions between two cylindrical-shaped aggrecans are strongly influenced by both the salt concentration and the pH. With increasing acidity, the polyelectrolytes of the aggrecan acquire charge and with decreasing salt concentration those charges become less screened. Consequently the interactions increase in size and range with increasing acidity and decreasing salt concentration. The size and range of the forces offers a possible explanation to the aggregation behavior of aggrecans and for their ability to resist compressive forces in cartilage. Likewise, the interdigitation of two aggrecan molecules is strongly affected by the salt concentration as well as the pH. With increasing pH, the number of charges increases, causing the repulsions between the polymers to increase, leading to a lower interdigitation of the two cylindrical polymer layers of the aggrecan molecules. The low interdigitation in charged polyelectrolytes layers provides an explanation for the good lubrication properties of polyelectrolyte layers in general and cartilage in particular.     

Biophysical characterization of the influence of salt on tetrameric SecB.

SecB is a tetrameric chaperone, with a monomeric molecular mass of 17 kDa, that is involved in protein translocation in Escherichia coli. It has been hypothesized that SecB undergoes a conformational change as a function of the salt concentration. To gain more insight into the salt-dependent behavior of SecB, we studied the protein in solution by dynamic light scattering, size exclusion chromatography, analytical ultracentrifugation, and small angle neutron scattering. The results clearly demonstrate the large influence of the salt concentration on the behavior of SecB. At high salt concentration, SecB is a non-spherical protein with a radius of gyration of 3.4 nm. At low salt concentration the hydrodynamic radius of the protein is apparently decreased, whereas the ratio of the frictional coefficients is increased. The protein solution behaves in a non-ideal way at low salt concentrations, as was shown by the analytical ultracentrifugation data and a pronounced interparticle effect observed by small angle neutron scattering. A possible explanation is a change in surface charge distribution dependent on the salt concentration in the solvent. We summarize our data in a model for the salt-dependent conformation of tetrameric SecB.     

pK values of histidine residues in ribonuclease Sa: effect of salt and net charge

The primary goal of this study was to gain a better understanding of the effect of environment and ionic strength on the pK values of histidine residues in proteins. The salt-dependence of pK values for two histidine residues in ribonuclease Sa (RNase Sa) (pI=3.5) and a variant in which five acidic amino acids have been changed to lysine (5K) (pI=10.2) was measured and compared to pK values of model histidine-containing peptides. The pK of His53 is elevated by two pH units (pK=8.61) in RNase Sa and by nearly one pH unit (pK=7.39) in 5K at low salt relative to the pK of histidine in the model peptides (pK=6.6). The pK for His53 remains elevated in 1.5M NaCl (pK=7.89). The elevated pK for His53 is a result of screenable electrostatic interactions, particularly with Glu74, and a non-screenable hydrogen bond interaction with water. The pK of His85 in RNase Sa and 5K is slightly below the model pK at low salt and merges with this value at 1.5M NaCl. The pK of His85 reflects mainly effects of long-range Coulombic interactions that are screenable by salt. The tautomeric states of the neutral histidine residues are changed by charge reversal. The histidine pK values in RNase Sa are always higher than the pK values in the 5K variant. These results emphasize that the net charge of the protein influences the pK values of the histidine residues. Structure-based pK calculations capture the salt-dependence relatively well but are unable to predict absolute histidine pK values.     

Donnan effect as measured by sedimentation equilibrium for the protein cytochrome c.

The protein turkey-heart cytochrome c is used as a model protein to study charge effects in sedimentation equilibrium experiments in three-component solutions. Data are given for the dependence of the apparent M (1–υ ρ) on ρ in solutions of KCl, RbCl, CsCl, and triethylamine hydrochloride. The results show the Donnan effect to have a significant influence on the apparent molecular weight, found by extrapolation of the data to a solution density of one. The apparent molecular weights are for protein at infinite dilution. A theoretical treatment is presented where the magnitude of this effect can be predicted accurately from the formal net charge of the protein as computed from the amino acid composition. The results are shown to be important in computing the preferential hydration of the protein in concentrated salt solutions. For such systems the Donnan effect should be subtracted from the total interaction coefficient for multicomponent system in order to obtain the preferential hydration.     

