An Axiomatization of Minimal Curb Sets

Norde et al.[Games Econ.Behav. 12 (1996) 219] proved that none of the equilibrium concepts in the literature on equilibrium selection in finite strategic games satisfying existence is consistent.A transition to set-valued solution concepts overcomes the inconsistency problem: there is a multiplicity of consistent set-valued solution concepts that satisfy nonemptiness and recommend utility maximization in one-player games.The minimal curb sets of Basu and Weibull [Econ.Letters 36 (1991) 141] constitute one such solution concept; this solution concept is axiomatized in this article.Minimal curb set;Consistency

Self-consistent-field calculations of proteinlike incorporations in polyelectrolyte complex micelles

Self-consistent field theory is applied to model the structure and stability of polyelectrolyte complex micelles with incorporated protein (molten globule) molecules in the core. The electrostatic interactions that drive the micelle formation are mimicked by nearest-neighbor interactions using Flory-Huggins X parameters. The strong qualitative comparison with experimental data proves that the Flory-Huggins approach is reasonable. The free energy of insertion of a proteinlike molecule into the micelle is nonmonotonic: there is (i) a small repulsion when the protein is inside the corona; the height of the insertion barrier is determined by the local osmotic pressure and the elastic deformation of the core, (ii) a local minimum occurs when the protein molecule is at the core-corona interface; the depth (a few kBT's) is related to the interfacial tension at the core-corona interface and (iii) a steep repulsion (several kBT) when part of the protein molecule is dragged into the core. Hence, the protein molecules reside preferentially at the core-corona interface and the absorption as well as the release of the protein molecules has annealed rather than quenched characteristics. Upon an increase of the ionic strength it is possible to reach a critical micellization ionic (CMI) strength. With increasing ionic strength the aggregation numbers decrease strongly and only few proteins remain associated with the micelles near the CM

Rheological Behavior of Food Emulsions Mixed with Saliva: Effect of Oil Content, Salivary Protein Content, and Saliva Type

In this paper, we studied the effect of saliva on the rheological properties of ß-lactoglobulin- and lysozyme-stabilized emulsions, prepared at pH¿=¿6.7 in relation to variation of emulsions- and saliva-related parameters. The effect of oil¿volume fraction (2.5% w/w to 10% w/w), salivary protein concentration (0.1 to 0.8 mg ml¿1), and the use of both stimulated and unstimulated saliva was investigated. Viscosity and storage modulus were measured before (¿ emul and G¿emul, respectively) and after addition of saliva (¿ mix and G¿mix). To better estimate the changes due to saliva-induced flocculation of the emulsions, the ratios ¿ mix/¿ emul, G¿mix/G¿emul were calculated. In addition, tan ¿ (=the ratio of the loss and storage moduli) was investigated to evaluate the viscoelastic behavior of the emulsion/saliva mixtures. Increasing the oil¿volume fraction and salivary protein concentration resulted in an increase in ¿ mix/¿ emul and G¿mix/G¿emul, while a decrease in tan ¿ of the emulsion/saliva mixtures is occurring. When compared with unstimulated saliva, mixing ß-lactoglobulin-stabilized emulsions with stimulated saliva led to a reduction in ¿ mix/¿ emul and G¿mix/G¿emul, and an augment of tan ¿ at all measured deformations. In case of lysozyme-stabilized emulsions, the use of stimulated saliva increased G¿mix/G¿emul for ¿

Biopolymer Adsorption, with Special Reference to the Serum Albumin-Polystyrene Latex System

A study has been made of the adsorption of human serum albumin (HSA) on emursifier-free, negatively charged polystyrene (PS) latices. The adsorption has been followed directly and microcalorimetrically. Important variables are: pH, temperature, csalt and the surface charge a0 of the latex. Although all adsorption isotherms have a platform, the Langmuir theory is inadequate to account for them. Distinction must be made between the initial stages of adsorption, solely determined by the HSA-PS interaction and the later stages, where lateral interaction between adsorbed HSA molecules plays also an important role. The adsorption platform as a function of pH is maximal in the isoelectric point. Here the adsorbed amount is roughly compatible with side-on native HSA molecules. Both below and above the i. e. p. adsorption proceeds in a more unfolded conformation but a spread monolayer is never reached. The adsorption is largely driven by a net entropy gain, both in the initial and later states of the process. Besides this, there is a recognizable influence of the electrostatic attraction between the latex surface and local positive excesses inside the molecule

