Chemically reacting systems of the type A + B ⇄ AB. II. Osmometry

The osmotic pressure equation for nonideal, associating systems of the type nA +mB ? A_nB_m, has been derived, by using the assumption yA _nB _m/yA ⁿyB ^m = 1. This treatment can also be applied to related associations such as nA + mB ? AB + AB₂ + A₂B + …. From osmotic pressure experiments on the pure reactants it is possible to obtain the molecular weights (M_A and M_B) of the reactants and also the virial coefficients (B_AA and B_BB) of the reactants. The osmotic pressure of a nonreacting mixture of A and B can be calculated from these measurements. It can be used along with osmotic pressure measurements on equilibrium mixtures of A and B to obtain expressions containing the equilibrium constant (or constants) and the cross-virial coefficients (B_AB and B_BA). Several procedures are described for the evaluation of the equilibrium constant (or constants) and the B_AB or B_BA terms. It appears that this procedure is a general one which is applicable to associations of the type nA + mB ? AB + A₂B + AB₂ + …. By correcting for nonideal behavior, one should then be able to apply it to any method available for analyzing ideal associations of the types considered here. In addition it is possible, subject to certain restrictions, to analyze associations of the type 3A + B ? A₂ + AB.     

Rapid-equilibrium rate equations for the enzymatic catalysis of A+B=P+Q over a range of pH

This article shows how pKs for the enzymatic site and enzyme-substrate complexes can be obtained from kinetic experiments on the reaction A+B=P+Q, with and without the consumption of hydrogen ions. The rapid-equilibrium rate equation makes it possible to obtain the pKs and chemical equilibrium constants involved in the mechanism, the apparent equilibrium constant K' for the catalyzed reaction, and the number of hydrogen ions consumed in the rate-determining reaction. Experimentally-determined Michaelis constants can be adjusted for the pKs of the substrates A, B, P, and Q so that it is easier to obtain the pKs of E, EA, EB, EAB, EQ, and EPQ, and the chemical equilibrium constants. Reaction rates are discussed for the forward reaction ordered A+B=ordered P+Q with zero, one, or two hydrogen ions consumed in the rate-determining reaction and for random A+B=ordered P+Q with zero, one, or two hydrogen ions consumed in the rate-determining reaction. When hydrogen ions are consumed in the rate-determining reaction, there is a new factor 10(n)(pH) in the rate equation, where n is the number of hydrogen ions consumed in the rate-determining reaction for the forward reaction. The integer n can be obtained from rate measurements over a range of pH, but it cannot be determined from thermodynamic measurements.     

The determination of equilibrium constants for heterogeneous macromolecular interactions. Systems forming 2:1 complexes

In developing a method for analyzing the heterogeneous association nA + mB in equilibrium AnBm, we have specifically investigated the case of n = 2, m = 1 for both the specific case of no appreciable intermediates and the more general case allowing intermediates. Computer-simulated three-dimensional surfaces of the 2:1 model generated from total concentrations of species A and B and the resulting weight-average molecular weights were analyzed with a Gauss-Newton nonlinear least-squares minimization routine. The surfaces generated included normalized random error of varying standard deviations imposed upon both the concentrations and weight-average molecular weights. For comparison purposes, these surfaces were analyzed not only by using the correct 2:1 model, but also by an incorrect (1:1) model and by the other (incorrect) 2:1 model. Except for those situations where the 'experimental' noise was consistently higher than the concentration of one of the species, correct K values were obtained and the correct model was easily distinguished from the incorrect model. The computer routine similarly distinguished between data correctly described as 1:1 and the same data incorrectly analyzed as either 2:1 model. For those cases in which a microscopic Ki value predicts an association such that all species involved for that particular Ki are in appreciable amounts, the Ki value is returned correctly. Correct overall equilibrium constants are also converged upon as long as adequate amounts of A2B, B and A are present.     

Kinetics studies on the interaction between ouabain and (Na+,K+)-ATPase.

