Effect of charge regulation and conformational equilibria in the 2 stretching properties of weak polyelectrolytes

Weak polyelectrolytes can modulate their charge in response to external perturbations, such as changes in the pH, ionic strength (I), or electrostatic interactions with other charged species, a phenomenon known as charge regulation (CR). On the other hand, it is well established that CR is highly coupled with the conformational degrees of freedom. In this paper, the influence of CR in the stretching properties of weak polyelectrolytes is analyzed, and the possibility of CR induced by mechanical stretching is explored. With this aim, we make use of a minimal model, which captures the fundamental aspects present in the stretching of a flexible weak linear polyelectrolyte: internal angle rotation, bond stretching, bond bending, and proton binding, which is the paradigmatic mechanism of CR. The angle rotation is described by using the rotational isomeric state approximation, while for protonation, the site binding model is assumed. Mechanical stretching is studied by performing semi-grand canonical Monte Carlo simulations at different pH and ionic strength conditions. The simulations simultaneously provide both conformational (bond state probabilities, persistence length lP, and chain elongation) and protonation properties (degree of protonation θ and the effective protonation constant Kc). The obtained force−extension curves suggest that the pH value and the ionic strength I have a significant effect on polyelectrolyte stretching. Three different force regimes can be observed. For large forces (F > 100 pN for typical force constants), the force−extension curve is almost independent of the pH and I. For low forces, the persistence length lP is force-independent, although it strongly increases with the pH value. Under this regime, linear and Pincus scaling behaviors are observed. Finally, in the intermediate-force regime, both rotational and protonation degrees of freedom are mechanically activated, and the picture becomes more complicated. It is found that lP increases with F and, under certain conditions, a significant increase of θ with F is observed, indicating that CR could in principle be induced by means of mechanical stretching. This fact can be explained by analyzing the coupling between θ and the probability of a bond to be in the gauche state P(g). P(g) decreases with F as the bonds adopt the trans conformation so that the electrostatic repulsion is reduced and θ increases. Finally, the intricate interplay between short-range and long-range interactions is analyzed, leading to apparently contradictory behaviors (P(g) and lp simultaneously decrease with I), which can only be explained by CR and the presence of complex spatial correlations

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 Dlong versus 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 (a) for streptavidin diffusion among D10, D400 and D700 dextran obstacles. Dlong, the short-time diffusion coefficient (Dshort) and a are obtained from the BD simulations by using a new empirical expression, able to describe the full temporal evolution of the diffusion coefficient

Dealing with long-range interactions in the determination of polyelectrolyte ionization properties. Extension of the transfer matrix formalism to the full range of ionic strengths

The ionization state of charged macromolecules in solution is usually determined by the extent of the binding processes. These processes are very sensitive to the ionic strength of the medium, which are of long-range nature. The ionization properties of weak polyelectrolytes can be described by means of Ising-type models, which is only feasible when long-range interactions are neglected. Here, this formalism is extended to include long-range interactions by introducing a modified free energy involving only effective short-range interaction parameters. These parameters can be systematically calculated by using the Gibbs-Bogoliubov variational principle. The technique is illustrated with the calculation of titration curves of homogeneous and heterogeneous polyelectrolytes in a wide range of ionic strengths. The correction of the site protonation free energy (first order correction) is enough to obtain an excellent agreement between theory and Monte Carlo simulations. Corrections to other cluster parameters (higher order corrections) are also implemented. In general, the correction to a particular parameter represents the average change in the long-range energy when a new interaction is created in the polyelectrolyte. The method presented here represents an improvement in the description of the ionization state of polyelectrolytes that can be relevant in a wide range of areas.represents the average change in the long range energy when a new interaction (of the type described by the cluster parameter), is created in the polyelectrolyte. The method presented here represents an improvement in the description of the ionization state of charged macromolecules that can be relevant in a wide range of areas such as biochemistry, environmental chemistry, materials science, etc

Monte Carlo simulation study of diffusion controlled reactions in three dimensional crowded media

Published data reveal that the rate coefficients of diffusion controlled reactions taking place in crowded media are time dependent. Within this study we have performed on lattice 3D Monte Carlo simulations concerning Michaelis-Menten enzymatic reactions in crowded media, such as the cyto- plasmatic region of the cells. We have considered the same size and mobility of the reactant particles and different crowding conditions using distinct concentrations and sizes of the immobile obstacles. The results we have obtained indicate a fractal like kinetics with the degree of fractality that changes with the concentration and dimension of the obstacles. The simulation data also reflect that, depending on the temporal scale, molecular crowding can bring positive or negative effects on reaction kinetics. Comparing the cases studied, for short periods of time the value of the initial rate constant generally increases with the degree of crowding. For longer periods of time and larger distances, molecular crowding slows down the reaction kinetics in every case, due to smaller diffusion coefficients of the reactants, having a more intense effect for the cases with higher degree of crowding

Severity of post-cardiac surgery acute kidney injury and long-term mortality: is chronic kidney disease the missing link?

While the retrospective cohort study by Lopez-Delgado and colleagues suggests a strong association of the RIFLE classification and long-term mortality of acute kidney injury (AKI) after post-cardiac surgery, it has a number of limitations. The numbers of patients with pre-existing chronic kidney disease (CKD) or with non-recovery of renal function, de novo CKD or progression of CKD to stage V are not given. The authors used an obsolete definition of CKD and a modified RIFLE classification system for definition and grading of AKI. Taken together, numerous studies underscore the strong association between AKI and de novo CKD. Severity, duration and frequency of AKI as well as age, comorbidities and pre-existing CKD are known risk factors for the development and/or progression of CKD. Careful analyses of the cumulative mortality curves reported by Lopez-Delgado and colleagues or by our group revealed a triphasic pattern. In the early phase, survival rates drop steeply due to critical illness, followed by a phase of smaller decline (caused by patient characteristics and development of CKD) and later on by a flatter survival curve attributable to the high cardiovascular mortality of progressive CKD. Physicians need to consider the long-term sequels of severe AKI. Lopez Delgado and colleagues's study provides further arguments for an early follow-up of survivors of AKI by nephrologists