John Warren Williams

The osmotic, sedimentation, and diffusion coefficients of sonicated sodium DNA in aqueous solutions which were rendered rigorously free of salts have been obtained in order to study the polyelectrolyte effect on these parameters. Both native and heat denatured DNA's were studied. All three parameters were found to be independent of concentration between 2 and 10 mmole/1. The osmotic coefficient gives the fraction of counterions not immobilized by the polyelectrolyte potential, under conditions of equilibrium. The value (ca. 0.18) obtained for this fraction agrees very well with that predicted by a theory of rodlike polyelectrolytes. A simplified model that permits the computation of fractions of mobile ions from sedimentation and diffusion coefficients, when applied to the experimental data, showed that under these conditions of flow between 0.5 to 0.9 of counterions are not immobilized. The experimental data also showed that for native DNA the translation frictional coefficient seems to have different values in sedimentation and diffusion, which agrees with a finding reported for another saltfree polyelectrolyte. For denatured DNA, however, the values were found to be equal: no satisfactory explanation could be found for this difference of behavior.     

Polyelectrolyte behavior of carrageenans in aqueous solutions

Osmotic coefficients of sodium, potassium, and calcium counterions have been determined in aqueous solutions on kappa-, iota-, and lambda-carrageenans at 25°C. The experimental results are correlated with the calculated ones from the limiting law of Manning. An orderd secondary structure exists in kappa- and iota-carrageenans. Its stability is discussed as a function of temperature, ionic strength, and the nature of the counterions.     

Electrooptical study of the electric polarizability of rodlike fragments of DNA

The anisotropy of electrical polarizability of rodlike fragments of DNA has been studied by a number of electro-optical methods: Kerr effect (combined with flow birefringence), light scattering, diehroism, and fluorescence in an electric field. The most sensitive technique (Kerr effect) has been used to study the variation of the polarizability with the nature and concentration of counteroins. DNA fragments constitute a truly rigid polyelectrolyte of known structure. The value obtained can then be quantitatively compared to the predictions of those of the theories of the longitudinal polarizability of rigid polyelectrolytes which are based on true molecular parameters. The comparison emphasizes the role of the counterion–counterion repulsion. Oosawa's theory seems to represent the best approach but fails to explain the differences observed between monovalent and divalent ions.     

Interactions of mono- and divalent counterions with alkali- and enzyme-deesterified pectins in salt-free solutions

The free fractions of monovalent and divalent counterions were determined on salt-free solutions of pectins. The effects of charge density, distribution of the carboxyl groups, polymer concentration, and the nature of the counterion were investigated by determinating the calcium and sodium activity coefficients (with specific electrodes) and by measuring the transport parameters (by conductimetry). Poor agreement for calcium ions was found with the Manning theory. The strong binding of these ions to highly charged polymers, which is ascribed to a dimerization process was demonstrated in very dilute solutions.     

A new model of counterion condensation in polyelectrolyte solutions. III. Theoretical predictions of competitive condensation between counterions of different valences

Our model has been extended for theoretical estimation of competitive condensation of counterions of different valences onto polyelectrolytes in solution. The estimations are compared with those obtained from Manning theory and with experimental data on counterion activity coefficients. The agreement with the data for sodium polystyrenesulfonate/MgCl2, CaCl2 is satisfactory.     

THE ELIMINATION OF DISCREPANCIES BETWEEN OBSERVED AND CALCULATED P.D. OF PROTEIN SOLUTIONS NEAR THE ISOELECTRIC POINT WITH THE AID OF BUFFER SOLUTIONS

1. It had been noticed in the previous experiments on the influence of the hydrogen ion concentration on the P.D. between protein solutions inside a collodion bag and aqueous solutions free from protein that the agreement between the observed values and the values calculated on the basis of Donnan''s theory was not satisfactory near the isoelectric point of the protein solution. It was suspected that this was due to the uncertainty in the measurements of the pH of the outside aqueous solution near the isoelectric point. This turned out to be correct, since it is shown in this paper that the discrepancy disappears when both the inside and outside solutions contain a buffer salt. 2. This removes the last discrepancy between the observed P.D. and the P. D. calculated on the basis of Donnan''s theory of P.D. between membrane equilibria, so that we can state that the P.D. between protein solutions inside collodion bags and outside aqueous solutions free from protein can be calculated from differences in the hydrogen ion concentration on the opposite sides of the membrane, in agreement with Donnan''s formula.     