The association and dissociation rate constants for the interaction of [3H]-ouabain with partially purified rat brain (Na+,K+)-ATPase (ATP phosphohydrolase, EC 3.6.1.3) in vitro were estimated from the time course of the [3H]-ouabain binding observed in the presence of Na+, Mg2+ and ATP by a polynomial approximation-curve-fitting technique. The reduction of the association rate constant by K+ was greater than its reduction of the dissociation rate constant. Thus, the affinity of Na+,K+)-ATPase for ouabain was reduced by K+. The binding-site concentration was unaffected by K+. Consistent with these findings, the addition of KCl to an incubation mixture at the time when [3H]-ouabain binding to (Na+,K+)ATPase is close to equilibrium, caused an immediate decrease in bound ouabain concentration, apparently shifting towards a new, lower equilibrium concentration. Dissociation rate constants which were estimated following the termination of the ouabain-binding reaction were different from those estimated with above methods and may not be useful in predicting the ligand effects on equilibrium of the ouabain-enzyme interaction.     

A kinetic study of cyclic adenosine 3':5'-monophosphate binding and mode of activation of protein kinase from Drosophila melanogaster embryos.

Cyclic AMP-dependent protein kinase and its regulatory subunit were isolated from Drosophila melanogaster embryos. The profiles of cyclic AMP binding by these proteins were significantly different. In order to explain such a difference and to find the mode of enzyme activation by cyclic AMP, a kinetic study of cyclic AMP binding was carried out. First, the association rate constant k1 and dissociation rate constant k-1 in the cyclic AMP-regulatory subunit interaction at 0 degrees C were estimated to be 2.3 X 10(6)M-1s-1 and 1.1 X 10(-3)s-1, respectively. Secondly, the three possible modes of enzyme activation by cyclic AMP were mathematically considered and could be described by a unique formula: r=APt + BQt (A + B=1) in which the parameters A, B, P, and Q are equivalent to rate constants in the sense that the rate constants are simply expressed by these parameters. Thirdly, the values of the parameters and subsequently the values of rate constants involved in the possible mechanisms were evaluated using a curve-fitting technique and compared with experimental observation. It was then found that the following mechanism was the only one which fitted the experimental observations. Namely, RC + L k3 equilibrium k-3 LRC k4 equilibrium k-4 RL + C where R, C, and L represent the regulatory and catalytic subunits and cyclic AMP as a ligand. Thus, our results indicate that in the presence of cyclic AMP the active enzyme (C) is released from a ternary intermediate which is the primary product of the cyclic AMP-holoenzyme interaction. The estimated values of the rate constants are: k3=3.5 X 10(6)M-1s-1;k-3=7.3 X 10(-1)s-1;and k4=3.8 X 10(-2)s. These estimates indicate that the reaction LRC leads to RL + C is relatively slow and limits the rate of the overall reaction. By comparing k-3 and k4, it is apparent that a large part of newly formed ternary intermediate reverts to the holoenzyme.     

The interaction of magnesium ions with teichoic acid.

The binding of Mg2+ to the wall teichoic acid of Lactobacillus buchneri N.C.I.B. 8007 was measured by equilibrium dialysis at controlled ionic concentration and pH. In an aqueous solution containing 10mM-NaCl at pH 5.0 one Mg2+ ion was bound for every two phosphate groups of the teichoic acid, with an apparent association constant, Kassoc. = 2.7 x 10(3) M-1. On lowering the pH below the pKa of the phosphate groups the amount of bound Mg2+ decreased concomitantly with decreasing ionization of the phosphate groups. Both the amount of Mg2+ bound to the teichoic acid and the apparent association constants were similar in the presence of 10 mM concentrations of NaCl or KCl but decreased markedly in the presence of 10 mM-CaCl2 because of competition between Ca2+ and Mg2+ for the binding sites. A similar effect was found when the concentration of NaCl was increased from 0 to 50 mM. The results are discussed in relation to the function of teichoic acid in the walls of Gram-positive bacteria.     

