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. 2024 Oct 3;20(20):9190–9208. doi: 10.1021/acs.jctc.4c00868

Changing Your Martini Can Still Give You a Hangover

Timothy D Loose 1, Patrick G Sahrmann 1, Thomas S Qu 1, Gregory A Voth 1,*
PMCID: PMC11500708  PMID: 39361008

Abstract

graphic file with name ct4c00868_0015.jpg

The Martini 3.0 coarse-grained force field, which was parametrized to better capture transferability in top-down coarse-grained models, is analyzed to assess its accuracy in representing thermodynamic and structural properties with respect to the underlying atomistic representation of the system. These results are compared to those obtained following the principles of statistical mechanics that start from the same underlying atomistic system. To this end, the potentials of mean force for lateral association in Martini 3.0 binary lipid bilayers are decomposed into their entropic and enthalpic components and compared to those of corresponding atomistic bilayers that have been projected onto equivalent coarse-grained mappings but evolved under the fully atomistic forces. This is accomplished by applying the reversible work theorem to lateral pair correlation functions between coarse-grained lipid beads taken at a range of different temperatures. The entropy-enthalpy decompositions provide a metric by which the underlying statistical mechanical properties of Martini can be investigated. Overall, Martini 3.0 is found to fail to properly partition entropy and enthalpy for the PMFs compared to the mapped all-atom results, despite changes made to the force field from the Martini 2.0 version. This outcome points to the fact that the development of more accurate top-down coarse-grained models such as Martini will likely necessitate temperature-dependent terms in the corresponding CG force-field; although necessary, this may not be sufficient to improve Martini. In addition to the entropy-enthalpy decompositions, Martini 3.0 produces an incorrect undulation spectrum, in particular at intermediate length scales of biophysical pertinence.

Introduction

Despite the continual advances in computing power, the simulation of many large, relevant biological processes remains tantalizingly out of grasp. For example, the maturation of HIV-1 viral particles occurs on the time scale of minutes, far outside the reach of conventional all-atom molecular dynamics (AA-MD) even though ∼100 million atom AA-MD simulations of the assembled virus capsid have been done.1,2 For this reason, there is an ever-present need to enhance the speed at which MD simulations can give a result. The two major paths for accomplishing this are enhanced free energy sampling, in which computation is sped up by weighting the statistics of the system of interest in favor of sampling desired phenomena, and coarse-graining (CG), in which the entire system is simplified by collapsing groups of atoms into individual CG “beads”.

CG models can be divided into two categories: bottom-up and top-down. Bottom-up CG involves parametrizing interactions between beads based on all-atom molecular dynamics data algorithmically by minimizing the difference between the CG model and the mapped atomistic data.3−5 Top-down CG on the other hand involves parametrizing each interaction by hand in order to match certain target properties.6−9 Top-down CG models may be easy to implement due to model libraries, but bottom-up CG models are more founded10 in statistical mechanics and may be easier to extend, as anyone can systematically generate their own model of a given system provided they have sufficient AA data. The overall sampling advantage of CG models leads them to often be used as a replacement for AA-MD models. In this vein, by guaranteeing at least a theoretical connection between the CG model and the underlying AA model which it replaces, the bottom-up CG approach can provide a basis upon which to judge the consistency of the CG model with the underlying all-atom system via statistical mechanics.

Martini, first developed by Marrink and co-workers in 2007,7 is a top-down CG model parametrized via matching partitioning free energies of various compounds between polar and nonpolar phases. The resulting model was a simple CG mapping of 4-heavy atoms to 1 CG bead that could be utilized to represent a variety of different molecules, which was extended to include small molecules, proteins, lipids, and carbohydrates.11,12 This model also generally relies on a treatment of the bulk solvent as large CG beads which represent a collection of 4 water molecules. These solvent beads tend to freeze at or around room temperature, a problem that was resolved via adding smaller “anti-freeze” particles that disrupt nucleation points for Martini ice. Later, a “Dry” Martini model was introduced which avoids representing solvent altogether, further enhancing the efficiency of the model at the cost of accuracy.13 (Solvent-free CG models such as this are common both in top-down and bottom-up CG due to the fact that in nearly all biophysical systems, the majority of the simulation is composed of water molecules.) Most recently, Martini 3.0 was released, which addressed previous concerns about temperature dependence as well as expanded the overall number of possible interaction types.14

