The release of monovalent counterions by addition of divalent counterions in coulombic interaction system

The additivity rule of counterion activity or osmotic pressure in rodlike polyelectrolyte solutions has been discussed on the basis of the Fokker-Planck and Poisson equations in relation to the fluctuation of counterion distribution. This new theory has concluded that the additivity rule of counterion activity is less applicable than that of osmotic pressure due to the electric expansion force acting on the free-volume surface resulting from the fluctuation of counterion distribution. The theory has introduced an approximate relation between the counterion activities in the mixture solution of divalent and monovalent counterions, such that Deltaa+ = DeltaC++ - Deltaa++, in which Deltaa+ represents the increase of activity of monovalent counter-ions resulting from the addition of divalent counterionsDeltaC++, (in molar) to the solution, and Deltaa++ means the increase of the divalent counterion activity (in molar) in this process. This relation has been experimentally examined for Na-PSS solutions in the process of Cu2+ ion addition by the use of Na+ and Cu2+ sensitive electrodes, and it has been turned out that the relation is established in the low charge state of polyion.     

DNA like-charge attraction and overcharging by divalent counterions in the presence of divalent co-ions

Strongly correlated electrostatics of DNA systems has drawn the interest of many groups, especially the condensation and overcharging of DNA by multivalent counterions. By adding counterions of different valencies and shapes, one can enhance or reduce DNA overcharging. In this paper, we focus on the effect of multivalent co-ions, specifically divalent co-ions such as SO\(_{4}^{2-}\). A computational experiment of DNA condensation using Monte Carlo simulation in grand canonical ensemble is carried out where the DNA system is in equilibrium with a bulk solution containing a mixture of salt of different valency of co-ions. Compared to systems with purely monovalent co-ions, the influence of divalent co-ions shows up in multiple aspects. Divalent co-ions lead to an increase of monovalent salt in the DNA condensate. Because monovalent salts mostly participate in linear screening of electrostatic interactions in the system, more monovalent salt molecules enter the condensate leads to screening out of short-range DNA–DNA like charge attraction and weaker DNA condensation free energy. The overcharging of DNA by multivalent counterions is also reduced in the presence of divalent co-ions. Strong repulsions between DNA and divalent co-ions and among divalent co-ions themselves lead to a depletion of negative ions near the DNA surface as compared to the case without divalent co-ions. At large distances, the DNA–DNA repulsive interaction is stronger in the presence of divalent co-ions, suggesting that divalent co-ions’ role is not only that of simple stronger linear screening.     

DNA G-quadruplexes are uniquely stable in the presence of denaturants and monovalent cations

Ions in the Hofmeister series exhibit varied effects on biopolymers. Those classed as kosmotropes generally stabilize secondary structure, and those classed as chaotropes generally destabilize secondary structure. Here, we report that several anionic chaotropes exhibit unique effects on one DNA secondary structure - a G quadruplex. These chaotropes exhibit the expected behaviour (destabilization of secondary structure) in two other structural contexts: a DNA duplex and i-Motifs. Uniquely among secondary structures, we observe that G quadruplexes are comparatively insensitive to the presence of anionic chaotropes, but not other denaturants. Further, the presence of equimolar NaCl provided greater mitigation of the destabilization caused by other non-anionic denaturants. These results are consistent with the presence of monovalent cations providing an especially pronounced stabilizing effect to G quadruplexes when studied in denaturing solution conditions.     

Thermodynamic properties of polyelectrolyte solutions containing mixtures of monovalent and trivalent counterions

The osmotic coefficients, heats of dilution, and volume changes on dilution of aqueous solutions containing mixtures of polystyrenesulfonic acid and its lanthanum salt have been determined at 25°C. The curve representing the osmotic coefficient as a function of the equivalent fraction of the acid has a maximum; the corresponding curves for the enthalpy and volume changes on dilution have a sigmoidal shape. Experimental results have been compared with predictions of the theory based on the cell model with cylindrical symmetry. A semiquantitative agreement between theory and experiment has been found.     