PH-dependence of the steady-state rate of a two-step enzymic reaction.

1. The pH-dependence is considered of a reaction between E and S that proceeds through an intermediate ES under "Briggs-Haldane' conditions, i.e. there is a steady state in ES and [S]o greater than [E]T, where [S]o is the initial concentration of S and [E]T is the total concentration of all forms of E. Reactants and intermediates are assumed to interconvert in three protonic states (E equilibrium ES; EH equilibrium EHS; EH2 equilibrium EH2S), but only EHS provides products by an irreversible reaction whose rate constant is kcat. Protonations are assumed to be so fast that they are all at equilibrium. 2. The rate equation for this model is shown to be v = d[P]/dt = (kcat.[E]T[S]o/A)/[(KmBC/DA) + [S]o], where Km is the usual assembly of rate constants around EHS and A-D are functions of the form (1 + [H]/K1 + K2/[H]), in which K1 and K2 are: in A, the molecular ionization constants of ES; in B, the analogous constants of E; in C and D, apparent ionization constants composed of molecular ionization constants (of E or ES) and assemblies of rate constants. 3. As in earlier treatments of this type of reaction which involve either the assumption that the reactants and intermediate are in equilibrium or the assumption of Peller & Alberty [(1959) J. Am. Chem. Soc. 81, 5907-5914] that only EH and EHS interconvert directly, the pH-dependence of kcat. is determined only by A. 4. The pH-dependence of Km is determined in general by B-C/A-D, but when reactants and intermediate are in equilibrium, C identical to D and this expression simplifies to B/A. 5. The pH-dependence of kcat./Km, i.e. of the rate when [S]o less than Km, is not necessarily a simple bell-shaped curve characterized only by the ionization constants of B, but is a complex curve characterized by D/B-C. 6. Various situations are discussed in which the pH-dependence of kcat./Km is determined by assemblies simpler than D/B-C. The special situation in which a kcat./Km-pH profile provides the molecular pKa values of the intermediate ES complex is delineated.     

Thermodynamics of the hydrolysis of sucrose

A thermodynamic investigation of the hydrolysis of sucrose to fructose and glucose has been performed using microcalorimetry and high-pressure liquid chromatography. The calorimetric measurements were carried out over the temperature range 298-316 K and in sodium acetate buffer (0.1 M, pH 5.65). Enthalpy and heat capacity changes were obtained for the hydrolysis of aqueous sucrose (process A): sucrose(aq) + H2O(liq) = glucose(aq) + fructose (aq). The determination of the equilibrium constant required the use of a thermochemical cycle calculation involving the following processes: (B) glucose 1-phosphate2-(aq) = glucose 6-phosphate2-(aq); (C) sucrose(aq) + HPO4(2-)(aq) = glucose 1-phosphate2-(aq) + fructose(aq); and (D) glucose 6-phosphate2-(aq) + H2O(liq) = glucose(aq) + HPO4(2-)(aq). The equilibrium constants determined at 298.15 K for processes B and C are 17.1 +/- 1.0 and 32.4 +/- 3.0, respectively. Equilibrium data for process D was obtained from the literature, and in conjunction with the data for processes B and C, used to calculate a value of the equilibrium constant for the hydrolysis of aqueous sucrose. Thus, for process A, delta G0 = -26.53 +/- 0.30 kJ mol-1, K0 = (4.44 +/- 0.54) x 10(4), delta H0 = -14.93 +/- 0.16 kJ mol-1, delta So = 38.9 +/- 1.2 J mol-1 K-1, and delta CoP = 57 +/- 14 J mol-1 K-1 at 298.15 K. Additional thermochemical cycles that bear upon the accuracy of these results are examined.     

