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.     

Effect of finite ionic size on the solution of the Poisson-Boltzmann equation: Application to the binding of divalent metal ions to DNA

The nonlinear Poisson-Boltzmann equation is solved for a cylindrical polyelectrolyte solution containing mono- and divalent counterions and monovalent coions. The finite size of the ions is taken into account by the introduction of the distances of closest approach between the ionic charges and the surface of the polyelectrolyte. The choice of these distances is based on the physicochemical properties of the polyelectrolyte and ions in solution. The effects of the finite ionic size on the distribution of the counterions around the polyelectrolyte and on the local ion concentration and the integrated charge fraction of the divalent cations in the vicinity of the polyelectrolyte are discussed. Theoretical predictions regarding the overall extent of binding and the extent of inner-sphere binding of divalent counterions to rodlike polyions are compared with the results of nmr studies of the binding of divalent metal ions to DNA.     

Adsorption of DNA to mica mediated by divalent counterions: a theoretical and experimental study

The adsorption of DNA molecules onto a flat mica surface is a necessary step to perform atomic force microscopy studies of DNA conformation and observe DNA-protein interactions in physiological environment. However, the phenomenon that pulls DNA molecules onto the surface is still not understood. This is a crucial issue because the DNA/surface interactions could affect the DNA biological functions. In this paper we develop a model that can explain the mechanism of the DNA adsorption onto mica. This model suggests that DNA attraction is due to the sharing of the DNA and mica counterions. The correlations between divalent counterions on both the negatively charged DNA and the mica surface can generate a net attraction force whereas the correlations between monovalent counterions are ineffective in the DNA attraction. DNA binding is then dependent on the fractional surface densities of the divalent and monovalent cations, which can compete for the mica surface and DNA neutralizations. In addition, the attraction can be enhanced when the mica has been pretreated by transition metal cations (Ni(2+), Zn(2+)). Mica pretreatment simultaneously enhances the DNA attraction and reduces the repulsive contribution due to the electrical double-layer force. We also perform end-to-end distance measurement of DNA chains to study the binding strength. The DNA binding strength appears to be constant for a fixed fractional surface density of the divalent cations at low ionic strength (I < 0.1 M) as predicted by the model. However, at higher ionic strength, the binding is weakened by the screening effect of the ions. Then, some equations were derived to describe the binding of a polyelectrolyte onto a charged surface. The electrostatic attraction due to the sharing of counterions is particularly effective if the polyelectrolyte and the surface have nearly the same surface charge density. This characteristic of the attraction force can explain the success of mica for performing single DNA molecule observation by AFM. In addition, we explain how a reversible binding of the DNA molecules can be obtained with a pretreated mica surface.     

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.     

Monte Carlo and Poisson–Boltzmann calculations of the fraction of counterions bound to DNA

The counterion density and the condensation region around DNA have been examined as functions of both ion size and added-salt concentration using Metropolis Monte Carlo (MC) and Poisson–Boltzmann (PB) methods. Two different definitions of the “bound” and “free” components of the electrolyte ion atmosphere were used to compare these approaches. First, calculation of the ion density in different spatial regions around the polyelectrolyte molecule indicates, in agreement with previous work, that the PB equation does not predict an invariance of the surface concentration of counterions as electrolyte is added to the system. Further, the PB equation underestimates the counterion concentration at the DNA surface, compared to the MC results, the difference being greatest in the grooves, where ionic concentrations are highest. If counterions within a fixed radius of the helical axis are considered to be bound, then the fraction of polyelectrolyte charge neutralized by counterions would be predicted to increase as the bulk electrolyte concentration increases. A second categorization—one in which monovalent cations in regions where the average electrostatic potential is ledd than ?kT are considered to be bound—provides an informative basis for comparison of MC and PB with each other and with counterion-condensation theory. By this criterion, PB calculations on the B from of DNA indicate that the amount of bound counterion charge per phosphate group is about .67 and is independent of salt concentration. A particularly provocative observatiob is that when this binding criterion is used, MC calculations quantitatively reproduce the bound fraction predicated by counterion-condensation theory for all-atom models of B-DNA and A-DNA as well as for charged cylindera of varying lineat charge densities. For example, for B-DNA and A-DNA, the fractions of phosphate groups neutralized by 2 Å hard sphere counterions are 0.768 and .817, respectively. For theoretical studies, the rediys enclosing the region in which the electrostatic potential is calculated studies, the radius enclosing the region in which the electrostatic potential is calculated to be less than ?kT is advocated s a more suitable binding or condensation radius that enclosing the fraction of counterions given by (1 – ξ^?1). A comparsion of radii calculated using both of these definitions is presented. © 1994 John Wiley & Sons, Inc.     

