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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., (Copyright 1999 John Wiley & Sons, Inc.)

Voltammetric speciation data for the potassium/zinc/polymethacrylate system, recently obtained for various charge densities of the polyelectrolyte (Díaz-Cruz et al., Anal. Chim. Acta, 264 (1992) 163) and for different concentrations of monovalent counterions (van den Hoop and van Leeuwen, Anal. Chim. Acta, 273 (1993) 275), are compared with theoretical predictions computed according to a new thermodynamic model developed by Paoletti et al. (Biophys. Chem., 41 (1991) 73) and recently extended by Benegas and Paoletti (in preparation). The model allows: (i) the simultaneous condensation of both monovalent and divalent counterions and (ii) can account for a certain specific affinity of the polyelectrolyte for one type of the counterion over the other. For various charge densities of the polyelectrolyte, experimentally obtained speciation data for the K/Zn/PMA system agree well with theoretical predictions by considering an extra reduced molar affinity energy of -4RT for the Zn(2+) polyelectrolyte binding. The agreement between experimental and theoretical values for the distribution of Zn(2+) ions over the free and bound state becomes less perfect for relatively high concentrations of monovalent counterions.

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.

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.

An analysis is given of the theoretical approach to the quantitative description of proton dissociation curves for weak polyacids. The basic model of the counterion condensation theory has been used, with the modification reported in the preceding study (S. Paoletti, A. Cesàro, C. Arce Samper and J.C. Benegas, Biophys. Chem. 34 (1989) 301). In this paper we demonstrate the effect of relaxing the hypothesis of a rigid conformation on the polyelectrolytic properties of weak polyacids. As an application of the present approach, a description is given of the titration curves for two weak polyacids, poly(DL-glutamic acid) (PDLGA) and poly(L-aspartic acid) (PLAA).

The cooperative conformational transition of poly(L-glutamic acid) induced by pH is monitored by the titration curves from literature. The polyelectrolytic approach described in the preceding article (A. Cesàro, S. Paoletti and J.C. Benegas, Biophys. Chem. 39 (1991) 1) is used to fit the experimental curves under various conditions of ionic strength and temperature, with the sole assumption that each polymeric state is characterized by a proper conformational flexibility. The helix-coil transition of the system becomes molecularly defined by the balance between the non-ionic conformational energy and the repulsive electrostatic energy of the two forms. Implications of the results of the theoretical model on the energetics of the cooperative order-disorder transition are discussed.

We describe a 41-year-old man with an unusual presentation of tuberculous joint disease involving 3 peripheral joints: right knee, wrist and first metatarsophalangeal. Periarticular "cold" tuberculous abscesses were observed in the ulnar aspect of his right hand and on the lateral aspect of his first right metatarsal bone. Mycobacterium tuberculosis was isolated from his knee and both abscesses. Synovial biopsies taken from these 3 joints showed typical tuberculous granulomata. M. tuberculosis was also isolated from 3 urine samples. Neither immunodeficiency, or a predisposing condition for tuberculosis could be demonstrated. Combined surgical and antibiotic treatment was effective.

The charge-induced conformational transition of poly(alpha-L-glutamic acid) (PLGA) is considered in this paper from the point of view of proton dissociation. Equations for the excess electrostatic Gibbs energy of dissociation (i.e., delta pKa) are derived as a function of the degree of ionization, alpha. These analytical equations are used to describe some experimental dissociation curves at different polymer and salt concentrations. The dependence of the calculated delta pKa with respect to the ionic strength for the two conformational states, alpha-helical and extended coil, respectively, is rather satisfactorily explained. Even more interesting are the predictions which are derived from this approach for the transition point, alpha tr which is found to be ionic-strength dependent, in full agreement with the experimental results.

A statistical model is presented in which an ionic polymer is taken as a linear arrangement of flexible segments (similar to the spring-bead model). This model is used to represent semi-flexible linear ionic polysaccharides in solution. The distribution of end-to-end distances is taken from Monte Carlo calculations of the amylosic chain conformation and combined with Manning's counterion condensation theory of linear polyelectrolytes. The excess thermodynamic properties are then calculated as a function of the degree of ionization and of a number of physical variables. The results show that the statistical average of thermodynamic functions taken over the conformational states is not equivalent to the thermodynamic function of the average conformation. This has important implications for the correct comparison of theoretical prediction with the experimental results.