Analysis of Ter-Ter enzyme kinetic mechanisms by computer simulation of isotope exchange at chemical equilibrium: development and application of ISOTER, a personal-computer-based program

A convenient, personal-computer-based program has been developed that allows simulation of isotopic exchange kinetics at chemical equilibrium catalyzed by a three reactant-three product (TerTer) enzyme system: A + B + C integral of P + Q + R. This program, ISOTER, utilizes a rapid algebraic method to calculate the exchange rate between any reactant-product pair as a function of the substrate concentration and avoids altogether the necessity of deriving an explicit (but cumbersome and impractical) equation for exchange rate. ISOTER was used to generate model saturation patterns for 16 different TerTer kinetic mechanisms, varying different combinations of reactant-product pairs in constant ratio at equilibrium: [all substrates], [A, P], [B, Q], and [C, R], while holding the nonvaried components constant. These model studies indicate that virtually every one of these mechanisms can be distinguished from the others. In addition, ISOTER has been used to fit multiple sets of experimental data for Escherichia coli glutamine synthetase, which produced a set of rate constants consistent with the previously proposed "preferred order random" kinetic mechanism.     

A simplified analysis of Scatchard plots for systems with two interacting binding sites

A simple graphical method for calculating stoichiometric and site binding constants for systems with two initially equivalent interacting sites is derived from a modified Scatchard equation. The binding constants can be calculated from Scatchard plots (r/[A] as a function of r) using the values of r/[A] (r is the molar ratio of bound ligands to total protein and [A] is the equilibrium concentration of free ligand) when r = 0 and r = 1 (half-saturation). The applicability of the method to the adsorption of bilirubin by peptide pendants immobilized on a polyacrylamide support is demonstrated.     

Equilibrium binding constants for Tl+ with gramicidins A, B and C in a lysophosphatidylcholine environment determined by 205Tl nuclear magnetic resonance spectroscopy.

Nuclear Magnetic Resonance (NMR) 205Tl spectroscopy has been used to monitor the binding of Tl+ to gramicidins A, B, and C packaged in aqueous dispersions of lysophosphatidylcholine. For 5 mM gramicidin dimer in the presence of 100 mM lysophosphatidylcholine, only approximately 50% or less of the gramicidin appears to be accessible to Tl+. Analysis of the 205Tl chemical shift as a function of Tl+ concentration over the 0.65-50 mM range indicates that only one Tl+ ion can be bound by gramicidin A, B, or C under these experimental conditions. In this system, the Tl+ equilibrium binding constant is 582 +/- 20 M-1 for gramicidin 1949 +/- 100 M-1 for gramicidin B, and 390 +/- 20 M-1 for gramicidin C. Gramicidin B not only binds Tl+ more strongly but it is also in a different conformational state than that of A and C, as shown by Circular Dichroism spectroscopy. The 205Tl NMR technique can now be extended to determinations of binding constants of other cations to gramicidin by competition studies using a 205Tl probe.     

Thermodynamics of the reduction of NADP with 2-propanol catalyzed by an NADP-dependent alcohol dehydrogenase

The apparent equilibrium constant of the biochemical reaction, 2-propanol+NADP(ox) = acetone+NADP(red), was determined at I = 0.25 M over a wide range of pH (5.63 to 8.02) and temperature (5 to 40 degrees C). The reaction was catalyzed by an NADP-dependent alcohol dehydrogenase. The results were used to calculate thermodynamic quantities for the chemical (ionic) reference reaction: 2-propanol+NADP(ox)(3-) = acetone+NADP(red)(4-)+H(+). The thermodynamic quantities for this reference reaction are as follows: equilibrium constant K = (5.98+/-0.46) x 10(-10); standard molar Gibbs energy change Delta(r)G(0) = (52.65+/-0.19) kJmol(-1); standard molar enthalpy change Delta(r)H(0) = (38.9+/-0.6) kJmol(-1); and standard molar entropy change Delta(r)S(0) = -(46.1+/-2.2)J K(-1)mol(-1). All of these results pertain to 25 degrees C (298.15 K) and I = 0. The results also lead, in conjunction with tabulated thermodynamic quantities, to the standard electromotive force E(0) = -0.140 V for the reduction of NADP(ox)(3-) to NADP(red)(4-).     

