The explicit bonding reaction ensemble Monte Carlo method.

We present the explicit bonding Reaction ensemble Monte Carlo (eb-RxMC) method, designed to sample reversible bonding reactions in macromolecular systems in thermodynamic equilibrium. Our eb-RxMC method is based on the reaction ensemble method; however, its implementation differs from the latter by the representation of the reaction. In the eb-RxMC implementation, we are adding or deleting bonds between existing particles, instead of inserting or deleting particles with different chemical identities.

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.

Charge Regulation Triggers Condensation of Short Oligopeptides to Polyelectrolytes.

Electrostatic interactions between charged macromolecules are ubiquitous in biological systems, and they are important also in materials design. Attraction between oppositely charged molecules is often interpreted as if the molecules had a fixed charge, which is not affected by their interaction. Less commonly, charge regulation is invoked to interpret such interactions, i.

Sequestration of Small Ions and Weak Acids and Bases by a Polyelectrolyte Complex Studied by Simulation and Experiment.

Mixing of oppositely charged polyelectrolytes can result in phase separation into a polymer-poor supernatant and a polymer-rich polyelectrolyte complex (PEC). We present a new coarse-grained model for the Grand-reaction method that enables us to determine the composition of the coexisting phases in a broad range of pH and salt concentrations. We validate the model by comparing it to recent simulations and experimental studies, as well as our own experiments on poly(acrylic acid)/poly(allylamine hydrochloride) complexes.

Explaining Giant Apparent pK_{a} Shifts in Weak Polyelectrolyte Brushes.

Recent experiments on weak polyelectrolyte brushes found marked shifts in the effective pK_{a} that are linear in the logarithm of the salt concentration. Comparing explicit-particle simulations with mean-field calculations we show that for high grafting densities the salt concentration effect can be explained using the ideal Donnan theory, but for low grafting densities the full shift is due to a combination of the Donnan effect and the polyelectrolyte effect. The latter originates from electrostatic correlations that are neglected in the Donnan picture and that are only approximately included in the mean-field theory.

Reply to the 'Comment on "Simulations of ionization equilibria in weak polyelectrolyte solutions and gels"' by J. Landsgesell, L. Nová, O. Rud, F. Uhlík, D. Sean, P. Hebbeker, C. Holm and P. Košovan, , 2019, , 1155-1185.

Levin and Bakhshandeh suggested in their comment that (1), we stated in our recent review that pH-p is a universal parameter for titrating systems, that (2), we omitted to mention in our review the broken symmetry of the constant pH algorithm, and that (3), a constant pH simulation must include a grand-canonical exchange of ions with the reservoir. As a reply to (1), we point out that Levin and Bakhshandeh misquoted and hence invalidated our original statement. We therefore explain in detail under which circumstances pH-p can be a universal parameter, and also demonstrate why their numerical example is not in contradiction to our statement.

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.

Both Charge-Regulation and Charge-Patch Distribution Can Drive Adsorption on the Wrong Side of the Isoelectric Point.

The mechanism of protein-polyelectrolyte complexation on the wrong side of the isoelectric point has long puzzled researchers. Two alternative explanations have been proposed in the literature: (a) the charge-patch (CP) mechanism, based on the inhomogeneous distribution of charges on the protein, and (b) the charge-regulation (CR) mechanism, based on the variable charge of weak acid and base groups, which may invert the protein charge in the presence of another highly charged object. To discern these two mechanisms, we simulated artificially constructed short peptides, containing acidic and basic residues, arranged in a blocklike or alternating sequence.

Reversible multilayered vesicle-like structures with fluid hydrophobic and interpolyelectrolyte layers.

Hydrophobic blocks of amphiphilic block copolymers often form glassy micellar cores at room temperature with a rigid structure that limits their applications as nanocapsules for targeted delivery. Nevertheless, we prepared and analyzed core/shell micelles with a soft core, formed by a self-assembled block copolymer consisting of a hydrophobic block and a polycation block, poly(lauryl acrylate)-block-poly(trimethyl-aminoethyl acrylate) (PLA-QPDMAEA), in aqueous solution. By light and small-angle neutron scattering, by transmission electron microscopy and by fluorescence spectroscopy, we showed that these core/shell micelles are spherical and cylindrical with a fluid-like PLA core and a positively charged outer shell and that they can encapsulate and release hydrophobic solutes.

