Polyelectrolyte-nanoparticle mutual charge regulation and its influence on their complexation

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. The conformational averages can be performed in a systematic way by means of the Conformational Contraction Equations (CCEs), which relate the SB parameters to the underlying conformational equilibrium. The conditions for the convergence of the CCE are evaluated in the presence of both Short Range (SR) and Long Range (LR) electrostatic interactions. Two analytically solvable models based on the Freely Jointed Chain (FJC), involving only SR interactions, are analyzed at first. Despite the large chain flexibility, the resulting SB model reproduces the ionization properties with high accuracy. In the case of independent bonds, a very flexible chain can be exactly replaced by an effective rigid object with neighboring pairwise interactions. In general, however, triplet and higher order interactions emerge at the SB level. When LR electrostatic interactions are introduced and combined with the FJC large chain flexibility, the convergence of the CCE for long chains becomes problematic since the SB free energy must be truncated. Similar conclusions are reached for the freely rotating chain and rotational isomeric state models.

Charge regulation of nanoparticles in the presence of multivalent electrolytes

We explore the charge regulation (CR) of spherical nanoparticles immersed in an asymmetric electrolyte of a specified pH. Using a recently developed reactive canonical Monte Carlo (MC) simulation method, titration isotherms are obtained for suspensions containing monovalent, divalent, and trivalent coions. A theory based on the modified Poisson-Boltzmann approximation, which incorporates the electrostatic ion solvation free energy and discrete surface charge effects, is used to compare with the simulation results. A remarkably good agreement is found without any fitting parameters, both for the ion distributions and titration curves, suggesting that ionic correlations between coions and hydronium ions at the nanoparticle surface play only a minor role in determining the association equilibrium between hydroniums and the functional sites on the nanoparticle surface. On the other hand, if suspension contains multivalent counterions, we observe a large deviation between theory and simulations, showing that the electrostatic correlations between counterions and hydronium ions at the nanoparticle surface are very significant and must be properly taken into account to correctly describe CR for such solutions.

pyMBE: The Python-based molecule builder for ESPResSo

We present the Python-based Molecule Builder for ESPResSo (pyMBE), an open source software application to design custom coarse-grained (CG) models, as well as pre-defined models of polyelectrolytes, peptides, and globular proteins in the Extensible Simulation Package for Research on Soft Matter (ESPResSo). The Python interface of ESPResSo offers a flexible framework, capable of building custom CG models from scratch. As a downside, building CG models from scratch is prone to mistakes, especially for newcomers in the field of CG modeling, or for molecules with complex architectures. The pyMBE module builds CG models in ESPResSo using a hierarchical bottom-up approach, providing a robust tool to automate the setup of CG models and helping new users prevent common mistakes. ESPResSo features the constant pH (cpH) and grand-reaction (G-RxMC) methods, which have been designed to study chemical reaction equilibria in macromolecular systems with many reactive species. However, setting up these methods for systems, which contain several types of reactive groups, is an error-prone task, especially for beginners. The pyMBE module enables the automatic setup of cpH and G-RxMC simulations in ESPResSo, lowering the barrier for newcomers and opening the door to investigate complex systems not studied with these methods yet. To demonstrate some of the applications of pyMBE, we showcase several case studies where we successfully reproduce previously published simulations of charge-regulating peptides and globular proteins in bulk solution and weak polyelectrolytes in dialysis. The pyMBE module is publicly available as a GitHub repository (https://github.com/pyMBE-dev/pyMBE), which includes its source code and various sample and test scripts, including the ones that we used to generate the data presented in this article.

On the Validity of Constant pH Simulations

Constant pH (cpH) simulations are now a standard tool for investigating charge regulation in coarse-grained models of polyelectrolytes and colloidal systems. Originally developed for studying solutions with implicit ions, extending this method to systems with explicit ions or solvents presents several challenges. Ensuring proper charge neutrality within the simulation cell requires performing titration moves in sync with the insertion or deletion of ions, a crucial aspect often overlooked in the literature. Contrary to the prevailing views, cpH simulations are inherently grand-canonical, meaning that the controlled pH is that of the reservoir. The presence of the Donnan potential between the implicit reservoir and the simulation cell introduces significant differences between titration curves calculated for open and closed systems; the pH of an isolated (closed) system is different from the pH of the reservoir for the same protonation state of the polyelectrolyte. To underscore this point, in this paper, we will compare the titration curves calculated using the usual cpH algorithm with those from the exact canonical simulation algorithm. In the latter case, titration moves adhere to the correct detailed balance condition, and pH is calculated using the recently introduced surface Widom insertion algorithm. Our findings reveal a very significant difference between the titration isotherms obtained using the standard cpH algorithm and the canonical titration algorithm, emphasizing the importance of using the correct simulation approach when studying charge regulation of polyelectrolytes, proteins, and colloidal particles.