Humic acid protein complexation

Interactions of purified Aldrich humic acid (PAHA) with lysozyme (LSZ) are investigated. In solution LSZ is moderately positively and PAHA negatively charged at the investigated pH values. The proton binding of PAHA and of LSZ is determined by potentiometric proton titrations at various KCl concentrations. It is also measured for two mixtures of PAHA¿LSZ and compared with theoretically calculated proton binding assuming no mutual interaction. The charge adaptation due to PAHA¿LSZ interaction is relatively small and only significant at low and high pH. Next to the proton binding, the mass ratio PAHA/LSZ at the iso-electric point (IEP) of the complex at given solution conditions is measured together with the pH using the Mütek particle charge detector. From the pH changes the charge adaptation due to the interaction can be found. Also these measurements show that the net charge adaptation is weak for PAHA¿LSZ complexes at their IEP. PAHA/LSZ mass ratios in the complexes at the IEP are measured at pH 5 and 7. At pH 5 and 50 mmol/L KCl the charge of the complex is compensated for 30¿40% by K+; at pH 7, where LSZ has a rather low positive charge, this is 45¿55%. At pH 5 and 5 mmol/L KCl the PAHA/LSZ mass ratio at the IEP of the complex depends on the order of addition. When LSZ is added to PAHA about 25% K+ is included in the complex, but no K+ is incorporated when PAHA is added to LSZ. The flocculation behavior of the complexes is also different. After LSZ addition to PAHA slow precipitation occurs (6¿24 h) in the IEP, but after addition of PAHA to LSZ no precipitation can be seen after 12 h. Clearly, PAHA/LSZ complexation and the colloidal stability of PAHA¿LSZ aggregates depend on the order of addition. Some implications of the observed behavior are discussed

Staphylococcus aureus-Fibronectin Interactions with and without Fibronectin-Binding Proteins and Their Role in Adhesion and Desorption

Adhesion and residence-time-dependent desorption of two Staphylococcus aureus strains with and without fibronectin (Fn) binding proteins (FnBPs) on Fn-coated glass were compared under flow conditions. To obtain a better understanding of the role of Fn-FnBP binding, the adsorption enthalpies of Fn with staphylococcal cell surfaces were determined using isothermal titration calorimetry (ITC). Interaction forces between staphylococci and Fn coatings were measured using atomic force microscopy (AFM). The strain with FnBPs adhered faster and initially stronger to an Fn coating than the strain without FnBPs, and its Fn adsorption enthalpies were higher. The initial desorption was high for both strains but decreased substantially within 2 s. These time scales of staphylococcal bond ageing were confirmed by AFM adhesion force measurement. After exposure of either Fn coating or staphylococcal cell surfaces to bovine serum albumin (BSA), the adhesion of both strains to Fn coatings was reduced, suggesting that BSA suppresses not only nonspecific but also specific Fn-FnBP interactions. Adhesion forces and adsorption enthalpies were only slightly affected by BSA adsorption. This implies that under the mild contact conditions of convective diffusion in a flow chamber, adsorbed BSA prevents specific interactions but does allow forced Fn-FnBP binding during AFM or stirring in ITC. The bond strength energies calculated from retraction force-distance curves from AFM were orders of magnitude higher than those calculated from desorption data, confirming that a penetrating Fn-coated AFM tip probes multiple adhesins in the outermost cell surface that remain hidden during mild landing of an organism on an Fn-coated substratum, like that during convective diffusional flow

Proteins at interfaces : the adsorption of human plasma albumin and bovine pancreas ribonuclease on polystyrene latices