For many researchers, Martini has evidently become their “go-to” CG model for several reasons. It has a large library of molecules, easy-to-use tools, and a 4 heavy atom to 1 CG bead resolution which retains a reasonable amount of chemical specificity while simultaneously offering a significant speedup over AA-MD simulations, especially when utilizing the solvent-free “dry” Martini models. This pregenerated library of molecule types makes using Martini follow a very similar workflow to using standard AA force fields. Additionally, the reduction in degrees of freedom results in a smoother free energy surface upon which the system evolves, speeding up diffusion and thus sampling beyond a simple uplift in integration rate.15 Many complex systems have been built and studied within the Martini framework, including a 63-component asymmetric plasma membrane model16 and more recently, an entire “cell”,17 both of which remain challenging to model.18,19

However, there are several disadvantages to using the Martini force field. The 4 to 1 mapping scheme employed still leads to issues of chemical specificity. Notably, there is a degeneracy of molecules that map to certain Martini topologies. For example, both 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC) and 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) map to the same Martini molecule. For this reason, the Martini model lacks a certain level of rigorous connection to the underlying atomistic representation and thus leads one to the conclusion that Martini is a semiphenomenological model rather than a model which seeks to represent the chemical properties of each of its molecules. Issues stemming from the 4 to 1 mapping scheme also emerge with Martini “water”. As previously mentioned, each Martini water bead represents 4 water molecules, which causes inaccurate freezing behavior to occur near room temperature, as well as issues pertaining to diffusion and the hydration of solute molecules, all of which are critically important to the study of biophysical systems (see, e.g., refs (20−23)). In addition, by representing liquid water as consisting of CG beads that “tie up” four actual water molecules, one obviously also ties up (and omits) the exchange entropy of those atomistic water molecules. The consequences of this simple, self-evident fact seem to have not been explored to any large degree to the best of our knowledge.

Due to its popularity, it is also important to understand Martini’s limitations as a CG model. Not only does this allow the scientific community to better interpret results from Martini simulations, but it also helps guide its use toward applications in which it could be sufficiently accurate, as well as help guide the development of more accurate top-down CG models in the future. Recently, an analysis of Martini 2.0 and dry Martini lipids was performed which suggests that the models are limited not only in structural bilayer properties but more critically in the thermodynamic (enthalpy-entropy) decomposition of their potentials of mean force (PMF).24 More specifically, in the case of a 1,2-Dioleoyl-sn-glycero-3-phosphocholine (DOPC)/Cholesterol bilayer, Martini 2.0 failed to properly partition the entropy and enthalpy of the CG PMF for the lateral association for the head groups as well as the glycerol beads.

At the time that this data was collected, Martini 3.0 cholesterol is unavailable, and thus this paper focuses on bilayers without cholesterol. However, as lipid bilayers are an excellent case study for the association of long amphipathic molecules, which are very similar to the parametrization methodology used for Martini originally (water/octanol partitioning), we chose to keep the focus of this work on lipid bilayers. Moreover, instead of simulating a pure DOPC bilayer as a comparison to all-atom MD data, simulations of two binary lipid mixtures were simulated to study the thermodynamic properties of the Martini interactions. The first system is a 70:30 mixture of DOPC and 1,2-dioleoyl-sn-glycero-3-phospho-l-serine (DOPS). Analysis of this mixture provides insight into Martini’s ability to partition charged and uncharged lipids. In this case, the heterogeneity of the bilayer is localized within the head groups of the membrane. The second system is a 50:50 mixture of DOPC and 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), to study Martini’s ability to capture saturated lipid tails interacting with unsaturated ones. While the prior study24 focused its analysis purely on the interactions between lipid head and glycerol groups, the current work extends this treatment to the analysis of the lipid tails as well. It is expected that in general Martini 3.0 will capture the lateral association of lipid tails more accurately than the head groups because they are well described by Lennard-Jones potentials (the core of the Martini parametrization scheme) as one might expect, although currently there is no study that directly analyzes Martini’s capacity in this regard from a statistical mechanical standpoint.

In this work we analyze Martini 3.0 according to CG mapped atomistic models, using the two membrane systems to probe how Martini lipids capture temperature transferability and higher-order structural properties including the undulation spectrum as well as structural lipid order parameters. First, the theory connecting the RDF to the decomposition of entropy and enthalpy in CG PMFs is discussed. We then describe the computational details of the work, including details necessary to reproduce each MD simulation performed, and details justifying the method by which we calculated the RDFs used in the entropy-enthalpy decompositions. Results for the entropy-enthalpy decompositions and undulation spectrum for each system are then presented, followed by an analysis of how these results show that the latest release of Martini still cannot capture thermodynamic transferability, likely without having an explicit temperature dependence built into the interactions in the model.

