Collection of Partition Coefficients in Hexadecyltrimethylammonium Bromide, Sodium Cholate, and Lithium Perfluorooctanesulfonate Micellar Solutions: Experimental Determination and Computational Predictions.

This study focuses on determining the partition coefficients (logP) of a diverse set of 63 molecules in three distinct micellar systems: hexadecyltrimethylammonium bromide (HTAB), sodium cholate (SC), and lithium perfluorooctanesulfonate (LPFOS). The experimental log p values were obtained through micellar electrokinetic chromatography (MEKC) experiments, conducted under controlled pH conditions. Then, Quantum Mechanics (QM) and machine learning approaches are proposed for the prediction of the partition coefficients in these three micellar systems. In the applied QM approach, the experimentally obtained partition coefficients were correlated with the calculated values for the case of the 15 solvent mixtures. Using Density Function Theory (DFT) with the B3LYP functional, we calculated the solvation free energies of 63 molecules in these 16 solvents. The combined data from the experimental partition coefficients in the three micellar formulations showed that the 1-propanol/water combination demonstrated the best agreement with the experimental partition coefficients for the SC and HTAB micelles. Moreover, we employed the SVM approach and k-means clustering based on the generation of the chemical descriptor space. The analysis revealed distinct partitioning patterns associated with specific characteristic features within each identified class. These results indicate the utility of the combined techniques when we want an efficient and quicker model for predicting partition coefficients in diverse micelles.

Molecular dynamics simulations of an α-synuclein NAC domain fragment with a ff14IDPSFF IDP-specific force field suggest ß-sheet intermediate states of fibrillation.

For the discovery of treatments against synucleinopathies, it is necessary to unravel and fully understand the mechanism of fibrillation of proteins involved. Among them, α-synuclein (αS) plays a key role in the development of these diseases through its aggregation into oligomers found in Lewy bodies. However, its structural disorder as an intrinsically disordered protein (IDP) makes its characterization by experimental techniques arduously difficult. Atomistic simulations aim to provide insights into this blank canvas and, fortunately, some studies have already suggested promising mechanisms. Still, it is urgent to consider the IDP features in simulations, so recently a lot of force fields designed to deal with IDPs have been developed. In this study, we have carried out a total of 12 µs simulations of an αS core fragment using a popular ff14SB AMBER force field and the ff14IDPSFF variation that includes a grid-based energy correction map (CMAP) method. The predicted chemical shifts from the simulations and those measured from the αS protein in the NMR solution indicate that ff14IDPSFF reproduces the experimental data more accurately. Moreover, structural analysis exhibits opposite trends between secondary structure propensities. The ff14SB force field preserves the α-helices found in the micelle-bound αS structure, which is used as an initial conformation, while ff14IDPSFF stands out with increased structural disorder and the formation of ß-sheets, which suggests that the IDP-specific force field can capture more suitable conformations representing the possible intermediate states of the fibrillation process.

Influence of macromolecular crowding on the charge regulation of intrinsically disordered proteins.

In this work we study the coupling between ionization and conformational properties of two IDPs, histatin-5 and ß-amyloid 42, in the presence of neutral and charged crowders. The latter is modeled to resemble bovine serum albumin (BSA). With this aim, semi-grand canonical Monte Carlo simulations are performed, so that the IDP charge is a dynamic property, undergoing protonation/deprotonation processes. Both ionization properties (global and specific amino acid charge and binding capacitance) and radius of gyration are analyzed in a large range of pH values and salt concentrations. Without crowder agents, the titration curve of histatin-5, a polycation, is salt-dependent while that of ß-amyloid 42, a polyampholyte, is almost unaffected. The salt concentration is found to be particularly relevant at pH values where the protein binding capacitance (directly linked with charge fluctuation) is larger. Upon addition of neutral crowders, charge regulation is observed in histatin-5, while for ß-amyloid 42 this effect is very small. The main mechanism for charge regulation is found to be the effective increase in the ionic strength due to the excluded volume. In the presence of charged crowders, a significant increase in the charge of both IDPs is observed in almost all the pH range. In this case, the IDP charge is altered not only by the increase in the effective ionic strength but also by its direct electrostatic interaction with the charged crowders.

