Specific interactions versus counterion condensation. 2. Theoretical treatment within the counterion condensation theory

Polyuronates such as pectate and alginate are very well-known examples of biological polyelectrolytes undergoing, upon addition of divalent cations, an interchain association that acts as the junction of an eventually formed stable hydrogel. In the present paper, a thermodynamic model based on the counterion condensation theory has been developed to account for this cation-induced chain pairing of negatively charged polyelectrolytes. The strong interactions between cross-linking ions and uronate moieties in the specific binding site have been described in terms of chemical bonding, with complete charge annihilation between the two species. The chain-pairing process is depicted as progressively increasing with the concentration of cross-linking counterions and is thermodynamically defined by the fraction of each species. On these bases, the total Gibbs energy of the system has been expressed as the sum of the contributions of the Gibbs energy of the (single) chain stretches and of the (associated) dimers, weighted by their respective fractions 1 - theta and theta. In addition, the model assumes that the condensed divalent counterions exhibit an affinity free-energy for the chain, G(C)(aff,0), and the junction, G(D)(aff,0), respectively. Moreover, a specific Gibbs energy of chemical bonding, G(bond,0), has been introduced as the driving force for the formation of dimers. The model provides the mathematical formalism for calculating the fraction, theta, of chain dimers formed and the amount of ions condensed and bound onto the polyelectrolyte when two different types of counterions (of equal or different valence) are present. The effect of the parameter G(bond,0) has been investigated and, in particular, its difference from G(C,D)(aff,0) was found to be crucial in determining the distribution of the ions into territorial condensation and chemical bonding, respectively. Finally, the effect of the variation of the molar ratio between cross-linking ions and uronic groups in the specific binding sites, sigma0, was evaluated. In particular, a remarkable decrease in the amount of condensed counterions has been pointed out in the case of sigma0 = 1/3, with respect to the value of sigma0 = 1/4, characterizing the traditional "egg-box" structure, as a result of the drop of the charge density of the polyelectrolyte induced by complete charge annihilation.     

Thermodynamics of the conformational transition of biopolyelectrolytes: the case of specific affinity of counterions.

A formal development of the Counterion Condensation theory (CC) of linear polyelectrolytes has been performed to include specific (chemical) affinity of condensed counterions, for polyelectrolyte charge density values larger than the critical value of condensation. It has been conventionally assumed that each condensed counterion exhibits an affinity free-energy difference for the polymer, (DeltaG(aff)). Moreover, the model assumes that the enthalpic and entropic contributions to DeltaG(aff), i.e., DeltaH(aff) and DeltaS(aff), are both independent of temperature, ionic strength and polymer concentration. Equations have been derived relative to the case of the thermally induced, ionic strength dependent, conformational transition of a biopolyelectrolyte between two conformations for which chemical affinity is supposed to take place. The experimental data of the intramolecular conformational transition of the ionic polysaccharide kappa-carrageenan in dimethylsulfoxide (DMSO) have been successfully compared with the theoretical predictions. This novel approach provides the enthalpic and entropic affinity values for both conformations, together with the corresponding thermodynamic functions of nonpolyelectrolytic origin pertaining to the biopolymer backbone change per se, i.e., DeltaH(n.pol) and DeltaS(n.pol), according to a treatment previously shown to be successful for lower values of the biopolyelectrolyte linear charge density. The ratio of DeltaH(n.pol) to DeltaS(n.pol) was found to be remarkably constant independent of the value of the dielectric constant of the solvent, from formamide to water to DMSO, pointing to the identity of the underlying conformational process.     

Alginate degradation by bacteria isolated from the gut of sea urchins and abalones

Degradation of alginate and its constituents, polymannuronate (polyM) and polyguluronate (polyG), by gut bacteria isolated from sea urchins and abalones in the northern part of Japan, were investigated. Bacterial counts in the guts of sea urchin S. intermedius, were 10⁵ to 10⁸ CFU/g, and in abalone H. discus hannai, counts ranged from 10⁶ to 10⁹ CFU/g. More than 80% of total 600 isolates were found to have alginolytic activity. The alginolytic bacteria were predominantly fermentative, but some differences were observed in their substrate specificity as well as between the flora in the gut of sea urchins and the abalones. Seventy percent of the alginolytic bacteria from the sea urchins showed no degrading preference for polyM or polyG blocks, and were able to degrade both the substrates simultaneously. Most of the alginolytic bacteria (96.6%) from sea urchins belonged to the genus Vibrio. The majority of alginolytic bacteria (68.0% on average) from abalones only degraded polyG and they were predominantly non-motile fermenters. From these results, it appeared that a different type of association exists between alginolytic gut microflora and the marine algal feeders with respect to the level of contribution by bacteria to the host's digestion of alginate. Correspondence to: T. Sawabe     

Evaluation of the counterion condensation theory of polyelectrolytes.