Theory

It is first helpful to clearly state the motivation for the following studies. Martini is a model, and as such one might assert that it cannot be incompatible with statistical mechanics since it is merely a model. In that view, as a model it may be incompatible with the observable reality of the system it aims to describe—as defined by the underlying atomistic system and its interactions—but it is not incompatible with statistical mechanics per se. However, in this paper we are not exploring these semantic differences. Instead, we are comparing the behavior and accuracy of Martini 3.0 with that of CG systems studied exactly through the principles and results of statistical mechanics, in which atomistic scale interactions give rise to higher length scale properties (structure and thermodynamics). To the extent Martini does not agree with these calculations for the same system(s) it claims to represent, it might be considered to be “incompatible” in that vein.

According to statistical mechanics, there is an inherent thermodynamic state dependence incurred when creating a molecular model at a CG resolution.10,25,26 That is, the effective Hamiltonian describing the CG configurational distribution is dependent on the thermodynamic state, e.g. temperature.27−30 Simulating a CG model outside of this state point (or whichever point the model was designed for) can lead to unphysical behavior as the PMF of the system will fail to correlate with the conditioned PMF of the corresponding system.28

Statistical mechanics offers a quantitative way to probe these PMFs via entropy-enthalpy decompositions. By the reversible work theorem, the radial distribution function can be connected to the PMF of association between two CG sites as31

graphic file with name ct4c00868_m001.jpg 1

In eq 1, β is equal to 1/kBT, g(r) refers to the RDF, and w(r) is the value of the PMF at some distance r. As the PMF is a free energy, it can be expressed as a sum of two components, an enthalpic term (ΔH), and an entropic term, −TΔS such that

graphic file with name ct4c00868_m002.jpg 2

where the reference point is r = ∞.For each value of r, the values of ΔH and ΔS can be estimated via linear regression of the PMF with respect to temperature, where the intercept represents enthalpy, and the slope corresponds to the negative of the entropic component.29

For CG models such as Martini, this analysis provides insight into how the missing configurational mapping entropy is accounted for in the model.32 Additionally, such analysis provides an indication where the model fails (i.e., head vs tail groups) and also how such models might be improved to increase their statistical mechanical accuracy. We hypothesize that as Martini was parametrized with hydrophilic/hydrophobic partitioning in mind, the tail groups of Martini lipids should perform better in this regard than the head groups, as lipid tails provide a similar chemical environment to octanol. However, this is dependent on Martini’s ability to generalize from a system in which the hydrophobes are shorter and have little to no lateral organization to a lipid bilayer in which there is far more ordering present. It is possible that errors in the organization of the head groups, to which the tails are attached, could also limit the ability of Martini lipids to associate correctly.

While entropy-enthalpy decompositions offer statistical mechanical insight into the thermodynamics and transferability of the Martini model, there is also the problem of representability in CG models.28 Representability refers to a CG model’s capacity to properly represent quantifiable observables from the AA regime. There are many observables that are patently impossible to correctly calculate for any CG model, such as entropy, due to the loss of entropy incurred when CG mapping is performed, as discussed earlier. However, many observables are representable for CG models, such as the location of alpha carbons in a CG protein which is mapped down to an alpha-carbon resolution.28 Previous studies of Martini 2.0 lipids have also used the height fluctuation spectrum and especially the bending modulus as a metric for Martini representability as well a gauge of its accuracy in capturing equilibrium properties of lipid bilayers. Analysis of bending behavior of membranes relies on a lipid patch large enough to properly sample low wavelength modes, as it is only at long ranges that molecular systems of lipids begin to share behavior with continuum models. Due to the size of the membrane patches considered in this work, we do not consider analysis of the bending modulus and instead only the undulation spectrum. In previous efforts, it has been shown that for Martini CG mappings, the position of the phosphorus atom in lipid heads is represented well by the position of Martini-mapped phosphate groups.24 This is logical, as the phosphate CG bead is made up of the phosphorus atom and the four covalently bonded oxygens. As the phosphate moiety is tetrahedral and thus the phosphorus atom occupies roughly the center of mass of the entire moiety, it is reasonable that the average phosphate bead z coordinate is an effective metric to use in the calculation of the midplane of the bilayer and undulation spectrum.

