Induced asymmetries in membranes

Abstract

Lipid asymmetry in plasma membrane of eukaryotes is ubiquitous. The first measurements reported compositional asymmetry: phosphatidylethanolamine and phosphatidylserine are mostly on the cytoplasmic leafet, while phosphatidylcholine and sphingomyelin are mostly on the exoplasmic leaflet. More recent experiments using lipidomics have evidenced the presence of saturation asymmetry between the two leaflets. A question that naturally arises is why such an asymmetry? To complicate matters, it is still largely unknown in which leaflet cholesterol lies. Here, we use chemical potentials to mimic flippase proteins responsible for maintenance of compositional asymmetry in silico. We show that saturation asymmetry naturally arises as a byproduct of phospholipid number asymmetry and sphingomyelin contents, thereby showing that some reported asymmetries may naturally result from others and do not necessarily require being externally driven. We also show that plasmalogen lipids’ tendency to be highly unsaturated is also natural. Additionally, we tackle the problem of cholesterol and show that, while it is influenced by all asymmetries, the resulting cholesterol asymmetry tends to be fairly mild.

Significance

While existence of lipid asymmetry in eukaryotic membrane is well established, the relations between asymmetry, regulation, and membrane properties are generally nebulous. Here, using simulations, we show that some asymmetries may simply be byproducts that do not require active maintenance.

Introduction

Lipid asymmetry in the plasma membrane, measured more than 40 years ago, is now considered a ubiquitous feature of living cells (1). Some of the functionality is known; for instance, phosphatidylserine (PS) in eukaryotes is located on the cytoplasmic leaflet, and its presence on the exoplasmic leaflet signals apoptosis. Most of the functionality of this asymmetry is unknown, in particular which aspects are tightly controlled by cells versus which are natural consequences of other aspects (2). Cholesterol distribution provides an example of such a contentious point, where experimental measurement techniques result in widely different results and where there is no agreement on whether it is a result of other asymmetries or is enforced by the cell (3).

There have been recent efforts to develop synthetic asymmetric membranes, which have led to a now-established protocol for their synthesis (4). These membranes show novel behavior, including stiffening (5), which has recently been attributed to the presence of differential stress (6), which can be directly induced by an imbalance of the number of lipids on each leaflet. Control over such parameters is currently out of reach of experimental techniques, and direct comparison between in vivo measurements and synthetic membranes is therefore challenging. In this context, a recent publication has even highlighted two new observations (7). First, the saturation distribution of acyl tails of phosphatidylcholine (PC) is also asymmetric, with higher unsaturated contents on the exoplasmic leaflet. Second, transmembrane domains of proteins are similarly asymmetric; domains that locate to the exoplasmic leaflet are generally thinner than their cytoplasmic counterparts. Given that we know so little about properties of asymmetric membranes, it is not clear whether we should be surprised by these results.

In parallel, we have recently explored the idea that cells do not directly regulate most of membrane lipids. Rather, phospholipids are freely transported from one membrane to another, leading to equilibration of chemical potentials across membranes (8). When investigating such systems using simulations, regulation implies that lipid chemical nature changes as simulation progresses. In coarse-grained models such as MARTINI (9), it is possible to change both the headgroup and the fatty tails of lipids, as illustrated in Fig. 1. In this picture, the overall membrane content of a particular lipid chemistry is controlled by the chemical potential of said lipid, which is, in turn, dependent on other processes such as the Lands’ cycle. Specific lipid membrane composition is driven by control components, such as cholesterol and membrane proteins. Recently, we have shown that coupling chemical potentials to order parameters, such as which leaflet a lipid resides on, can emulate the effect of flippase proteins on the plasma membrane (10).

Figure 1.

Transformations between glycerophospholipids during simulations in the MARTINI coarse-grained force field. (A) Glycerophospholipid heads, glycerol shown in purple, phosphate group in yellow, and esterified moiety in blue. The esterified moeity can either be a P₅ bead (serine), Q₀ bead (choline), or Q_d bead (ethanolamine). Plasmalogens, characterized by an ether linkage, are represented by a C₅ bead on the glycerol linker due to higher hydrophobicity than esters. We forbid PS plasmalogens by numerically disabling any transition to such lipids. Changes in charges are uncompensated, leading to varying bilayer charges over the course of simulations. (B) Lipid tails, unsaturations located at dark gray beads. Beads corresponding to saturated bonds are represented by C₁ beads, whereas unsaturations correspond to C₃ beads. Tails are free to change nature over time; left: sn-1-palmitoyl-sn-2-dihomo-$\gamma$-linoleoyl-, right: sn-1-oleoyl-sn-2-all-cis-8,11,14,17-eicosatetraenoyl-. Not all combinations and lipid unsaturation positions are allowed; see supporting material for details. To see this figure in color, go online.

One can then ask, if we impose some asymmetry by emulating flippases, what is the natural composition of the membrane? In other words, if the cell pays energy in order to forcefully drag PC and sphingomyelin (SM) molecules to the exoplasmic leaflet, what does it gain without additional investment? In order to answer this question, we explore here the natural asymmetries that arise from imposing different chemical potential on the exoplasmic leaflet than on the cytoplasmic leaflet. In particular, we show that two asymmetries presented in (7) are natural in the sense that they arise from other asymmetries. First, plasmalogen lipids are generally less saturated than their esterified counterparts (7). Second, both incorporation of SM and phospholipid number asymmetry create a saturation asymmetry in PC where molecules on the exoplasmic leaflet show a different saturation than on the cytoplasmic side. We also discuss cholesterol asymmetry and how it subtly depends on various parameters such as SM and phospholipid number asymmetry. We also show that, while significant asymmetries are measured, they are much milder than what some of the published experimental measurements suggest.

