MOLSIM: A modular molecular simulation software

Translocation of Antimicrobial Peptides across Model Membranes: The Role of Peptide Chain Length

Cushioned lipid bilayers are structures consisting of a lipid bilayer supported on a solid substrate with an intervening layer of soft material. They offer possibilities for studying the behavior and interactions of biological membranes more accurately under physiological conditions. In this work, we continue our studies of cushion formation induced by histatin 5 (24Hst5), focusing on the effect of the length of the peptide chain. 24Hst5 is a short, positively charged, intrinsically disordered saliva peptide, and here, both a shorter (14Hst5) and a longer (48Hst5) peptide variant were evaluated. Experimental surface active techniques were combined with coarse-grained Monte Carlo simulations to obtain information about these peptides. Results show that at 10 mM NaCl, both the shorter and the longer peptide variants behave like 24Hst5 and a cushion below the bilayer is formed. At 150 mM NaCl, however, no interaction is observed for 24Hst5. On the contrary, a cushion is formed both in the case of 14Hst5 and 48Hst5, and in the latter, an additional thick, diffuse, and highly hydrated layer of peptide and lipid molecules is formed, on top of the bilayer. Similar trends were observed from the simulations, which allowed us to hypothesize that positively charged patches of the amino acids lysine and arginine in all three peptides are essential for them to interact with and translocate over the bilayer. We therefore hypothesize that electrostatic interactions are important for the interaction between the solid-supported lipid bilayers and the peptide depending on the linear charge density through the primary sequence and the positively charged patches in the sequence. The understanding of how, why, and when the cushion is formed opens up the possibility for this system to be used in the research and development of new drugs and pharmaceuticals.

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.

Monte Carlo simulation of the ionization and uptake behavior of cationic oligomers into pH-responsive polyelectrolyte microgels of opposite charge - a model for oligopeptide uptake and release

External stimuli can tune the uptake and release of guest molecules in microgels. Especially their pH responsiveness makes microgels exciting candidates for drug delivery systems. When both microgel and guest molecules are pH-responsive, predicting the electrostatically driven uptake can be complex since the ionization depends on many parameters. In this work, we performed Metropolis Monte Carlo simulations while systematically varying the pK of the monomers, the concentrations of microgel and guest molecules to obtain a better understanding of the uptake of weak cationic oligomers as a model for oligopeptides into a weak anionic polyelectrolyte microgel. Further, we varied the chain length of the oligomers. The polyelectrolyte networks can take up oligomers when both the network and the oligomers are charged. The presence of both species in the system leads to a mutual enhancement of their ionization. The uptake induces a release of counterions and results in complex formation between the oligomers and the network, leading to the collapse of the networks. Longer oligomers enhance the ionization of the network and, therefore, the complexation. A higher microgel concentration increases the uptake only around the isoelectric point but prevents the uptake due to lower entropy gain at counterion release at higher pH. The results give an insight into the uptake of cationic oligomers into oppositely charged polyelectrolyte microgels and provide hints for the design of anionic microgels as carriers for guest molecules e.g. antimicrobial peptides.

DNA Condensation by Peptide-Conjugated PAMAM Dendrimers. Influence of Peptide Charge

Nucleic acid delivery to cells is an important therapeutic strategy that requires the transport of nucleic acids to intracellular compartments and their protection from enzymatic degradation. This can be achieved through the complexation of the nucleic acids with polycations. Poly(amidoamine) (PAMAM) dendrimers and peptide-conjugated dendrimers have been investigated as delivery vectors. Inspired by these studies and the role of flexible peptide domains in protein-DNA interactions, we studied the impact of conjugating two peptides (tails) to generation 2 (G2) PAMAM dendrimers on DNA condensation and polyplex formation. Using gel electrophoresis, dye exclusion assays, atomic force microscopy, and Monte Carlo simulations, it is shown that the steric impact of neutral peptide tails is to hinder the formation of DNA-G2 polyplexes composed of multiple DNA chains. If the tails are negatively charged, which results in overall neutral G2 conjugates, then the interaction of G2 with DNA is hindered. Increasing the net positive charge of the tails resulted in the complexation capacity of G2 with the DNA being restored. While DNA complexation is obtained for a similar net charge balance for G2 and G2 conjugates with positive tails, fewer of the latter are required to achieve a comparable condensation degree. Furthermore, it is shown that about 40% of the DNA remains accessible to binding by small molecules. Overall, this shows that tuning the net charge of peptide tails conjugated to PAMAM dendrimers offers a handle to control the complexation capacity of DNA, which can be explored as a novel route for optimization as gene delivery vehicles.