The adsorption from (aqueous) solution of proteins is very complex. The interfacial behaviour of proteins is determined by the properties of, and the mutual interactions between, the adsorbing interface, the protein molecules, the solvent (water) molecules and other solutes (e.g. ions). Virtually all kinds of interactions are involved, viz. electrostatic, hydrogen bonding, hydrophobic, van der Waals, etcetera.Due to the intricate nature of the adsorption process, and also to the specificity in structure and conformational stability of protein molecules, no general theories satisfactorily describing protein adsorption have yet been developed. Furthermore, all the proposed hypotheses concerning the structure of proteins at interfaces are difficult to verify since most of the techniques that can be applied for the conformational analysis of proteins in bulk solution are not suitable for studying proteins at interfaces. Even in a qualitative sense, protein adsorption is often not well understood. The intention of this study was to gain more insight in the factors that govern the adsorption of proteins from solution.In chapter 3 the adsorption of proteins in relation to their properties in solution was discussed on the basis of data reported in the literature. Although certain aspects of protein adsorption seem rather controversial, some general features may be recognized.As is typical for the adsorption of macromolecules, proteins generally attach irreversibly to the adsorbent. With hydrophilic interfaces polar interactions seem to dominate, but with hydrophobic interfaces non-polar interactions appear to govern the adsorption process. As a rule, the affinity between the protein and the adsorbent surface increases with their increasing hydrophobic content. This is due primarily to the increasing entropy gain resulting from hydrophobic bonding.The structure of a protein molecule in the adsorbed state is largely determined by its structural stability in bulk solution. The less stable the structure in solution, the more likely it is to be perturbed by the interface. The tendency of a protein molecule to change its structure on adsorption increases with increasing importance of hydrophobic interactions as a factor stabilizing the protein structure in solution. In these terms, the feature, often observed, that the plateau level of adsorption tends to a maximum in the isoelectric region of the protein in solution, may be explained.The conformational stability on varying the pH for HPA molecules is much less than for RNase molecules. Since the hydrophobicity of HPA is greater than that of RNase, for HPA the relative contribution from intramolecular hydrophobic interactions to the stabilization of the molecular structure in solution is expected to be greater than in the case of RNase.In chapter 2 the preparation and characterization of negatively charged polystyrene latices was described. The latices were prepared in the absence of any emulsifying agents. By this procedure 'clean' polystyrene surfaces containing no spurious materials were obtained. The charge on the polystyrene surface is essentially due to the presence of negatively charged sulphate (-OSO 3-) groups. By adjusting the polymerization conditions the latex surface charge could be varied in a controlled way. Obviously, the hydrophobicity of the polystyrene surface decreases with increasing surface charge density. There are some experimental indications that oligomers of styrene containing -OSO 3-end groups are adsorbed on the polystyrene particles. However, no conclusive evidence has been obtained to ascertain whether the presence of these oligomers renders the polystyrene surface 'hairy' or smooth.The electrophoresis of the polystyrene particles was studied in the presence of KNO 3 . From the electrophoretic mobility the electrokinetic potential and electrokinetic charge density were calculated. It appears that, especially for high surface charge densities, the surface charge is to a large extent compensated by charge located within the plane of shear of the particle. This implies considerable specific adsorption of K +ions at the polystyrene surface.In chapter 4 a description has been given of the determination of isotherms for the adsorption from solution of HPA and RNase onto polystyrene surfaces, under various conditions of pH (i.e. charge on the protein molecule), charge on the polystyrene surface, ionic strength (0.01 M and 0.05 M KNO 3 , without adding buffers) and temperature (5°C, 22°C and 37°C).In all cases, dilution experiments indicated that the proteins adsorb irreversibly.The affinity between HPA and the polystyrene surface, as judged from the initial slopes of the isotherms, reflects the Coulombic interaction between the adsorbate and the adsorbent. Thus, the initial part of the isotherm is steeper, the larger the charge difference between the HPA molecules and the polystyrene surface.The effect of temperature on the adsorption of HPA was found to be dependent on pH. Away from the isoelectric point in solution, at low degrees of coverage of the polystyrene surface, a steady increase of the amount adsorbed was observed on increasing the temperature. This suggests that, at least under these conditions, the adsorption is endothermic and, hence, that the adsorption process is driven by an entropy gain. In the isoelectric: region (pH ca. 4.6 for HPA) the adsorption mechanism seems to be different. At this pH the initial adsorption isotherms, at 5°C, and 22°C, are virtually identical but increasing the temperature to 37°C leads to a greater affinity between HPA and polystyrene. Moreover, it was found that the lateral repulsion between adsorbed