We compare free energies of counterion distributions in polyelectrolyte solutions predicted from the cylindrical Poisson-Boltzmann (PB) model and from the counterion condensation theories of Manning: CC1 (Manning, 1969a, b), which assumes an infinitely thin region of condensed counterions, and CC2 (Manning, 1977), which assumes a region of finite thickness. We consider rods of finite radius with the linear charge density of B-DNA in 1-1 valent and 2-2 valent salt solutions. We find that under all conditions considered here the free energy of the CC1 and the CC2 models is higher than that of the PB model. We argue that counterion condensation theory imposes nonphysical constraints and is, therefore, a poorer approximation to the underlying physics based on continuum dielectrics, point-charge small ions, Poisson electrostatics, and Boltzmann distributions. The errors in counterion condensation theory diminish with increasing distance from, or radius of, the polyion.     

Limiting-laws of polyelectrolyte solutions. Ionic distribution in mixed-valency counterions systems. I: The model

An extension of the counterion-condensation (CC) theory of linear polyelectrolytes has been developed for the case of a system containing a mixture of counterions of different valency, i and j. The main assumption in the derivation of the model is that the relative amount of the condensed counterions of the type i and j is strongly correlated and it is determined by the overall physical bounds of the system. The results predicted by the model are consistent, in the limiting cases of single species component, with those of the original CC theory. The most striking results are obtained for the cases of low charge density and excess of counterion species: in particular, an apparent positive "binding" cooperativity of divalent ions is revealed for small, increasing additions of M2+ ions to a solution containing a swamping amount of monovalent salt and a polyelectrolyte of low charge density. Apparent "competitive binding" of mono- and divalent ions derives as a bare consequence of the electrostatic interactions. Theoretical calculations of experimentally accessible quantities, namely single-(counter) ion activity coefficients, confirm the surprising predictions at low charge density, which qualitatively agree with the measured quantities.     

Purification and partial characterization of an extracellular alginate lyase from <Emphasis Type="Italic">Aspergillus oryzae</Emphasis> isolated from brown seaweed

The extracellular enzyme alginate lyase produced from marine fungus Aspergillus oryzae isolated from brown alga Dictyota dichotoma was purified, partially characterized, and evaluated for its sodium alginate depolymerization abilities. The enzyme characterization studies have revealed that alginate lyase consisted of two polypeptides with about 45 and 50 kDa each on 10% sodium dodecyl sulfate polyacrylamide gel electrophoresis and showed 140-fold higher activity than crude enzyme under optimized pH (6.5) and temperature (35°C) conditions. Zn²⁺, Mn²⁺, Cu²⁺, Mg²⁺, Co²⁺ and NaCl were found to enhance the enzyme activity while (Ca²⁺, Cd²⁺, Fe²⁺, Hg²⁺, Sr²⁺, Ni²⁺), glutathione, and metal chelators (ethylenediaminetetraacetic acid and ethylene glycol tetraacetic acid) suppressed the activity. Fourier transform infrared and thin-layer chromatography analysis of depolymerized sodium alginate indicated the enzyme specificity for cleaving at the β-1,4 glycosidic bond between polyM and polyG blocks of sodium alginate and therefore resulted in estimation of relatively higher polyM content than polyG. Comparison of chemical shifts in ¹³C nuclear magnetic resonance spectra of both polyM and polyG from that of sodium alginate also showed further evidence for enzymatic depolymerization of sodium alginate.     

Counterion-induced condesation of deoxyribonucleic acid. a light-scattering study.

The addition of the trivalent or tetravalent cations spermidine or spermine to a solution of T7 DNA in aqueous solution causes an alteration of the DNA from its extended coil form to a condensed form. If performed at low DNA concentration and at low ionic strengths, this transformation results in a monomolecular collapse to form a particle with a hydrodynamic radius of about 500 A. We have monitored this change using quasielastic and total intensity light scattering. In a solution of 50% methanol in water, the divalent cations Mg2+ and putrescine also can cause the condensation of DNA. Using Manning's (1978) counterion condensation theory, we calculate a striking unity among these disparate ions: the collapse occurs in each case when from 89 to 90% of the DNA phosphate charges are neutralized by condensed counterions.     