Comparative Performance of Computer Simulation Models of Intrinsically Disordered Proteins at Different Levels of Coarse-Graining

Coarse-graining is commonly used to decrease the computational cost of simulations. However, coarse-grained models are also considered to have lower transferability, with lower accuracy for systems outside the original scope of parametrization. Here, we benchmark a bead-necklace model and a modified Martini 2 model, both coarse-grained models, for a set of intrinsically disordered proteins, with the different models having different degrees of coarse-graining. The SOP-IDP model has earlier been used for this set of proteins; thus, those results are included in this study to compare how models with different levels of coarse-graining compare. The sometimes naive expectation of the least coarse-grained model performing best does not hold true for the experimental pool of proteins used here. Instead, it showed the least good agreement, indicating that one should not necessarily trust the otherwise intuitive notion of a more advanced model inherently being better in model choice.

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.

Ionisation and swelling behaviour of weak polyampholyte core-shell networks - a Monte Carlo study

The network charge of polyampholyte microgels can be tuned by varying the pH of the surrounding solution, and a charge reversal from a positively charged microgel at low pH to a negatively charged microgel at high pH can be achieved. In a titration experiment, it is difficult to tell apart the ionisation of the acidic and basic monomers in the network and to determine the distribution of charges in the network, whereas using Metropolis Monte Carlo simulations, both the degree of ionisation and the distribution of ionised monomers can be determined separately for both species. Building on our earlier work on alternating polyampholyte microgels, we now investigated the pH-dependent ionisation and the swelling behaviour of polyampholyte core-shell microgels under good solvent conditions. For this purpose, we performed Metropolis Monte Carlo simulations for a bead-spring model using the constant-pH method. As in our previous study on alternating microgels, the width of the U-shaped curve of the microgels volume as a function of pH depends on the relative dissociation constants of acid and base, and the microgel volume can be approximated by a linear function of the total network charge. Due to the spatial separation of acid and base in core-shell systems, the ionisation is less enhanced compared to a microgel with an alternating distribution of the two species. Nevertheless, we still see an influence of the presence of one species on the ionisation behaviour of the other species under good solvent conditions. Furthermore, the isoelectric point is shifted towards higher pH, which is caused by a higher charge density in the core compared to that in the shell. Added salt changes the Donnan equilibrium, which determines the counterion distribution within and outside of the microgel. At the same time, it contributes to the electrostatic screening of the network charges, leading to a narrowing of the U-shaped volume transition curve.

Clustering and cross-linking of the wheat storage protein α-gliadin: A combined experimental and theoretical approach

Our aim was to understand mechanisms for clustering and cross-linking of gliadins, a wheat seed storage protein type, monomeric in native state, but incorporated in network while processed. The mechanisms were studied utilizing spectroscopy and high-performance liquid chromatography on a gliadin-rich fraction, in vitro produced α-gliadins, and synthetic gliadin peptides, and by coarse-grained modelling, Monte Carlo simulations and prediction algorithms. In solution, gliadins with α-helix structures (dip at 205 nm in CD) were primarily present as monomeric molecules and clusters of gliadins (peaks at 650- and 700-s on SE-HPLC). At drying, large polymers (R_g 90.3 nm by DLS) were formed and β-sheets increased (14% by FTIR). Trained algorithms predicted aggregation areas at amino acids 115-140, 150-179, and 250-268, and induction of liquid-liquid phase separation at P- and Poly-Q-sequences (Score = 1). Simulations showed that gliadins formed polymers by tail-to-tail or a hydrophobic core (Kratky plots and R_ee = 35 and 60 for C- and N-terminal). Thus, the N-terminal formed clusters while the C-terminal formed aggregates by disulphide and lanthionine bonds, with favoured hydrophobic clustering of similar/exact peptide sections (synthetic peptide mixtures on SE-HPLC). Mechanisms of clustering and cross-linking of the gliadins presented here, contribute ability to tailor processing results, using these proteins.