HPA molecules tends to be maximum in the isoelectric region of the protein in solution. This argues against a conformation of the adsorbed molecules that is independent of pH.The adsorption isotherms for RNase all show a high-affinity character. Therefore, the effect of charge or temperature on the initial parts of the isotherms could not be measured.Unlike for RNase, the isotherms for HPA, in some cases, show steps. This reflects transitions in the mode of adsorption at intermediate surface coverages.For both HPA and RNase, the isotherms show plateau levels at sufficiently large concentrations in bulk solution. However, HPA and RNase differ markedly in the way the plateau levels depend on the pH of adsorption. In the case of HPA, the maximum amount adsorbed, as a function of pH, is more or less symmetrical with respect to its isoelectric point in solution, with a pronounced maximum at this pH value. With RNase the maximum adsorption is much less dependent on pH. Thus, at least for HPA, the plateau level of adsorption is predominantly determined by the net charge of the dissolved molecule. Based on a consideration of all the results, it was concluded that the reduction in the plateau level of adsorption with increasing pH beyond the isoelectric point, is due to a greater amount of structural rearrangement in the protein molecule, rather than to increased distances between the adsorbed molecules. Hence, it was assumed that the plateau level of adsorption corresponds to complete monolayers of protein molecules, structurally perturbed to varying degrees. Indeed, the influence of temperature and ionic strength on the structural stability of the protein in solution is generally reflected in the amount adsorbed.In the case of RNase it was found that the maximum amount adsorbed decreases significantly at pH values ≥9.5, where this protein possesses a considerable net negative charge.On increasing the negative charge of the polystyrene surface an increase in the adsorption of HPA and RNase was observed, even at pH values where the protein is also negatively charged. The reasons underlying this feature are not clear, but it indicates that the Coulombic interaction between the protein and the polystyrene surface is not a dominant factor in the adsorption process.Based on the assumption of structural rearrangements in the adsorbing protein molecules, it was concluded that the fraction of the protein in actual contact with the polystyrene surface increases with decreasing amount adsorbed. It was further argued that, after structural rearrangements, the adsorbed protein molecules retain a rather compact structure. Hence, the thickness of the adsorbed layers of HPA and RNase decreases with decreasing amount adsorbed. In the case of HPA the protein volume fraction in the adsorbed layer seems to be larger than for RNase.The electrostatic effects, i.e. the various roles played by the charged groups of the protein and the polystyrene surface as well as by the ions in solution, have been discussed in chapter 5. This discussion refers to adsorption saturation.Hydrogen ion titrations show that, as a result of adsorption, the dissociation of carboxyl groups in HPA and RNase molecules is suppressed. It was deduced that in both these proteins the average position of the carboxyl groups is relatively close to the negatively charged polystyrene surface. In the case of RNase, this effect is essentially independent of the pH of adsorption, whereas for HPA this suppression of dissociation of the carboxyl groups increases the further the pH is from the isoelectric point of HPA in solution. Hence, it would seem that the structural rearrangements accompanying the adsorption process lead to a larger fraction of the carboxyl groups located close to the polystyrene surface.In the case of RNase it was found that, after adsorption, a smaller number of positively charged groups (i.e. imidazole and amino groups) are titratable. It was assumed that this is due to the formation of strong ion pairs between these groups and the negatively charged sulphate groups at the polystyrene surface. In this respect, the experiments with HPA were not conclusive, but it is probable that the same kind of ion pairing occurs with this protein as well.The involvement of ions in the adsorption process was investigated by electrophoresis of the polystyrene particles and the protein molecules, before and after adsorption. Calculation of the electrokinetic charges revealed that, coincident with the adsorption of either protein, a net increase in negative charge results at low pH, and a net increase in positive charge at high pH.In order to analyze this redistribution of charge, a simple model for the protein- covered polystyrene particles was adopted. According to this model the average position of the negatively charged sulphate groups is taken to be the plane defining the polystyrene surface. The adsorbed protein layer, considered to have a rather compact structure, totally covers the adsorbent surface. The adsorbed layer is divided into three regions. In the innermost region, adjacent to the polystyrene surface, a fraction of the charged groups of the protein (e.g. carboxyl groups and positively charged groups that have formed ion pairs with negatively charged groups of the polystyrene surface), as well as specifically adsorbed ions, are located. The thickness of this region is comparable with the difference between the hydrodynamic radius of the bare polystyrene particle and the radius of the solid particle (i.e. the thickness of the shear layer). By analogy with the interior of dissolved protein molecules, the central region of the adsorbed protein layer