Light-induced currents from oriented purple membrane: II. Proton and cation contributions to the photocurrent

The sign of B2, the micro-second component of the photocurrent from oriented purple membrane, is that of positive charge moving away from the purple membrane in the direction of proton release. B2 could be due to internal dipole or proton movement, proton release, or metal cation release. We found that the waveform of B2 is virtually insensitive to changes in the salt concentration as long as it is >40 mM KCl, >5 mM CaCl₂, or >0.5 mM LaCl₃. However, below these limits, B2's apparent rate of decay increases as the salt concentration decreases without any change in the initial amplitude. This salt dependence suggests that B2 is due to a positive charge, either a metal cation or a proton, moving from the membrane into the solution. That the positive charge is not a metal cation is suggested by the waveform of B2 remaining unchanged upon replacing the cations both in solution and in the binding sites of the purple membrane. Direct evidence that the positive charge movement is due to protons was obtained by examining the correlation of B2 with the proton dependent processes of bacteriorhodopsin in buffers and dyes. Based on these observations, we suggest that most, if not all, of the intrinsic B2 component of the photocurrent at moderate salt concentration is due to proton release.

The photocurrents from purple membranes whose surface potential has been reduced by delipidation or chemical modification of carboxyl groups with methyl esters were found to be only modestly changed. This suggests that the salt effect is not through its modulation of the surface potential. Rather, we propose that in low salt B2 represents the sum of a proton release from the surface of the purple membrane and a second current component, due to cations moving back towards the membrane, which is only important in low salt. The cation counter current is induced by proton release which creates a transient uncompensated negative charge on the membrane.

     

Correlation for the partition behavior of proteins in aqueous two-phase systems: effect of surface hydrophobicity and charge

Correlations to describe the effect of surface hydrophobicity and charge of proteins with their partition coefficient in aqueous two-phase systems were investigated. Polyethylene glycol (PEG) 4000/phosphate, sulfate, citrate, and dextran systems in the presence of low (0.6% w/w) and high (8.8% w/w) levels of NaCl were selected for a systematic study of 12 proteins. The surface hydrophobicity of the proteins was measured by ammonium sulfate precipitation as the inverse of their solubility. The hydrophobicity values measured correlated well with the partition coefficients, K, obtained in the PEG/salt systems at high concentration of NaCl (r = 0.92-0.93). In PEG/citrate systems the partition coefficient correlated well with protein hydrophobicity at low and high concentrations of NaCl (r = 0.81 and 0.93, respectively). The PEG/citrate system also had a higher hydrophobic resolution than other systems to exploit differences in the protein's hydrophobicity. The surface charge and charge density of the proteins was determined over a range of pH (3-9) by electrophoretic titration curves; PEG/salt systems did not discriminate well between proteins of different charge or charge density. In the absence of NaCl, K decreased slightly with increased positive charge. At high NaCl concentration, K increased as a function of positive charge. This suggested that the PEG-rich top phase became more negative as the concentration of NaCl in the systems increased and, therefore, attracted the positively charged proteins. The effect of charge was more important in PEG/dextran systems at low concentrations of NaCl. In the PEG/dextran systems at lower concentration of NaCl, molecular weight appeared to be the prime determinant of partition, whereas no clear effect of molecular weight could be found in PEG/salt systems.     

Composition effect on peptide interaction with lipids and bacteria: variants of C3a peptide CNY21

The effect of peptide hydrophobicity and charge on peptide interaction with model lipid bilayers was investigated for the C3a-derived peptide CNY21 by fluorescence spectroscopy, circular dichroism, ellipsometry, z-potential, and photon correlation spectroscopy measurements. For both zwitterionic and anionic liposomes, the membrane-disruptive potency for CNY21 variants increased with increasing net positive charge and mean hydrophobicity and was completely lost on elimination of all peptide positive charges. Analogous effects of elimination of the peptide positive net charge in particular were found regarding bacteria killing for both Pseudomonas aeruginosa and Bacillus subtilis. The peptides, characterized by moderate helix content both in buffer and when attached to the liposomes, displayed high adsorption for the net positively charged peptide variants, whereas adsorption was non-measurable for the uncharged peptide. That electrostatically driven adsorption represents the main driving force for membrane disruption in lipid systems was also demonstrated by a drastic reduction in both liposome leakage and peptide adsorption with increasing ionic strength, and this salt inactivation can be partly avoided by increasing the peptide hydrophobicity. This increased electrolyte resistance translates also to a higher antibacterial effect for the hydrophobically modified variant at high salt concentration. Overall, our findings demonstrate the importance of the peptide adsorption and resulting peptide interfacial density for membrane-disruptive effects of these peptides.     