The release of monovalent counterions by addition of divalent counterions in coulombic interaction system of polyions (II)

In this work, the increase in activity. Deltaa+ of a monovalent counterion (Na+) resulting from the addition or a divalent ion (Cu2+) was experimentally investigated in sulfate or sulfonate polyelectrolyte solutions. It was found that in the case of polyvinylsulfonate, a+ was expressed by Deltaa+ = Delta(C++ -a++). where C(++) and a(++) represent the molar concentration and activity of added Cu2+ respectively, while in the case of dextran sulfate, the expression or Deltaa+ became Deltaa+ =2Delta(C++-a++). Considering that interactions between these cations and sulfate or sulfonale groups are Durely electrostatic, these results were analyzed in relation to the conformation of the polyelectrolytes.     

Exchange of counterions in DNA condensation

We measured the fluorescence intensity of DNA-bound fluorescent dyes YO-PRO-1 (oxazole yellow) and YOYO-1 (dimer of oxazole yellow) at various spermidine concentrations to determine how counterions on DNA are exchanged in the process of DNA condensation. A decrease of fluorescence intensity was observed with an increase of spermidine. Considering the chemical equilibrium under the competition between the dye and spermidine for counterion condensation on DNA, the theoretical curve well describes the decrease of the fluorescence intensity. These results indicate that dyes are exchanged for spermidine at the binding site on DNA; that is, the exchange of counterions occurs. The parameters associated with the decrease of the fluorescence intensity show that the relative affinity of the dye and spermidine for DNA depends on the state of DNA. Moreover, YOYO-1 prevents the DNA condensation, but the effect of YO-PRO-1 on the condensation is very slight, though both dyes intercalate for DNA; the high affinity of YOYO-1 compared to YO-PRO-1 enables prevention of the condensation.     

The effect of counterions on melittin aggregation.

Melittin, a surface-active polypeptide from bee venom, has an overall hydrophobic N-terminus, with basic residues clustered at the C-terminus. In aqueous solution melittin exists as a mixture of monomer and tetramer, the monomer adopting a predominantly random-coil configuration, whereas the tetramer is rich in alpha-helix. The tendency of melittin to aggregate is dependent on the counter-anions present in solution, the effect being most marked with phosphate, decreasing in the order HPO4(2-) greater than SO4(2-) greater than ClO4- greater than Cl-.     

Quantifying aggregation of IgE-FcepsilonRI by multivalent antigen

Aggregation of cell surface receptors by multivalent ligand can trigger a variety of cellular responses. A well-studied receptor that responds to aggregation is the high affinity receptor for IgE (FcepsilonRI), which is responsible for initiating allergic reactions. To quantify antigen-induced aggregation of IgE-FcepsilonRI complexes, we have developed a method based on multiparameter flow cytometry to monitor both occupancy of surface IgE combining sites and association of antigen with the cell surface. The number of bound IgE combining sites in excess of the number of bound antigens, the number of bridges between receptors, provides a quantitative measure of IgE-FcepsilonRI aggregation. We demonstrate our method by using it to study the equilibrium binding of a haptenated fluorescent protein, 2,4-dinitrophenol-coupled B-phycoerythrin (DNP25-PE), to fluorescein isothiocyanate-labeled anti-DNP IgE on the surface of rat basophilic leukemia cells. The results, which we analyze with the aid of a mathematical model, indicate how IgE-FcepsilonRI aggregation depends on the total concentrations of DNP25-PE and surface IgE. As expected, we find that maximal aggregation occurs at an optimal antigen concentration. We also find that aggregation varies qualitatively with the total concentration of surface IgE as predicted by an earlier theoretical analysis.     

Conductometric analysis of the competition between monovalent and divalent counterions in their interaction with polyelectrolytes

A procedure is described for the analysis of the conductivity of solutions of anionic polyelectrolytes in which both mono- and divalent counterions are present. The method is based on analysis of the relation between the overall conductivity of the system and the conductivity of the individual monovalent cations which are only electrostatically (non-specifically) bound. The system is described in terms of the two-state approach, implying that the counterions are considered to be either fully bound to the polyion or completely free. The potentialities of the proposed method are explored by studying solutions of alkali polyacrylates with and without added zinc nitrate at several alkali nitrate concentrations. The results give a picture of the composition of the counterionic atmosphere around the polyion in systems with both mono- and divalent counterions present. To a certain degree, the divalent ion Zn(II) was found to be bound quantitatively by the polyion. The composition of the counterionic atmosphere around the polyion was largely independent of alkali nitrate concentration when the latter was present in not too large an excess with respect to both Zn(II) and the charged monomers.     

