Modulation of the electrostatic potential around α-lactalbumin using oligoelectrolyte chains, pH and salt concentration.

In this study, we conducted a comprehensive computational investigation of the interaction between α-lactalbumin, a small globular protein, and strong anionic oligoelectrolyte chains with a polymerization degree from 2 to 9. Both the protein and oligoelectrolyte chains are represented using coarse-grained models, and their properties were calculated by the Monte Carlo method under constant pH conditions. We were able to estimate the effects of this interaction on the electrostatic potential around the protein. At acidic pH, the protein had a net positive charge; therefore, the electrostatic potential around it was also positive. To neutralize or reverse this electrostatic potential, oligoelectrolyte chains with a minimum size of six monomers were necessary. Simultaneously, low salt concentrations were required as elevated salt levels led to a significant attenuation of the electrostatic interactions and the corresponding electrostatic potential.

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.

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.

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.

Interaction between ß-Lactoglobuline and Weak Polyelectrolyte Chains: A Study Using Monte Carlo Simulation.

Complexation between the ß-lactoglobulin and a weak acid polyelectrolyte (PE) has been studied using Monte Carlo simulations. Different coarse-grained models were used to represent the system, and two different acidic constants were used on the PE model. The protein-PE interaction is quantified considering the average PE monomers adsorbed on the protein as a function of pH. A maximum in the interaction between macromolecules was found, which is explained as a function of the titration behavior of the ß-lactoglobuline and weak PE. We also found that there was a direct relation between the pH range of monomers adsorbed and the change on dissociation profile of the protein and weak PE compared to isolated conditions. The complexation of protein-PE increased both the dissociation degree of the PE chain and the protein net charge. This benefits the monomer adsorption on the protein surface.

On the reasons for α-lactalbumin adsorption on a charged surface: a study by Monte Carlo simulation.

This work studies α-lactalbumin adsorption on a charged substrate using Monte Carlo simulation. The protein is represented by a coarse-grained model with enough components as to reproduce the complex behavior of α-lactalbumin on electrically-charged substrates. The simulation results in particular can reproduce protein adsorption when both the protein and the substrate are negatively charged. The energetic and entropic contributions to the free energy of the adsorption process are estimated and analyzed. The effects of the charge regulation mechanism, the localization of titratable groups in α-lactalbumin as well as the distribution of small ions around the interface are studied in detail. Both the asymmetrical distribution of the charged groups of the protein and the counterion distribution play predominant roles in α-lactalbumin adsorption on a substrate with the same sign of electrical charge.

Adsorption of three-domain antifreeze proteins on ice: a study using LGMMAS theory and Monte Carlo simulations.

In the present work, the adsorption of three-domain antifreeze proteins on ice is studied by combining a statistical thermodynamics based theory and Monte Carlo simulations. The three-domain protein is modeled by a trimer, and the ice surface is represented by a lattice of adsorption sites. The statistical theory, obtained from the exact partition function of non-interacting trimers adsorbed in one dimension and its extension to two dimensions, includes the configuration of the molecule in the adsorbed state, and allows the existence of multiple adsorption states for the protein. We called this theory "lattice-gas model of molecules with multiple adsorption states" (LGMMAS). The main thermodynamics functions (partial and total adsorption isotherms, Helmholtz free energy and configurational entropy) are obtained by solving a non-linear system of j equations, where j is the total number of possible adsorption states of the protein. The theoretical results are contrasted with Monte Carlo simulations, and a modified Langmuir model (MLM) where the arrangement of the adsorption sites in space is immaterial. The formalism introduced here provides exact results in one-dimensional lattices, and offers a very accurate description in two dimensions (2D). In addition, the scheme is capable of predicting the proportion between coverage degrees corresponding to different conformations in the same energetic state. In contrast, the MLM does not distinguish between different adsorption states, and shows severe discrepancies with the 2D simulation results. These findings indicate that the adsorbate structure and the lattice geometry play fundamental roles in determining the statistics of multistate adsorbed molecules, and consequently, must be included in the theory.

Protonation of ß-lactoglobulin in the presence of strong polyelectrolyte chains: a study using Monte Carlo simulation.

In this work, the molecular interaction between the protein ß-lactoglobulin and strong polyelectrolyte chains was studied using Monte Carlo simulations. Different coarse-grained models were used to represent the system components. Both net charge and protonation of the isolated dimeric protein were analyzed as a function of pH. The acid-base equilibrium of each titratable group was distinctively modified by the presence of polyanion or polycation chains. The complexation on the wrong side of pI was more evident with the polycation than with the polyanion. It was mainly due to a charge regulation mechanism, where the reversion in net charge of the protein was more pronounced at the left of isoelectric point of the protein. The glutamic and aspartic groups play a key role in this charge reversion. Both polyanion and polycation were spatially adsorbed in different region on the protein surface, suggesting the importance of the surface charge distribution of the protein.

Adsorption thermodynamics of two-domain antifreeze proteins: theory and Monte Carlo simulations.