Macromolecular diffusion in crowded media beyond the hard-sphere model.

The effect of macromolecular crowding on diffusion beyond the hard-core sphere model is studied. A new coarse-grained model is presented, the Chain Entanglement Softened Potential (CESP) model, which takes into account the macromolecular flexibility and chain entanglement. The CESP model uses a shoulder-shaped interaction potential that is implemented in the Brownian Dynamics (BD) computations. The interaction potential contains only one parameter associated with the chain entanglement energetic cost (Ur). The hydrodynamic interactions are included in the BD computations via Tokuyama mean-field equations. The model is used to analyze the diffusion of a streptavidin protein among different sized dextran obstacles. For this system, Ur is obtained by fitting the streptavidin experimental long-time diffusion coefficient Dlongversus the macromolecular concentration for D50 (indicating their molecular weight in kg mol-1) dextran obstacles. The obtained Dlong values show better quantitative agreement with experiments than those obtained with hard-core spheres. Moreover, once parametrized, the CESP model is also able to quantitatively predict Dlong and the anomalous exponent (α) for streptavidin diffusion among D10, D400 and D700 dextran obstacles. Dlong, the short-time diffusion coefficient (Dshort) and α are obtained from the BD simulations by using a new empirical expression, able to describe the full temporal evolution of the diffusion coefficient.

Ionization and Conformational Equilibria of Citric Acid: Delocalized Proton Binding in Solution.

The microspeciation of citric acid is studied by analyzing NMR titration data. When the site binding (SB) model, which assumes fully localized proton binding to the carboxylic groups, is used to obtain microscopic energy parameters (dissociation constants, pair and triplet interaction energies between charged carboxylate groups), contradictory results are obtained. The resulting macroscopic constants are in very good agreement with the values reported in the literature using potentiometry. However, the found pair interaction energy between the terminal carboxylates and the triplet interaction energy are physically meaningless. To solve this apparent contradiction, we consider the possibility of delocalized proton binding, so that the proton can be exchanged at high velocity in the NMR time scale through short, strong, low-barrier (SSLB) hydrogen bonds. With this aim, ab initio MP2 calculations using the SMD polarizable continuum model for the solvent were performed and the fully roto-microspeciation elucidated. First, fully localized proton binding was assumed, and the resulting microstate probabilities are in reasonable agreement with those reported in previous works that use selective blocking of the carboxylic groups. They are, however, in clear disagreement with the microstate probabilities derived from the NMR titration data, which predict, within a very narrow confidence interval, a unique microspecies for the symmetric di-ionized form. Moreover, counterintuitively, the interaction between terminal charged groups is much larger than that between central and terminal groups. As a consequence, we have explored the possibility of delocalized proton binding by calculating the energy of intermediate proton positions between two carbolxylic groups. The results reveal that the exchange of the proton through the hydrogen bonds is in some cases produced without energetic barrier. This effect is specially relevant in the di-ionized form, with all the most stable conformations forming a SSLB, which together would constitute the only microstate detected by NMR. An alternative reaction scheme for the ionization process, based on proton delocalization, is proposed.

Ammoniacal nitrogen recovery from swine slurry using a gas-permeable membrane: pH control strategies and feed-to-trapping volume ratio.