The iso-competition point for counterion competition binding to DNA: calculated multivalent versus monovalent cation binding equivalence.

In this paper we introduce an important parameter called the iso-competition point (ICP), to characterize the competition binding to DNA in a two-cation-species system. By imposing the condition of charge neutralization fraction equivalence theta1 = ZthetaZ upon the two simultaneous equations in Manning's counterion condensation theory, the ICPs can be calculated. Each ICP, which refers to a particular multivalent concentration where the charge fraction on DNA neutralized from monovalent cations equals that from the multivalent cations, corresponds to a specific ionic strength condition. At fixed ionic strength, the total DNA charge neutralization fractions thetaICP are equal, no matter whether the higher valence cation is divalent, trivalent, or tetravalent. The ionic strength effect on ICP can be expressed by a semiquantitative equation as ICPZa/ICPZb = (Ia/Ib)Z, where Ia, Ib refers to the instance of ionic strengths and Z indicates the valence. The ICP can be used to interpret and characterize the ionic strength, valence, and DNA length effects on the counterion competition binding in a two-species system. Data from our previous investigations involving binding of Mg2+, Ca2+, and Co(NH3)63+ to lambda-DNA-HindIII fragments ranging from 2.0 to 23.1 kbp was used to investigate the applicability of ICP to describe counterion binding. It will be shown that the ICP parameter presents a prospective picture of the counterion competition binding to polyelectrolyte DNA under a specific ion environment condition.     

Molecular characterization of monovalent and multivalent hapten-protein conjugates for analysis of the antigen--antibody interaction

We prepared a hapten-protein conjugate using (4-hydroxy-3-nitrophenyl)acetyl (NP) hapten and hen egg lysozyme (HEL) or bovine serum albumin (BSA) and defined hapten modification sites on the former protein based on results of reverse-phase high-performance liquid chromatography (HPLC) and mass spectrometric analyses performed after enzymatic digestion. The most reactive residue for aminoacetylation in HEL was found to be Lys33, and the second was Lys96 or Lys97. The homogeneous NP-HEL conjugates were purified by HPLC and used for examining the effect of hapten valence on the antigen-antibody interaction. We also examined the molecular nature of NP conjugates of BSA. Analysis using mass spectroscopy showed that the mass distribution of NP-BSA conjugates was limited, although it became broader with an increase in NP valence. Surface plasmon resonance biosensor measurements were employed in measuring antigen-antibody interactions. The results showed that the apparent binding avidity depends on hapten valence, hapten density, size of carrier proteins, and intrinsic binding affinity of the antibody.     

DNA and its counterions: a molecular dynamics study

The behaviour of mobile counterions, Na⁺ and K⁺, was analysed around a B-DNA double helix with the sequence CCATGCGCTGAC in aqueous solution during two 50 ns long molecular dynamics trajectories. The movement of both monovalent ions remains diffusive in the presence of DNA. Ions sample the complete space available during the simulation time, although individual ions sample only about one-third of the simulation box. Ions preferentially sample electronegative sites around DNA, but direct binding to DNA bases remains a rather rare event, with highest site occupancy values of <13%. The location of direct binding sites depends greatly on the nature of the counterion. While Na⁺ binding in both grooves is strongly sequence-dependent with the preferred binding site in the minor groove, K⁺ mainly visits the major groove and binds close to the centre of the oligomer. The electrostatic potential of an average DNA structure therefore cannot account for the ability of a site to bind a given cation; other factors must also play a role. An extensive analysis of the influence of counterions on DNA conformation showed no evidence of minor groove narrowing upon ion binding. A significant difference between the conformations of the double helix in the different simulations can be attributed to extensive α/γ transitions in the phosphate backbone during the simulation with Na⁺. These transitions, with lifetimes over tens of nanoseconds, however, appear to be correlated with ion binding to phosphates. The ion-specific conformational properties of DNA, hitherto largely overlooked, may play an important role in DNA recognition and binding.     