In this paper we develop the statistical thermodynamics of two-domain antifreeze proteins adsorbed on ice. We use a coarse-grained model and a lattice network in order to represent the protein and ice, respectively. The theory is obtained by combining the exact analytical expression for the partition function of non-interacting linear k-mers adsorbed in one dimension, and its extension to higher dimensions. The total and partial adsorption isotherms, and the coverage and temperature dependence of the Helmholtz free energy and configurational entropy are given. The formalism reproduces the classical Langmuir equation, leads to the exact statistical thermodynamics of molecules adsorbed in one dimension, and provides a close approximation for two-dimensional systems. Comparisons with analytical data obtained using the modified Langmuir model (MLM) and Monte Carlo simulations in the grand canonical ensemble were performed in order to test the validity of the theoretical predictions. In the MC calculations, the different mechanisms proposed in the literature to describe the adsorption of two-domain antifreeze proteins on ice were analyzed. Indistinguishable results were obtained in all cases, which verifies the thermodynamic equivalence of these mechanisms and allows the choice of the most suitable mechanism for theoretical studies of equilibrium properties. Even though a good qualitative agreement is obtained between MLM and MC data, it is found that the new theoretical framework offers a more accurate description of the phenomenon of adsorption of two-domain antifreeze proteins.

Lysozyme adsorption in pH-responsive hydrogel thin-films: the non-trivial role of acid-base equilibrium.

We develop and apply a molecular theory to study the adsorption of lysozyme on weak polyacid hydrogel films. The theory explicitly accounts for the conformation of the network, the structure of the proteins, the size and shape of all the molecular species, their interactions as well as the chemical equilibrium of each titratable unit of both the protein and the polymer network. The driving forces for adsorption are the electrostatic attractions between the negatively charged network and the positively charged protein. The adsorption is a non-monotonic function of the solution pH, with a maximum in the region between pH 8 and 9 depending on the salt concentration of the solution. The non-monotonic adsorption is the result of increasing negative charge of the network with pH, while the positive charge of the protein decreases. At low pH the network is roughly electroneutral, while at sufficiently high pH the protein is negatively charged. Upon adsorption, the acid-base equilibrium of the different amino acids of the protein shifts in a nontrivial fashion that depends critically on the particular kind of residue and solution composition. Thus, the proteins regulate their charge and enhance adsorption under a wide range of conditions. In particular, adsorption is predicted above the protein isoelectric point where both the solution lysozyme and the polymer network are negatively charged. This behavior occurs because the pH in the interior of the gel is significantly lower than that in the bulk solution and it is also regulated by the adsorption of the protein in order to optimize protein-gel interactions. Under high pH conditions we predict that the protein changes its charge from negative in the solution to positive within the gel. The change occurs within a few nanometers at the interface of the hydrogel film. Our predictions show the non-trivial interplay between acid-base equilibrium, physical interactions and molecular organization under nanoconfined conditions, which leads to non-trivial adsorption behavior that is qualitatively different from what would be predicted from the state of the proteins in the bulk solution.

Reversible precipitation of casein micelles with a cationic hydroxyethylcellulose.

The cationic hydroxyethylcellulose Polyquaternium 10 (PQ10) was found to produce a dose-dependent destabilization of casein micelles from whole or skim milk without affecting the stability of most of the whey proteins. The anionic phosphate residues on caseins were not determinant in the observed interaction since the destabilization was also observed with dephosphorylated caseins to the same extent. However, the precipitation process was completely inhibited by rising NaCl concentration, indicating an important role of electrostatic interactions. Furthermore, the addition of 150 mM NaCl solubilized preformed PQ10-casein complexes, rendering a stable casein suspension without a disruption of the internal micellar structure as determined by dynamic light scattering. This casein preparation was found to contain most of the Ca2+ and only 10% of the lactose originally present in milk and remained as a stable suspension for at least 4 months at 4 degrees C. The final concentration of PQ10 determined both the size of the casein-polymer aggregates and the amount of milkfat that coprecipitates. The presence of PQ10 in the aggregates did not inhibit the activity of rennet or gastrointestinal proteases and lipases, nor did it affect the growth of several fermentative bacteria. The cationic cellulose PQ10 may cause a reversible electrostatic precipitation of casein micelles without disrupting their internal structure. The reversibility of the interaction described opens the possibility of using this cationic polysaccharide to concentrate and resuspend casein micelles from whole or skim milk in the production of new fiber-enriched lactose-reduced calcium-caseinate dairy products.

Aggregation of casein micelles by interactions with chitosans: a study by Monte Carlo simulations.

Recently, it was found that the addition of chitosan, a cationic polymer, to whole or skim milk produces the destabilization and coagulation of casein micelles which takes place without modifications in the milk pH or in the stability of most of the whey proteins. In the present work, Monte Carlo simulations are employed to show that the phase separation of casein micelles induced by chitosan can be explained by a depletion mechanism, where an effective attraction between the casein micelles is induced by the presence of chitosan molecules. This interaction is described on the basis of Vrij's model, where the depletion of polymer from the gap between neighboring casein micelles originates an effective attractive interaction that leads to a phase transition. This model, that considers volume restriction effects, accounts for several qualitative and even quantitative aspects of the experimental data for the coagulation of casein through chitosan addition.