Methods

The two aforementioned lipid systems were simulated at four different temperatures to gather data necessary for entropy-enthalpy decompositions and undulation spectrum calculations. For each lipid mixture, an atomistic simulation was performed using the CHARMM36 M force field in GROMACS33 at 290, 305, 320, and 335 K.34 All simulations were prepared using the CHARMM-GUI membrane builder browser-based tool.35,36 Each system consisted of 1140 lipid molecules and was first annealed to the appropriate temperature before being simulated for 200 ns under constant NPT conditions. All membranes were solvated in 0.15 M NaCl. The DOPC/DOPS AA membrane was solvated with 41040 TIP3P37 waters, 432 Na ions, and 90 Cl ions, and the DOPC/DOPS MARTINI membrane was solvated with 9729 CG waters, 468 Na ions, and 126 Cl ions. The DOPC/DPPC AA membrane was solvated with 38389 TIP3P waters, 101 Na ions, and 101 Cl ions, and the DOPC/DPPC MARTINI membrane was solvated with 11643 CG waters, 156 Na ions, and 156 Cl ions. Each trajectory was stripped of water and each leaflet was analyzed separately for the calculation of lateral entropy enthalpy decompositions; interleaflet correlations were not considered due to the inherent anisotropy of the bilayer system. For the undulation spectrum calculations, the 305 K split trajectories were combined to obtain a full bilayer. The AA simulations were then mapped to Martini CG resolution using a center of geometry mapping scheme in order to more directly compare the Martini and AA models.14,25,26 We note that in our original work which was the basis for this manuscript,38 a center of mass mapping was employed and that similar conclusions were reached as in the following results. The reference distribution implied by the mapping operator, Inline graphic, is given by the following relation in eq 3

graphic file with name ct4c00868_m004.jpg 3

where pr(rn) is the Boltzmann distribution of the atomistic degrees of freedom, RN are the CG configurational degrees of freedom, and the bold-faced delta function denotes a product of all the delta functions involving all of the CG mapping operators.

For the CG models, the process was largely the same. The Martini 3.0 force field was utilized,14 with each system simulated at 290, 305, 320, and 335 K. However, each simulation was stopped after 100 ns of NPT integration. It was found that due to Martini’s faster lipid diffusion, less sampling was required to obtain converged RDFs. The membrane patches simulated in this study were larger than those used in a previous analysis24 of Martini 2, in which lipid patches containing 268 DOPC molecules and 70 cholesterol molecules were used, which necessitated much longer simulations in order to obtain RDFs that converged to the degree necessary to calculate accurate entropy-enthalpy decompositions.

xy-RDFs

To properly study the equilibrium properties of lateral association in the lipid membrane, all radial distribution functions used in this work were projected onto the two dimensions parallel to the plane of the lipid membrane on a per-leaflet basis. These RDFs are hereby referred to as xy-RDFs. By projecting the RDFs in this way, the anisotropic nature of the bilayer is properly handled. If full 3-dimensional RDFs were calculated, the results would not normalize to 1 as a proper RDF does, but to 0, as there is no particle density above or below the membrane. This also guarantees that the PMFs calculated via the reversible work theorem correspond to the PMF of lateral association, which is of particular interest for membrane systems. The RDF calculations were performed for each leaflet individually, as the distance between beads on different monolayers projected onto the xy plane is not hindered by steric constraints. To calculate the xy-RDFs for the CG beads of the AA systems, the lipid atoms were mapped onto a Martini-equivalent CG resolution. This way, the AA reference simulations were as close to the Martini system as possible. Each mapped AA trajectory was split into separate trajectories containing a single lipid leaflet, and the xy-RDFs were calculated for each leaflet and averaged to obtain a converged RDF for the entire simulation. Figures 1–6 depict the RDFs of both models at 305 K.

Figure 1.

Figure 1

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Lateral RDFs for DOPC-DOPC interactions in the DOPC/DOPS system. CG beads are labeled according to the following scheme. Choline: NC3, phosphate: PO4, glycerols: GL1 and GL2, saturated tail beads: C1A, C3A, and C4A, unsaturated tail beads: D2A. Martini 3.0 RDFs (green) are compared to mapped CHARMM36 data (red).

Figure 6.

Figure 6

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Lateral RDFs for DPPC-DOPC interactions in the DOPC/DPPC system. Beads are labeled according to the following scheme. Choline: NC3, phosphate: PO4, glycerols: GL1 and GL2, saturated tail beads: C1A, C2A, C3A, and C4A. Martini 3.0 RDFs (green) are compared to mapped CHARMM36 data (red).

For the calculation of lateral association RDFs and entropy-enthalpy decompositions, each bead in each tail was treated distinctly. All results presented utilize the correlations between the beads labeled as part of the “A” tail in the Martini mapping. Because the A and B tails are identical, this result is consistent across each tail, and figures comparing the B tails can be found in the Supporting Information.