Gas-permeable membrane (GPM) technology is gaining interest to recover nitrogen from residual effluents due to its effectiveness, simple operation and capacity of producing a nutrient rich product with fertilising value. In this study, a GPM contactor was used at 25 °C to recover total ammoniacal nitrogen (TAN) from swine slurry as a concentrated (NH4)2SO4 solution. Firstly, a synthetic solution was tested on a wide pH range (6-12). Results showed that the ammonia mass transfer constants (Km) increased from 7.9·10-9 to 1.2·10-6 m/s as the pH increased. The reagent consumption to control the pH per mole nitrogen recovered had a minimum at pH 9, which showed a Km value of 3.0·10-7 m/s. Secondly, various pH control strategies were tested using swine slurry, including (i) no pH control, (ii) pH control at 8.5, 9.0 and 10.0, and (iii) an initial spike of the NaOH equivalent to the required to control the pH at 9. The test without pH control reached a TAN recovery of around 60%, which could be an interesting strategy when high nitrogen recoveries or short operating times are not required. The pH control at 9 stood out as the most favourable operating condition due to its high Km and lower reagent consumption. Thirdly, several feed-to-trapping volume ratios ranging from 1:1 to 15:1 were tested using swine slurry at pH 9. These assays revealed that a GPM process with a high feed-to-trapping volume ratio fastens the recovery of 99% of TAN as a high purity (NH4)2SO4 solution containing 40 g N/L.

Unusual Aspects of Charge Regulation in Flexible Weak Polyelectrolytes.

This article reviews the state of the art of the studies on charge regulation (CR) effects in flexible weak polyelectrolytes (FWPE). The characteristic of FWPE is the strong coupling of ionization and conformational degrees of freedom. After introducing the necessary fundamental concepts, some unconventional aspects of the the physical chemistry of FWPE are discussed. These aspects are: (i) the extension of statistical mechanics techniques to include ionization equilibria and, in particular, the use of the recently proposed Site Binding-Rotational Isomeric State (SBRIS) model, which allows the calculation of ionization and conformational properties on the same foot; (ii) the recent progresses in the inclusion of proton equilibria in computer simulations; (iii) the possibility of mechanically induced CR in the stretching of FWPE; (iv) the non-trivial adsorption of FWPE on ionized surfaces with the same charge sign as the PE (the so-called "wrong side" of the isoelectric point); (v) the influence of macromolecular crowding on CR.

Immunometabolic actions of trabectedin and lurbinectedin on human macrophages: relevance for their anti-tumor activity.

In recent years, the central role of cell bioenergetics in regulating immune cell function and fate has been recognized, giving rise to the interest in immunometabolism, an area of research focused on the interaction between metabolic regulation and immune function. Thus, early metabolic changes associated with the polarization of macrophages into pro-inflammatory or pro-resolving cells under different stimuli have been characterized. Tumor-associated macrophages are among the most abundant cells in the tumor microenvironment; however, it exists an unmet need to study the effect of chemotherapeutics on macrophage immunometabolism. Here, we use a systems biology approach that integrates transcriptomics and metabolomics to unveil the immunometabolic effects of trabectedin (TRB) and lurbinectedin (LUR), two DNA-binding agents with proven antitumor activity. Our results show that TRB and LUR activate human macrophages toward a pro-inflammatory phenotype by inducing a specific metabolic rewiring program that includes ROS production, changes in the mitochondrial inner membrane potential, increased pentose phosphate pathway, lactate release, tricarboxylic acids (TCA) cycle, serine and methylglyoxal pathways in human macrophages. Glutamine, aspartate, histidine, and proline intracellular levels are also decreased, whereas oxygen consumption is reduced. The observed immunometabolic changes explain additional antitumor activities of these compounds and open new avenues to design therapeutic interventions that specifically target the immunometabolic landscape in the treatment of cancer.

Molecular dynamics simulation of the spherical electrical double layer of a soft nanoparticle: effect of the surface charge and counterion valence.