is assumed to be electrically neutral. The outermost region, extending to the plane of shear of the covered particle, then contains the remainder of the electrokinetic charge of the protein-covered particle. For the purpose of analysis a homogeneous distribution of charge in both the innermost and the outermost regions was assumed. The permittivities of each of these three regions of the adsorbed layer were taken to be adjustable parameters.On the basis of this model, the charge effects in the innermost and the outermost region, resulting from the transfer of ions to or from the solution phase, were calculated. It was reasoned that a net uptake of cations (i.e. K +) from solution into the region adjacent to the polystyrene surface occurs, whereas in the outermost region of the adsorbed protein layer there is a net increase in the binding of anions (i.e. NO 3-).In chapter 6 a thermodynamic analysis of the adsorption process was made. The net enthalpy change, at maximum adsorption of the two proteins, was measured under various conditions. For RNase and, in most cases, for HPA this enthalpy change was found to be positive. This leads to the conclusion that the adsorption process is governed by an increase of entropy.The experimentally obtained adsorption enthalpy was interpreted in terms of the contributions resulting from the various factors that are known to be involved in the overall adsorption process. In view of the experimental results reported in the previous chapters, the following factors were considered:a. changes in the degree of protonation of the adsorbed and the dissolved protein molecules (especially their carboxyl groups),b. redistribution of charge due to overlap of electric fields of the protein and the polystyrene surface,c. changes in the medium of the ions that are transferred from the solution to the adsorbed layer,d. van der Waals interactions between the polystyrene particle and the adsorbed protein layer,e. dehydration of hydrophobic parts of the polystyrene surface,f. those resulting from structural changes in the adsorbing protein molecules, including changes in the state of hydration and interactions between specific groups of the protein and the polystyrene surface.The changes in the thermodynamic functions of state due to the factors a. - e. were estimated on the basis of the model proposed for the adsorbed layer. Due to lack of detailed knowledge concerning the nature of structural changes in the adsorbing protein molecules, the thermodynamic effects resulting from factor f. are not directly assessable. However, an estimate of the contribution made by this factor to the net adsorption enthalpy may be obtained by subtracting the sum of the calculated enthalpy changes due to the factors a. - e. from the experimental value of the adsorption enthalpy. The degree of accuracy to which the enthalpy resulting from structural changes can then, therefore, be determined, depends on the accuracy of the estimates for the other constituent terms (a.-e.) as well as on the accuracy of the experimental value; it will also contain contributions from any other factors that may have been overlooked. Nevertheless, for both HPA and RNase, the enthalpy resulting from factor f., obtained in this way, seems to show a definite relationship to the amount of protein adsorbed (i.e. to the extent of rearrangement of the protein structure). For both proteins this enthalpy effect was found always to be positive.The mechanisms proposed for the adsorption of HPA and RNase on polystyrene are, in a qualitative sense, consistent with the effect of temperature on the overall adsorption enthalpy.Due to the irreversibility of the process, the standard Gibbs free energy of adsorption of HPA and RNase onto polystyrene could not be established from the adsorption isotherms, but it must be negative for adsorption to occur.It was concluded that the ionic medium effect (factor c. ) opposes protein adsorption. For polystyrene latices having a large negative surface charge the redistribution of charge (factor b.) also opposes the adsorption process, but this effect decreases with decreasing surface charge density. Dehydration of hydrophobic areas of the polystyrene surface (factor e.) favours the adsorption process primarily on account of the resulting entropy gain. The contributions from changes in the degree of protonation of the protein (factor a.) and from the van der Waals interaction between the adsorbed protein layer and the polystyrene particle (factor d.) to the Gibbs free energy of adsorption seem to be of minor importance. It was further argued that the Gibbs free energy change resulting from structural rearrangements in the protein (factor f.) is negative. Since the enthalpy change due to this factor was found to be positive, the entropy effect involved must also be positive. This entropy gain may originate e.g. from variations in the number and the kind of amino acid residues exposed to the aqueous phase, and from increased rotational freedom in the protein molecule.Altogether, it appears that a net increase of entropy, associated with factors e. and f., dominates the adsorption from aqueous solution of HPA and RNase onto negatively charged polystyrene surfaces.The model assumed for the adsorbed layer and the distribution of charge therein, seems to fit the experimental observations rather well; at least, the thermodynamic analysis based on this model is not incompatible with the experimental data.Finally, the thermodynamic analysis of the adsorption processes under investigation leads to conclusions, which one may expect to be of general validity with regard to the interaction between proteins and interfaces