Effects of MgATP and MgADP on the cross-bridge kinetics of rabbit soleus slow-twitch muscle fibers.

The elementary steps surrounding the nucleotide binding step in the cross-bridge cycle were investigated with sinusoidal analysis in rabbit soleus slow-twitch muscle fibers. The single-fiber preparations were activated at pCa 4.40, ionic strength 180 mM, 20 degrees C, and the effects of MgATP (S) and MgADP (D) concentrations on three exponential processes B, C, and D were studied. Our results demonstrate that all apparent (measured) rate constants increased and saturated hyperbolically as the MgATP concentration was increased. These results are consistent with the following cross-bridge scheme: [cross-bridge scheme: see text] where A = actin, M = myosin, S = MgATP, and D = MgADP. AM+S is a collision complex, and AM*S is its isomerized form. From our studies, we obtained K0 = 18 +/- 4 mM-1 (MgADP association constant, N = 7, average +/- sem), K1a = 1.2 +/- 0.3 mM-1 (MgATP association constant, N = 8 hereafter), k1b = 90 +/- 20 s-1 (rate constant of ATP isomerization), k-1b = 100 +/- 9 s-1 (rate constant of reverse isomerization), K1b = 1.0 +/- 0.2 (equilibrium constant of isomerization), k2 = 21 +/- 3 s-1 (rate constant of cross-bridge detachment), k-2 = 14.1 +/- 1.0 s-1 (rate constant of reversal of detachment), and K2 = 1.6 +/- 0.3 (equilibrium constant of detachment). K0 is 8 times and K1a is 2.2 times those in rabbit psoas, indicating that nucleotides bind to cross-bridges more tightly in soleus slow-twitch muscle fibers than in psoas fast-twitch muscle fibers. These results indicate that cross-bridges of slow-twitch fibers are more resistant to ATP depletion than those of fast-twitch fibers. The rate constants of ATP isomerization and cross-bridge detachment steps are, in general, one-tenth to one-thirtieth of those in psoas.     

Kinetic characteristics of the ATP-pyrophosphate isotope exchange catalyzed by RNA ligase from T4 bacteriophage

The dependence of initial rate v0 of ATP--PPi exchange reaction catalyzed by RNA-ligase of bacteriophage T4 on the concentration of ATP(s), pyrophosphate (z) and Mgcl2 has been determined. The dependence of v0 on s and z described by the equation v0 = k-1k2E0/(k-1 + K2) (1 + K1/s + k2/z) has been obtained for the reaction of E + S in equilibrium ES in equilibrium E1 + Z, where E--enzyme, E1--adenylylenzyme, S--ATP, Z--pyrophosphate, K1 and K2--constants of equilibrium, k-1, k2--velocity constants of transition of ES to E + S and E1 + Z, E0--complete concentration of enzyme. The low inhibition of the ATP--PPi exchange by the acceptor A(pA)2 and donors pAp, p(Ap)3, pCp has been shown. The dependence of v0 on the concentration of MgCl2 is consent with the incorporation of only dimagnesium salts of substrates in the isotope-exchange reaction.     

Murine B7 antigen provides a sufficient costimulatory signal for antigen-specific and MHC-restricted T cell activation.

We have previously shown that the murine B7 (mB7) molecule, when expressed in Chinese hamster ovary cells in stable fashion, can costimulate with anti-CD3 mAb or Con A to induce T cell activation. We have now derived, by gene transfection, Chinese hamster ovary cell lines that express the I-Ad molecule, either alone or in context with mB7. We have analyzed these transfectants for their capacity to present Ag to murine CD4+ T lymphocytes. I-Ad/mB7-double transfectants were able to stimulate mixed lymphocyte reactions and to present peptide Ag to specific T cells. Chinese hamster ovary cells that expressed only the I-Ad molecule were not able to stimulate T cell proliferation in these systems. Thus, the mB7 protein is a sufficient costimulatory molecule for the physiologic, Ag-dependent/MHC-restricted activation of murine CD4+ T cells. Stimulation of T cell bulk cultures resulted predominantly in the production of IL-2 and not of IL-4. The costimulatory activity of mB7 is not, however, restricted to the IL-2-secreting subset. We have identified one IL-4-secreting T cell clone, CDC35, which is responsive to mB7 triggering. Finally, we present experiments that suggest that mB7 and peptide/MHC complexes need to be expressed on the same cell for optimal induction of T cell activation.     