Molecular dynamics simulations were performed to study the ion and water distribution around a spherical charged nanoparticle. A soft nanoparticle model was designed using a set of hydrophobic interaction sites distributed in six concentric spherical layers. In order to simulate the effect of charged functionalyzed groups on the nanoparticle surface, a set of charged sites were distributed in the outer layer. Four charged nanoparticle models, from a surface charge value of -0.035 C m(-2) to -0.28 C m(-2), were studied in NaCl and CaCl(2) salt solutions at 1 M and 0.1 M concentrations to evaluate the effect of the surface charge, counterion valence, and concentration of added salt. We obtain that Na(+) and Ca(2+) ions enter inside the soft nanoparticle. Monovalent ions are more accumulated inside the nanoparticle surface, whereas divalent ions are more accumulated just in the plane of the nanoparticle surface sites. The increasing of the the salt concentration has little effect on the internalization of counterions, but significantly reduces the number of water molecules that enter inside the nanoparticle. The manner of distributing the surface charge in the nanoparticle (uniformly over all surface sites or discretely over a limited set of randomly selected sites) considerably affects the distribution of counterions in the proximities of the nanoparticle surface.

Adsorption of flexible proteins in the 'wrong side' of the isoelectric point: Casein macropeptide as a model system.

We analyze the conditions of the adsorption of a flexible peptide onto a charged substrate in the 'wrong side' of the isoelectric point (WSIP), i.e. when surface and peptide charges have the same sign. As a model system, we focus on the casein macropeptide (CMP), both in the aglycosylated (aCMP) and fully glycosydated (gCMP) forms. We model the substrate as a uniformly charged plane while CMP is treated as a bead-and-spring model including electrostatic interactions, excluded volume effects and acid/base equilibria. Adsorption coverage, aminoacid charges and concentration profiles are computed by means of Monte Carlo simulations at fixed pH and salt concentration. We conclude that for different reasons the CMP can be adsorbed to both positively and negatively charged surfaces in the WSIP. For negatively charged surfaces, WSIP adsorption is due to the patchy distribution of charges: the peptide is attached to the surface by the positively charged end of the chain, while the repulsion of the surface for the negatively charged tail is screened by the small ions of the added salt. This effect increases with salt concentration. Conversely, a positively charged substrate induces strong charge regulation of the peptide: the acidic groups are deprotonated, and the peptide becomes negatively charged. This effect is stronger at low salt concentrations and it is more intense for gCMP than for aCMP, due to the presence of the additional sialic groups in gCMP.

New insights into diffusion in 3D crowded media by Monte Carlo simulations: effect of size, mobility and spatial distribution of obstacles.

Particle diffusion in crowded media was studied through Monte Carlo simulations in 3D obstructed lattices. Three particular aspects affecting the diffusion, not extensively treated in a three-dimensional geometry, were analysed: the relative particle-obstacle size, the relative particle-obstacle mobility and the way of having the obstacles distributed in the simulation space (randomly or uniformly). The results are interpreted in terms of the parameters that characterize the time dependence of the diffusion coefficient: the anomalous diffusion exponent (α), the crossover time from anomalous to normal diffusion regimes (τ) and the long time diffusion coefficient (D*). Simulation results indicate that there are a more anomalous diffusion (smaller α) and a lower long time diffusion coefficient (D*) when obstacle concentration increases, and that, for a given total excluded volume and immobile obstacles, the anomalous diffusion effect is less important for bigger size obstacles. However, for the case of mobile obstacles, this size effect is inverted yielding values that are in qualitatively good agreement with in vitro experiments of protein diffusion in crowded media. These results underline that the pattern of the spatial partitioning of the obstacle excluded volume is a factor to be considered together with the value of the excluded volume itself.

A semi-grand canonical Monte Carlo simulation model for ion binding to ionizable surfaces: proton binding of carboxylated latex particles as a case study.