Changes in the Form Factor and Size Distribution of Nanogels in Crowded Environments

Particle size disparities suppress crystallization. However, soft deformable nanogels can change the size of the larger particles in suspension and crystallize even at a high initial size-polydispersity. Using neutron scattering with contrast variation, the response of individual nanogels in crowded environments was probed, and an increase of the parameter describing size-polydispersity was found, which is often interpreted as deformation. Here, computer simulations are used to generate deformed nanogels and the corresponding form factor. The data are fitted with the spherical model used to analyze scattering data. The fits show the same qualitative increase of the parameter related to the size-polydispersity with increasing particle deformation. Starting from the simulated deformed spheres, we also reproduce experimental scattering data. A further analysis of the particle shows that the size disparities between nanogels do not increase significantly. In contrast, their shapes strongly vary from one nanogel to the other.

Influence of Charge Lipid Head Group Structures on Electric Double Layer Properties

In this study we derived a model for a multicomponent lipid monolayer in contact with an aqueous solution by means of a generalized classical density functional theory and Monte Carlo simulations. Some of the important biological lipid systems were studied as monolayers composed of head groups with different shapes and charge distributions. Starting from the free energy of the system, which includes the electrostatic interactions, additional internal degrees of freedom are included as positional and orientational entropic contributions to the free energy functional. The calculus of variation was used to derive Euler–Lagrange equations, which were solved numerically by the finite element method. The theory and Monte Carlo simulations predict that there are mainly two distinct regions of the electric double layer: (1) the interfacial region, with thickness less than or equal to the length of the fully stretched conformation of the lipid head group, and (2) the outside region, which follows the usual screening of the interface. In the interfacial region, the electric double layer is strongly perturbed, and electrostatic profiles and ion distributions have functionality distinct to classical mean-field theories. Based purely on Coulomb interactions, the theory suggests that the dominant effect on the lipid head group conformation is from the charge density of the interface and the structured lipid mole fraction in the monolayer, rather than the salt concentration in the system.

Monte Carlo simulations of weak polyampholyte microgels: pH-dependence of conformation and ionization

We performed Metropolis Monte Carlo simulations to investigate the impact of varying acid and base dissociation constants on the pH-dependent ionization and conformation of weak polyampholyte microgels under salt-free conditions and under explicit consideration of the chemical ionization equilibria of the acidic and basic groups and their electrostatic interaction. Irrespective of their relative acid and base dissociation constant, all of the microgels undergo a pH-dependent charge reversal from positive to negative with a neutral charge at the isoelectric point. This charge reversal is accompanied by a U-shaped swelling transition of the microgels with a minimum of their size at the point of charge neutrality. The width of the U-shaped swelling transition, however, is found to depend on the chosen relative acid and base dissociation constants through which the extent of the favorable electrostatic intramolecular interaction of the ionized acidic and basic groups is altered. The pH-dependent swelling transition of the microgels is found to become broader, the stronger the intramolecular electrostatic interaction of the oppositely charged ionized species is. In addition, the intramolecular charge compensation of the acidic and basic groups of the microgels allows their counterions to abandon the microgel and the associated gain in translational entropy further amplifies the broadening of the pH-dependent swelling transition. The analysis of the radial ionization profiles of the acidic and basic groups of the differently composed microgels reveals a variety of radial ionization patterns with a dependence on the overall charge of the microgels.

Impact of Arginine-Phosphate Interactions on the Reentrant Condensation of Disordered Proteins

Re-entrant condensation results in the formation of a condensed protein regime between two critical ion concentrations. The process is driven by neutralization and inversion of the protein charge by oppositely charged ions. Re-entrant condensation of cationic proteins by the polyvalent anions, pyrophosphate and tripolyphosphate, has previously been observed, but not for citrate, which has similar charge and size compared to the polyphosphates. Therefore, besides electrostatic interactions, other specific interactions between the polyphosphate ions and proteins must contribute. Here, we show that additional attractive interactions between arginine and tripolyphosphate determine the re-entrant condensation and decondensation boundaries of the cationic, intrinsically disordered saliva protein, histatin 5. Furthermore, we show by small-angle X-ray scattering (SAXS) that polyvalent anions cause compaction of histatin 5, as would be expected based solely on electrostatic interactions. Hence, we conclude that arginine-phosphate-specific interactions not only regulate solution properties but also influence the conformational ensemble of histatin 5, which is shown to vary with the number of arginine residues. Together, the results presented here provide further insight into an organizational mechanism that can be used to tune protein interactions in solution of both naturally occurring and synthetic proteins.

