Solubilization in Mixed Micelles Studied by Molecular Dynamics Simulations and COSMOmic

Collection of Partition Coefficients in Hexadecyltrimethylammonium Bromide, Sodium Cholate, and Lithium Perfluorooctanesulfonate Micellar Solutions: Experimental Determination and Computational Predictions

This study focuses on determining the partition coefficients (logP) of a diverse set of 63 molecules in three distinct micellar systems: hexadecyltrimethylammonium bromide (HTAB), sodium cholate (SC), and lithium perfluorooctanesulfonate (LPFOS). The experimental log p values were obtained through micellar electrokinetic chromatography (MEKC) experiments, conducted under controlled pH conditions. Then, Quantum Mechanics (QM) and machine learning approaches are proposed for the prediction of the partition coefficients in these three micellar systems. In the applied QM approach, the experimentally obtained partition coefficients were correlated with the calculated values for the case of the 15 solvent mixtures. Using Density Function Theory (DFT) with the B3LYP functional, we calculated the solvation free energies of 63 molecules in these 16 solvents. The combined data from the experimental partition coefficients in the three micellar formulations showed that the 1-propanol/water combination demonstrated the best agreement with the experimental partition coefficients for the SC and HTAB micelles. Moreover, we employed the SVM approach and k-means clustering based on the generation of the chemical descriptor space. The analysis revealed distinct partitioning patterns associated with specific characteristic features within each identified class. These results indicate the utility of the combined techniques when we want an efficient and quicker model for predicting partition coefficients in diverse micelles.

COSMO Models for the Pharmaceutical Development of Parenteral Drug Formulations

The aqueous solubility of active pharmaceutical ingredients is one of the most important features to be considered during the development of parenteral formulations in the pharmaceutical industry. Computational modelling has become in the last years an integral part of pharmaceutical development. In this context, ab initio computational models, such as COnductor-like Screening MOdel (COSMO), have been proposed as promising tools for the prediction of results without the effective use of resources. Nevertheless, despite the clear evaluation of computational resources, some authors had not achieved satisfying results and new calculations and algorithms have been proposed over the years to improve the outcomes. In the development and production of aqueous parenteral formulations, the solubility of Active Pharmaceutical Ingredients (APIs) in an aqueous and biocompatible vehicle is a decisive step. This work aims to study the hypothesis that COSMO models could be useful in the development of new parenteral formulations, mainly aqueous ones.

Partition of the Reactive Species of the Suzuki-Miyaura Reaction between Aqueous and Micellar Environments

The Suzuki-Miyaura reaction between the aryl halide (1) and the phenyl boronic acid (2), in the presence of the palladium(0) complex (3) as catalyst, gives the cross-coupling product (4) in quantitative yield when performed in basic aqueous solution of the nonionic surfactant Kolliphor-EL (K-EL). The partition between the aqueous and micellar environments of the species of this reaction has been investigated by means of Molecular Dynamics (MD) simulations. Starting from the K-EL molecules dispersed in water, a micelle model has been generated by MD simulations, adopting the 2016H66 force field. Reagent and product species have been described with the same force field, once the reliability of this force field has been tested comparing the n-octanol/water partition free energies calculated from the MD and Free Energy Perturbation (FEP) method with those obtained from the quantum-mechanical SMD method. The potential of mean force for the transfer process between water and the micellar phase of the different species has been calculated by the MD simulations and the Umbrella Sampling (US) method. The overall picture that emerges from these results confirms that the molecular species involved in this reaction prefers the micellar environment and concentrates in different but close zones of the micelle. This supports the experimental evidence that the use of suitable surfactant agents promotes reactivity, allowing micelles to behave as nanoreactors in which reactive species are solubilized and enhance their local concentration.

Machine learning hybrid approach for the prediction of surface tension profiles of hydrocarbon surfactants in aqueous solution

HYPOTHESIS

Predicting the surface tension (SFT)-log(c) profiles of hydrocarbon surfactants in aqueous solution is computationally non-trivial, and empirically challenging due to the diverse and complex architecture and interactions of surfactant molecules. Machine learning (ML), combining a data-based and knowledge-based approach, can provide a powerful means to relate molecular descriptors to SFT profiles.

EXPERIMENTS

A dataset of SFT for 154 model hydrocarbon surfactants at 20-30 °C is fitted to the Szyszkowski equation to extract three characteristic parameters (Γ_max,K_L and critical micelle concentration (CMC)) which are correlated to a series of 2D and 3D molecular descriptors. Key (∼10) descriptors were selected by removing co-correlation, and employing a gradient-boosted regressor model to rank feature importance and carry out recursive feature elimination (RFE). The hyperparameters of each target-variable model were fine-tuned using a randomised cross-validated grid search, to improve predictive ability and reduce overfitting.