Influence of monovalent cations on the activity of T4 DNA ligase in the presence of polyethylene glycol.

Monovalent cations such as Na+ and K+ inhibit the activity of T4 DNA ligase. However, the extent of inhibition varies with the terminal sequence of the duplex DNA used as substrate; in many cases, ligation of DNA is completely inhibited at 200 mM. The activity of the ligase is stimulated by raising the concentration of polyethylene glycol 6000 from 0 to 15% (w/v) when NaC1 and KC1 were both absent. Ligation was reduced as the concentration of NaC1 or KC1 was raised in a mixture containing 5 or 15% PEG 6000. With 10% PEG 6000, both cohesive- and blunt-end ligation of this ligase increased at high concentrations of salt (150-200 mM NaC1, or 200-250 mM KC1). Further, with 10% PEG 6000, inter- and intramolecular ligation occurred at low salt concentrations (0-100 mM NaC1, or 0-150 mM KC1); only linear oligomers were formed by intermolecular ligation at the high concentrations.     

The release of monovalent counterions by addition of divalent countemons to aqueous solutions of maleic acid copolymer

Divalent cation binding and the release of monovalent cations accompanying the cation binding were experimentally studied by ion-selective electrode methods in aqueous solutions of copolymer of maleic acid and ethyl vinyl ether. It was found that in the process of Ca2+ addition, all the Ca2+ added was bound to polyions and the initially condensed Na+ was released in proportion to the concentration of the added Ca2+ up to the critical concentration of added Ca2+ at which the condensation of Ca2+ ceases. Values of the structural charge density parameter xi(s), were determined from the end-points of condensation of Ca2+. The process of Na+ release by adding Ca2+ was analyzed on the basis of the counterion condensation theory by using these xi(s) values. In addition, the relationship between the activity coefficient gamma-- of Ca2+ and degree of neutralization alpha in salt-free solutions was obtained from the Manning theory. Agreement between the calculated and experimental values was excellent in both cases.     

Hydration structure and dynamics of B- and Z-DNA in the presence of counterions via molecular dynamics simulations

Following our previous attempts at understanding the structural and dynamical properties of water and counterions hydrating nucleic acids, we have performed molecular dynamics simulations for B- and Z-DNA. In these simulations, the nucleic acids were held rigid. In the case of B-DNA, one turn of B-DNA double helix was considered in the presence of 1500 water molecules and 20 counterions (K⁺). The simulations were performed for 4.0 ps after equilibrating the system. For Z-DNA, we considered one turn of the double helix in the presence of 1851 water molecules and 24 counterions (K⁺). The simulations were carried out for 3.5 ps after equilibration. The average temperature of these simulations was ～ 360 K for Z-DNA and ～ 345 K for B-DNA. In these simulations the hydrogen atoms were explicitly taken into account. For both simulations, a fifth-order predictor-corrector was used for solving the translational equations of motion. The rotational motion of the water molecules was represented in terms of quaternion algebra and the rotational equations of motion were solved with a second-order quaternion method using a sixth-order predictor-corrector method. A time step of 0.5 · 10^?15 s was used in these simulations. The structural and the dynamical properties of water solvating the counterions, and the phosphate groups of the DNA, were computed to understand the hydration structure. Diffusion coefficients and velocity correlation functions were calculated for both ions and the water molecules. The velocity correlation functions for the ions exhibit a caged behavior. The dipole correlation functions for the water molecules indicate that the water molecules close to the helix retain the memory of their initial orientations for longer periods of time than those away from the helix. During the time period of our simulation (3–4 ps) the ion probability distributions show a well-defined pattern and suggest limited mobility for the ions, being close to the helix.     