THE COMBINATION OF SALTS AND PROTEINS. I

1. It has been found that the ratios of the total concentrations of Ca, Mg, K, Zn, inside and outside of gelatin particles do not agree with the ratios calculated according to Donnan''s theory from the hydrogen ion activity ratios. 2. E.M.F. measurements of Zn and Cl electrode potentials in such a system show, however, that the ion activity ratios are correct, so that the discrepancy must be due to a decrease in the ion concentration by the formation of complex ions with the protein. 3. This has been confirmed in the case of Zn by Zn potential measurements in ZnCl₂ solutions containing gelatin. It has been found that in 10 per cent gelatin containing 0.01 M ZnCl₂ about 60 per cent of the Zn⁺⁺ is combined with the gelatin. 4. If the activity ratios are correctly expressed by Donnan''s equation, then the amount of any ion combined with a protein can be determined without E.M.F. measurements by determining its distribution in a proper system. If the activity ratio of the hydrogen ion and the activity of the other ion in the aqueous solution are known, then the activity and hence the concentration of the ion in the protein solution can be calculated. The difference between this and the total molar concentration of the ion in the protein represents the amount combined with the protein. 5. It has been shown that in the case of Zn the values obtained in this way agree quite closely with those determined by direct E.M.F. measurements. 6. The combination with Zn is rapidly and completely reversible and hence is probably not a surface effect. 7. Since the protein combines more with Zn than with Cl, the addition of ZnCl₂ to isoelectric gelatin should give rise to an unequal ion distribution and hence to an increase in swelling, osmotic pressure, and viscosity. This has been found to be the case.     

Predicting the Activity Coefficients of Free-Solvent for Concentrated Globular Protein Solutions Using Independently Determined Physical Parameters

The activity coefficient is largely considered an empirical parameter that was traditionally introduced to correct the non-ideality observed in thermodynamic systems such as osmotic pressure. Here, the activity coefficient of free-solvent is related to physically realistic parameters and a mathematical expression is developed to directly predict the activity coefficients of free-solvent, for aqueous protein solutions up to near-saturation concentrations. The model is based on the free-solvent model, which has previously been shown to provide excellent prediction of the osmotic pressure of concentrated and crowded globular proteins in aqueous solutions up to near-saturation concentrations. Thus, this model uses only the independently determined, physically realizable quantities: mole fraction, solvent accessible surface area, and ion binding, in its prediction. Predictions are presented for the activity coefficients of free-solvent for near-saturated protein solutions containing either bovine serum albumin or hemoglobin. As a verification step, the predictability of the model for the activity coefficient of sucrose solutions was evaluated. The predicted activity coefficients of free-solvent are compared to the calculated activity coefficients of free-solvent based on osmotic pressure data. It is observed that the predicted activity coefficients are increasingly dependent on the solute-solvent parameters as the protein concentration increases to near-saturation concentrations.     

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.     

Analysis of circular dichroism spectra of homopurine: homopyrimidine DNA's for sequence information and comparison of results with heterobase DNA

Procedures are developed which make a first neighbor frequency analysis possible from a CD spectrum of homopyrimidine: homopurine DNA's. The contribution to the CD spectrum from the various first neighbor frequencies present in homopyrimidine: homopurine-type DNA's has been determined, and hence the CD spectrum for any DNA of this type with known first neighbor frequencies can easily be calculated. An identical analysis is presented for the determination of extinction coefficients. It is further shown that unlike the more usual heteropurine–pyrimidine DNA's a random sequence does not lead to a simplified formalism. Finally, it is concluded that the homopyrimidine: homopurine DNA's have a structure that is different from that of the more usual heterobase DNA's. A procedure capable of determining first neighbor frequencies from a CD spectrum for heterobase and/or homopurine: homopyrimidine DNA's is described. This procedure is used to determine that there is only minimal interference between these two types of DNA in the first neighbor analysis.     

