Amphiphilic molecules self-assemble in solution to form a variety of micellar aggregates of molecules that behave in a concerted fashion. Such systems pose a severe challenge for simulation, since prediction of the critical micelle concentration and the distribution of aggregates requires attainment of equilibrium between all states of aggregation, from the isolated molecule in solution to aggregates comprising thousands of molecules in the tail of the micelle size distribution. Furthermore, these micelles are typically dilute in solution, so that for every aggregate of a few hundred micelle molecules, there are tens of thousands of solvent molecules. One approach to problems of this type is to reduce the level of complexity through coarse-graining of the system representation. However, such coarse-graining generally comes with a loss of fidelity in system representation. Here, we discuss a coarse-graining strategy based on an implicit representation of the solvent molecules. Loss of thermodynamic information is mitigated by introducing a density dependent term in the intermolecular potential function that accounts for the free energy otherwise associated with the solvent. The resulting Density-Dependent Implicit Solvent (DDIS) potentials are quite simple, and are shown to capture both the structure and chemical potential of solutions of amphiphilic molecules, allowing the direct simulation of critical micelle concentrations and aggregate size distributions. The more general utility of density-dependent potentials for coarse-graining applications will also be discussed.
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