Finite-Size Effects and Optimal System Sizes in Simulations of Surfactant Micelle Self-Assembly

Ion-Induced PIP2 Clustering with Martini3: Modification of Phosphate-Ion Interactions and Comparison with CHARMM36

Phosphatidylinositol 4,5-bisphosphate (PIP2) is a critical lipid for cellular signaling. The specific phosphorylation of the inositol ring controls protein binding as well as clustering behavior. Two popular models to describe ion-mediated clustering of PIP2 are Martini3 (M3) and CHARMM36 (C36). Molecular dynamics simulations of PIP2-containing bilayers in solutions of potassium chloride, sodium chloride, and calcium chloride, and at two different resolutions are performed to understand the aggregation and the model parameters that drive it. The average M3 clusters of PIP2 in bilayers of 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine and PIP2 bilayers in the presence of K+, Na+, or Ca2+ contained 2.2, 2.6, and 6.4 times more PIP2 than C36 clusters, respectively. Indeed, the Ca2+-containing systems often formed a single large aggregate. Reparametrization of the M3 ion-phosphate Lennard-Jones interaction energies to reproduce experimental osmotic pressure of sodium dimethyl phosphate (DMP), K[DMP], and Ca[DMP]2 solutions, the same experimental target as C36, yielded comparably sized PIP2 clusters for the two models. Furthermore, C36 and the modified M3 predict similar saturation of the phosphate groups with increasing Ca2+, although the coarse-grained model does not capture the cooperativity between K+ and Ca2+. This characterization of the M3 behavior in the presence of monovalent and divalent ions lays a foundation to study cation/protein/PIP2 clustering.

SANS Spectra with PLUMED: Implementation and Application to Metainference

Using small-angle scattering with either X-ray or neutron sources has become common in the investigation of soft-matter systems. These experiments provide information about the coarse shape of the scattered objects, but obtaining more-detailed information can usually only be achieved with the aid of molecular simulations. In this Application Note, we report the implementation of an extension in PLUMED to compute the small-angle neutron scattering (SANS), which can be used for data processing as well for enhanced sampling, in particular with the metainference method to bias simulations and sample structures with a resulting spectrum in agreement with an experimental reference. Our implementation includes a resolution function that can be used to smear the SANS intensities according to beamline error sources and is compatible with both all-atom and coarse-grained simulations. Scripts to aid in the calculation of the scattering lengths when the system is coarse-grained and to aid in preparing the inputs are provided. We illustrate the use of the implementation with metainference by performing coarse-grained simulations of beta-octylglucoside and dodecylphosphocholine micelles in water. With different software and different Hamiltonians, we show that the metainference SANS bias can drive micelles to be split and to change shapes to achieve a better agreement with the experimental reference.

Effects of surfactant adsorption on the wettability and friction of biomimetic surfaces

The properties of solid-liquid interfaces can be markedly altered by surfactant adsorption. Here, we use molecular dynamics (MD) simulations to study the adsorption of ionic surfactants at the interface between water and heterogeneous solid surfaces with randomly arranged hydrophilic and hydrophobic regions, which mimic the surface properties of human hair. We use the coarse-grained MARTINI model to describe both the hair surfaces and surfactant solutions. We consider negatively-charged virgin and bleached hair surface models with different grafting densities of neutral octadecyl and anionic sulfonate groups. The adsorption of cationic cetrimonium bromide (CTAB) and anionic sodium dodecyl sulfate (SDS) surfactants from water are studied above the critical micelle concentration. The simulated adsorption isotherms suggest that cationic surfactants adsorb to the surfaces via a two-stage process, initially forming monolayers and then bilayers at high concentrations, which is consistent with previous experiments. Anionic surfactants weakly adsorb via hydrophobic interactions, forming only monolayers on both virgin and medium bleached hair surfaces. We also conduct non-equilibrium molecular dynamics simulations, which show that applying cationic surfactant solutions to bleached hair successfully restores the low friction seen with virgin hair. Friction is controlled by the combined surface coverage of the grafted lipids and the adsorbed CTAB molecules. Treated surfaces containing monolayers and bilayers both show similar friction, since the latter are easily removed by compression and shear. Further wetting MD simulations show that bleached hair treated with CTAB increases the hydrophobicity to similar levels seen for virgin hair. Treated surfaces containing CTAB monolayers with the tailgroups pointing predominantly away from the surface are more hydrophobic than bilayers due to the electrostatic interactions between water molecules and the exposed cationic headgroups.

