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

Abstract

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 parametrized 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 are quite different, pointing to a number of possible consequences for realistic modeling of membrane processes. Taken as a whole, the results presented here show disagreement in the enthalpic and entropic driving forces driving lateral structure in lipid bilayers as well as quantitative differences in association of embedded amphipathic helices, which can help direct future efforts to parametrize CG models with better agreement to the all-atom systems they aspire to represent.

Martini 3 Coarse‐Grained Force Field: Small Molecules

“…Despite the numerous improvements and even wider applications opened up by Martini 3, limitations of this coarse‐graining approach must be kept in mind. Certain limitations apply generally to the Martini force field, [ 8,24,75 ] and include a nonquantitative agreement with experimental free energies of solvation and narrower fluid ranges due to the use of the 12‐6 Lennard‐Jones potential, and an entropy–enthalpy imbalance—due to enthalpy compensating for the loss of degrees of freedom upon coarse‐graining—which is known to affect the temperature dependence of several properties, [ 10,24 ] Other limitations pertain more specifically to the systems subject of the present study, namely small‐molecules containing ring‐like structures described by finer mappings. As shown in Section 3.4, conformations driven by quadrupolar interactions, such as T‐shaped stacking, are not captured by standard Martini models due to the lack of specific electrostatic interactions.…”

Mechanistic Understanding from Molecular Dynamics in Pharmaceutical Research 2: Lipid Membrane in Drug Design

“…Coarse-grained simulations have also been successfully used in the study of nanoparticles partitioning into lipid bilayers, e.g., [652,653] or where large-scale screening is performed for hundreds of drugs [654][655][656][657][658]. It should be noted that the MARTINI model was recently reparametrized (MARTINI 3) [659] to fix problems related to the imbalance of interactions between beads of various sizes leading to unrealistically strong interactions, e.g., proteinprotein interactions [660][661][662].…”

A Data-Driven Dimensionality Reduction Approach to Compare and Classify Lipid Force Fields

“…The density profiles of the phosphate groups show a large variability both in height and in width (top right in Figure 2 ). This can be likely imputed to differences in the CG beads, and in the bead–bead interactions, used in the different CG FFs, slightly different approximations in the enthalpy/entropy balance in the models (that unavoidably accompany the various CG schemes 58 ) can, for example, make the thermal vibrations larger/smaller, broadening/narrowing the density distributions. A great variability is present in membrane compressibility (bottom left in Figure 2 ), irrespective of the FF resolution.…”

“…Recently, it was shown that Martini 2.2 and Dry Martini CG FFs, respectively, tend, on average, to overstructure and understructure the bilayers compared to AA FFs. 58 However, all these analyses and comparisons provide evidence that is limited to the average characterization of the bilayers, while, on the other hand, it has been shown that the behavior of complex supramolecular assemblies (such as also lipid bilayers) may be strongly controlled by local events, or fluctuations, that cannot be captured with average evaluations. 39,40,61 To move our investigation to a deeper level, similarly to a recent study 37 where typical ice nucleation sites were probed in a QM-based liquid water model by means of a SOAP analysis, we investigated the transition of a lipid bilayer between the liquid phase and the gel phase.…”