Dielectric continuum model examination of real-space electrostatic treatments

Electrostatic interaction is long ranged; thus, the accurate calculation is not an easy task in molecular dynamics or Monte Carlo simulations. Though the rigorous Ewald method based on the reciprocal space has been established, real-space treatments have recently become an attractive alternative because of the efficient calculation. However, the construction is not yet completed and is now a challenging subject. In an earlier theoretical study, Neumann and Steinhauser employed the Onsager dielectric continuum model to explain how simple real-space cutoff produces artificial dipolar orientation. In the present study, we employ this continuum model to explore the fundamental properties of the recently developed real-space treatments of three shifting schemes. The result of the distance-dependent Kirkwood function G_K(R) showed that the simple bare cutoff produces a well-known hole-shaped artifact, whereas the shift treatments do not. Two-dimensional mapping of electric field well explained how these shift treatments remove the hole-shaped artifact. Still, the shift treatments are not sufficient because they do not produce a flat G_K(R) profile unlike ideal no-cutoff treatment. To test the continuum model results, we also performed Monte Carlo simulations of dipolar particles. The results found that the continuum model could predict the qualitative tendency as to whether each electrostatic treatment produces the hole-shaped artifact of G_K(R) or not. We expect that the present study using the continuum model offers a stringent criterion to judge whether the primitive electrostatic behavior is correctly described or not, which will be useful for future construction of electrostatic treatments.

Influence of macromolecular crowding on the charge regulation of intrinsically disordered proteins

In this work we study the coupling between ionization and conformational properties of two IDPs, histatin-5 and β-amyloid 42, in the presence of neutral and charged crowders. The latter is modeled to resemble bovine serum albumin (BSA). With this aim, semi-grand canonical Monte Carlo simulations are performed, so that the IDP charge is a dynamic property, undergoing protonation/deprotonation processes. Both ionization properties (global and specific amino acid charge and binding capacitance) and radius of gyration are analyzed in a large range of pH values and salt concentrations. Without crowder agents, the titration curve of histatin-5, a polycation, is salt-dependent while that of β-amyloid 42, a polyampholyte, is almost unaffected. The salt concentration is found to be particularly relevant at pH values where the protein binding capacitance (directly linked with charge fluctuation) is larger. Upon addition of neutral crowders, charge regulation is observed in histatin-5, while for β-amyloid 42 this effect is very small. The main mechanism for charge regulation is found to be the effective increase in the ionic strength due to the excluded volume. In the presence of charged crowders, a significant increase in the charge of both IDPs is observed in almost all the pH range. In this case, the IDP charge is altered not only by the increase in the effective ionic strength but also by its direct electrostatic interaction with the charged crowders.

The Effects of Chain Length on the Structural Properties of Intrinsically Disordered Proteins in Concentrated Solutions

Intrinsically disordered proteins (IDP) are proteins that sample a heterogeneous ensemble of conformers in solution. An estimated 25–30% of all eukaryotic proteins belong to this class. In vivo, IDPs function under conditions that are highly crowded by other biological macromolecules. Previous research has highlighted that the presence of crowding agents can influence the conformational ensemble sampled by IDPs, resulting in either compaction or expansion. The effects of self-crowding of the disordered protein Histatin 5 has, in an earlier study, been found to have limited influence on the conformational ensemble. In this study, it is examined whether the short chain length of Histatin 5 can explain the limited effects of crowding observed, by introducing (Histatin 5)₂, a tandem repeat of Histatin 5. By utilizing small-angle X-ray scattering, it is shown that the conformational ensemble is conserved at high protein concentrations, in resemblance with Histatin 5, although with a lowered protein concentration at which aggregation arises. Under dilute conditions, atomistic molecular dynamics and coarse-grained Monte Carlo simulations, as well as an established scaling law, predicted more extended conformations than indicated by experimental data, hence implying that (Histatin 5)₂ does not behave as a self-avoiding random walk.

