Electrostatic and specific binding to macromolecular ligands

Proton Binding Characteristics of Dissolved Organic Matter Extracted from the North Atlantic

Marine dissolved organic matter (DOM) presents key thermodynamic properties that are not yet fully constrained. Here, we report the distribution of binding sites occupied by protons (i.e., proton affinity spectra) and parametrize the median intrinsic proton binding affinities (log K̅H) and heterogeneities (m), for DOM samples extracted from the North Atlantic. We estimate that 11.4 ± 0.6% of C atoms in the extracted marine DOM have a functional group with a binding site for ionic species. The log K̅H of the most acidic groups was larger (4.01-4.02 ± 0.02) than that observed in DOM from coastal waters (3.82 ± 0.02), while the chemical binding heterogeneity parameter increased with depth to values (m1= 0.666 ± 0.009) ca. 10% higher than those observed in surface open ocean or coastal samples. On the contrary, the log K̅H for the less acidic groups shows a difference between the surface (10.01 ± 0.08) and deep (9.22 ± 0.35) samples. The latter chemical groups were more heterogeneous for marine than for terrestrial DOM, and m2 decreased with depth to values of 0.28 ± 0.03. Binding heterogeneity reflects aromatic carbon compounds' persistence and accumulation in diverse, low-abundance chemical forms, while easily degradable low-affinity groups accumulate more uniformly in the deep ocean.

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.

The electrostatic potential inside and around α-lactalbumin: Fluctuations and mean-field models

The electrostatic potential (EP) generated by the protein α-lactoalbumin in the presence of added salt is computed as a thermal average at a given point in space. With this aim, constant pH Monte Carlo (MC) simulations are performed within the primitive model, namely, the solvent is treated as a continuum dielectric. The study of the thermal and spatial fluctuations of the EP reveals that they are remarkably high inside the protein. The calculations indicate that fluctuations inside the protein are mainly due to the asymmetric distribution of the charge groups, while the charge fluctuations of the titratable groups play a minor role. The computed EP matches very well with the one obtained from the Poisson equation for the average charge density in spherical symmetry. The Tanford–Kirkwood multipole expansion reproduces the simulated angular-averaged potential rather accurately. Surprisingly, two of the simplest mean-field models, the linear Poisson–Boltzmann (PB) equation and Donnan potential, provide good estimations of the average EP in the effective protein surface (surface EP). The linear PB equation predicts a linear relationship between charge and surface EP, which is numerically reproduced only if the small ions within the protein are taken into account. On the other hand, the partition coefficients of the small ions inside and outside the protein predicted by Donnan theory reproduce reasonably well the simulation results.

Proton binding to humic nano particles: electrostatic interaction and the condensation approximation

Proton binding to "carboxylic" and "phenolic" sites of humic nano particles (HNPs) is determined by the total proton affinity that is due to a specific and an electrostatic affinity. Both affinities are accounted for in the bi-modal Langmuir-Freundlich (bi-LF)-equation extended with a Boltzmann factor that includes the electrostatic site potential(s), y. For y → 0 the equation reduces to the bi-LF Master Curve (MC). Commonly, an electrical double layer model is used to obtain y, e.g., the bi-LF-Donnan-V_app (monocomponent NICA-Donnan) model and bi-LF-soft-particle-Poison-Boltzmann-Theory (SPBT). A new method is presented that combines the "condensation approximation" (CA) with the MC concept (CA-MC). With the CA, the proton binding curve and MC can be transformed in, respectively, the total and specific affinity distribution. The difference at a given charge density provides the electrostatic affinity and CA-potentials vs. charge density. The MC can be obtained theoretically or by using the convention that the electrostatic interaction is negligible at 1 M salt concentration. For five HNPs CA-potentials corresponding with the bi-LF-SPBT are compared with results of the bi-LF-Donnan-V_app model using the MC(SPBT). The bi-LF-Donnan-V_app model fails when the Debye length > hydrated particle radius. The CA-MC(1M) method does not require characteristics of the HNPs. Combination of the bi-LF-eq. with the CA-MC(1 M) method gives the bi-LF-CA-MC(1 M) model. The CA-MC(1 M) differs from the MC(SPBT); therefore, resulting parameters can only be compared when the same method is used.

Addressing the electrostatic component of protons binding to aquatic nanoparticles beyond the Non-Ideal Competitive Adsorption (NICA)-Donnan level: Theory and application to analysis of proton titration data for humic matter

HYPOTHESIS

Charge descriptors of aquatic nanoparticles (NPs) are evaluated from proton titration curves measured at different salt concentrations and routinely analysed by the Non-Ideal Competitive Adsorption-Donnan (NICAD) model. This model, however, suffers from approximations regarding particle electrostatics, which may bias particle charge estimation. Implementation of Poisson-Boltzmann (PB) theory within consistent treatment of NPs protolytic data is expected to address NICAD shortcomings.

EXPERIMENTS

An alternative to NICAD is elaborated on the basis of nonlinearized PB equation for soft particle electrostatics to properly unravel the electrostatic and chemical components of proton binding to NPs. A numerical package is developed for automated analysis of proton titration curves and proton affinity spectra at different salt concentrations. The performance of the method is illustrated for humic matter nanoparticles with different charge and size, and compared to that of NICAD.