The nature of conformational correlations in alpha- and beta-anomers of nucleic acid components in aqueous solution by nuclear magnetic resonance

The solution distribution of combinations of the sugar ring puckering domains, C2'endo(S), C3'endo(N), and C4'-C5' rotamers, +sc(g+), ap(t), -sc(g-), in alpha and beta-anomers in ribo- and deoxyribo- pyrimidine nucleic acid components can be determined from vicinal coupling constants (M. Remin, J. Biomol. Str. Dyn. 2, 211 (1984). A general correlation pattern with a conformational constant lambda reflecting an intrinsic physical property of the sugar-side chain ensemble, is developed and expressed in terms of four principles: I) The +sc rotamer contributes to the C3'endo population to a higher extent (1-Yt) than to C2'endo, (1-Yt-Yg-/Xs). II) The ap rotamer contributes to both C2'endo and C3'endo populations to the same extent (Yt). III) The -sc rotamer contributes only to the C2'endo population, (Yg-/Xs). IV) The molar fractions Xs, Yt and Yg- of conformations C2'endo, ap and -sc, respectively, are strongly correlated, lambda = (Yg-/Xs)/Yt approximately 0.5, and therefore Yt is a basic variable parameter which determines all others in the correlation pattern. In alpha-anomers, regardless of the type and conformation of the sugar ring and base, the molar fraction Yt = 0.37 +/- 0.02. This finding means that different alpha-anomers show one correlation pattern free of the influence of the base. In beta-anomers, structure and conformation of the base are important factors which modulate (through Yt) the correlation pattern, conserving its fundamental features. Yt is considerably increased by a syn-oriented pyrimidine base, but decreases when the base is anti. The transition from anti to syn orientation of the base is followed by destabilization of (C2'endo, +sc) in favor of (C3'endo, ap). The principles of conformational correlations rationalize a variety of correlations observed in the past.     

Effects of calcium binding and of EDTA and CaEDTA on the clotting of bovine fibrinogen by thrombin

Studies were carried out at pH 7.0 and gamma/2 0.15 before addition of CaCl2 or EDTA. Clotting time, tau, at 3.03 microM fibrinogen and 0.91 u/ml thrombin was determined for equilibrium systems. With added Ca2+, tau decreases, from tau 0 at 0 added Ca2+ (mean, 29.7 +/- 3 s), by approximately 3 s at 5 mM added Ca2+. With added EDTA, tau increases sigmoidally from tau 0 at 0 EDTA to a maximum (mean tau m = 142 +/- 23 s) at approximately 200 microM EDTA. tau then decreases slightly to a minimum at approximately 1.3 mM and finally increases to infinity at approximately 10 mM EDTA. Between 0 and 1.3 mM EDTA, effects on clotting time are completely reversed by adding Ca2+ and, after equilibration at 400 microM EDTA, tau is independent of EDTA concentration. Thus, up to 400 microM EDTA, effects on clotting time are attributed to decreasing fibrinogen bound Ca2+. Between 5 mM Ca2+ and 200 microM EDTA it is assumed that an equilibrium distribution of fibrinogen species having 3, 2, 1, or 0 bound calcium ions is established and that a clotting time is determined by the sum of products of species fractional abundance and pure species clotting time. Analysis indicates that pure species clotting times increase proportionately with decreasing Ca2+ binding, binding sites are nearly independent, and the microscopic association constant for the first bound Ca2+ is approximately 4.9 X 10(6) M-1. Effects of adding Ca2+ at times t1 after thrombin addition to systems initially equilibrated at 200 microM EDTA were determined. Analysis of the relation between tau and t1 indicates that as Ca2+ binding decreases, rate constants for release of B peptides decrease less than those for release of A peptides. As EDTA concentration is increased above 1.3 mM, inhibitory effects of EDTA and CaEDTA progressively increase.     