Glutenin and Gliadin, a Piece in the Puzzle of their Structural Properties in the Cell Described through Monte Carlo Simulations

Gluten protein crosslinking is a predetermined process where specific intra- and intermolecular disulfide bonds differ depending on the protein and cysteine motif. In this article, all-atom Monte Carlo simulations were used to understand the formation of disulfide bonds in gliadins and low molecular weight glutenin subunits (LMW-GS). The two intrinsically disordered proteins appeared to contain mostly turns and loops and showed "self-avoiding walk" behavior in water. Cysteine residues involved in intramolecular disulfide bonds were located next to hydrophobic peptide sections in the primary sequence. Hydrophobicity of neighboring peptide sections, synthesis chronology, and amino acid chain flexibility were identified as important factors in securing the specificity of intramolecular disulfide bonds formed directly after synthesis. The two LMW-GS cysteine residues that form intermolecular disulfide bonds were positioned next to peptide sections of lower hydrophobicity, and these cysteine residues are more exposed to the cytosolic conditions, which influence the crosslinking behavior. In addition, coarse-grained Monte Carlo simulations revealed that the protein folding is independent of ionic strength. The potential molecular behavior associated with disulfide bonds, as reported here, increases the biological understanding of seed storage protein function and provides opportunities to tailor their functional properties for different applications.

Structural behavior of amphiphilic polyion complexes interacting with saturated lipid membranes investigated by coarse-grained molecular dynamic simulations

Neutral polyelectrolyte complexes (PECs) made from an amphiphilic multiblock copolymer of type (A_nB_n)_m and an oppositely charged polyion and interacting with a dipalmitoylphosphatidylcholine (DPPC) lipid membrane.

Molecular aggregation in liquid acetic acid: insight from molecular dynamics/quantum mechanics modelling of structural and NMR properties

The 1H NMR signal of the acidic proton in acetic acid molecules shows a marked upfield shift in the neat liquid as compared to that in low-concentration acetic acid solution in inert solvents where acetic acid cyclic dimers predominate. The underlying reasons for this phenomenon are analyzed in this work by considering classical molecular dynamics simulations and combined quantum mechanics/molecular mechanics calculations of the 1H NMR chemical shift of the acidic proton in the neat liquid and in the cyclic dimer of acetic acid in cyclohexane solution. Recorded trajectories were quantitatively analyzed in terms of different types of molecular aggregates formed in the neat liquid by using a geometrical definition of the hydrogen bond. Both the geometrical analysis and the computational NMR results indicate that the cyclic dimer cannot be the dominating aggregation pattern for acetic acid molecules in the neat liquid. The applied computational approach reproduces the lowering of the 1H NMR chemical shift of the acidic proton in acetic acid when going from cyclohexane solution to the neat liquid very well. The presence of acetic acid aggregates with hydrogen bonding between hydroxyl moieties and of monomeric acetic acid molecules in the neat liquid is found to lead to the observed lowering of the chemical shift, with lesser contribution from the formation of open acetic acid aggregates.

Role of Protein Self-Association on DNA Condensation and Nucleoid Stability in a Bacterial Cell Model

Bacterial cells do not have a nuclear membrane that encompasses and isolates the genetic material. In addition, they do not possess histone proteins, which are responsible for the first levels of genome condensation in eukaryotes. Instead, there is a number of more or less specific nucleoid-associated proteins that induce DNA bridging, wrapping and bending. Many of these proteins self-assemble into oligomers. The crowded environment of cells is also believed to contribute to DNA condensation due to excluded volume effects. Ribosomes are protein-RNA complexes found in large concentrations in the cytosol of cells. They are overall negatively charged and some DNA-binding proteins have been reported to also bind to ribosomes. Here the effect of protein self-association on DNA condensation and stability of DNA-protein complexes is explored using Monte Carlo simulations and a simple coarse-grained model. The DNA-binding proteins are described as positively charged dimers with the same linear charge density as the DNA, described using a bead and spring model. The crowding molecules are simply described as hard-spheres with varying charge density. It was found that applying a weak attractive potential between protein dimers leads to their association in the vicinity of the DNA (but not in its absence), which greatly enhances the condensation of the model DNA. The presence of neutral crowding agents does not affect the DNA conformation in the presence or absence of protein dimers. For weakly self-associating proteins, the presence of negatively charged crowding particles induces the dissociation of the DNA-protein complex due to the partition of the proteins between the DNA and the crowders. Protein dimers with stronger association potentials, on the other hand, stabilize the nucleoid, even in the presence of highly charged crowders. The interactions between protein dimers and crowding agents are not completely prevented and a few crowding molecules typically bind to the nucleoid.