Results and Discussion

Lateral Association

System 1: DOPC/DOPS

Figure 1 shows comparisons between Martini and AA xy-RDFs for the lateral association between DOPC molecules. Martini matches the distributions of the tail beads, although it produces overstructured results compared to the AA system. The biggest difference in the RDFs of the tail groups comes in the D2A group. In this case, Martini fails to capture the magnitude of the first peak properly. For the head groups, Martini 3.0 largely fails to reproduce the RDFs of the CG mapped AA lipids. Figure 2, which shows the same RDFs between DOPS molecules, exhibits similar results. However, there is a further deviation between AA CG mapped and Martini in associations between DOPS serine groups (named CNO in Martini). In this case, the AA bilayer exhibits a much larger amount of structuring around 0.5 nm. Figure 3 shows the xy- RDFs between the two lipid species. These RDFs do not exhibit additional deviations beyond the single-component RDFs.

Figure 2.

Figure 2

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Lateral RDFs for DOPS-DOPS interactions in the DOPC/DOPS system. Beads are labeled according to the following scheme. Serine: CNO, phosphate: PO4, glycerols: GL1 and GL2, saturated tail beads: C1A, C3A, and C4A, unsaturated tail beads: D2A. Martini 3.0 RDFs (green) are compared to mapped CHARMM36 data (red).

Figure 3.

Figure 3

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Lateral RDFs for DOPC-DOPS interactions in the DOPC/DOPS system. Beads are labeled according to the following scheme. Choline: NC3, serine: CNO, phosphate: PO4, glycerols: GL1 and GL2, saturated tail beads: C1A, C3A, and C4A, unsaturated tail beads: D2A. Martini 3.0 RDFs (green) are compared to mapped CHARMM36 data (red).

System 2: DOPC/DPPC

The DOPC/DPPC system for the most part shows similar results for lateral association. Figures 4 and 5 show results for DOPC-DOPC and DOPC-DPPC association. For the most part, Martini can capture the structuring of lipid tails with peaks at the correct distances and magnitude. The head groups, as in the DOPC/DOPS system, are largely inaccurate. However, there were no large deviations seen in the DOPS-DOPS serine–serine RDF in the previous system, but larger inaccuracies are seen in the DPPC-DPPC tail interactions, shown in Figure 6. As opposed to RDFs from the previous system and in DOPC interactions in this system, DPPC-DPPC tail interactions fail to capture peak locations for each bead. This is not limited to the first peak either, each subsequent peak is also located further away than in the CHARMM reference data, suggesting that Martini DPPC tails are effectively larger than they should be.

Figure 4.

Figure 4

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Lateral RDFs for DOPC-DPPC interactions in the DOPC/DPPC system. Beads are labeled according to the following scheme. Choline: NC3, phosphate: PO4, glycerols: GL1 and GL2, saturated tail beads: C1A, C2A, C3A, and C4A, unsaturated tail beads: D2A. Martini 3.0 RDFs (green) are compared to mapped CHARMM36 data (red).

Figure 5.

Figure 5

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Lateral RDFs for DOPC-DOPC interactions in the DOPC/DPPC system. Beads are labeled according to the following scheme. Choline: NC3, phosphate: PO4, glycerols: GL1 and GL2, saturated tail beads: C1A, C3A, and C4A, unsaturated tail beads: D2A. Martini 3.0 RDFs (green) are compared to mapped CHARMM36 data (red).

Entropy-Enthalpy Decompositions

The PMF is a free energy so according to eq 2 one can decompose it into enthalpic [ΔH(r)] and entropic [ −TΔS(r)] contributions. In the following, these are calculated for the CG mapped all-atom reference and the Martini 3 model.

System 1: DOPC/DOPS

Figure 7 shows entropy-enthalpy decompositions for headgroup DOPC-DOPS interactions. While the PMFs for the glycerol groups are decomposed accurately at least at long ranges, the phosphate-phosphate and choline-serine decompositions exhibit large deviations from the CG mapped atomistic data. Figure 8 shows the decompositions for the tail group DOPC-DOPS interactions. While there are deviations in the peak locations and heights, overall, the tail groups are captured reasonably well with the Martini 3.0 model. Of note, the errors for each value of r are shown as well. For clarity, we only compare Martini 3.0 and CHARMM entropies and enthalpies in regions where the standard error is less than 0.5 kBT. At lower r values, these errors raise in magnitude due to the lack of sampling in these regimes. In certain cases, no sampling for certain bins was obtained, and the data are not plotted for these regimes. Figure 9 shows decompositions for the head groups of the DOPC-DOPC interactions in the DOPC/DOPS system. Again, phosphate beads are poorly captured by Martini 3.0 while the glycerol beads are qualitatively similar. Interestingly, the choline groups show an additional feature that is not present in choline–choline decompositions for the second system: a strong peak after the initial well which is not observed at all in the CG mapped atomistic data.