FINDINGS

The ML models correlate favourably with test experimental data, with R²= 0.69-0.87, and the merits and limitations of the approach are discussed based on 'unseen' hydrocarbon surfactants. The incorporation of a knowledge-based framework provides an appropriate smoothing of the experimental data which simplifies the data-driven approach and enhances its generality. Open-source codes and a brief tutorial are provided.

Detailed Calorimetric Analysis of Mixed Micelle Formation from Aqueous Binary Surfactants for Design of Nanoscale Drug Carriers

While numerous papers have been published according to the binary surfactant mixtures, only a few articles provide deeper information on the composition dependence of the micellization, and even less work attempts to apply the enhanced feature of the mixed micelles. The most important parameter of the self-assembled surfactants is the critical micelle concentration (cmc), which quantifies the tendency to associate, and provides the Gibbs energy of micellization. Several techniques are known for determining the cmc, but the isothermal titration calorimetry (ITC) can be used to measure both cmc and enthalpy change (Δ_micH) accompanying micelle formation. Outcomes of our calorimetric investigations were evaluated using a self-developed routine for handling ITC data and the thermodynamic parameters of mixed micelle formation were obtained from the nonlinear modelling of temperature- and composition- dependent enthalpograms. In the investigated temperature and micelle mole fractions interval, we observed some intervals where the cmc is lower than the ideal mixing model predicted value. These equimolar binary surfactant mixtures showed higher solubilization ability for poorly water-soluble model drugs than their individual compounds. Thus, the rapid and fairly accurate calorimetric analysis of mixed micelles can lead to the successful design of a nanoscale drug carrier.

Solvation of nonionic poly(ethylene oxide) surfactant Brij 35 in organic and aqueous-organic solvents

HYPOTHESIS

By combining the experimental small- and wide-angle x-ray scattering (SWAXS) method with molecular dynamics simulations and the theoretical 'complemented-system approach' it is possible to obtain detailed information about the intra- and inter-molecular structure and dynamics of the solvation and hydration of the surfactant in organic and mixed solvents, e.g., of the nonionic surfactant Brij 35 (C₁₂E₂₃) in alcohols and aqueous alcohol-rich ternary systems. This first application of the complemented-system approach to the surfactant system will promote the use of this powerful methodology that is based on experimental and calculated SWAXS data in studies of colloidal systems. By applying high-performance computing systems, such an approach is readily available for studies in the colloidal domain.

EXPERIMENTS

SWAXS experiments and MD simulations were performed for binary Brij 35/alcohol and ternary Brij 35/water/alcohol systems with ethanol, n-butanol and n-hexanol as the organic solvent component at 25 °C.

FINDINGS

We confirmed the presence of solvated Brij 35 monomers in the studied organic media, revealed their preferential hydration and discussed their structural and dynamic features at the intra- and inter-molecular levels. Anisotropic effective surfactant molecular conformations were found. The influence of the hydrophobicity of the organic solvent on the hydration phenomena of surfactant molecules was explained.

Molecular Dynamics Simulations on Interindividual Variability of Intestinal Fluids: Impact on Drug Solubilization

Efficient delivery of oral drugs is dependent on their solubility in human intestinal fluid, a complex and dynamic fluid that contains colloidal structures composed of small molecules. These structures solubilize poorly water-soluble compounds, increasing their apparent solubility, and possibly their bioavailability. In this study, we conducted coarse-grained molecular dynamics simulations with data from duodenal fluid samples previously acquired from five healthy volunteers. In these simulations, we observed the self-assembly of mixed micelles of bile salts, phospholipids, and free fatty acids. The micelles were ellipsoids with a size range of 4–7 nm. Next, we investigated micelle affinities of three model drugs. The affinities in our simulation showed the same trend as literature values for the solubility enhancement of drugs in human intestinal fluids. This type of simulations is useful for studies of events and interactions taking place in the small intestinal fluid.

Predicting Partition Coefficients of Neutral and Charged Solutes in the Mixed SLES-Fatty Acid Micellar System

Sodium laureth sulfate (SLES) and fatty acids are common ingredients in many cosmetic products. Understanding how neutral and charged fatty acid compounds partition between micellar and water phases is crucial to achieve the optimal design of the product formulation. In this paper, we first study the formation of mixed SLES and fatty acid micelles using molecular dynamics (MD) simulations. Micelle/water partition coefficients of neutral and charged fatty acids are then calculated using COSMOmic as well as a MD approach based on the potential of mean force (PMF) calculations performed using umbrella sampling (US). The combined US/PMF approach was performed with both the additive, non-polarizable CHARMM general force field (CGenFF) and the classical Drude polarizable force field. The partition coefficients for the neutral solutes are shown to be accurately calculated with the COSMOmic and additive CGenFF US/PMF approaches, while only the US/PMF approach with the Drude polarizable force field accurately calculated the experimental partition coefficient of the charged solute. These results indicate the utility of the Drude polarizable force field as a tool for the rational development of mixed micelles.