Molecular basis of the apparent near ideality of urea solutions

Activity coefficients of urea solutions are calculated to explore the mechanism of its solution properties, which form the basis for its well-known use as a strong protein denaturant. We perform free energy simulations of urea solutions in different urea concentrations using two urea models (OPLS and KBFF models) to calculate and decompose the activity coefficients. For the case of urea, we clarify the concept of the ideal solution in different concentration scales and standard states and its effect on our subsequent analysis. The analytical form of activity coefficients depends on the concentration units and standard states. For both models studied, urea displays a weak concentration dependence for excess chemical potential. However, for the OPLS force-field model, this results from contributions that are independent of concentration to the van der Waals and electrostatic components whereas for the KBFF model those components are nontrivial but oppose each other. The strong ideality of urea solutions in some concentration scales (incidentally implying a lack of water perturbation) is discussed in terms of recent data and ideas on the mechanism of urea denaturation of proteins.     

Polyion-counterion interaction behavior for sodium carboxymethylcellulose in methanol-water mixed solvent media

Precise measurements on the electrical conductivities have been reported for solutions of sodium carboxymethylcellulose in methanol-water mixed solvent media. The conductivity vs. concentration data have been analyzed on the basis of the scaling theory approach for semidilute polyelectrolyte conductivity. The effects of the temperature, the medium, and the polymer concentration on the fractions of uncondensed counterions, the polyion conductivities, the standard state free energies of counterion association, and the coefficients of friction between the polyion and the solvent have also been investigated and the results have been interpreted from the viewpoints of polyion-countreion interactions, effective charge on the polyion, solvation of counterions and the polyionic sites, and counterion dissociation.     

Activity coefficients of antibiotics in aqueous NaCl solutions at 298.2 K

Data at 298.2 K for aqueous NaCl solutions containing either D-phenylglycin, D-(p-hydroxy)phenylglycine, 6-amino penicillanic acid (6-APA), amoxicillin or ampicillin, are reported. The mean ionic activity coefficients of NaCl were determined from measurements of the responses of a sodium and a chloride ion-selective electrode. The activity coefficients of the precursors or the antibiotics were calculated from the values of the mean ionic activity coefficients using the exact cross differential relation between them. The correlation of solubility data using the activity coefficients measured in this work shows the same puzzling results previously observed in systems containing amino acids.     

Effect of counterions on complex coacervation

In a recent paper, we developed a thermodynamic theory on the complex coacervation in the absence of low molecular ions, under the assumption that the coacervation is a condensation phenomenon of aggregates of polyanion and polycation in the aqueous solution, by obtaining the interaction potential U_S between these aggregates on the basis of Flory's method. In this paper, we have extended the theory to a more complicated phenomenon of the counterion-containing solutions. This treatment has led the interaction potential having an additional contribution to U_S resulting from an entropy increase by the counterion distribution. The phase diagram between solution (sol) and separated phase has been obtained as a function of the difference of charges between polyanion and polycation. It has been found that the presence of counterions sensitively suppresses the coacervation.     

Specific helix stabilization of poly(L-glutamic acid) in mixed counterion systems

The coil–helix transitions of poly (L -glutamic acid) in aqueous alcohol solutions have been investigated for mixed counterion systems. It has been found that coexistence of two kinds of counterion species, i.e., two alkali metal counterions, alkali and alkaline earth metal, and two alkaline earth metals, specifically stabilizes or destabilizes the helix conformation depending upon the combination of the counterion species. The most striking enhancement of the helix content was observed for the combination of Li⁺ and K⁺ counterions. It has been suggested that the helix stabilization is attributed to the reduction of the free energy in the contact ion pair formation between the polymer charges and the counterions in the mixed counterion systems. © 1993 John Wiley & Sons, Inc.     

Some speculations on the rate of adhesion of cells to coverslips

Suspensions of mouse tumour cells were cultured over glass coverslips, and their rate of adhesion to the coverslips measured. The interaction energies between the cell and coverslip surfaces were computed according to DLVO-theory, on the basis of experimentally determined parameters, for a wide range of values of Hamaker's coefficients. The secondary attractive minimum was computed to occur when the two surfaces were separated by 40–85 Å. It was observed that 50% of the cells adhered to the coverslips after 30 minutes, although it was calculated that they could gravitate to the position of the secondary minima in approximately 5 minutes. We have discussed this delay of 25 minutes in terms of the mechanisms of cell adhesion to the coverslips.     

Statistical determination of the average values of the extinction coefficients of tryptophan and tyrosine in native proteins.