Figure 7.

Figure 7

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Entropy-enthalpy decompositions of DOPC-DOPS headgroup interactions for the DOPC/DOPS system. Standard errors at each r value are shown. Beads are labeled according to the following scheme. Choline: NC3, phosphate: PO4, glycerols: GL1 and GL2. Martini 3.0 decompositions (green) are compared to mapped CHARMM36 data (red).

Figure 8.

Figure 8

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Entropy-enthalpy decompositions of DOPC-DOPS tail group interactions for the DOPC/DOPS system. Standard errors at each r value are shown. Beads are labeled according to the following scheme. Lipid tail beads in descending order: C1A, C2A, C3A, and C4A. Martini 3.0 decompositions (green) are compared to mapped CHARMM36 data (red).

Figure 9.

Figure 9

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Entropy-enthalpy decompositions of DOPC-DOPC headgroup interactions for the DOPC/DOPS system. Standard errors at each r value are shown. Beads are labeled according to the following scheme. Choline: NC3, phosphate: PO4, glycerols: GL1 and GL2. Martini 3.0 decompositions (green) are compared to mapped CHARMM36 data (red).

System 2: DOPC/DPPC

The mixed DOPC-DPPC interactions show similar trends as the second system simulated for both phosphate and glycerol groups, shown in Figure 10. In the case of phosphate, the Martini 3.0 lipids produce significant structuring which is not present in the CG mapped atomistic system. The glycerol groups on the other hand show a rough qualitative agreement with the all-atom lipids at long ranges. The choline–choline decompositions on the other hand are much closer to the reference simulation than the serine-choline decompositions in the DOPC/DOPS system. Aside from some slight structuring at long ranges which is not present in the atomistic data, the decompositions have roughly the same features.

Figure 10.

Figure 10

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Entropy-enthalpy decompositions of DOPC-DPPC headgroup interactions for the DOPC/DPPC system. Standard errors at each r value are shown. Beads are labeled according to the following scheme. Choline: NC3, phosphate: PO4, glycerols: GL1 and GL2. Martini 3.0 decompositions (green) are compared to mapped CHARMM36 data (red).

The tail–tail decompositions for the mixed DOPC-DPPC interactions, detailed in Figure 11, follow the trends of their corresponding RDFs. The under-structuring of tails by Martini 3.0 is worse in this system than in the DOPC/DOPS system, and the locations of the peaks are all different from the AA reference data. This error is the most prominent in the C2A-D2A interactions in contrast with the DOPC/DOPS system. Interactions between molecules of the same species follow the same trends with one major exception: The interactions between atomistic CG mapped DPPC tails exhibit much higher contributions both in the enthalpic and temperature-dependent entropic terms than those between DOPC molecules and the DOPC-DOPS tail interactions, as shown in Figure 12. Martini 3.0 fails to capture this entirely, and the DPPC tails seem to behave much closer to those of DOPC. Effectively, the Martini DPPC tails are much less temperature dependent, meaning they are missing an accurate entropic component.

Figure 11.

Figure 11

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Entropy-enthalpy decompositions of DOPC-DPPC tail group interactions for the DOPC/DPPC system. Standard errors at each r value are shown. Beads are labeled according to the following scheme. Unsaturated tail bead: D2A, saturated tail beads in descending order: C1A, C2A, C3A, and C4A. Martini 3.0 decompositions (green) are compared to mapped CHARMM36 data (red).

Figure 12.

Figure 12

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Entropy-enthalpy decompositions of DPPC-DPPC tail group interactions for the DOPC/DPPC system. Standard errors at each r value are shown. Beads are labeled according to the following scheme. Tail beads in descending order: C1A, C2A, C3A, and C4A. Martini 3.0 decompositions (green) are compared to mapped CHARMM36 data (red).

Lipid Order Parameters

Key order parameters which describe membrane structuring are reported for DOPC/DOPS and DOPC/DPPC in Tables 1 and 2, respectively. These order parameters include the membrane thickness, acyl chain order parameter, and Nelson-Halperin order parameter. The membrane thickness is reported as the distance between PO4 headgroup bead types across leaflets. Each membrane was binned into a 5 × 5 grid and each thickness per bin was calculated, with the bin-averaged thickness reported. In this work, the acyl chain order parameter is represented as the second order Legendre polynomial describing the angle the GL1-C4A bond makes with the bilayer normal, i.e., the z-axis, and is computed as

graphic file with name ct4c00868_m005.jpg 4

Table 1. Lipid Order Parameters for the DOPC/DOPS Membrane Systems for the CHARMM36 AA and Martini 3.0 Models across the Simulated Temperatures.

