Modeling the Gibbs–Donnan effect during ultrafiltration and diafiltration processes using the Poisson–Boltzmann theory in combination with a basic Stern model

Donnan equilibrium in charged slit-pores from a hybrid nonequilibrium molecular dynamics/Monte Carlo method with ions and solvent exchange

Ion partitioning between different compartments (e.g., a porous material and a bulk solution reservoir), known as Donnan equilibrium, plays a fundamental role in various contexts such as energy, environment, or water treatment. The linearized Poisson-Boltzmann (PB) equation, capturing the thermal motion of the ions with mean-field electrostatic interactions, is practically useful to understand and predict ion partitioning, despite its limited applicability to conditions of low salt concentrations and surface charge densities. Here, we investigate the Donnan equilibrium of coarse-grained dilute electrolytes confined in charged slit-pores in equilibrium with a reservoir of ions and solvent. We introduce and use an extension to confined systems of a recently developed hybrid nonequilibrium molecular dynamics/grand canonical Monte Carlo simulation method ("H4D"), which enhances the efficiency of solvent and ion-pair exchange via a fourth spatial dimension. We show that the validity range of linearized PB theory to predict the Donnan equilibrium of dilute electrolytes can be extended to highly charged pores by simply considering renormalized surface charge densities. We compare with simulations of implicit solvent models of electrolytes and show that in the low salt concentrations and thin electric double layer limit considered here, an explicit solvent has a limited effect on the Donnan equilibrium and that the main limitations of the analytical predictions are not due to the breakdown of the mean-field description but rather to the charge renormalization approximation, because it only focuses on the behavior far from the surfaces.

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.

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.

Predicting Formulation Conditions During Ultrafiltration and Dilution to Drug Substance Using a Donnan Model with Homology-Model Based Protein Charge

In the manufacturing of therapeutic monoclonal antibodies (mAbs), the final steps of the purification process are typically ultrafiltration/diafiltration (UF/DF), dilution, and conditioning. These steps are developed such that the final drug substance (DS) is formulated to the desired mAb, buffer, and excipient concentrations. To develop these processes, process and formulation development scientists often perform experiments to account for the Gibbs-Donnan and volume-exclusion effects during UF/DF, which affect the output pH and buffer concentration of the UF/DF process. This work describes the development of an in silico model for predicting the DS pH and buffer concentration after accounting for the Gibbs-Donnan and volume-exclusion effects during the UF/DF operation and the subsequent dilution and conditioning steps. The model was validated using statistical analysis to compare model predictions against experimental results for nine molecules of varying protein concentrations and formulations. In addition, our results showed that the structure-based in silico approach used to calculate the protein charge was more accurate than a sequence-based approach. Finally, we used the model to gain fundamental insights about the Gibbs-Donnan effect by highlighting the role of the protein charge concentration (the protein concentration multiplied with protein charge at the formulation pH) on the Gibbs-Donnan effect. Overall, this work demonstrates that the Gibbs-Donnan and volume-exclusions effects can be predicted using an in silico model, potentially alleviating the need for experiments.

An Intercompany Perspective on Practical Experiences of Predicting, Optimizing and Analyzing High Concentration Biologic Therapeutic Formulations

Developing high-dose biologic drugs for subcutaneous injection often requires high-concentration formulations and optimizing viscosity, solubility, and stability while overcoming analytical, manufacturing, and administration challenges. To understand industry approaches for developing high-concentration formulations, the Formulation Workstream of the BioPhorum Development Group, an industry-wide consortium, conducted an inter-company collaborative exercise which included several surveys. This collaboration provided an industry perspective, experience, and insight into the practicalities for developing high-concentration biologics. To understand solubility and viscosity, companies desire predictive tools, but experience indicates that these are not reliable and experimental strategies are best. Similarly, most companies prefer accelerated and stress stability studies to in-silico or biophysical-based prediction methods to assess aggregation. In addition, optimization of primary container-closure and devices are pursued to mitigate challenges associated with high viscosity of the formulation. Formulation strategies including excipient selection and application of studies at low concentration to high-concentration formulations are reported. Finally, analytical approaches to high concentration formulations are presented. The survey suggests that although prediction of viscosity, solubility, and long-term stability is desirable, the outcome can be inconsistent and molecule dependent. Significant experimental studies are required to confirm robust product definition as modeling at low protein concentrations will not necessarily extrapolate to high concentration formulations.

In-line monitoring of protein concentration with MIR spectroscopy during UFDF

Rapid increase of product titers in upstream processes has presented challenges for downstream processing, where purification costs increase linearly with the increase of the product yield. Hence, innovative solutions are becoming increasingly popular. Process Analytical Technology (PAT) tools, such as spectroscopic techniques, are on the rise due to their capacity to provide real-time, precise analytics. This ensures consistent product quality and increased process understanding, as well as process control. Mid-infrared spectroscopy (MIR) has emerged as a highly promising technique within recent years, owing to its ability to monitor several critical process parameters at the same time and unchallenging spectral analysis and data interpretation. For in-line monitoring, Attenuated Total Reflectance-Fourier Transform Infrared Spectroscopy (ATR-FTIR) is a method of choice, as it enables reliable measurements in a liquid environment, even though water absorption bands are present in the region of interest. Here, we present MIR spectroscopy as a monitoring tool of critical process parameters in ultrafiltration/diafiltration (UFDF). MIR spectrometer was integrated in the UFDF process in an in-line fashion through a single-use flow cell containing a single bounce silicon ATR crystal. The results indicate that the one-point calibration algorithm applied to the MIR spectra, predicts highly accurate protein concentrations, as compared with validated offline analytical methods.

Interdependence of Kinetics and Fluid Dynamics in the Design of Photocatalytic Membrane Reactors

Photocatalytic membrane reactors (PMRs) are a promising technology for wastewater reclamation. The principles of PMRs are based on photocatalytic degradation and membrane rejection, the different processes occurring simultaneously. Coupled photocatalysis and membrane filtration has made PMRs suitable for application in the removal of emerging contaminants (ECs), such as diclofenac, carbamazepine, ibuprofen, lincomycin, diphenhydramine, rhodamine, and tamoxifen, from wastewater, while reducing the likelihood of byproducts being present in the permeate stream. The viability of PMRs depends on the hypotheses used during design and the kinetic properties of the systems. The choice of design models and the assumptions made in their application can have an impact on reactor design outcomes. A design’s resilience is due to the development of a mathematical model that links material and mass balances to various sub-models, including the fluid dynamic model, the radiation emission model, the radiation absorption model, and the kinetic model. Hence, this review addresses the discrepancies with traditional kinetic models, fluid flow dynamics, and radiation emission and absorption, all of which have an impact on upscaling and reactor design. Computational and analytical descriptions of how to develop a PMR system with high throughput, performance, and energy efficiency are provided. The potential solutions are classified according to the catalyst, fluid dynamics, thickness, geometry, and light source used. Two main PMR types are comprehensively described, and a discussion of various influential factors relating to PMRs was used as a premise for developing an ideal reactor. The aim of this work was to resolve potential divergences that occur during PMRs design as most real reactors do not conform to the idealized fluid dynamics. Lastly, the application of PMRs is evaluated, not only in relation to the removal of endocrine-disrupting compounds (EDCs) from wastewater, but also in dye, oil, heavy metals, and pesticide removal.