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.     

Counterion exchange reactions on DNA: Monte Carlo and Poisson-Boltzmann analysis

In solutions containing DNA and cations of more than one type, the competitive interactions of these cations with DNA can be modeled as an ion exchange process that can be described quantitatively by means of the theoretical approach reported in this paper. Under conditions of experimental interest the radial distribution function of each type of counterion is calculated from the results of canonical Monte Carlo (MC) simulations using the primitive model for DNA (having a helical charge distribution) and for the electrolyte ions. These ions consist of monovalent coions, monovalent counterions intended to represent Na⁺, and counterions of a second type designated M^z+, having variable size and charge (z ≥ 1). The competitive association of these counterions with DNA is described in terms of D, a parameter analogous to an ion exchange equilibrium quotient. Values of D are calculated from the results of our MC simulations and compared with corresponding predictions of the Poisson–Boltzmann (PB) cell model and with results inferred from analyses of previously published nmr measurements. Over typical experimental concentration ranges (0.02M < [Na⁺] < 0.20M, 0.001 < [M^z+] < 0.160M), D^MC and D^PB both are predicted to be relatively independent of the bulk ion concentrations. For various specifications of the size and charge of the competing cation (M^z+), D^MC and D^PB exhibit similar trends, although the MC simulations consistently predict that the cations bearing a higher charge density than that of Na⁺ are somewhat stronger competitors than indicated by the PB calculations. For monovalent and divalent competitors of varying radii, theoretical predictions of D are compared with values obtained by fitting nmr measurements. If the hard-sphere radii specified in the simulations are the (hydrated) ionic radii determined from conductance measurements, then the MC predictions and the corresponding nmr results are in reasonable agreement for various monovalent competitors and for a divalent polyamine, but not for Ca²⁺ and Mg²⁺.     

Limiting laws and counterion condensation in polyelectrolyte solutions: IV. The approach to the limit and the extraordinary stability of the charge fraction

The limiting laws for polyelectrolyte solutions developed in previous papers of this series have been amply confirmed by measurement. A surprising result of the accumulated data is that the limiting polyelectrolyte charge fraction (fraction of fixed charges uncompensated by condensed counterions in the limit of zero concentration), persists up to concentrations of 0.1 M or even higher. Here the theory is extended in a simple manner to finite concentrations, and the stability of the charge fraction is found to be firmly based on consequences of the long-range polyelectrolyte field. The associated counterions are assumed to translate freely in a region centered on the contour axis of the polyion. The numerical value of the free volume is determined self-consistently from the axial charge density of the polyelectrolyte and is used as the general framework within which specific binding effects are treated.     