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.

Structural characterization, stability, and cytocompatibility study of chitosan BaTiO3@ZnO:Er heterostructures

New imaging agents are required in cancer diagnosis to enhance the diagnostic accuracy, classification, and therapeutic management of tumors. Nanomaterials have emerged as a promising alternative to developing new nanostructures with imaging applications. In this study, a heterostructure based on barium titanate (BT), zinc oxide (ZnO), and erbium (Er) was prepared and coated with Chitosan (CS) to investigate their stability and compatibility with biological systems. The structure, particle morphology, luminescence properties, stability, and cytotoxicity of different nanoparticles (NPs) were assessed. The results demonstrated the formation of a [BT@ZnO:Er]-CS heterostructure, which is consistent with the relative intensities and positions of peaks in the X-ray diffraction (XRD) with an average crystallite size of ~76 nm. The electrokinetic measurement results indicate that the coated NPs are the most stable and have an average size close to 200 nm when the pH is between 3 and 5. Finally, we presented a cytotoxicity study of naked and CS-coated NPs. The results indicate that naked NPs exhibit varying cellular toxicity, as indicated by decreased cell viability, morphological changes, and an increase in an apoptotic marker. The CS-coated NPs prevented the cytotoxic effect of the naked NPs, demonstrating the significance of CS as a stabilizing agent.

Theory of Charge Regulation of Colloidal Particles in Electrolyte Solutions

We present a theory that enables us to (i) calculate the effective surface charge of colloidal particles and (ii) efficiently obtain titration curves for different salt concentrations. The theory accounts for the shift of pH of solution due to the presence of 1:1 electrolyte. It also accounts self-consistently for the electrostatic potential produced by the deprotonated surface groups. To examine the accuracy of the theory, we have performed extensive reactive Monte Carlo simulations, which show excellent agreement between theory and simulations without any adjustable parameters.

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.

Anionically Functionalized Glycogen Encapsulates Melittin by Multivalent Interaction

We developed acid-functionalized glycogen conjugates as supramolecular carriers for efficient encapsulation and inhibition of a model cationic peptide melittin─the main component of honeybee venom. For this purpose, we synthesized and characterized a set of glycogens, functionalized to various degrees by several different acid groups. These conjugates encapsulate melittin up to a certain threshold amount, beyond which they precipitate. Computer simulations showed that sufficiently functionalized conjugates electrostatically attract melittin, resulting in its efficient encapsulation in a broad pH range around the physiological pH. Hemolytic assays confirmed in vitro that the effective inhibition of melittin's hemolytic activity occurs for highly functionalized samples, whereas no inhibition is observed when using low-functionalized conjugates. It can be concluded that functional glycogens are promising carriers for cationic molecular cargos or antidotes against animal venoms under conditions, in which suitable properties such as biodegradability and biocompatibility are crucial.

Reactive Monte Carlo simulations for charge regulation of colloidal particles

We use a reactive Monte Carlo simulation method and the primitive model of electrolyte to study acid-base equilibrium that controls charge regulation in colloidal systems. The simulations are performed in a semi-grand canonical ensemble in which colloidal suspension is in contact with a reservoir of salt and strong acid. The interior of colloidal particles is modeled as a low dielectric medium, different from the surrounding water. The effective colloidal charge is calculated for different numbers of surface acidic groups, pH, salt concentrations, and types of electrolyte. In the case of potassium chloride, the titration curves are compared with the experimental measurements obtained using potentiometric titration. A good agreement is found between simulations and experiments. In the case of lithium chloride, the specific ionic adsorption is taken into account through the partial dehydration of lithium ion.