Dynamical Oligomerisation of Histidine Rich Intrinsically Disordered ProteinS Is Regulated through Zinc-Histidine Interactions

Intrinsically disordered proteins (IDPs) can form functional oligomers and in some cases, insoluble disease related aggregates. It is therefore vital to understand processes and mechanisms that control pathway distribution. Divalent cations including Zn²⁺ can initiate IDP oligomerisation through the interaction with histidine residues but the mechanisms of doing so are far from understood. Here we apply a multi-disciplinary approach using small angle X-ray scattering, nuclear magnetic resonance spectroscopy, calorimetry and computations to show that that saliva protein Histatin 5 forms highly dynamic oligomers in the presence of Zn²⁺. The process is critically dependent upon interaction between Zn²⁺ ions and distinct histidine rich binding motifs which allows for thermodynamic switching between states. We propose a molecular mechanism of oligomerisation, which may be generally applicable to other histidine rich IDPs. Finally, as Histatin 5 is an important saliva component, we suggest that Zn²⁺ induced oligomerisation may be crucial for maintaining saliva homeostasis.

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. After discussing the advantages and limitations of both methods, we review the existing simulation literature. We discuss coarse-grained simulations of weak polyelectrolytes with respect to ionization equilibria, conformational properties, and the effects of salt, both in good and poor solvent conditions. This is followed by a discussion of branched star-like weak polyelectrolytes and weak polyelectrolyte gels. At the end we touch upon the interactions of weak polyelectrolytes with other polymers, surfaces, nanoparticles and proteins. Although proteins are an important class of weak polyelectrolytes, we explicitly exclude simulations of protein ionization equilibria, unless they involve protein-polyelectrolyte interactions. Finally, we try to identify gaps and open problems in the existing simulation literature, and propose challenges for future development.

Do the properties of gels constructed by interlinking triply-responsive microgels follow from those of the building blocks?

Microgels (MGs) are swellable crosslinked polymer colloids. They can also be used as the only building block to construct nanostructured hydrogels which are denoted as doubly crosslinked microgels (DX MGs). Here, new triply responsive DX MGs comprised of interlinked MGs of oligo(ethylene glycol)methacrylate (OEGMA), 2-(2-methoxyethoxy)ethyl methacrylate (MEO₂MA), methacrylic acid (MAA) and a o-nitrobenzyl-based UV photocleavable crosslinker are investigated. The MGs swelled or collapsed in response to temperature and pH changes. These behaviours were rationalised with a generic model using Monte Carlo simulations. The MGs also degraded when UV irradiated due to photocleavage of nPh. DX MGs were assembled from the MGs to give injectable gels that were not cytotoxic to nucleus pulposus cells. Comparison of the responsive properties of the DX MGs and MGs showed that the temperature and pH responses of the former were mostly governed by the latter. However, two key differences were found. Firstly, whilst increasing the crosslinker mol% in the MG building blocks (x) did not change MG particle swelling, the compression modulus (E) and swelling of the DX MG gels were strongly affected by x. The E value for the gels was tuneable using x which is a potentially useful new observation for DX MGs. Secondly, UV irradiation of the DX MGs enhanced gel mechanical photostability in contrast to the behaviour of the MGs. We find that the properties of the DX MGs do not simply follow those of the parent MGs and propose mechanisms to account for the differences. The new family of multi-responsive DX MGs presented in this study have potential application for soft tissue repair as injectable gels or as gel implants which report sterilisation.

