Coarse-grained Force Fields from the Perspective of Statistical Mechanics: Better Understanding the Origins of a MARTINI Hangover

The popular MARTINI coarse-grained model is used as a test case to analyze the adherence of top-down coarse-grained molecular dynamics models (i.e., models primarily parameterized to match experimental results) to the known features of statistical mechanics for the underlying all-atom representations. Specifically, the temperature dependence of various pair distribution functions, and hence their underlying potentials of mean force via the reversible work theorem, are compared between MARTINI 2.0, Dry MARTINI, and all-atom simulations mapped onto equivalent coarse-grained sites for certain lipid bilayers. It is found that the MARTINI models do not completely capture the lipid structure seen in atomistic simulations as projected onto the coarse-grained mappings, and that issues of accuracy and temperature transferability arise due to an incorrect enthalpy-entropy decomposition of these potentials of mean force. The potential of mean force for the association of two amphipathic helices in a lipid bilayer is also calculated and, especially at shorter ranges, the MARTINI and all-atom projection results differ substantially. The former is much less repulsive and hence will lead to a higher probability of MARTINI helix association in the MARTINI bilayer than occurs in the actual all-atom case. Additionally, the bilayer height fluctuation spectra are calculated for the MARTINI model and - compared to the all-atom results - it is found that the magnitude of thermally averaged amplitudes at intermediate length scales is quite different, pointing to a number of possible consequences for realistic modeling of membrane processes. Taken as a whole, the results presented here can point the way for future coarse-grained model parameterization efforts that might bring top-down coarse-grained models into better agreement with the statistical mechanics of the actual all-atom systems they aspire to represent.