Application of polyelectrolyte theories for analysis of DNA melting in the presence of Na+ and Mg2+ ions.

Numerical calculations, using Poisson-Boltzmann (PB) and counterion condensation (CC) polyelectrolyte theories, of the electrostatic free energy difference, DeltaGel, between single-stranded (coil) and double-helical DNA have been performed for solutions of NaDNA + NaCl with and without added MgCl2. Calculations have been made for conditions relevant to systems where experimental values of helix coil transition temperature (Tm) and other thermodynamic quantities have been measured. Comparison with experimental data has been possible by invoking values of Tm for solutions containing NaCl salt only. Resulting theoretical values of enthalpy, entropy, and heat capacity (for NaCl salt-containing solutions) and of Tm as a function of NaCl concentration in NaCl + MgCl2 solutions have thus been obtained. Qualitative and, to a large extent, quantitative reproduction of the experimental Tm, DeltaHm, DeltaSm, and DeltaCp values have been found from the results of polyelectrolyte theories. However, the quantitative resemblance of experimental data is considerably better for PB theory as compared to the CC model. Furthermore, some rather implausible qualitative conclusions are obtained within the CC results for DNA melting in NaCl + MgCl2 solutions. Our results argue in favor of the Poisson-Boltzmann theory, as compared to the counterion condensation theory.     

The binding of divalent metal ions to polyelectrolytes in mixed counterion systems. II. Dextransulfate-Mg2+ and dextransulfate-Ca2+ in solutions containing added NaCl or KCl

Measurements of magnesium and calcium ion activities in solutions of the polyelectrolyte dextransulfate, with added sodium chloride or potassium chloride are presented. A two wavelength dye spectrophotometric method is used. Dextransulfate concentrations Cp (expressed as moles sulfate ion/litre) vary between 0.001 and 0.007, total ionic strengths between 0.005 and 0.08 mole/XXX. Divalent metal ion concentrations are varied between 0 and 1.2 Cp. The results for the metal ion activities are expressed in the form of parameters theta2 = C2/Cp (C(2bp) = bound divalent metal ion concentration) and K2 = theta2/(C2-C2b). For each divalent/univalent counterion pair the values obtained for theta2 and K2 as a function of C2,Cp, and ionic strength are compared to predictions of the "two variable theory" developed for these mixed counterion systems by Manning. This comparison shows that the observed decrease in theta2 with increasing ionic strength at fixed C2 and Cp is generally well predicted by the two variable theory. The extent of divalent ion binding at a given C2, Cp, and ionic strength is largest for the Ca/Na counterion combination, and lowest for the Mg/K combination.     

The role of counterion on the thermotropic phase behavior of DODAB and DODAC vesicles

Dioctadecyldimethylammonium bromide and chloride surfactants (DODAX, X representing Br(-) or Cl(-) counterions) assemble in water, above their melting temperatures (T(m)), as cationic unilamellar vesicles at the typical surfactant concentration of 1.0mM. The larger T(m) of DODAC (49 degrees C) relative to DODAB (45 degrees C) has been attributed to the differing affinity and binding specificity of the counterions to the vesicle interfaces. In this communication it is reported differential scanning calorimetry (DSC), conductimetry and dynamic light scattering (DLS) data for mixtures of DODAB and DODAC in water at 1.0mM total surfactant concentration and varying surfactant concentration, to investigate the effect of counterion on the pre-, main- and post-transition temperatures (T(s), T(m) and T(p)), and the data compared to the neat surfactants in water. Accordingly, T(m) increases sigmoidally from 45.8 to 48.9 degrees C when DODAC molar fraction (x(DODAC)) is varied from 0 to 1. Neat DODAB exhibits in addition to T(m), T(s) and T(p) that are inhibited by DODAC. The main peak width DeltaT(1/2) does not depend on the surfactant molar fraction but the melting enthalpy change DeltaH is smaller for DODAB-rich dispersions due to the stronger affinity of Br(-). The conductivity and the apparent hydrodynamic diameter as well do not vary much with x(DODAB), indicating that the surface charge density is similar for DODAB and DODAC, evidencing the role of the counterion binding specificity and affinity on the properties of DODAX vesicles.     

