Alternative methods for determining the critical micelle concentration (cmc) are investigated using canonical and grand canonical Monte Carlo simulations of a lattice surfactant model. A common measure of the cmc is the "free" (unassociated) surfactant concentration in the presence of micellar aggregates. Many prior simulations of micellizing systems have observed a decrease in the free surfactant concentration with overall surfactant loading for both ionic and nonionic surfactants, contrary to theoretical expectations from mass-action models of aggregation. In the present study, we investigate a simple lattice nonionic surfactant model in implicit solvent, for which highly reproducible simulations are possible in both the canonical (NVT) and grand canonical (μVT) ensembles. We confirm the previously observed decrease of free surfactant concentration at higher overall loadings and propose an algorithm for the precise calculation of the excluded volume and effective concentration of unassociated surfactant molecules in the accessible volume of the solution. We find that the cmc can be obtained by correcting the free surfactant concentration for volume exclusion effects resulting from the presence of micellar aggregates. We also develop an improved method for determination of the cmc based on the maximum in curvature for the osmotic pressure curve determined from μVT simulations. Excellent agreement in cmc and other micellar properties between NVT and μVT simulations of different system sizes is observed. The methodological developments in this work are broadly applicable to simulations of aggregating systems using any type of surfactant model (atomistic/coarse grained) or solvent description (explicit/implicit).

Colloidal particles, amphiphiles and functionalized nanoparticles are examples of systems that frequently exhibit short-range attraction coupled with long-range repulsion. We vary the ratio of attraction and repulsion in a simple isotropic model with competing interactions, using molecular simulations, and observe significant differences in the properties of the self-assembled clusters that form. We report conditions that lead to the self-assembly of clusters of a preferred size, accompanied by a change in the slope of the pressure with respect to density, similar to micelles formed by amphiphilic molecules. We also report conditions where repulsion dominates, clusters of a preferred size form and the pressure vs. density slope is unaffected by self-assembly. We investigate cluster structure by calculating the size distributions, free colloid density, cluster shape and density profiles. The system dynamics are characterized by cluster life-times. We do not find qualitative differences in structure or dynamics of the clusters, regardless the pressure behavior. Therefore, thermodynamic and structural quantities are required to classify the different clustering characteristics that are observable in systems with competing interactions. Our results have implications in terms of development of design principles for stable cluster self-assembly.

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The binding free energy of 4-bromophenol (4-BP), an inhibitor that binds in the internal binding site in dehaloperoxidase-hemoglobin (DHP) was calculated using Molecular Dynamics (MD) methods combined with pulling or umbrella sampling. The effects of systematic changes in the pulling speed, pulling force constant and restraint force constant on the calculated potential of mean force (PMF) are presented in this study. The PMFs calculated using steered molecular dynamics (SMD) were validated by umbrella sampling (US) in the strongly restrained regime. A series of restraint force constants ranging from 1000 down to 5 kJ/(mol nm(2)) were used in SMD simulations. This range was validated using US, however noting that weaker restraints give rise to a broader sampling of configurations. This comparison was further tested by a pulling simulation conducted without any restraints, which was observed to have a value closest to the experimentally measured free energy for binding of 4-BP to DHP based on ultraviolet-visible (UV-vis) and resonance Raman spectroscopies. The protein-inhibitor system is well suited for fundamental study of free energy calculations because the DHP protein is relatively small and the inhibitor is quite rigid. Simulation configuration structures are compared to the X-ray crystallography structures of the binding site of 4-BP in the distal pocket above the heme.

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