DOPC/DOPS
temperature (K) AA Martini 3.0
Membrane Thickness (nm)
290 3.96 3.84
305 3.93 3.81
320 3.89 3.77
335 3.86 3.73
P2
290 0.55/0.54 0.51/0.52
305 0.54/0.53 0.49/0.50
320 0.53/0.51 0.47/0.48
335 0.52/0.50 0.45/0.45
|ψ6|
290 0.38/0.37 0.37/0.37
305 0.37/0.37 0.36/0.36
320 0.37/0.37 0.36/0.36
335 0.37/0.37 0.36/0.36
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Table 2. Lipid Order Parameters for the DOPC/DPPC Membrane Systems for the CHARMM36 AA and Martini 3.0 Models across the Simulated Temperatures.

DOPC/DPPC
temperature (K) AA Martini 3.0
Membrane Thickness (nm)
290 4.07 3.97
305 3.95 3.90
320 3.90 3.84
335 3.85 3.79
P2
290 0.54/0.67 0.49/0.57
305 0.52/0.61 0.46/0.53
320 0.50/0.57 0.45/0.50
335 0.49/0.55 0.42/0.48
|ψ6|
290 0.38/0.43 0.37/0.38
305 0.37/0.39 0.36/0.37
320 0.37/0.38 036/0.37
335 0.37/0.37 0.36/0.36
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The acyl chain order parameter ranges from [−0.5, 1] where −0.5 indicates orthogonal orientation and a value of 1 is when the vectors are parallel.39 The Nelson-Halperin order parameter quantifies the degree of hexatic packing in lipid tails.40 In this work, the Nelson-Halperin order parameters for the C2A and C2B CG beads for DOPC/DOPS and the D2A and D2B beads of DPPC were calculated. To calculate the Nelson-Halperin order parameter for CG bead i, the six nearest neighbors of the CG bead were identified and fit to a plane via singular value decomposition.41,42 The order parameter, Inline graphic, was then calculated from the angle each distance vector makes with respect to an arbitrary reference vector, in this case, the x-axis, via the following equation

graphic file with name ct4c00868_m007.jpg 5

The absolute value of the order parameter |ψ6| quantifies the degree of hexatic ordering and ranges from [0, 1], with values of 0 indicating no hexatic ordering and values of 1 indicating ideal hexatic ordering.

Qualitatively, the Martini model follows the same trends across temperatures as the CHARMM36 AA model. For both models, as temperature is increased, the bilayer thickness decreases, acyl chain order parameters and Nelson-Halperin order parameters decrease as the lipid tails become less aligned with the bilayer normal and less hexatically packed. The two models show the biggest discrepancy in the bilayer thickness of DOPC/DOPS, as evident in Table 1 and the P2 values of DOPC/DPPC, as evident in Table 2. Although the correct trend with respect to temperature is followed, there are noticeable differences in the magnitude of these order parameters between the CHARMM36 AA and the Martini model.

Height Fluctuation Spectrum

As shown in Figures 13 and 14, Martini fails to capture the height fluctuation spectrum of CG mapped atomistic bilayers at intermediate to higher wavelengths. Figure 13 shows the full spectrum for the DOPC/DOPS system for both Martini 3.0 and CHARMM36 all-atom. Between q = 1 and q = 5 nm–1, the Martini bilayer shows fluctuations that are up to twice as large as the reference all-atom simulation. These fluctuations mediate interactions between proteins on the surface of membranes43 and thus can affect the interaction and aggregation of membrane bound proteins. This has consequences for processes such as membrane remodeling, which involve large quantities of proteins such as with N-BARs motifs which contain membrane targeting amphipathic helices.44−46

Figure 13.

Figure 13

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Height fluctuation spectrum for the DOPC/DOPS system.

Figure 14.

Figure 14

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Height fluctuation spectrum for the DOPC/DPPC system.

Figure 14 shows the same spectrum for the DOPC/DPPC system. In this case, the discrepancy between the atomistic and CG bilayers is even greater and persists to even higher frequency (shorter wavelength) modes.

Conclusions

Several conclusions can be drawn about Martini 3.0 membranes in general based on the lateral associations of the tail beads when compared to reference CG mapped AA data. For all systems studied in this work, Martini 3.0 consistently produces overstructured RDFs in comparison to the CG mapped all-atom reference (CHARMM36 force field). However, it is apparent that the entropy-enthalpy decompositions of the Martini model also consistently underestimate peak and well heights. Consequently, the Martini 3.0 model is less sensitive to changes in temperature due to the smaller magnitude of its entropic term but sometimes compensates for this via a lower enthalpy term. While it might be tempting to argue that Martini 3.0 fails to correctly capture the “hidden entropy” in a CG model (as manifest by a temperature dependence of the CG interactions, which Martini 3.0 does not have) as the origin of its inaccuracy, in a number of instances Martini 3.0 is inaccurate on those fronts compared to the CG mapped all-atom reference, the latter following the calculation principles of statistical mechanics.