Coarse-grained simulation studies on the adsorption of polyelectrolyte complexes upon lipid membranes

Conformations of a polyelectrolyte complex irreversibly bound to a zwitterionic lipid bilayer.

pH-Dependent Polyelectrolyte Bridging of Charged Nanoparticles

Systems comprised of polyelectrolytes and charged nanoparticles are of great technological interest, being common components in formulations among other uses. The colloidal stability of formulations is an important issue, and thus a lot of effort has been made to study the interactions of individual components in these systems. Here, the complexation and adsorption of an annealed (pH-dependent) polyelectrolyte to two spherical nanoparticles has been studied using coarse-grained Monte Carlo simulations. This has been done mainly by varying the solution pH and separation distance (concentration) between the nanoparticles. The polyelectrolyte charge distribution is seen to vary with nanoparticle separation distance, and its ability to bridge both nanoparticles changes with pH. The flexible polyelectrolyte creates compact, multilink bridges at short nanoparticle separation distances and evolves to a stretched single-link bridge at longer distances, where a larger fraction of the polyelectrolyte wraps around the nanoparticles. The annealed polyelectrolyte is also compared with a quenched polyelectrolyte of similar fixed fractional charge. Here, a difference is found in the adsorption ability at low pH/ionization due to the ability of the annealed polyelectrolytes to concentrate charges in the vicinity of the nanoparticle. At intermediate polyelectrolyte charge fractions and with increasing nanoparticle separation distances, the annealed system is able to link nanoparticles at larger distances as compared to the quenched, in good agreement with experimental observations. The results in this work contribute to the understanding of the effect of annealed polyelectrolytes and pH variations in the phase behavior of polyelectrolyte-nanoparticle systems, potentially aiding in the design and optimization of pH-responsive systems.

Reappearance of slow mode in mixtures of polyethylene glycol and poly(sodium methacrylate)

Mixtures of an anionic polyelectrolyte, poly(sodium methacrylate), NaPMA, and a neutral polymer, polyethylene glycol, PEG, were investigated by dynamic and static light scattering techniques at different concentrations and chain-lengths of PEG. The NaPMA standard with a narrow molecular weight distribution was chosen for the study. The so called slow-mode behaviour, characteristic of salt-free NaPMA solutions, vanishes as the simple salt, NaCl in this case, is added in a sufficient amount. However, in NaPMA-NaCl-PEG mixtures, the slow-mode signal is observed again. We assume that the dielectric constant of the mixture with PEG, which is substantially lower than that of pure water, causes the reappearance of the slow-mode signal through reinforced electrostatic interactions between NaPMA polyions. Monte Carlo simulations of a coarse-grained model of the system confirm stronger correlations between NaPMA molecules and thus qualitatively agree with experimental results.

Monte Carlo simulations of weak polyelectrolyte microgels: pH-dependence of conformation and ionization

In this study, we investigated the effect of pH on single weak acidic polyelectrolyte microgels under salt-free conditions with (i) varying microgel concentration, (ii) varying content of acidic groups and (iii) different crosslinking densities using Monte Carlo simulations under explicit consideration of the protonation/deprotonation reaction. We assessed both global properties, such as the degree of ionization, the degree of swelling and the counterion distribution, and local properties such as the radial network ionization profile and the ionization along the polymer chains as a function of pH. We found a pronounced suppression of the pH-dependent ionization of the microgels, as compared to the ideal titration behavior and a shift of the titration curve to a higher pH originating in the proximity of acidic groups in the microgel. In contrast to macroscopic gels, counterions can leave the microgel, resulting in an effective charge of the network, which hinders the ionization. A decreasing microgel concentration leads to an increased effective charge of the microgel and a more pronounced shift of the titration curve. The number of acidic groups showed only a weak effect on the ionization behavior of the microgels. For two different microgels with different crosslinking densities, similar scaling of the gel size was observed. A distinct transition from an uncharged and unswollen to a highly charged and expanded polymer network was observed for all investigated microgels. The degree of swelling mainly depends on the degree of ionization. An inhomogeneous distribution of the degree of ionization along the radial profile of the microgel was found.