An experimental test of the discreteness-of-charge effect in positive and negative lipid bilayers

The electrostatic properties of charged bilayers and the bilayer component of biological membranes are often described theoretically by assuming the charge is smeared uniformly over the surface. This is one of the fundamental assumptions in the Gouy-Chapman-Stern (GCS) theory. However, the average distance between the charged phospholipids in a typical biological membrane is 2-3 nm, which is 2-3 times the Debye length in a 0.1 M salt solution. Existing discreteness-of-charge theories predict significant deviations from the GCS theory for the adsorption of ions to such membranes. We considered the predictions of the simplest discreteness-of-charge theory [Nelson, A. P., & McQuarrie, D. A. (1975) J. Theor. Biol. 55, 13-27], in which the charges are assumed to be fixed in a square lattice and the potential is described by the linearized Poisson-Boltzmann relation. This theory predicts deviations that are larger for counterions than for co-ions and much larger for divalent than for monovalent counterions. We tested these predictions by measuring the adsorption of a fluorescent monovalent anion and a paramagnetic divalent cation to both positive and negative membranes, which we demonstrated experimentally had the same average surface potential. All our experimental results with probes, including those obtained on membranes in the gel rather than in the liquid-crystalline state, agreed with the predictions of the GCS theory rather than with the discreteness-of-charge theory. A simple calculation indicates that the agreement between the experimental results and the predictions of the GCS theory could be due to the finite size of the lipids.     

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.     

The electroanalytical approach to lipid peroxide determinations

An electroanalytical method for the determination of lipid peroxides in physiological material is described. The technique is based on electrochemical detection for HPLC as the means for enhancing sensitivity. Samples containing organic peroxides, including lipid peroxides, can be analyzed directly using a modified polarographic detector (Lloyd, J.B.F.; Optimization of the operational parameters of the supported mercury drop electrode detector in high performance liquid chromatography. Anal. Chim. Acta 154:121-131; 1983.) for reversed phase HPLC determinations. Detection limits for fatty acid hydroperoxides were found to be in the low nanogram range.     

A molecular dynamics simulation study of polyamine– and sodium–DNA. Interplay between polyamine binding and DNA structure

Four different molecular dynamics (MD) simulations have been performed for infinitely long ordered DNA molecules with different counterions, namely the two natural polyamines spermidine(3+) (Spd³⁺) and putrescine(2+) (Put²⁺), the synthetic polyamine diaminopropane(2+) (DAP²⁺), and the simple monovalent cation Na⁺. All systems comprised a periodical hexagonal cell with three identical DNA decamers, 15 water molecules per nucleotide, and counterions balancing the DNA charge. The simulation setup mimics the DNA state in oriented DNA fibers, previously studied using NMR and other experimental methods. In this paper the interplay between polyamine binding and local DNA structure is analyzed by investigating how and if the minor groove width of DNA depends on the presence and dynamics of the counterions. The results of the MD simulations reveal principal differences in the polyamine–DNA interactions between the natural [spermine(4+), Spd³⁺, Put²⁺] and the synthetic (DAP²⁺) polyamines.Abbreviations DAP diaminopropane - DDD Drew–Dickerson dodecamer - MD molecular dynamics - Put putrescine - RDF radial distribution function - Spd spermidine - Spm spermine     

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.     

Thermodynamics of single-stranded RNA binding to oligolysines containing tryptophan.

