When can flexible weak polyelectrolytes be treated as effective rigid objects?

Conformational and ionization equilibria of flexible weak polyelectrolytes (PEs) are, in general, strongly coupled. In this article, we analyze the effect of averaging over (or "contracting") the conformational degrees of freedom so that the original flexible molecule is replaced by an effective rigid object with the same ionization properties. As a result, one obtains the so-called Site Binding (SB) model, much easier to treat both theoretically and computationally, and extensively used to characterize the ionization properties of PE.

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.

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.

Monte Carlo simulations of enzymatic reactions in crowded media. Effect of the enzyme-obstacle relative size.

We perform Monte Carlo simulations in three-dimensional (3D) lattice in order to study diffusion-controlled and mixed activation-diffusion reactions following an irreversible Michaelis-Menten scheme in crowded media. The simulation data reveal the rate coefficient dependence on time for diffusion-controlled bimolecular reactions developing in three-dimensional media with obstacles, as predicted by fractal kinetics approach. For the cases of mixed activation-diffusion reactions, the fractality of the reaction decreases as the activation control increases.

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.

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*).

Effect of crowding by dextrans on the hydrolysis of N-Succinyl-L-phenyl-Ala-p-nitroanilide catalyzed by α-chymotrypsin.

Traditionally, studies on the diffusion-controlled reaction of biological macromolecules have been carried out in dilute solutions (in vitro). However, in an intracellular environment (in vivo), there is a high concentration of macromolecules, which results in nonspecific interactions (macromolecular crowding). This affects the kinetics and thermodynamics of the reactions that occur in these systems.

Diffusion of alpha-chymotrypsin in solution-crowded media. A fluorescence recovery after photobleaching study.

Fluorescence recovery after photobleaching (FRAP) is one of the most powerful and used techniques to study diffusion processes of macromolecules in membranes or in bulk. Here, we study the diffusion of alpha-chymotrypsin in different crowded (Dextran) in vitro solutions using a confocal laser scanning microscope. In the considered experimental conditions, confocal FRAP images could be analyzed applying the uniform circular disk approximation described for a nonscanning microscope generalized to take into account anomalous diffusion.

Model-independent link between the macroscopic and microscopic descriptions of multidentate macromolecular binding: relationship between stepwise, intrinsic, and microscopic equilibrium constants.

The binding of ions or other small molecules to macromolecules and surfaces can be macroscopically characterized by means of the stepwise (or stoichiometric) equilibrium constants, which can be obtained experimentally from coverage versus concentration data. The present work presents a novel, simple, and direct interpretation of the stepwise constants in terms of the microscopic, site-specific, stability constants. This formalism can be applied to the most general case, including the heterogeneity of the sites, interactions among them, multicomponent adsorption, and so forth, and, in particular, to chelate complexation.

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.

Conditional affinity spectra of Pb2+-humic acid complexation from data obtained with AGNES.

The new electroanalytical technique AGNES (Absence of Gradients and Nernstian Equilibrium Stripping) has been applied to follow Pb2+ complexation to Purified Aldrich Humic Acid. A refined methodology of AGNES, allowing considerably larger gains, reached free metal ion concentrations down to subnanomolar values in a reasonable deposition time due to the lability and mobility of these complexes. Further insights into the meaning of the binding data, fitted to a NICA (Non Ideal Competitive Adsorption) isotherm, can be obtained with the concept of conditional affinity spectrum (CAS).

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.

A hierarchical approach to cooperativity in macromolecular and self-assembling binding systems.

The study of complex macromolecular binding systems reveals that a high number of states and processes are involved in their mechanism of action, as has become more apparent with the sophistication of the experimental techniques used. The resulting information is often difficult to interpret because of the complexity of the scheme (large size and profuse interactions, including cooperative and self-assembling interactions) and the lack of transparency that this complexity introduces into the interpretation of the indexes traditionally used to describe the binding properties. In particular, cooperative behaviour can be attributed to very different causes, such as direct chemical modification of the binding sites, conformational changes in the whole structure of the macromolecule, aggregation processes between different subunits, etc.

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.

Affinity distribution functions in multicomponent heterogeneous adsorption. Analytical inversion of isotherms to obtain affinity spectra.

An analytical approach for the interpretation of multicomponent heterogeneous adsorption or complexation isotherms in terms of multidimensional affinity spectra is presented. Fourier transform, applied to analyze the corresponding integral equation, leads to an inversion formula which allows the computation of the multicomponent affinity spectrum underlying a given competitive isotherm. Although a different mathematical methodology is used, this procedure can be seen as the extension to multicomponent systems of the classical Sips's work devoted to monocomponent systems.