The results presented in the previous section show that Martini 3.0 fails to a certain degree in several areas which are sensitive to bilayer composition. The two systems studied provide insight into how lipid bilayers partition entropy and enthalpy in different regions of the membrane. For the DOPC/DOPS system, the heterogeneity from the different lipid species emerges from the presence of a choline group in DOPC versus a serine group in DOPS. Structurally, Martini fails to capture peaks in the serine–serine RDF while consistently also failing to reproduce the structural correlations of the phosphate headgroup. While the choline–choline decompositions are qualitatively similar for the CG all-atom reference and Martini 3.0 in the DOPC/DPPC system, the presence of DOPS in this membrane causes Martini to have peaks that are not seen at all in the CG mapped all-atom data. It can be concluded that the heterogeneity of the membrane itself, and Martini’s inability to properly represent serine, disrupts the otherwise reasonable choline–choline association.

On the other hand, the DOPC/DPPC system exhibits heterogeneity localized within the hydrophobic core of the bilayer. In this case, the lack of double bonds in DPPC creates a bilayer with more flexible tails which are capable of unkinked conformations. Despite this, Martini 3.0 DPPC appears to have a larger effective size based on the locations of peaks in the DPPC-DPPC tail RDFs and entropy-enthalpy decompositions. In addition, CG mapped all-atom DPPC is more sensitive to temperature, noted by the increased magnitude of its entropy-enthalpy decompositions in the tail groups. The entropic aspect of this is likely a root cause of disagreement, as Martini 3.0 tails cannot account well for the conformational entropy of AA lipid tails. This lack of entropy then requires a lowered enthalpy to compensate to ensure that the PMF is similar enough to better capture the RDFs. While the previously mentioned system issues seemed in part to stem from the heterogeneity of the lipid heads, in the case of the DOPC/DPPC membrane these stem mostly from the DPPC lipids themselves and do not seem to affect the mixed lipid interactions as much.

Lastly, at intermediate undulation wavelengths, Martini 3.0 gives excessive amplitudes relative to the all-atom reference. The origin of this spurious behavior is unclear, but it may be tied to the Martini 3.0 use of CG water beads that try to represent four water molecules as being somehow tied together, and thus the Martini 3.0 membrane may be too “bouncy” at those length scales, a behavior that could have significant consequences for membrane protein–protein interactions at the CG level. We additionally note that a recent study has found that the surface tension of Martini CG water is approximately a third of that observed experimentally, which may explain, in part, the erroneous undulation spectrum of Martini 3.0 at intermediate wavelengths.47

Overall, the additions to Martini 3.0 in the context of lipid bilayers do not seem to greatly improve on the behavior of the Martini 2.0 lipids. Martini 3.0 partitioning of entropy and enthalpy into lateral association PMFs still has inaccuracies relative to a CG mapped all-atom reference, and the new systems analyzed in this work bring to light additional issues related to Martini membrane properties. It seems unlikely that a Martini model can begin to resolve these issues without first incorporating explicit temperature dependence into the CG force field,29,48 as well as rethinking the Martini solvent model. These issues are inherently connected to the inherent statistical mechanical nature of CG models.3−5 If such models cannot reproduce the effects of the entropic contributions from the atomistic scale fluctuations that are coarse-grained (the “missing” or “hidden” entropy), then one may expect failures in representing any real system at the CG level. The connection between the PMFs of lateral association and the nonbonded CG pair potential, which is itself a conditioned PMF in the low density limit, suggests that a linear temperature dependence of the CG pair potentials29 may be sufficient to recapitulate the effects of the missing entropy at the CG resolution and could, as a start, possibly lead to more accurate and potentially more transferrable CG models.

Acknowledgments

This work was supported by an award from the National Institute of General Medical Science (NIGMS) of the National Institutes of Health (NIH), grant R01GM063796. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. Simulations were performed using computing resources provided by the University of Chicago Research Computing Center (RCC).

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jctc.4c00868.

  • Additional plots of entropy-enthalpy decompositions for DOPC-DOPS and DOPC-DPPC systems (PDF)

Author Contributions

† T.D.L. and P.G.S. contributed equally.

The authors declare no competing financial interest.

Supplementary Material

ct4c00868_si_001.pdf (1.4MB, pdf)

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