In this paper, we present a computer simulation study of the ion binding process at an ionizable surface using a semi-grand canonical Monte Carlo method that models the surface as a discrete distribution of charged and neutral functional groups in equilibrium with explicit ions modelled in the context of the primitive model. The parameters of the simulation model were tuned and checked by comparison with experimental titrations of carboxylated latex particles in the presence of different ionic strengths of monovalent ions. The titration of these particles was analysed by calculating the degree of dissociation of the latex functional groups vs. pH curves at different background salt concentrations. As the charge of the titrated surface changes during the simulation, a procedure to keep the electroneutrality of the system is required. Here, two approaches are used with the choice depending on the ion selected to maintain electroneutrality: counterion or coion procedures. We compare and discuss the difference between the procedures. The simulations also provided a microscopic description of the electrostatic double layer (EDL) structure as a function of pH and ionic strength. The results allow us to quantify the effect of the size of the background salt ions and of the surface functional groups on the degree of dissociation. The non-homogeneous structure of the EDL was revealed by plotting the counterion density profiles around charged and neutral surface functional groups.

Unravelling Constant pH Molecular Dynamics in Oligopeptides with Explicit Solvation Model.

An accurate description of the protonation state of amino acids is essential to correctly simulate the conformational space and the mechanisms of action of proteins or other biochemical systems. The pH and the electrochemical environments are decisive factors to define the effective pKa of amino acids and, therefore, the protonation state. However, they are poorly considered in Molecular Dynamics (MD) simulations. To deal with this problem, constant pH Molecular Dynamics (cpHMD) methods have been developed in recent decades, demonstrating a great ability to consider the effective pKa of amino acids within complex structures. Nonetheless, there are very few studies that assess the effect of these approaches in the conformational sampling. In a previous work of our research group, we detected strengths and weaknesses of the discrete cpHMD method implemented in AMBER when simulating capped tripeptides in implicit solvent. Now, we progressed this assessment by including explicit solvation in these peptides. To analyze more in depth the scope of the reported limitations, we also carried out simulations of oligopeptides with distinct positions of the titratable amino acids. Our study showed that the explicit solvation model does not improve the previously noted weaknesses and, furthermore, the separation of the titratable amino acids in oligopeptides can minimize them, thus providing guidelines to improve the conformational sampling in the cpHMD simulations.

Unveiling the Effect of Low pH on the SARS-CoV-2 Main Protease by Molecular Dynamics Simulations.

(1) Background: Main Protease (Mpro) is an attractive therapeutic target that acts in the replication and transcription of the SARS-CoV-2 coronavirus. Mpro is rich in residues exposed to protonation/deprotonation changes which could affect its enzymatic function. This work aimed to explore the effect of the protonation/deprotonation states of Mpro at different pHs using computational techniques. (2) Methods: The different distribution charges were obtained in all the evaluated pHs by the Semi-Grand Canonical Monte Carlo (SGCMC) method. A set of Molecular Dynamics (MD) simulations was performed to consider the different protonation/deprotonation during 250 ns, verifying the structural stability of Mpro at different pHs. (3) Results: The present findings demonstrate that active site residues and residues that allow Mpro dimerisation was not affected by pH changes. However, Mpro substrate-binding residues were altered at low pHs, allowing the increased pocket volume. Additionally, the results of the solvent distribution around Sγ, Hγ, Nδ1 and Hδ1 atoms of the catalytic residues Cys145 and His41 showed a low and high-water affinity at acidic pH, respectively. It which could be crucial in the catalytic mechanism of SARS-CoV-2 Mpro at low pHs. Moreover, we analysed the docking interactions of PF-00835231 from Pfizer in the preclinical phase, which shows excellent affinity with the Mpro at different pHs. (4) Conclusion: Overall, these findings indicate that SARS-CoV-2 Mpro is highly stable at acidic pH conditions, and this inhibitor could have a desirable function at this condition.

On the Use of the Discrete Constant pH Molecular Dynamics to Describe the Conformational Space of Peptides.