Molecular dynamics study of solubilization of cyclohexane, benzene, and phenol into mixed micelles composed of sodium dodecyl sulfate and octaethylene glycol monododecyl ether

Molecular dynamics calculations of a mixed micelle composed of sodium dodecyl sulfate (SDS) and octaethylene glycol monododecyl ether (C₁₂ E₈ ) were performed for six compositions (SDS/C₁₂ E₈ = 100/0, 80/20, 60/40, 40/60, 20/80, and 0/100) to investigate the composition dependence of the mixed micelle structure and solubilization of cyclohexane, benzene, and phenol molecules by the micelle. The radial density distribution of the hydrophilic polyoxyethylene (POE) group of C₁₂ E₈ as a function of distance from the micelle center is very sharp for micelles with high SDS content because the POE group captures a Na⁺ ion in solution and wraps around it to form a compact crown-ether-like complex. The hydrophobic dodecyl groups of SDS and C₁₂ E₈ were separately distributed in the mixed micelle core. ΔG(r) evaluated for each solute showed that despite the structural changes of the micelle the binding strength of the solute molecules to the micelle did not change significantly. © 2019 Wiley Periodicals, Inc.

Protobiotic Systems Chemistry Analyzed by Molecular Dynamics

Systems chemistry has been a key component of origin of life research, invoking models of life's inception based on evolving molecular networks. One such model is the graded autocatalysis replication domain (GARD) formalism embodied in a lipid world scenario, which offers rigorous computer simulation based on defined chemical kinetics equations. GARD suggests that the first pre-RNA life-like entities could have been homeostatically-growing assemblies of amphiphiles, undergoing compositional replication and mutations, as well as rudimentary selection and evolution. Recent progress in molecular dynamics has provided an experimental tool to study complex biological phenomena such as protein folding, ligand-receptor interactions, and micellar formation, growth, and fission. The detailed molecular definition of GARD and its inter-molecular catalytic interactions make it highly compatible with molecular dynamics analyses. We present a roadmap for simulating GARD's kinetic and thermodynamic behavior using various molecular dynamics methodologies. We review different approaches for testing the validity of the GARD model by following micellar accretion and fission events and examining compositional changes over time. Near-future computational advances could provide empirical delineation for further system complexification, from simple compositional non-covalent assemblies towards more life-like protocellular entities with covalent chemistry that underlies metabolism and genetic encoding.

Micellization and Partition Equilibria in Mixed Nonionic/Ionic Micellar Systems: Predictions with Molecular Models

In practical applications, surfactant solutions are mostly used in mixtures of nonionic and ionic surfactants because they have improved characteristics compared to those of single surfactant solutions. By adjusting the composition of the micelles and the pH value, the solubilization of solutes can be enhanced. Nevertheless, the partitioning of solutes between nonionic/ionic mixed micelles and the aqueous phase is studied to a much lesser extent than for single surfactant solutions. Theoretical methods to predict partition equilibria in mixed micelles are of interest for screening studies. For those, the composition of the mixed micelle has to be known. Here we investigate mixtures of TX-114 (Triton X-114), Brij35 (C12E23), SDS (sodium dodecyl sulfate), and CTAB (cetyltrimethylammonium bromide). First, to investigate the surfactant compositions in the micelles, molecular dynamics (MD) self-assembly simulations were applied. Thereafter, the predictive COSMO-RS model, which applies the pseudophase approach, and its extension to anisotropic systems termed COSMOmic were compared for the prediction of partition equilibria in mixed micelles, where various molar ratios of the surfactants were considered. It could be demonstrated that both methods are applicable and lead to reasonable predictions for neutral molecules. However, taking into account the three-dimensional structure of the micelle is beneficial because the calculations with COSMOmic are in better agreement with experimental results. Because the partitioning behavior of ionizable molecules in mixed micelles is of particular interest, the partitioning of ionized isovanillin in mixed Brij35/CTAB micelles at different micelle compositions was calculated with COSMOmic. Using a thermodynamic cycle, the position-dependent pK_a of isovanillin within the micelle is calculated on the basis of COSMOmic free energy profiles. As a result, the protolytic equilibrium of isovanillin within the micelles can be taken into account, which is crucial for the reliable prediction of partition coefficients.