Spectroscopic measurement of protein concentration requires knowledge of the value of the relevant extinction coefficient. If the amino acid composition of a protein is known, however, extinction coefficients can be calculated approximately, provided that the values of the molar absorptivities for tryptophan and tyrosine residues in the protein are known. We have applied a matrix linear regression procedure and a mapping of average absolute deviations between experimental and calculated values to find molar extinction coefficients (epsilon M, 1 cm, 280 nm) of 5540 M-1 cm-1 for tryptophan and 1480 M-1 cm-1 for tyrosine residues in an "average" protein, as defined by a set of experimentally determined extinction coefficients for more than 30 proteins. Use of these values provides a significant improvement in extinction coefficient estimation over that obtained with the commonly used values obtained from solutions of model compounds in guanidine-HCl. The consistency of these results when compared to the large deviations often observed between experimentally determined extinction coefficients suggest that this method may offer acceptable accuracy in the initial estimation of molar absorptivities of globular proteins.     

Study of the self-diffusion coefficients of cations in the presence of an acidic polysaccharide

Self-diffusion coefficient measurements have been applied to the study of Na⁺, Ca⁺⁺, and Sr⁺⁺ in the presence of a linear acidic polysaccharide extracted from cartilage, i.e., chondroitin sulfate. A series of experimental determinations was made with and without supporting electrolytes, and an analysis of experiments involving the separation of the electrostatic interaction terms by an extension of Manning's theory produced results showing the preponderant nature of these electrostatic terms. The specificity of each type of ion or the influence of the pH can be considered merely as higher order corrections with respect to the preceding interactions. Counterion concentration ranges and pH ranges were determined, where either the alkaline-earth counterions become free and hence move with their normal diffusion rate, or these cations are associated with the polyelectrolyte molecule, thus giving a diffusion coefficient similar to that of the macromolecule, or the apparent diffusion coefficients vary between these two extreme diffusion rates as a function of the association equilibria. This variation can be expressed as a function of the linear charge density parameter ξ related to the structure of the polyelectrolyte, the value of which was determined and found in good agreement with published values.     

Sodium counter ion activity of poly-S-carboxyethyl-L-cysteine

Counterion activity of poly-S-carboxyethyl-L-cysteine in salt-free solutions neutralized to various degrees with sodium hydroxide was determined either directly from the e.m.f measurements of concentration cells formed across a Na–glass electrode, or from the potentiometric titrations at different sodium chloride concentrations assuming the additivity rule. From e.m.f. measurements, the activity coefficient of counterions was confirmed to display the β-structure random coil transition of the polymer. For random coil state, both methods gave identical results. Observed values of the activity coefficient was generally smaller than those for other randomly coiled polypeptides. The activity coefficient was found to decrease with the increase of the polymer concentration. The activity coefficient of counterions for β-structure was extremely small as compared with that for random coil at the same degree of neutralization. The activity coefficient obtained from titrations was almost independent of degree of neutralization and increased with the increase of the polymer concentration.     

Limiting-laws of polyelectrolyte solutions. Ionic distribution in mixed-valency counterions systems. II. A comparison of conductometric data and theoretical predictions

The competitive binding of monovalent and divalent counterions (M+ and M2+, respectively) has been studied by a conductometric procedure as described by De Jong et al. (Biophysical Chemistry 27 (1987) 173) for aqueous solutions of alkali metal polymethacrylates in the presence of Ca (NO3)2 or Mg(NO3)2. The experimentally obtained fractions of conductometrically free counterions are compared with theoretical values computed according to a new thermodynamic model recently developed by Paoletti et al. (Biophysical Chemistry, 41 (1991) 73). For the systems studied, the fractions of free monovalent and divalent counterions can be fairly well described by the theory. In fact, the results support the assumption that under the present conditions the conductometrically obtained distribution parameters (l) and (2) approximate the equilibrium fractions of free monovalent and divalent counterions. For a degree of neutralization of 0.8 and a molar concentration ratio of divalent counterions and charged groups on the polyion up to 0.25, the mean M+/M2+, exchange ratio nu has been found to be 1.39 +/- 0.03 and 1.33 +/- 0.03 for the alkali metal/Ca/PMA and alkali metal/Mg/PMA systems, respectively. These values agree well with the theoretical value, which for this particular case is 1.38.