Solvent pH is an important property that defines the protonation state of the amino acids and, therefore, modulates the interactions and the conformational space of the biochemical systems. Generally, this thermodynamic variable is poorly considered in Molecular Dynamics (MD) simulations. Fortunately, this lack has been overcome by means of the Constant pH Molecular Dynamics (CPHMD) methods in the recent decades. Several studies have reported promising results from these approaches that include pH in simulations but focus on the prediction of the effective pKa of the amino acids. In this work, we want to shed some light on the CPHMD method and its implementation in the AMBER suitcase from a conformational point of view. To achieve this goal, we performed CPHMD and conventional MD (CMD) simulations of six protonatable amino acids in a blocked tripeptide structure to compare the conformational sampling and energy distributions of both methods. The results reveal strengths and weaknesses of the CPHMD method in the implementation of AMBER18 version. The change of the protonation state according to the chemical environment is presumably an improvement in the accuracy of the simulations. However, the simulations of the deprotonated forms are not consistent, which is related to an inaccurate assignment of the partial charges of the backbone atoms in the CPHMD residues. Therefore, we recommend the CPHMD methods of AMBER program but pointing out the need to compare structural properties with experimental data to bring reliability to the conformational sampling of the simulations.

Effect of pH on the Supramolecular Structure of Helicobacter pylori Urease by Molecular Dynamics Simulations.

The effect of pH on the supramolecular structure of Helicobacter pylori urease was studied by means of molecular dynamics simulations at seven different pHs. Appropriate urease charge distributions were calculated using a semi-grand canonical Monte Carlo (SGCMC) procedure that assigns each residue's charge state depending on the assigned individual pKa obtained by PROPKA. The effect of pH on protein stability has been analyzed through root-mean-square deviation (RMSD), radius of gyration (RG), solvent-accessible surface area (SASA), hydrogen bonds (HB) and salt bridges (SB). Urease catalyses the hydrolysis of urea in 12 active sites that are covered by mobile regions that act like flaps. The mobility of these flaps is increased at acidic pHs. However, extreme acidic conditions cause urease to have the least number of stabilizing interactions. This initiates the process of denaturalization, wherein the four (αß)3 subunits of the global structure ((αß)3)4 of urease start to separate.

Role of Charge Regulation and Fluctuations in the Conformational and Mechanical Properties of Weak Flexible Polyelectrolytes.

This work addresses the role of charge regulation (CR) and the associated fluctuations in the conformational and mechanical properties of weak polyelectrolytes. Due to CR, changes in the pH-value modifies the average macromolecular charge and conformational equilibria. A second effect is that, for a given average charge per site, fluctuations can alter the intensity of the interactions by means of correlation between binding sites. We investigate both effects by means of Monte Carlo simulations at constant pH-value, so that the charge is a fluctuating quantity. Once the average charge per site is available, we turn off the fluctuations by assigning the same average charge to every site. A constant charge MC simulation is then performed. We make use of a model which accounts for the main fundamental aspects of a linear flexible polyelectrolyte that is, proton binding, angle internal rotation, bond stretching and bending. Steric excluded volume and differentiated treatment for short-range and long-range interactions are also included. This model can be regarded as a kind of "minimal" in the sense that it contains a minimum number of parameters but still preserving the atomistic detail. It is shown that, if fluctuations are activated, gauche state bond probabilities increase and the persistence length decreases, so that the polymer becomes more folded. Macromolecular stretching is also analyzed in presence of CR (the charge depends on the applied force) and without CR (the charge is fixed to the value at zero force). The analysis of the low force scaling behavior concludes that Pincus exponent becomes pH-dependent. Both, with and without CR, a transition from 1/2 at high pH-values (phantom chain) to 3/5 at low pH-values (Pincus regime) is observed. Finally, the intermediate force stretching regime is investigated. It is found that CR induces a moderate influence in the force-extension curves and persistence length (which in this force regime becomes force-dependent). It is thus concluded that the effect of CR on the stretching curves is mainly due to the changes in the average charge at zero force. It is also found that, for the cases studied, the effect of steric excluded volume is almost irrelevant compared to electrostatic interactions.

Competitive Cd2+/H+ complexation to polyacrylic acid described by the stepwise and intrinsic stability constants.