Effect of secondary structure on the potential of mean force for poly-L-lysine in the alpha-helix and beta-sheet conformations

Because poly-L-lysine (PLL) can exist in the alpha-helix or beta-sheet conformation depending on solution preparation and solution conditions, PLL is a suitable candidate to probe the dependence of protein interactions on secondary structure. The osmotic second virial coefficient and weight-average molecular weight are reported from low-angle laser-light scattering measurements for PLL as a function of NaCl concentration, pH, and alpha-helix or beta-sheet content. Interactions between PLL molecules become more attractive as salt concentration increases due to screening of PLL charge by salt ions and at low salt concentration become more attractive as pH increases due to decreased net charge on PLL. The experimental results show that interactions are stronger for the beta-sheet conformation than for the alpha-helix conformation. A spherically-symmetric model for the potential of mean force is used to account for specific interactions not described by DLVO theory and to show how differences in secondary structure affect PLL interactions.     

Visualizing ion relaxation in the transport of short DNA fragments

Ion relaxation plays an important role in a wide range of phenomena involving the transport of charged biomolecules. Ion relaxation is responsible for reducing sedimentation and diffusion constants, reducing electrophoretic mobilities, increasing intrinsic viscosities, and, for biomolecules that lack a permanent electric dipole moment, provides a mechanism for orienting them in an external electric field. Recently, a numerical boundary element method was developed to solve the coupled Navier-Stokes, Poisson, and ion transport equations for a polyion modeled as a rigid body of arbitrary size, shape, and charge distribution. This method has subsequently been used to compute the electrophoretic mobilities and intrinsic viscosities of a number of model proteins and DNA fragments. The primary purpose of the present work is to examine the effect of ion relaxation on the ion density and fluid velocity fields around short DNA fragments (20 and 40 bp). Contour density as well as vector field diagrams of the various scalar and vector fields are presented and discussed at monovalent salt concentrations of 0.03 and 0.11 M. In addition, the net charge current fluxes in the vicinity of the DNA fragments at low and high salt concentrations are briefly examined and discussed.     

Partitioning of α-lactalbumin and β-lactoglobulin in aqueous two-phase systems of polyvinylpyrrolidone and potassium phosphate

In the present study, the partitioning of α-lactalbumin, β-lactoglobulin, and cheese whey proteins in aqueous two-phase system of polyvinylpyrrolidone-potassium phosphate is investigated. The partitioning of proteins in this system depends on the polymer and salt weight percents in feed, temperature, and pH. The orthogonal central composite design is used to study the effects of different parameters on partitioning of α-lactalbumin and β-lactoglobulin. A second order model is proposed to determine the impact of these parameters. The results of the model show that the weight percent of the salt in feed has a large effect on the protein partitioning. The weight percent of polyvinylpyrrolidone in the feed increases the partitioning coefficients. By increasing the temperature, the viscosity of polyvinylpyrrolidone is reduced and the protein can easily be transferred from one phase to the other phase. The pH of the aqueous two phase system can alter the protein partitioning coefficient through the variation of the protein net charge.     

Protein diffusion in crowded electrolyte solutions

We report on a combined cold neutron backscattering and spin-echo study of the short-range and long-range nanosecond diffusion of the model globular protein bovine serum albumin (BSA) in aqueous solution as a function of protein concentration and NaCl salt concentration. Complementary small angle X-ray scattering data are used to obtain information on the correlations of the proteins in solution. Particular emphasis is put on the effect of crowding, i.e. conditions under which the proteins cannot be considered as objects independent of each other. We thus address the question at which concentration this crowding starts to influence the static and in particular also the dynamical behaviour. We also briefly discuss qualitatively which charge effects, i.e. effects due to the interplay of charged molecules in an electrolyte solution, may be anticipated. Both the issue of crowding as well as that of charge effects are particularly relevant for proteins and their function under physiological conditions, where the protein volume fraction can be up to approximately 40% and salt ions are ubiquitous. The interpretation of the data is put in the context of existing studies on related systems and of existing theoretical models.