铽(Ⅲ)与人血清脱铁转铁蛋白结合的荧光光谱研究

在ｐＨ７．４０．１ｍｏｌ／ＬＨｅｐｅｓ及室温条件下,使用荧光光谱进行了Ｔｂ３＋对人血清脱铁转铁蛋白的滴定．结果表明Ｔｂ３＋与人血清脱铁转铁蛋白结合后,其５４９ｎｍ处的荧光强度增强约１０５倍．在５４９ｎｍ处Ｔｂ３＋－脱铁转铁蛋白络合物的摩尔荧光强度是（９．６５±０．０５）×１０４ｍｏｌ－１Ｌ,Ｔｂ３＋可占据脱铁转铁蛋白的两个金属离子结合部位,优先占据脱铁转铁蛋白的Ｃ端结合部位,条件平衡常数是ｌｇＫＣ＝９．９６±０．２０,ｌｇＫＮ＝６．３７±０．１６．Ｔｂ３＋与Ｒ３＋Ｅ（ＲＥ＝Ｎｄ、Ｓｍ、Ｅｕ和Ｇｄ）间的线性自由能关系表明稀土离子占据脱铁转铁蛋白的Ｃ端结合部位时受离子大小的影响     

A triphasic theory for the swelling and deformation behaviors of articular cartilage

Swelling of articular cartilage depends on its fixed charge density and distribution, the stiffness of its collagen-proteoglycan matrix, and the ion concentrations in the interstitium. A theory for a tertiary mixture has been developed, including the two fluid-solid phases (biphasic), and an ion phase, representing cation and anion of a single salt, to describe the deformation and stress fields for cartilage under chemical and/or mechanical loads. This triphasic theory combines the physico-chemical theory for ionic and polyionic (proteoglycan) solutions with the biphasic theory for cartilage. The present model assumes the fixed charge groups to remain unchanged, and that the counter-ions are the cations of a single-salt of the bathing solution. The momentum equation for the neutral salt and for the intersitial water are expressed in terms of their chemical potentials whose gradients are the driving forces for their movements. These chemical potentials depend on fluid pressure p, salt concentration c, solid matrix dilatation e and fixed charge density cF. For a uni-uni valent salt such as NaCl, they are given by mu i = mu io + (RT/Mi)ln[gamma 2 +/- c(c + cF)] and mu w = mu wo + [p-RT phi (2c + cF) + Bwe]/pwT, where R, T, Mi, gamma +/-, phi, pwT and Bw are universal gas constant, absolute temperature, molecular weight, mean activity coefficient of salt, osmotic coefficient, true density of water, and a coupling material coefficient, respectively. For infinitesimal strains and material isotropy, the stress-strain relationship for the total mixture stress is sigma = - pI-TcI + lambda s(trE)I + 2 musE, where E is the strain tensor and (lambda s, mu s) are the Lamé constants of the elastic solid matrix. The chemical-expansion stress (-Tc) derives from the charge-to-charge repulsive forces within the solid matrix. This theory can be applied to both equilibrium and non-equilibrium problems. For equilibrium free swelling problems, the theory yields the well known Donnan equilibrium ion distribution and osmotic pressure equations, along with an analytical expression for the "pre-stress" in the solid matrix. For the confined-compression swelling problem, it predicts that the applied compressive stress is shared by three load support mechanisms: 1) the Donnan osmotic pressure; 2) the chemical-expansion stress; and 3) the solid matrix elastic stress. Numerical calculations have been made, based on a set of equilibrium free-swelling and confined-compression data, to assess the relative contribution of each mechanism to load support. Our results show that all three mechanisms are important in determining the overall compressive stiffness of cartilage.