Predicting Critical Micelle Concentrations with Molecular Dynamics Simulations and COSMOmic

Analyzing the Accuracy of Critical Micelle Concentration Predictions Using Deep Learning

This paper presents a novel approach to predicting critical micelle concentrations (CMCs) by using graph neural networks (GNNs) augmented with Gaussian processes (GPs). The proposed model uses learned latent space representations of molecules to predict CMCs and estimate uncertainties. The performance of the model on a data set containing nonionic, cationic, anionic, and zwitterionic molecules is compared against a linear model that works with extended connectivity fingerprints (ECFPs). The GNN-based model performs slightly better than the linear ECFP model when there is enough well-balanced training data and achieves predictive accuracy that is comparable to published models that were evaluated on a smaller range of surfactant chemistries. We illustrate the applicability domain of our model using a molecular cartogram to visualize the latent space, which helps to identify molecules for which predictions are likely to be erroneous. In addition to accurately predicting CMCs for some surfactant classes, the proposed approach can provide valuable insights into the molecular properties that influence CMCs.

First-principles prediction of critical micellar concentrations for ionic and nonionic surfactants

The concentration of surfactant in solution for which micelles start to form, also known as critical micelle concentration is a key property in formulation design. The critical micelle concentration can be determined experimentally with a tensiometer by measuring the surface tension of a concentration series. In analogy with experiments, in-silico predictions can be achieved through interfacial tension calculations. We present a newly developed method, which employs first principles-based interfacial tension calculations rooted in COSMO-RS theory, for the prediction of the critical micelle concentration of a set of nonionic, cationic, anionic, and zwitterionic surfactants in water. Our approach consists of a combination of two prediction strategies for modelling two different phenomena involving the removal of the surfactant hydrophobic tail from contact with water. The two strategies are based on regular micelle formation and thermodynamic phase separation of the surfactant from water and both are required to take into account a wide range of polarity in the hydrophilic headgroup. Our method yields accurate predictions for the critical micellar concentration, within one log unit from experiments, for a wide range of surfactant types and introduces possibilities for first-principles based prediction of formulation properties for more complex compositions.

Predicting Critical Micelle Concentrations for Surfactants Using Graph Convolutional Neural Networks

Surfactants are amphiphilic molecules that are widely used in consumer products, industrial processes, and biological applications. A critical property of a surfactant is the critical micelle concentration (CMC), which is the concentration at which surfactant molecules undergo cooperative self-assembly in solution. Notably, the primary method to obtain CMCs experimentally-tensiometry-is laborious and expensive. In this study, we show that graph convolutional neural networks (GCNs) can predict CMCs directly from the surfactant molecular structure. In particular, we developed a GCN architecture that encodes the surfactant structure in the form of a molecular graph and trained it using experimental CMC data. We found that the GCN can predict CMCs with higher accuracy on a more inclusive data set than previously proposed methods and that it can generalize to anionic, cationic, zwitterionic, and nonionic surfactants using a single model. Molecular saliency maps revealed how atom types and surfactant molecular substructures contribute to CMCs and found this behavior to be in agreement with physical rules that correlate constitutional and topological information to CMCs. Following such rules, we proposed a small set of new surfactants for which experimental CMCs are not available; for these molecules, CMCs predicted with our GCN exhibited similar trends to those obtained from molecular simulations. These results provide evidence that GCNs can enable high-throughput screening of surfactants with desired self-assembly characteristics.