A commentary on the screened-Oseen, counterion-condensation formalism of polyion electrophoresis

The use of linear theory, in particular, counterion condensation (CC) theory, in describing electrophoresis of polyelectrolyte chains, is criticized on several grounds. First, there are problems with CC theory in describing the equilibrium distribution of ions around polyelectrolytes. Second, CC theory is used to treat ion relaxation in a linear theory with respect to the polyion charge despite the fact that ion relaxation arises as a consequence of nonlinear charge effects. This nonlinearity has been well established by several investigators over the last 70 years for spherical, cylindrical, and arbitrarily shaped model polyions. Third, current use of CC theory ignores the electrophoretic hindrance as well as the ion relaxation for condensed counterions and only includes such interactions for uncondensed counterions. Because most of the condensed counterions lie outside the shear surface of the polyion (in the example of DNA), the assumption of ion condensation is artificial and unphysical. Fourth, the singular solution, based on a screened Oseen tensor, currently used in the above mentioned theories is simply wrong and fails to account for the incompressibility of the solvent. The actual singular solution, which has long been available, is discussed. In conclusion, it is pointed out that numerical alternatives based on classic electrophoresis theory (J.T.G. Overbeek, Kolloid-Beih, 1943, 54:287-364) are now available.     

Thermodynamic consequences of grafting enhanced affinity toward the mutated antigen onto an antibody. The case of anti-lysozyme antibody, HyHEL-10

In order to address the mechanism of enhancement of the affinity of an antibody toward an antigen from a thermodynamic viewpoint, anti-hen lysozyme (HEL) antibody HyHEL-10, which also recognize the mutated antigen turkey lysozyme (TEL) with reduced affinity, was examined. Grafting high affinity toward TEL onto HyHEL-10 was performed by saturation mutagenesis into four residues (Tyr(53), Ser(54), Ser(56), and Tyr(58)) in complementarity-determining region 2 of the heavy chain (CDR-H2) followed by selection with affinity for TEL. Several clones enriched have a Phe residue at site 58. Thermodynamic analyses showed that the clones selected had experienced a greater than 3-fold affinity increase toward TEL in comparison with wild-type Fv, originating from an increase in negative enthalpy change. Substitution of HyHEL-10 HTyr(58) with Phe led to the increase in negative enthalpy change and to almost identical affinity for TEL in comparison with mutants selected, indicating that mutations at other sites decrease the entropy loss despite little contribution to the affinity for TEL. These results suggest that the affinity of an antibody toward the antigen is enhanced by the increase in enthalpy change by some limited mutation, and excess entropy loss due to the mutation is decreased by other energetically neutral mutations.     

Differential hydration of dA.dT base pairing and dA and dT bulges in deoxyoligonucleotides

The role of water in the formation of stable duplexes of nucleic acids is being studied by determining the concurrent volume change, heats, and counterion uptake that accompany the duplexation process. The variability of the volume contraction that we have observed in the formation of a variety of homoduplexes suggests that sequence and conformation acutely affect the degree of hydration. We have used a combination of densimetric and calorimetric techniques to measure the change in volume and enthalpy resulting from the mixing of two complementary strands to form (a) fully paired duplexes with 10 or 11 base pairs and (b) bulged decameric duplexes with an extra dA or dT unmatched residue. We also monitored absorbance vs temperature profiles as a function of strand and salt concentration for all four duplexes. Relative to the decamer duplex, insertion of an extra dA.dT base pair to form an undecamer duplex results in a favorable enthalpy of -5.6 kcal/mol that is nearly compensated by an unfavorable entropy term of -5.1 kcal/mol. This enthalpy difference correlates with a differential uptake of water molecules, corresponding to an additional hydration of 16 mol of water molecules/mol of base pair. Relative to the fully paired duplexes, both bulged duplexes are 12-16 degrees C less stable and exhibit marginally larger counterion uptake on forming the duplex. The enthalpy change is slightly lower for the T-bulge duplex and less still for the A-bulge duplex. The volume change results indicate that an unmatched residue increases the amount of coulombic and/or structural hydration. The combined results strongly suggest that the destabilizing forces in bulged duplexes are partially compensated by an increase in hydration levels.     