Finite-Size Effects in Simulations of Peptide/Lipid Assembly

Molecular dynamics simulations are an attractive tool for understanding lipid/peptide self-assembly but can be plagued by inaccuracies when the system sizes are too small. The general guidance from self-assembly simulations of homogeneous micelles is that the total number of surfactants should be three to five times greater than the equilibrium aggregate number of surfactants per micelle. Herein, the heuristic is tested on the more complicated self-assembly of lipids and amphipathic peptides using the Cooke and Martini 3 coarse-grained models. Cooke model simulations with 50 to 1000 lipids and no peptide are dominated by finite-size effects, with usually one aggregate (micelle or nanodisc) containing most of the lipids forming at each system size. Approximately 200 systems of different peptide/lipid (P/L) ratios and sizes of up to 1000 lipids yield a "finite-size phase diagram" for peptide driven self-assembly, including a coexistence region of micelles and discs. Insights from the Cooke model are applied to the assembly of dimyristoylphosphatidylcholine and the ELK-neutral peptide using the Martini 3 model. Systems of 150, 450, and 900 lipids with P/L = 1/6.25 form mixtures of lipid-rich discs that agree in size with experiment and peptide-rich micelles. Only the 150-lipid system shows finite-size effects, which arise from the long-tailed distribution of aggregate sizes. The general rule of three to five times the equilibrium aggregate size remains a practical heuristic for the Cooke and Martini 3 systems investigated here.

Coarse-grained molecular dynamics simulations of immobilized micelle systems and their interactions with hydrophobic molecules

Micelles immobilized in polymer materials are of emerging interest in drug delivery, water treatment and other applications. Immobilization removes the need for membrane-based separation to eliminate micelles from the medium, enabling facile extraction and delivery in diverse industries. This work lays out a coarse-grained molecular dynamics simulations framework for the rapid identification of surfactants for use in immobilized micelle systems. Micelles are immobilized by constraining one end of the constituent surfactants in space, mimicking what would occur in a copolymer system. We demonstrate that constraints affect how the micelles interact with small hydrophobic molecules, making it important to account for their effects in various drug-micelle and pollutant-micelle simulations. Our results show that in several systems there is stronger interaction between hydrophobic small molecules and micelles in immobilized systems compared to unconstrained systems. These strengthened interactions can have important implications for the design of new micelle-based extraction and delivery processes.

Structural Insights into Self-Assembled Aerosol-OT Aggregates in Aqueous Media Using Atomistic Molecular Dynamics

In water, the surfactant dioctyl sulfosuccinate (Aerosol-OT or AOT) exhibits diverse aggregate structures, ranging from micelles to lamella. An atomic-level understanding, however, of the formation and structure of these aggregates is lacking. Herein, using atomistic molecular dynamics (MD) with microsecond-long simulations, self-assembly of AOT in water is studied for concentrations of 1, 7.2, and 20 wt % at 293 K and for 7.2 wt % at 353 K. Assembly proceeds through stepwise association and dissociation of single AOT molecules, and the fusion and fission of AOT clusters. At 293 K, AOT self-assembles into either (i) spherical micelles (1 wt %), (ii) biphasic systems consisting of rod-like and prolate spheroidal micelles (7.2 wt %), or (iii) bilayers (20 wt %). We hypothesize that the observed rod-like structure is a precursor to lamellar microdomains found experimentally in biphasic dispersions. Increasing temperature to 353 K at 7.2 wt % results in a system consisting of prolate micelles but no rod-like micelles. Simulated phase behavior agrees with previously published experimental observations. Individual aggregates formed during self-assembly are identified using graph theory. Structural metrics of these aggregates like the radius of gyration, shape anisotropy, and prolateness are presented. Trends in structural metrics quantitatively reflect how shapes and sizes of AOT aggregates vary with surfactant concentration and temperature. These simulations provide deeper insight into open questions in the scientific community and demonstrate a method to generate physics-based micelle structures that can be used to rationalize experimental observations.

Free energy of micellization of dodecyl phosphocholine (DPC) from molecular simulation: Hybrid PEACH-BAR method

A new method to extract the free energy of aggregation versus aggregate size from molecular simulation data is proposed and applied to a united atom model of the zwitterionic surfactant dodecyl phosphocholine in water. This system's slow dissociation rate and low critical micelle concentration (CMC of approximately 1-2 mM) make extraction of cluster free energies directly from simulation results using the "partition-enabled analysis of cluster histogram" (PEACH) method impractical. The new approach applies PEACH to a model with weakened attractions between aggregants, which allows sampling of a continuous range of cluster sizes, then recovers the free energy of aggregation under the original fully-attractive force field using the BAR free energy difference method. PEACH-BAR results are compared with free energy differences calculated via umbrella sampling, and are used to make predictions of CMC, average cluster size, and SAXS scattering profiles that are in fair agreement with experiment.