Influence of amino acid and peptide counterions on the conformation of DNA

We describe fibre diffraction studies on the interaction of DNA with different amino acids and peptides. The B form of DNA, with ten base-pairs per turn, is always found at high levels of humidity. We suggest that this pitch is observed because the DNA molecules are maintained in a straight position. In solution, the DNA molecules are bent and may have a larger pitch. The A form of DNA is never found upon dehydration. Instead, the B form may be either stabilized by the counterions or altered so that the number of base-pairs per helical turn decreases upon dehydration. Alteration is favoured either by small counterions that have a single charge or by large basic polypeptides and proteins. Stabilization is favoured by small counterions that have several charged groups. A third type of behaviour is found with some amino acids that contain hydrophobic groups, which destabilize the secondary structure of DNA, probably due to a modification of its intramolecular interactions. We have not detected any specific effect of amino acid side-chains, although the amino acid sequence has a clear influence on the interaction. We think that these observations are of interest in the pursuit of more detailed crystallographic studies on protein-DNA interactions.     

Dissociation and aggregation of calpain in the presence of calcium

Calpain is a heterodimeric Ca(2+)-dependent cysteine protease consisting of a large (80 kDa) catalytic subunit and a small (28 kDa) regulatory subunit. The effects of Ca(2+) on the enzyme include activation, aggregation, and autolysis. They may also include subunit dissociation, which has been the subject of some debate. Using the inactive C105S-80k/21k form of calpain to eliminate autolysis, we have studied its disassociation and aggregation in the presence of Ca(2+) and the inhibition of its aggregation by means of crystallization, light scattering, and sedimentation. Aggregation, as assessed by light scattering, depended on the ionic strength and pH of the buffer, on the Ca(2+) concentration, and on the presence or absence of calpastatin. At low ionic strength, calpain aggregated rapidly in the presence of Ca(2+), but this was fully reversible by EDTA. With Ca(2+) in 0.2 m NaCl, no aggregation was visible but ultracentrifugation showed that a mixture of soluble high molecular weight complexes was present. Calpastatin prevented aggregation, leading instead to the formation of a calpastatin-calpain complex. Crystallization in the presence of Ca(2+) gave rise to crystals mixed with an amorphous precipitate. The crystals contained only the small subunit, thereby demonstrating subunit dissociation, and the precipitate was highly enriched in the large subunit. Reversible dissociation in the presence of Ca(2+) was also unequivocally demonstrated by the exchange of slightly different small subunits between mu-calpain and m-calpain. We conclude that subunit dissociation is a dynamic process and is not complete in most buffer conditions unless driven by factors such as crystal formation or autolysis of active enzymes. Exposure of the hydrophobic dimerization surface following subunit dissociation may be the main factor responsible for Ca(2+)-induced aggregation of calpain. It is likely that dissociation serves as an early step in calpain activation by releasing the constraints upon protease domain I.     

Interplay of ion binding and attraction in DNA condensed by multivalent cations

We have measured forces generated by multivalent cation-induced DNA condensation using single-molecule magnetic tweezers. In the presence of cobalt hexammine, spermidine, or spermine, stretched DNA exhibits an abrupt configurational change from extended to condensed. This occurs at a well-defined condensation force that is nearly equal to the condensation free energy per unit length. The multivalent cation concentration dependence for this condensation force gives the apparent number of multivalent cations that bind DNA upon condensation. The measurements show that the lower critical concentration for cobalt hexammine as compared to spermidine is due to a difference in ion binding, not a difference in the electrostatic energy of the condensed state as previously thought. We also show that the resolubilization of condensed DNA can be described using a traditional Manning–Oosawa cation adsorption model, provided that cation–anion pairing at high electrolyte concentrations is taken into account. Neither overcharging nor significant alterations in the condensed state are required to describe the resolubilization of condensed DNA. The same model also describes the spermidine³⁺/Na⁺ phase diagram measured previously.     

Localisation and dynamics of sodium counterions around DNA in solution from molecular dynamics simulation

The localisation and dynamics of sodium counterions around the DNA duplex d(AGCGTACTAGTACGCT)₂ corresponding to the trp operator fragment used in the crystal structure of the half site complex has been studied by a 1.4 ns molecular dynamics simulation in explicit solvent. A continuous and well-defined counterion density is shown to be present around the minor groove, while density patches are found in the major groove in regions where DNA bending is observed. A residence time analysis reveals the dynamic nature of these distributions. The resulting picture agrees with previous theoretical and experimental studies of A-tract DNA sequences, and is consistent with the polyelectrolyte condensation model. Received: 12 August 1999 / Revised version: 11 November 1999 / Accepted: 7 December 1999