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.

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.

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.

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.