Divalent forms of CC49 single-chain antibody constructs in Pichia pastoris: expression, purification, and characterization

Single-chain variable fragments (scFvs) are tumor-recognition units that hold enormous potential in antibody-based therapeutics. Their clinical applications, however, require the large scale production and purification of biologically active recombinant scFvs. In the present study, we engineered and expressed divalent non-covalent [(scFv)(2)-His(6)] and covalent [sc(Fv)(2)-His(6)] scFvs of a tumor-associated monoclonal antibody (MAb) CC49 in Pichia pastoris. The purity and immunoreactivity of the scFvs were analyzed by SDS-PAGE, HPLC, and competitive ELISA. The binding affinity constant (K(A)), determined by surface plasmon resonance analysis using BIAcore, was 4.28 x 10(7), 2.75 x 10(7), and 1.14 x 10(8) M(-1) for (scFv)(2)-His(6), sc(Fv)(2)-His(6), and CC49 IgG, respectively. The expression of scFvs in P. pastoris was 30 to 40-fold higher than in Escherichia coli. Biodistribution studies in athymic mice bearing LS-174T human colon carcinoma xenografts showed equivalent tumor-targeting of CC49 dimers generated in yeast (scFv)(2)-His(6) and bacteria (scFv)(2) with 12.52% injected dose/gram (%ID/g) and 11. 42%ID/g, respectively, at 6 h post-injection. Interestingly, the pharmacokinetic pattern of dimeric scFvs in xenografted mice exhibited a slower clearance of His-tagged scFvs from the blood pool than scFvs lacking the His-tag (0.1 >/= p >/= 0.05). In conclusion, improved yields of divalent scFvs were achieved using the P. pastoris expression/secretion system. The in vitro and in vivo properties of these scFvs suggest possible therapeutic applications.     

Study of the DNA/ethidium bromide interactions on mica surface by atomic force microscope: influence of the surface friction

The influence of mica surface on DNA/ethidium bromide interactions is investigated by atomic force microscopy (AFM). We describe the diffusion mechanism of a DNA molecule on a mica surface by using a simple analytical model. It appears that the DNA diffusion on a mica surface is limited by the surface friction due to the counterion correlations between the divalent counterions condensed on both mica and DNA surfaces. We also study the structural changes of linear DNA adsorbed on mica upon ethidium bromide binding by AFM. It turns out that linear DNA molecules adsorbed on a mica surface are unable to relieve the topological constraint upon ethidium bromide binding. In particular, strongly adsorbed molecules tend to be highly entangled, while loosely bound DNA molecules appear more extended with very few crossovers. Adsorbed DNA molecules cannot move freely on the surface because of the surface friction. Therefore, the topological constraint increases due to the ethidium bromide binding. Moreover, we show that ethidium bromide has a lower affinity for strongly bound molecules due to the topological constraint induced by the surface friction.     

Measurement of Cationic and Intracellular Modulation of Integrin Binding Affinity by AFM-Based Nanorobot

Integrins are dynamic transmembrane cation-dependent heterodimers that both anchor cells in position and transduce signals into and out of cells. We used an atomic force microscope (AFM)-based nanorobotic system to measure integrin-binding forces in intact human intestinal epithelial Caco-2 cells. The AFM-based nanorobot enables human-directed, high-accuracy probe positioning and site-specific investigations. Functionalizing the AFM probe with an arginine-glycine-aspartate (RGD)-containing sequence (consensus binding sequence for integrins) allowed us to detect a series of peptide-cell membrane interactions with a median binding force of 115.1 ± 4.9 pN that were not detected in control interactions. Chelating divalent cations from the culture medium abolished these interactions, as did inhibiting intracellular focal adhesion kinase (FAK) using Y15. Adding 1 mM Mg²⁺ to the medium caused a rightward shift in the force-binding curve. Adding 1 mM Ca²⁺ virtually abolished the RGD-membrane specific interactions and blocked the Mg²⁺ effects. Cell adhesion assays demonstrated parallel effects of divalent cations and the FAK inhibitor on cell adhesion. These results demonstrate direct modulation of integrin-binding affinity by both divalent cations and intracellular signal inhibition. Additionally, three binding states (nonspecific, specific inactivated, and specific activated) were delineated from affinity measurements. Although other research has assumed that this process of integrin conformational change causes altered ligand binding, in this work we directly measured these three states in individual integrins in a physiologically based study.     