Role of p in Charge Regulation and Conformation of Various Peptide Sequences.

Peptides containing amino acids with ionisable side chains represent a typical example of weak ampholytes, that is, molecules with multiple titratable acid and base groups, which generally exhibit charge regulating properties upon changes in pH. Charged groups on an ampholyte interact electrostatically with each other, and their interaction is coupled to conformation of the (macro)molecule, resulting in a complex feedback loop. Their charge-regulating properties are primarily determined by the pKA of individual ionisable side-chains, modulated by electrostatic interactions between the charged groups.

Computer modeling of polymer stars in variable solvent conditions: a comparison of MD simulations, self-consistent field (SCF) modeling and novel hybrid Monte Carlo SCF approach.

Computer-aided modeling is a systematic approach to grasp the physics of macromolecules, but it remains essential to know when to trust the results and when not. For a polymer star, we consider three approaches: (i) Molecular Dynamics (MD) simulations and implementing a coarse-grained model, (ii) the self-consistent field approach based on a mean-field approximation and implementing the lattice model due to Scheutjens and Fleer (SF-SCF) and (iii) novel hybrid Monte Carlo self-consistent field (MC-SCF) method, which combines a coarse-grained model driven by a Monte Carlo method and a mean-field representation driven by SF-SCF. We compare the performance of these approaches under a wide range of solvent qualities.

Multivalent counterions accumulate in star-like polyelectrolytes and collapse the polymer in spite of increasing its ionization.

We used computer simulations to explore the dissociative and conformational behaviour of branched weak polyelectrolytes with multivalent counterions. We compared simulated titration curves and chain sizes in the presence of added salt of various valencies, keeping the total charge of salt constant. We showed that multivalent counterions enhance ionization of the weak polyelectrolytes, in spite of collapsing of the chains.

Interactions of star-like polyelectrolyte micelles with hydrophobic counterions.

Hydrophobicity of a counterion has a profound effect on the interaction with polyelectrolytes similar to that of multivalency. Specifically, understanding this interaction in weak polyelectrolyte micelles might assist in developing nanocarriers for pH-controlled encapsulation and release. We used star-like weak polyelectrolyte micelles of polystyrene-block-poly(2-vinyl pyridine) (PS-P2VP) with fixed aggregation number as a model polyelectrolyte, and cobalt bis(1,2-dicarbollide) (COSAN) as a model hydrophobic anion.

Simulations of ionization equilibria in weak polyelectrolyte solutions and gels.

This article recapitulates the state of the art regarding simulations of ionization equilibria of weak polyelectrolyte solutions and gels. We start out by reviewing the essential thermodynamics of ionization and show how the weak polyelectrolyte ionization differs from the ionization of simple weak acids and bases. Next, we describe simulation methods for ionization reactions, focusing on two methods: the constant-pH ensemble and the reaction ensemble.

Local pH and Effective p of a Polyelectrolyte Chain: Two Names for One Quantity?

In recent experiments, the "local pH" near polyelectrolyte chains was determined from the shift in the effective acidity constant of fluorescent pH indicators attached to the macromolecules. This indirect determination raises the question if the analyzed quantity was indeed the "local pH" and what this term actually means. In this study, we combined experiments and simulations to demonstrate that the shift in ionization constant is slightly lower than the difference between the pH and the "local pH".

Local pH and effective pK of weak polyelectrolytes - insights from computer simulations.

In this work we study the titration behavior of weak polyelectrolytes by computer simulations. We analyze the local pH near the chains at various conditions and provide molecular-level insight which complements the recent experimental determination of this quantity. Next, we analyze the non-ideal titration behaviour of weak polyelectrolytes in solution, calculate the effective ionization constant and compare the simulation results with theoretical predictions.

A self-consistent mean-field model for polyelectrolyte gels.

We present a novel approach to modeling polyelectrolyte gels, exploiting the analogy between star-branched polymers and polymer networks as a computationally inexpensive yet reliable alternative to full-scale simulations. In the numerical mean-field model of a star-like polymer we modify the boundary conditions to represent an infinite network. We validate the predictions of our new model against a coarse-grained simulation model.