The equilibrium binding to the synthetic RNA poly(U) of a series of oligolysines containing one, two, or three tryptophans has been examined as a function of pH, monovalent salt concentration (MX), temperature, and Mg2+. Oligopeptides containing lysine (K) and tryptophan (W) of the type KWKp-NH2 and KWKp-CO2 (p = 1-8), as well as peptides containing additional tryptophans or glycines, were studied by monitoring the quenching of the peptide tryptophan fluorescence upon binding poly(U). Equilibrium association constants, K(obs), and the thermodynamic quantities delta G(o)obs, delta H(o)obs, and delta S(o)obs describing peptide-poly(U) binding were measured as well as their dependences on monovalent salt concentration, temperature, and pH. In all cases, K(obs) decreases significantly with increasing monovalent salt concentration, with (delta log K(obs)/delta log [K+]) = -0.74 (+/- 0.04)z, independent of temperature and salt concentration, where z is the net positive charge on the peptide. The origin of these salt effects is entropic, consistent with the release of counterions from the poly(U) upon formation of the complex. Upon extrapolation to 1 M K+, the value of delta G(o)obs is observed to be near zero for all oligolysines binding to poly(U), supporting the conclusion that these complexes are stabilized at lower salt concentrations due to the increase in entropy accompanying the release of monovalent counterions from the poly(U). Only the net peptide charge appears to influence the thermodynamics of these interactions, since no effects of peptide charge distribution were observed. The binding of poly(U) to the monotryptophan peptides displays interesting behavior as a function of the peptide charge. The extent of tryptophan fluorescence quenching, Qmax, is dependent upon the peptide charge for z less than or equal to +4, and the value of Qmax correlates with z-dependent changes in delta H(o)obs and delta S(o)obs(1 M K+), whereas for z greater than or equal to +4, Qmax, delta H(o)obs, and delta S(o)obs (1 M K+) are constant. The correlation between Qmax and delta H(o)obs and delta S(o)obs(1 M K+) suggests a context (peptide charge)-dependence of the interaction of the peptide tryptophan with poly(U). However the interaction of the peptide tryptophan does not contribute substantially to delta G(o)obs for any of the peptides, independent of z, due to enthalpy-entropy compensations. Each of the tryptophans in multiple Trp-containing peptides appear to bind to poly(U) independently, with delta H(o)Trp = -2.9 +/- 0.7, although delta G(o)Trp is near zero due to enthalpy-entropy compensations.(ABSTRACT TRUNCATED AT 400 WORDS)     

Simultaneous measurement of Ca2+ influx and reversal potentials in recombinant N-methyl-D-aspartate receptor channels.

The Ca(2+) permeability of N-methyl-D-aspartate receptor (NMDA-R) channels was studied in human embryonic kidney cells transfected with the NR1-NR2A subunit combination. To determine the fractional Ca(2+) current (P(f)), measurements of fura-2-based Ca(2+) influx and whole-cell currents were made in symmetrical monovalent ion concentrations at membrane potentials between -50 mV and the reversal potential. The ratios of Ca(2+) flux over net whole-cell charge at 2, 5, and 10 mM external Ca(2+) concentrations ([Ca](o)) were identical at a membrane potential close to the reversal potential of the monovalent current component. Assuming unity of P(f) at this potential, the percentage of current carried by Ca(2+) was found to be 18.5 +/- 1.3% at 2 mM [Ca](o) and -50 mV. This value, which is higher than the ones reported previously, was confirmed in independent experiments in which a pure flux of Ca(2+) through NMDA-R channels was used to calibrate the Ca(2+) influx signals. The measured values of fractional Ca(2+) currents, which agree with the predictions of the Goldman-Hodgkin-Katz equations, are also compatible with a two-barrier model for ion permeation, in which the differences between the energy barriers for Ca(2+) and monovalent ions are similar on the external and internal membrane sides.     

Condensation of Co++ ions on chondroitin sulfate from transport coefficients and proton NMR measurements in aqueous solutions

The “condensed” counterions which characterize high-charge-density polyelectrolyte solutions can be analyzed into two subpopulations: (1) site-bound counterions and (2) atmospherically entrapped counterions. The distinction is achieved experimentally by combining the data from self-diffusion coefficient or electrical mobility measurements, which give the amount of “condensed” ions, and those from nmr, chemical shift measurements, which indicate the amount of site-bound ions. In the case of a solution of chondroitin sulfate with excess Co⁺⁺ counterions, it can be estimated that 20% of the structural charge of the polyion is neutralized by site-bound, dehydrated, condensed counterions, while a further 30% is neutralized by atmospherically entrapped, hydrated counterions.     