Spacer Chains Prevent the Intramolecular Complexation in Miktoarm Star Polymers

The influence of spacer chains on the intramolecular complexation in star-shaped heteroarm (miktoarm) polymers is investigated. To overcome the mutual attraction of different polymeric components present in a miktoarm star with different homopolymeric arms, spacer chains of different length are attached to the core of the star at three different positions. In most of the investigated cases, this leads to diblock copolymer arms within the miktoarm star. Hereby, the inner spacer separates the outer blocks from their attractively interacting homopolymeric arms. The effect on the intramolecular complexation and the structure of the star polymer is obtained by Monte Carlo simulations of a simple bead-spring model. Then, long spacers can completely prevent the complexation. Both, local shielding by the spacer chains and the increased distance between the complex-forming polymers due to the spacer chains inhibit the complex formation. For a range of spacer positions and lengths, an equilibrium between a system forming a complex and a complex free system is found. The spacer chains can be used as a tool to tune the intramolecular complexation.

Directed Self-Assembly of Polarizable Ellipsoids in an External Electric Field

The interplay between shape anisotropy and directed long-range interactions enables the self-assembly of complex colloidal structures. As a recent highlight, ellipsoidal particles polarized in an external electric field were observed to associate into well-defined tubular structures. In this study, we systematically investigate such directed self-assembly using Monte Carlo simulations of a two-point-charge model of polarizable prolate ellipsoids. In spite of its simplicity and computational efficiency, we demonstrate that the model is capable of capturing the complex structures observed in experiments on ellipsoidal colloids at low volume fractions. We show that, at sufficiently high electric field strength, the anisotropy in shape and electrostatic interactions causes a transition from three-dimensional crystal structures observed at low aspect ratios to two-dimensional sheets and tubes at higher aspect ratios. Our work thus illustrates the rich self-assembly behavior accessible when exploiting the interplay between competing long- and short-range anisotropic interactions in colloidal systems.

Shielded attractive shell model again: resummed thermodynamic perturbation theory for central force potential

The approach developed earlier to describe the dimerizing shielded attractive shell (SAS) primitive model of chemical association due to Cummings and Stell is generalized and extended to include a description of a polymerizing SAS model. Our extension is based on the combination of the resummed thermodynamic perturbation theory for central force (RTPT-CF) associating potential and self consistent scheme, which takes into account the changes in the system free volume due to association. Theoretical results for thermodynamical properties of the model at different bonding length, density and temperature are compared against newly generated computer simulation results. The theory gives very accurate predictions for the model with bonding length L (*) from the range 0  <  L (*)  <  0.6 at all values of the density and temperature studied, including the limit of infinitely large temperature.

Interactions between charged surfaces mediated by stiff, multivalent zwitterionic polymers

The interaction between like-charged objects in electrolyte solutions can be heavily altered by the presence of multivalent ions which possess a spatially distributed charge. In this work, we examine the influence of stiff, multivalent zwitterionic polymers on the interaction between charged surfaces using a splitting field theory previously shown to be accurate for the weak to the intermediate to the strong electrostatic coupling regimes. The theory is compared to Monte Carlo simulations and good agreement is found between both approaches. For surface separations shorter than the polymer length, the polymers are mainly oriented parallel to the surfaces, and the surface-surface interaction is repulsive. When the surface separation is comparable to the length of polymers, the polymers have two main orientations. The first corresponds to the polymers adsorbed onto the surface with their centers located near to or in contact with the surface; the second corresponds to polymers which are perpendicular to the charged surfaces, bridging both surfaces and leading to an attractive force between them. Increasing the surface charge density leads to more pronounced attraction via bridging. At surface separations greater than the polymer length, the polymers in the center of the system are still mainly perpendicular to the surfaces, due to "chaining" between zwitterions that enable them to bridge the surfaces at larger separations. This leads to an attractive interaction between the surfaces with a range significantly longer than the length of the polymers.

Depletion controlled surface deposition of uncharged colloidal spheres from stable bulk dispersions

The competition between surface adsorption and bulk aggregation was investigated for silica colloids dispersed in cyclohexane in contact with hydrophobized silica substrates. Central to this study is that the colloids and surfaces have the same material and surface properties. Colloid-colloid and colloid-surface interactions were controlled by addition of polymers providing depletion interaction. Bulk instability was determined by turbidity and viscosity measurements and surface adsorption by ellipsometry measurements. At increasing polymer concentration, strong surface adsorption occurred at polymer concentrations below that required for bulk phase separation. Complementary Monte Carlo simulations with the use of a new weak depletion theory support quantitatively the experimental observation of the existence of an interval of interaction strength at which aggregation in bulk is negligible while surface adsorption is substantial.