Stepwise constants can be used to describe competitive proton and metal binding to macromolecules with a large number of sites. With the aim of accessing information on the microscopic binding model, we report an expression that connects the stepwise constants to the site-specific metal constants. This expression holds for a very general complexation model including heterogeneity, interactions, and chelate complexation. Assuming bidentate binding of the Cd ions to adjacent carboxylate groups in poly(acrylic acid), stepwise and intrinsic stability constants for proton and cadmium binding were estimated from the experimental data. Intrinsic values were split into specific and electrostatic contributions (by means of the Poisson-Boltzmann equation under cylindrical geometry). Free of the electrostatic contribution, the remaining Cd binding energy showed almost no dependence on the coverage and ionic strength, and the corresponding average values allowed for a reasonable reproduction of raw binding data. Small systematic discrepancies from the homogeneous behavior are critically discussed.

Coupling of Charge Regulation and Conformational Equilibria in Linear Weak Polyelectrolytes: Treatment of Long-Range Interactions via Effective Short-Ranged and pH-Dependent Interaction Parameters.

The classical Rotational Isomeric State (RIS) model, originally proposed by Flory, has been used to rationalize a wide range of physicochemical properties of neutral polymers. However, many weak polyelectrolytes of interest are able to regulate their charge depending on the conformational state of the bonds. Recently, it has been shown that the RIS model can be coupled with the Site Binding (SB) model, for which the ionizable sites can adopt two states: protonated or deprotonated. The resulting combined scheme, the SBRIS model, allows for analyzing ionization and conformational equilibria on the same foot. In the present work, this approach is extended to include pH-dependent electrostatic Long-Range (LR) interactions, ubiquitous in weak polyelectrolytes at moderate and low ionic strengths. With this aim, the original LR interactions are taken into account by defining effective Short-Range (SR) and pH-dependent parameters, such as effective microscopic protonation constants and rotational bond energies. The new parameters are systematically calculated using variational methods. The machinery of statistical mechanics for SR interactions, including the powerful and fast transfer matrix methods, can then be applied. The resulting technique, which we will refer to as the Local Effective Interaction Parameters (LEIP) method, is illustrated with a minimal model of a flexible linear polyelectrolyte containing only one type of rotating bond. LEIP reproduces very well the pH dependence of the degree of protonation and bond probabilities obtained by semi-grand canonical Monte Carlo simulations, where LR interactions are explicitly taken into account. The reduction in the computational time in several orders of magnitude suggests that the LEIP technique could be useful in a range of areas involving linear weak polyelectrolytes, allowing direct fitting of the relevant physical parameters to the experimental quantities.

Competitive ion complexation to polyelectrolytes: determination of the stepwise stability constants. The Ca2+/H+/polyacrylate system.

This work presents a new methodology aimed at obtaining the stepwise stability constants corresponding to the binding of ions (or other small molecules) to macromolecular ligands having a large number of sites. For complexing agents with a large number of sites, very simple expressions for the stepwise stability constants arise. Such expressions are model-independent; that is, they allow the determination of the stepwise stability constants without making any previous assumption of the detailed complexation mechanism. The formalism is first presented for a single complexing ion and further extended to competitive systems where the competing ions can display, in general, different stoichiometric relationships. These ideas are applied to the analysis of experimental titrations corresponding to competitive binding of calcium ions to poly(acrylic acid) for different pH values and ionic strengths. Intrinsic stability constants were estimated from the stepwise stability constants (by removing the corresponding statistical factor), and split into specific and electrostatic contributions (by means of the Poisson-Boltzmann equation). After this treatment, the specific proton binding energies showed almost no dependence on the coverage and ionic strength. Likewise, for the range of concentrations studied, the specific component of the intrinsic stability constants of the calcium ions, calculated assuming bidentate binding of Ca to neighboring groups of a linear chain, is almost independent of the calcium and proton coverage and ionic strength.