Density functional theory for the nonspecific binding of salt to polyelectrolytes: thermodynamic properties

The thermodynamics of the nonspecific binding of salt to a polyelectrolyte molecule is studied using a density functional approach. The polyelectrolyte molecule is modeled as an infinite, inflexible, and impenetrable charged cylinder and the counterions and co-ions are modeled as charged hard spheres of equal diameter. The density functional theory is based on a hybrid approach where the hard-sphere contribution to the one-particle correlation function is evaluated nonperturbatively and the ionic contribution to the one-particle correlation function is evaluated perturbatively. The advantage of the approach is that analytical expressions are available for all the correlation functions. The calculated single ion preferential interaction coefficients, excess free energy, and activity coefficients show a nonmonotonic variation as a function of polyion charge in the presence of divalent ions. These properties display considerable departure from the predictions of the nonlinear Poisson-Boltzmann (NLPB) equation, with qualitative differences in some cases, which may be attributed to correlation effects neglected in the NLPB theory.     

Activity and properties of fructose bisphosphatase of turbellarian Phagocata sibirica

Activity and properties of fructose bisphosphatase (FBPase) was studied in the free-living turbellarian Phagocata sibirica. All subcellular fractions of P. sibirica (12 000 g cytosol, 105 000 g cytosol, mitochondria, and microsomes) have the FBPase activity. There was studied dependence of the FBPase reaction rate on the substrate concentration. For realization of the enzyme activity, the high affinity to substrate and presence of bivalent cations (Mg2+ or Mn2+) are necessary. The was studied the effect of various effectors as well as of monovalent (Na+, K+, Li+, and NH4+) and bivalent (Zn2+ and Cu2+) cations.     

Positively charged side chains in protein farnesyltransferase enhance catalysis by stabilizing the formation of the diphosphate leaving group

Protein farnesyltransferase (FTase) requires both Zn(2+) and Mg(2+) for efficient catalysis of the formation of a thioether bond between carbon-1 of farnesyldiphosphate (FPP) and the cysteine thiolate contained in the carboxy-terminal CaaX sequence of target proteins. Millimolar concentrations of Mg(2+) accelerate catalysis by as much as 700-fold in FTase. Although FTase lacks a typical DDXXD Mg(2+) binding site found in other enzymes that use Mg(2+) for diphosphate stabilization, D352beta in FTase has been implicated in binding Mg(2+) (Pickett et al. (2003) J. Biol. Chem. 278, 51243). Structural studies demonstrate that the diphosphate (PPi) group of FPP resides in a binding pocket made up of highly positively charged side chains, including residues R291beta and K294beta, prior to formation of an active conformation. Analysis of the Mg(2+) dependence of FTase mutants demonstrates that these positively charged residues decrease the Mg(2+) affinity up to 40-fold. In addition, these residues enhance the farnesylation rate constant by almost 80-fold in the presence of Mg(2+), indicating that these residues are not simply displaced by Mg(2+) during the reaction. Mutations at R291beta increase the pK(a) observed in the magnesium affinity, suggesting that this arginine stabilizes the deprotonated form of the PPi leaving group. Furthermore, binding and catalysis data using farnesylmonophosphate (FMP) as a substrate indicate that the side chains of R291beta and K294beta interact mainly with the beta-phosphate of FPP during the chemical reaction. These results allow refinement of the model of the Mg(2+) binding site and demonstrate that positive charge stabilizes the developing charge on the diphosphate leaving group.     

The effect of counter-ion substitution on the transport properties of polyelectrolyte solutions

The effects of counter-ion substitution in aqueous polyelectrolyte solutions (chondroitin sulfate) on the two main transport phenomena of the ionic species, self-diffusion and electrical mobility, were studied experimentally by tracer methods and dynamic light scattering. The data were analyzed with respect to counter-ion condensation and stoichiometric substitution of low-ionic counterions by high-ionic charge ones and compared to Manning's theory. Substitution effects on the apparent charge of the macro-ion were derived from the transport data using an extended Nernst-Einstein relationship and discussed in the light of the condensation effect in polyelectrolyte solutions. The effective charge of the polyion (i.e., its residual charge after condensation of counter-ions) and the charge difference between the substituting counter-ions appear determinant in the mechanism of substitution.