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

Wrapping nonspherical vesicles at bio-membranes

The wrapping of particles and vesicles by lipid bilayer membranes is a fundamental process in cellular transport and targeted drug delivery. Here, we investigate the wrapping behavior of nonspherical vesicles, such as ellipsoidal, prolate, oblate, and stomatocytes, by systematically varying the bending rigidity of the vesicle membrane and the tension of the initially planar membrane. Using the Helfrich Hamiltonian, triangulated membrane models, and energy minimization techniques, we predict multiple stable-wrapped states and identify the conditions for their coexistence. Our results demonstrate that softer vesicles bind more easily to initially planar membranes; however, complete wrapping requires significantly higher adhesion strength than rigid vesicles. As membrane tension increases, deep-wrapped states disappear at a triple point where shallow-wrapped, deep-wrapped, and complete-wrapped states coexist. The coordinates of the triple point are highly sensitive to the vesicle shape and stiffness. For stomatocytes, increasing stiffness shifts the triple point to higher adhesion strengths and membrane tensions, while for oblates, it shifts to lower values, influenced by shape changes during wrapping. Oblate shapes are preferred in shallow-wrapped states and stomatocytes in deep-wrapped states. In contrast to hard particles, where optimal adhesion strength for complete wrapping occurs at tensionless membranes, complete wrapping of soft vesicles requires finite membrane tension for optimal adhesion strength. These findings provide insights into the interplay between vesicle deformability, shape, and membrane properties, advancing our understanding of endocytosis and the design of advanced biomimetic delivery systems.

How To Correct Erroneous Symmetry-Breaking in Coarse-Grained Constant-pH Simulations

The constant-pH Monte Carlo method is a popular algorithm to study acid-base equilibria in coarse-grained simulations of charge regulating soft matter systems including weak polyelectrolytes and proteins. However, the method suffers from systematic errors in simulations with explicit ions, which lead to a symmetry-breaking between chemically equivalent implementations of the acid-base equilibrium. Here, we show that this artifact of the algorithm can be corrected a-posteriori by simply shifting the pH-scale. We present two analytical methods as well as a numerical method using Widom insertion to obtain the correction. By numerically investigating various sample systems, we assess the range of validity of the analytical approaches and show that the Widom approach always leads to consistent results, even when the analytical approaches fail. Overall, we provide practical guidelines on how to use constant-pH simulations to avoid systematic errors, including cases where special care is required, such as polyampholytes and proteins.

Exploring guest molecule uptake in pH-responsive polyelectrolyte microgels via Monte Carlo simulations

Understanding the interactions of guest molecules like proteins and nanoparticles with microgels is fundamental for using microgels as nanocarriers. However, understanding and predicting the system properties becomes increasingly difficult as the systems become more complex. In this study, we systematically investigated the uptake of these guest molecules in a pH-responsive polyelectrolyte microgel modeled as a bead-spring network using Monte Carlo simulations. To narrow down the complexity of the systems, we modeled the guest molecules as simple charged beads. The simulations included the variation of (i) guest molecule charge, (ii) size, and (iii) number, as well as the influence of (iv) the addition of salt. The effect of these parameters on the ionization, swelling, and guest molecule uptake was investigated. The uptake of guest molecules with higher charges enhanced the ionization of the microgel at low pH. The strongest effect was observed for beads with charge z = +15. For higher guest molecule charges, the polymer chains could not fully wrap around the guest molecules, to provide enough microgel charges to fully compensate for the repulsive interactions between the guest beads. In general, the uptake of guest molecules leads to a collapse of the microgel due to attractive electrostatic interactions. With the increasing size of the guest molecules, their excluded volume increases, and the microgel swells with their uptake. Adding monovalent salt slightly decreases the uptake at low ionization of the network due to electrostatic screening. The presence of salt ions with higher valency further decreases the uptake of guest molecules into a fully ionized microgel.

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.