Charge-controlled nano-structuring in partially collapsed star-shaped macromolecules.

Hydrophobic polyelectrolytes exhibit intra-molecular nano-scale self-organization instead of macroscopic phase separation because of the interplay between short-range hydrophobic attraction and long-range electrostatic repulsion. We aim to unravel how the morphology of the intra-molecular nanostructures can be controlled through the topology of the macromolecule on one hand and by adjustable ionization on the other hand. Specifically, we focus on hydrophobic star-branched polyelectrolytes, composed of either strong or weak acidic monomers.

Mean squared displacement from fluorescence correlation spectroscopy.

Under certain conditions, the mean squared displacement (MSD) can be retrieved from fluorescence correlation spectroscopy (FCS) measurements. However, in the general case this procedure is not valid, and the apparent MSD obtained from FCS data may substantially differ from the true one. In this work we discuss under which conditions this procedure can be applied.

The drag of the tails: Diffusion of sticky nanoparticles in dilute polymer solutions.

We devise a simple coarse-grained model of a nanoparticle exhibiting attractive interactions with a polymer in good solvent and use Monte Carlo simulations to study how adsorption of the polymer affects the hydrodynamic properties of the nanoparticle. We show that the hydrodynamic radius of the polymer-decorated nanoparticle increases with increasing polymer chain length or concentration. The slowdown of diffusion of the sticky nanoparticles is predicted to occur at polymer concentrations many orders of magnitude below the overlap concentration, in contrast with the case of non-sticky nanoparticles.

Coarse-grained simulations of an ionic liquid-based capacitor: II. Asymmetry in ion shape and charge localization.

In this work, which is a continuation of part I, we introduce a primitive model for an ionic liquid (IL) that can account for the planar shape of cations typical for ILs like imidazolium. The model consists of a spherical anion and a triangular cation consisting of three spheres, where one or all three vertices of the triangle can carry electric charge. We use molecular dynamics simulations to study the differential capacitance Cd of an ionic liquid confined between two planar electrodes.

Coarse-grained simulations of an ionic liquid-based capacitor: I. Density, ion size, and valency effects.

We introduce a hierarchy of generic coarse-grained models of ionic liquids of increasing complexity. We use them in molecular dynamics simulations to study the differential capacitance of a capacitor consisting of an ionic liquid between two planar electrodes. The primary goal is to explain the complex dependence of the differential capacitance Cd on the electrode potential U in simple terms, e.

Complex tracer diffusion dynamics in polymer solutions.

We employ fluorescence correlation spectroscopy (FCS) and coarse-grained molecular dynamics simulations to study the mobility of tracers in polymer solutions. Excluded volume interactions result in crowding-induced slowdown, depending only on the polymer concentration. With specific tracer-polymer attractions, the tracer is slowed down at much lower concentrations, and a second diffusion component appears that is sensitive to the polymer chain length.

Tracer diffusion in a crowded cylindrical channel.

Based on a coarse-grained model, we carry out molecular dynamics simulations to analyze the diffusion of a small tracer particle inside a cylindrical channel whose inner wall is covered with randomly grafted short polymeric chains. We observe an interesting transient subdiffusive behavior along the cylindrical axis at high attraction between the tracer and the chains, however, the long-time diffusion is always normal. This process is found to be enhanced for the case that we immobilize the grafted chains, i.

Self-assembly of poly(4-methylstyrene)-g-poly(methacrylic acid) graft copolymer in selective solvents for grafts: scattering and molecular dynamics simulation study.

Poly(4-methylstyrene)-g-poly(methacrylic acid) (P4MS-g-PMAA) graft copolymer was synthesized by the grafting-onto method from poly(4-methylstyrene), selectively brominated on methyl groups, and "living" poly(tert-butyl methacrylate). The average degree of polymerization of the backbone and the grafts and the average number of grafts per backbone were 251, 21, and 25, respectively. The self-assembly of P4MS-g-PMAA was studied in methanol and aqueous buffers (selective solvents for grafts).