Micelles, Rods, Liposomes, and Other Supramolecular Surfactant Aggregates: Computational Approaches

Surfactants are an interesting class of compounds characterized by the segregation of polar and apolar domains in the same molecule. This peculiarity makes possible a whole series of microscopic and macroscopic effects. Among their features, their ability to segregate particles (fluids or entire domains) and to reduce the surface/interfacial tension is the utmost important. The interest in the chemistry of surfactants never weakened; instead, waves of increasing interest have occurred every time a new field of application of these molecules has been discovered. All these special characteristics depend largely on the ability of surfactants to self-assemble and constitute supramolecular structures where their chemical properties are amplified. The possibility to obtain structural and energy information and, above all, the possibility of forecast the self-organizing mechanisms of surfactants have had a significant boost via computational chemistry. The molecular dynamics models, initially coarse-grained and subsequently (with the increasing computer power) using more accurate models, allowed, over the years, to better understand different aspects of the processes of dispersion, self-assembly, segregation of surfactant. Moreover, several other aspects have been investigated as the effect of the counterions of many ionic surfactants in defining the final supramolecular structures, the mobility of side chains, and the capacity of some surfactant to envelope entire proteins. This review constitutes a perspective/prospective view of these results. On the other hand, some comparison of in silico results with experimental information recently acquired through innovative analytical techniques such as ion mobility mass spectrometry which have been introduced.

Polymeric mixed micelles as nanomedicines: Achievements and perspectives

During the past few decades, polymeric micelles have raised special attention as novel nano-sized drug delivery systems for optimizing the treatment and diagnosis of numerous diseases. These nanocarriers exhibit several in vitro and in vivo advantages as well as increased stability and solubility to hydrophobic drugs. An interesting approach for optimizing these properties and overcoming some of their disadvantages is the combination of two or more polymers in order to assemble polymeric mixed micelles. This review article gives an overview on the current state of the art of several mixed micellar formulations as nanocarriers for drugs and imaging probes, evaluating their ongoing status (preclinical or clinical stage), with special emphasis on type of copolymers, physicochemical properties, in vivo progress achieved so far and toxicity profiles. Besides, the present article presents relevant research outcomes about polymeric mixed micelles as better drug delivery systems, when compared to polymeric pristine micelles. The reported data clearly illustrates the promise of these nanovehicles reaching clinical stages in the near future.

Effect of hydrostatic pressure on gas solubilization in micelles

Molecular dynamics simulations of anionic sodium decylsulfate and nonionic pentaethylene glycol monodecyl ether micelles in water have been performed to examine the impact of hydrostatic pressure on argon solubilization as a function of pressure. The potential-of-mean force between the micelles and argon demonstrates that nonpolar gases are attracted to the interiors of both micelles. The affinity of argon for micelle interiors, however, decreases with increasing pressure as a result of the comparatively higher molar volume of argon inside assemblies. We evaluate solubility enhancement coefficients, which describe the drop in the solute chemical potential as a function of the micellized surfactant concentration, to quantify the impact of micellization on gas solubilization. While argon is similarly attracted to the hydrophobic cores of both micelles, the gas is more effectively sequestered within nonionic micelles compared with anionic micelles as a result of salting out by charged head groups and accompanying counterions. The solubility enhancement coefficients of both micelles decrease with increasing pressure, reflecting the changing forces observed in the potentials-of-mean force. An analytical liquid drop model is proposed to describe the pressure dependence of argon solubilization within micelles that captures the simulation solubility enhancement coefficients after fitting an effective micelle radius for each surfactant.

Explicit- and implicit-solvent simulations of micellization in surfactant solutions

In this article, we focus on simulation methodologies to obtain the critical micelle concentration (cmc) and equilibrium distribution of aggregate sizes in dilute surfactant solutions. Even though it is now relatively easy to obtain micellar aggregates in simulations starting from a fully dispersed state, several major challenges remain. In particular, the characteristic times of micelle reorganization and transfer of monomers from micelles to free solution for most systems of practical interest exceed currently accessible molecular dynamics time scales for atomistic surfactant models in explicit solvent. In addition, it is impractical to simulate highly dilute systems near the cmc. We have demonstrated a strong dependence of the free surfactant concentration (frequently, but incorrectly, taken to represent the cmc in simulations) on the overall concentration for ionic surfactants. We have presented a theoretical framework for making the necessary extrapolations to the cmc. We find that currently available atomistic force fields systematically underpredict experimental cmc's, pointing to the need for the development of improved models. For strongly micellizing systems that exhibit strong hysteresis, implicit-solvent grand canonical Monte Carlo simulations represent an appealing alternative to atomistic or coarse-grained, explicit-solvent simulations. We summarize an approach that can be used to obtain quantitative, transferrable effective interactions and illustrate how this grand canonical approach can be used to interpret experimental scattering results.