5.2 Coarse graining
Coarse-grained molecular dynamics simulations employ intermediate resolution in order to balance chemical detail with system size. They offer sufficient size to study membrane-remodeling events while retaining the ability to self-assemble. Because they are capable of simulating mesoscopic length scales, they make contact with a wider variety of experiments. A complete coarse-grained model must include two components: a mapping from atomistic structures to coarse-grained beads and a set of potentials that describe the interactions between beads. The former defines the geometry or length scale of the resulting model, while the latter defines the potential energy function or the force field. The parameterization of the force field is essential to the performance of the model, which is only relevant insofar as it can reproduce experimental observables. Here we will describe the characteristic methods for developing CGMD models, namely the bottom-up structure- and force-matching and top-down free energy-based approaches. We note that excellent reviews have been written on coarse-grained methods with applications in other fields such as polymer physics, see, e.g., [72].
5.2.1 Structure and energy matching in the CMM-CG model: Klein and co-workers developed a coarse-grained model for phospholipid bilayers by matching the structural and thermodynamic properties of water, hydrocarbons and lipid amphiphile to experimental measurements and all-atom simulations [102]. The resulting force field, titled CMM-CG, has been used to investigate a range of polymer systems as well as those containing nonionic liquids and lipids. Classic coarse-grained methods propose pair potentials between CG beads according to the Boltzmann inversion method. In this method, a pair correlation function, or radial distribution function (RDF) g(r) defines the probability of finding a particle at distance r from a reference particle such that the conditional probability of finding the particle is ρ(r)=ρg(r), where ρ is the average number density of the fluid. The potential of mean force (PMF) between CG beads is then estimated by (Eq. 18) where gaa(r) is the RDF measured from atomistic simulation, and αn is a scaling factor (corresponding to the nth iteration of the estimate) designed to include the effect of interactions with the (necessarily) heterogeneous environment.