FINDINGS

Unlike NICAD, PB-based treatment successfully reproduces particle charge dependence on pH for practical salt concentrations from the thin to thick electric double layer limit. Donnan representation in NICAD leads to moderate to dramatic misestimations of proton affinity and binding heterogeneity depending on particle size to Debye layer thickness ratio. Interpretation of NPs protolytic properties with PB theory further avoids adjustment of the 'particle Donnan volume' empirically introduced in NICAD.

Equilibrium mono- and multicomponent adsorption models: From homogeneous ideal to heterogeneous non-ideal binding

Aqueous sorption processes play an important role in, for example, pollutant binding to natural nanoparticles, colloid stability, separation and enrichment of components and remediation processes. In this article, which is a tribute to Hans Lyklema, models of localized (ad)sorption of molecules and ions from aqueous solution on homogeneous and heterogeneous nanoparticles are presented. The discussed models range from ideal monocomponent sorption on homogeneous (Langmuir) and heterogeneous sites, to multicomponent ideal sorption on homogeneous and heterogeneous sites, multicomponent multisite ion complexation with charge distribution (CD-MUSIC) and non-ideal competitive adsorption on heterogeneous sites (NICA). Attention is also paid to lateral interaction, site-induced aggregation, binding stoichiometry and multilayer formation. Electrical double layer models are discussed in relation to ion binding on impermeable and permeable nanoparticles. Insight in models that can describe sorption of molecules and ions on nanoparticles leads to awareness of the limitations of using simple models for complex systems and is needed for the selection and application of an appropriate model for a given system. This is relevant for all practical sorption processes and for a better understanding of the role of natural nanoparticles in the binding of nutrients and pollutants.

Rigorous Physicochemical Framework for Metal Ion Binding by Aqueous Nanoparticulate Humic Substances: Implications for Speciation Modeling by the NICA-Donnan and WHAM Codes

Latest knowledge on the reactivity of charged nanoparticulate complexants toward aqueous metal ions is discussed in mechanistic detail. We present a rigorous generic description of electrostatic and chemical contributions to metal ion binding by nanoparticulate complexants, and their dependence on particle size, particle type (i.e., reactive sites distributed within the particle body or confined to the surface), ionic strength of the aqueous medium, and the nature of the metal ion. For the example case of soft environmental particles such as fulvic and humic acids, practical strategies are delineated for determining intraparticulate metal ion speciation, and for evaluating intrinsic chemical binding affinities and heterogeneity. The results are compared with those obtained by popular codes for equilibrium speciation modeling (namely NICA-Donnan and WHAM). Physicochemical analysis of the discrepancies generated by these codes reveals the a priori hypotheses adopted therein and the inappropriateness of some of their key parameters. The significance of the characteristic time scales governing the formation and dissociation rates of metal-nanoparticle complexes in defining the relaxation properties and the complete equilibration of the metal-nanoparticulate complex dispersion is described. The dynamic features of nanoparticulate complexes are also discussed in the context of predictions of the labilities and bioavailabilities of the metal species.

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.

Metal ion–humic acid nanoparticle interactions: role of both complexation and condensation mechanisms

A counterion condensation – Donnan electrostatic model provides a physicochemically consistent description of intraparticulate metal species distributions in humic acid nanoparticles.

Modeling ion binding to humic substances: elastic polyelectrolyte network model

A new model for the electrostatic contribution to ion binding to humic substances is proposed and applied to published data for proton binding to fulvic and humic acids. The elastic polyelectrolyte network model treats humic substance particles as composed by two parts, an external one directly in contact with the solution, and an internal part or gel fraction which is considered, from a statistical point of view, as a charged polymer network swelled by the electrolyte solution, in the framework of the Flory polymer network theory. The electrostatic effect is given by a Donnan-like potential, which can be regarded as an average value over the gel fraction of the humic particle. The gel fraction expands as the pH and humic charge are increased, determining the Donnan potential and consequently the ion activity inside the gel. The model was fitted to published experimental data with good agreement. The model predictions are discussed, and the behavior suggests, for some cases, the presence of a transition between closed and open structures attributed to the presence, at low pH, of intramolecular hydrogen bonds which are removed as the carboxylic sites become deprotonated.

Effective affinity distribution for the binding of metal ions to a generic fulvic acid in natural waters

The effective distribution of affinities (Conditional Affinity Spectrum, CAS) seen by a metal ion binding to a humic substance under natural water conditions is derived and discussed within the NICA-Donnan model. Analytical expressions for the average affinity of these distributions in general multi-ion mixtures are reported here for the first time. These expressions enable a simple evaluation of the effect of all interfering cations on the affinity distribution of a given one. We illustrate this methodology by plotting the affinity spectra of a generic fulvic acid for 14 different cations in the presence of major inorganic ions and trace metals at pH and concentration values representative of a river water. The distribution of occupied sites and their average affinity at the typical freshwater conditions are also reported for each ion. The CAS allows usto distinguish three groups of cations: (a) Al, H, Pb, Hg, and Cr, which are preferentially bound to the phenolic sites of the fulvic ligand; (b) Ca, Mg, Cd, Fe(II), and Mn, which display a greater effective affinity for carboxylic sites, in contrast to what would be expected from their individual complexation parameters; and (c) Fe(III), Cu, Zn, and Ni, for which phenolic and carboxylic distributions are overlapped.