Microcalorimetric investigation of the interaction of calmodulin with seminalplasmin and myosin light chain kinase

Flow microcalorimetric titrations of calmodulin with seminalplasmin at 25 degrees C revealed that the high affinity one-to-one complex in the presence of Ca2+ (Comte, M., Malnoe, A., and Cox, J. A. (1986) Biochem. J. 240, 567-573) is entirely enthalpy-driven (delta H0 = -50 kJ.mol-1; delta S0 = O J.K-1.mol-1; delta Cp0 = O J.K-1.mol-1) and is not influenced by the proton or Mg2+ concentration. The Sr2+- and Cd2+-promoted high affinity complexes are also exothermic for -49 and -45 kJ.mol-1, respectively. The observed low affinity interaction in the absence of divalent ions displays no enthalpy change. No enthalpy changes are observed when calmodulin and seminalplasmin are mixed in the presence of millimolar concentrations of Mg2+, Zn2+, or Mn2+. Enthalpy titrations of the 1:1 calmodulin-seminalplasmin complex with Ca2+ and of partly Ca2+-saturated calmodulin with seminalplasmin revealed that only the species calmodulin.Can greater than or equal to 2 is fully competent for high affinity interaction with seminalplasmin. Binding of the second Ca2+ is strongly enhanced (K2 greater than or equal to 5 X 10(7) M-1) as compared to that in free calmodulin (K2 = 2.6 X 10(5) M-1). This is essentially due to the concomitant strongly exothermic step of isomerization of the calmodulin-seminalplasmin complex from its low to its high affinity form. Binding of the remaining two Ca2+ to the high affinity seminalplasmin-calmodulin complex displays the same affinity constants and endothermic enthalpy change as in free calmodulin. A microcalorimetric study on the complex formation between Ca2+-saturated calmodulin and turkey gizzard myosin light chain kinase revealed that the interaction is strongly exothermic with an important overall gain of order (delta H0 = -85 kJ.mol-1; delta S0 = -122 J.K-1.mol-1) and occurs with significant proton uptake (0.44 H+ per mol at pH 7.5). The observed low affinity interaction (K = 2.2 X 10(5) M-1) in the absence of Ca2+ (Mamar-Bachi, A., and Cox, J. A. (1987) Cell Calcium 8, 473-482) displays neither a change in enthalpy nor in protonation.     

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.     

On the application of polyelectrolyte limiting laws to the helix-coil transition of DNA. IV. Depedence of helix stability on the concentration of divalent metal ions.

The molecular theory of the previous paper in this series is extended to determine the effect of divalent metal ions on helix stability relative to coil at fixed ionic strength and nucleotide phosphate concentration. Specification of the state of condensed counterions, as well as their concentration, is essential for the solution of this problem, and it is assumed that they translate freely within a thin cylindrical shell close to the polynucleotide. As a function of divalent counterion concentration m the relative stability of the helix is highly nonlinear. Although the overall trend is that the helix stability increases with addition of divalent metal ion, there is a narrow concentration range for which it decreases slightly. The behavior of the relative stability as a function of m is determined by the translational degrees of freedom of the counterions, both univalent and divalent, both condensed and uncondensed. Detailed comparison of the theory with data is not given here, but it is pointed out that the calculated values of the relative stability are consistent with the order of magnitude of the observed effect Mg²⁺ on the melting temperature.     

The effects of sodium and magnesium-ion interactions on chromatin structure and solubility

The effects of sodium and magnesium-ion interactions on chromatin structure and solubility were examined in isolated mouse liver nuclei. To facilitate this study, a simple assay of chromatin structure was developed, based on the absorbances at 260 nm (A260) and 320 nm (A320) of nuclei in test solutions. By subtracting the A320 from the A260, a single "spectral index" was obtained which served as a useful, but not absolute, indicator of chromatin structure. Electron microscopy verified the validity of this approach. The results indicate that either 200 mM NaCl or 0.5 mM MgCl2 were capable of preserving the native 20 to 30 nm chromatin fiber structure. Below 200 mM NaCl, the native fiber progressively uncoiled to the 10 nm unit fiber. The presence of 0.5 mM MgCl2 inhibited this uncoiling. Only divalent cations stabilized condensed chromatin (heterochromatin) within the nucleus. Monovalent and divalent cations interacted with one another at critical concentrations and modified their individual effects on chromatin structure; e.g., 10 to 25 mM NaCl interfered with the action of 0.5 to 1.5 mM MgCl2, causing a complete loss of condensed chromatin. Maximum solubility of micrococcal nuclease-digested chromatin occurred at 10 mM NaCl, which treatment allowed the chromatin to unfold to the 10 nm fiber. However, ionic conditions that disrupted condensed chromatin but maintained the native chromatin fiber morphology still resulted in relatively high yields of soluble chromatin. Minimum solubility occurred under conditions which preserved the structure of condensed chromatin.