Molecular simulations of lipid membrane partitioning and translocation by bacterial quorum sensing modulators

Quorum sensing (QS) is a bacterial communication process mediated by both native and non-native small-molecule quorum sensing modulators (QSMs), many of which have been synthesized to disrupt QS pathways. While structure-activity relationships have been developed to relate QSM structure to the activation or inhibition of QS receptors, less is known about the transport mechanisms that enable QSMs to cross the lipid membrane and access intracellular receptors. In this study, we used atomistic MD simulations and an implicit solvent model, called COSMOmic, to analyze the partitioning and translocation of QSMs across lipid bilayers. We performed umbrella sampling at atomistic resolution to calculate partitioning and translocation free energies for a set of naturally occurring QSMs, then used COSMOmic to screen the water-membrane partition and translocation free energies for 50 native and non-native QSMs that target LasR, one of the LuxR family of quorum-sensing receptors. This screening procedure revealed the influence of systematic changes to head and tail group structures on membrane partitioning and translocation free energies at a significantly reduced computational cost compared to atomistic MD simulations. Comparisons with previously determined QSM activities suggest that QSMs that are least likely to partition into the bilayer are also less active. This work thus demonstrates the ability of the computational protocol to interrogate QSM-bilayer interactions which may help guide the design of new QSMs with engineered membrane interactions.

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.

In Silico Prediction of the Thermodynamic Equilibrium of Solute Partition in Multiphase Complex Fluids: A Case Study of Oil-Water Microemulsion

Multiphase complex fluids such as micelles, microemulsions, and dispersions are ubiquitous in product formulations of foods, pharmaceuticals, cosmetics, and fine chemicals. Quantifying how active solutes partition in the microstructure of such multiphase fluids is necessary for designing formulations that can optimally deliver the benefits of functional actives. In this paper, we at first predict the structure of a heptane/butanol/sodium dodecyl sulfate droplet in water that self-assembled to form a microemulsion through the molecular dynamics (MD) simulation and subsequently investigate the thermodynamic equilibrium of solute partitioning using COSMOmic. To our knowledge, this is the first time that the MD/COSMOmic approach is used for predicting solute partitioning in a microemulsion. The predicted partition coefficients are compared to experimental values derived from retention measurements of the same microemulsion. We show that the experimental data of droplet-water partition coefficients (K_droplet/w) can be reliably predicted by the method that combines MD simulations with COSMOmic.

Molecular Modeling of Surfactant Micellization Using Solvent-Accessible Surface Area

We report a new implicit solvent simulation model for studying the self-assembly of surfactants, where the hydrophobic interactions were captured by calculating the relative changes of the solvent-accessible surface area (SASA) of the hydrophobic domains. Using histogram-reweighting grand canonical Monte Carlo simulations, we demonstrate that this approach allows us to match both the experimental critical micelle concentrations (cmc) and micellar aggregation numbers simultaneously with a single phenomenological surface tension γ_SASA for the poly(oxyethylene) monoalkyl ether (C _mE _n) surfactants in aqueous solutions. Excellent transferability is observed: the same model can accurately predict the experimental cmc and aggregation numbers for the C _mE _n surfactants with the alkyl lengths m between 6 and 12 and the poly(oxyethylene) lengths n between 1 and 9. The SASA-based implicit solvent model put forward in this work is general and may be applied to study more complex amphiphilic systems such as surfactants with branched alkyl chains or surfactant-hydrocarbon mixtures.

COSMOplex: self-consistent simulation of self-organizing inhomogeneous systems based on COSMO-RS

During the past 20 years, the efficient combination of quantum chemical calculations with statistical thermodynamics by the COSMO-RS method has become an important alternative to force-field based simulations for the accurate prediction of free energies of molecules in liquid systems. While it was originally restricted to homogeneous liquids, it later has been extended to the prediction of the free energy of molecules in inhomogeneous systems such as micelles, biomembranes, or liquid interfaces, but these calculations were based on external input about the structure of the inhomogeneous system. Here we report the rigorous extension of COSMO-RS to a self-consistent prediction of the structure and the free energies of molecules in self-organizing inhomogeneous systems. This extends the application range to many new areas, such as the prediction of micellar structures and critical micelle concentrations, finite loading effects in micelles and biomembranes, the free energies and structure of liquid interfaces, microemulsions, and many more related topics, which often are of great practical importance.

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.