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

The spontaneous formation of micelles in aqueous solutions is governed by the amphipathic nature of surfactants and is practically interesting due to the regular use of micelles as membrane mimics, for the characterization of protein structure, and for drug design and delivery. We performed a systematic characterization of the finite-size effect observed in single-component dodecylphosphocholine (DPC) micelles with the coarse-grained MARTINI model. Of multiple coarse-grained solvent models investigated using large system sizes, the nonpolarizable solvent model was found to most accurately reproduce SANS spectra of 100 mM DPC in aqueous solution. We systematically investigated the finite-size effect at constant 100 mM concentration in 23 systems of sizes 40-150 DPC, confirming the finite-size effect to manifest as an oscillation in the mean micelle aggregation number about the thermodynamic aggregation number as the system size increases. The oscillations in aggregation number mostly diminish once the system supports the formation of three micelles. Similar oscillations were observed in the estimated critical micelle concentration with a mean value of 1.10 mM, which is in agreement with experiment to 0.1 mM. The accuracy of using a multiscale simulation approach to avoid finite-size effects in the micelle size distribution and SANS spectra using MARTINI and CHARMM36 was explored using multiple long time scale 500 DPC coarse-grained simulations, which were back-mapped to CHARMM36 all-atom systems. It was found that the MARTINI model generally occupies more volume than the all-atom model, leading to the formation of micelles that are of a reasonable radius of gyration but are smaller in aggregation number. The systematic characterization of the finite-size effect and exploration of multiscale modeling presented in this work provide guidance for the accurate modeling of micelles in simulations.