Materials and methods

We simulate membranes using the MARTINI force field, with slight adjustments for polyunsaturated acyl chains as described in (8). All simulated membranes incorporate PC and phosphatidylethanolamine (PE), which are always in the same regulated ensemble, i.e., in the same semigrand canonical ensemble. The full list of acyl tails is available in the supporting material. We make use of the equal-binding approximation (see (8)) on the cytoplasmic leaflet, implying that chemical potentials of all lipid species are equal. This is simulated by using Monte-Carlo moves that swap the chemical nature of lipids during simulations, as shown in Fig. 1 (see (10) for further details). To emulate the flippase protein, we set the chemical potential of PC lipids on the exoplasmic leaflet to be 25 kJ/mol higher than other species, as in (10). Membranes incorporate 1,600 lipid molecules and 20% cholesterol (400 molecules), and all simulations ran for at least 10 μs. The temperature is fixed to $k_{B}T=2.5$ kJ/mol ($T\approx 301$ K). Changing the temperature affects lipid distribution, with higher temperatures typically linked to higher unsaturation levels (8).

We first investigate properties of the system in the presence of other phospholipids. In order to do so, we replace up to 240 lipids of the cytoplasmic leaflet with either PE-plasmalogen (PEp) or PS. We keep these molecules in a separate semigrand canonical ensemble, which means that the headgroup of these lipids is fixed but the acyl chains are free to change their chemical nature. Therefore, while the proportion of PEp and PS is fixed, the saturation contents are not conserved. No counterions are present for data reported in this article, which results in charged bilayers when PS is present. We ran simulations with 150 mM NaCl explicit counter ions and found no qualitative difference in behavior.

In a second numerical experiment, we investigate the effect of SM by replacing up to 240 lipids of the exoplasmic leaflet with SM molecules. Here, we allow the headgroup to vary between PC and PE, but this is subject to the same 25 kJ/mol chemical potential difference that applies to other lipids, with the consequence that SM headgroups are predominantly (>99%) PC. This is a consequence of the simulation setup; naturally occurring SMs possess PC headgroups. We expect this discrepancy to have negligible effects. Unlike for phospholipids, we do not allow the chemical nature of SM acyl tails to change. To reflect the highly saturated content of SM in cells, we choose highly saturated chains. Last, we investigate a system that incorporates all simple MARTINI phospholipids (PC, PE, PS, PEp, PCp) in a common semigrand canonical ensemble while replacing up to 400 lipids of the exoplasmic leaflet with SM. Within both of these numerical experiments, the proportion of SM lipids is fixed.

In addition to the chemical asymmetry, we also investigate effect of phospholipid number asymmetry. Membranes are created with a different number of lipids on each leaflet. A nonzero phospholipid number asymmetry implies an out-of-equilibrium condition. However, the relaxation timescale associated with lipid flip flop is larger than simulation times, and the simulation is therefore in a pseudoequilibrium situation where phospholipid number asymmetry is fixed throughout the simulation. Phospholipid number asymmetry is characterized using the same definition found in (6), i.e., $\delta =\left(N^{+}-N^{-}\right)/\left(N^{+}+N^{-}\right)$, where $+$ denotes the exoplasmic leaflet and $-$ the cytoplasmic leaflet. A positive value of $\delta$ therefore refers to a membrane with a larger number of lipids on the exoplasmic leaflet. Membranes in these articles possess values of $\delta$ in the range $\left[-\mathrm{5,5}\right]\%$. Asymmetries in the system can induce a cholesterol asymmetry between the leaflets. We characterize it either in absolute number, that is ${\delta }_{\text{chol}}=N_{\text{chol}}^{+}-N_{\text{chol}}^{-}$, or by its ratio between the two leaflets, given in terms of exoplasmic:cytoplasmic.

Software

We make use of the MARTINI force field (9), the HOOMD-Blue molecular dynamics engine (v.2.9.3) (26,27,28), the hoobas molecular builder (29), and the semigrand canonical ensemble package (10). Images were rendered using ovito (30). Analysis was done using in-house software.

Results

We first review trends observed in membranes with only PC and PE. These are fully described in (10). Leaflets with equal chemical potentials between lipids are dominated by PE in MARTINI due to the hydrogen bond model. The cytoplasmic leaflet is therefore mostly PE (87%). Conversely, the large chemical potential favors PC on the exoplasmic leaflet, resulting in almost exclusively PC on the leaflet (>99%).

In the absence of phospholipid number asymmetry $\left(\delta =0\right)$, we observe a mild cholesterol asymmetry of ${\delta }_{\text{chol}}=-15$. The PE-rich cytoplasmic leaflet therefore has a tendency to be enriched in cholesterol. This observation is not novel, and has been previously observed in simulations, with two proposed theoretical explanations. The first one relies on the preference of cholesterol for ordered domains and the observation that PE bilayers are slightly more ordered than PC (11). The second explanation comes from curvature: the intrinsic curvature of PE is larger than PC, and cholesterol can compensate this curvature difference (12) by increasing lipid order. These are not mutually exclusive and can be self-reinforcing for regulated ensembles: as the cholesterol fraction increases, so does the mean saturation of the leaflet and cholesterol solubility.

The presence of phospholipid number asymmetry creates differential stress in the membrane, as one leaflet is compressed and the other stretched. Under such stress, the cholesterol distribution is determined by a mixture of stress compensation, preferential partitioning, and entropy (6,13). In broad terms, cholesterol will tend to migrate toward the leaflet under tension in order to fill some of the voids. However, differential stress can also be created (or alleviated) via saturation asymmetry. Saturated lipids occupy a lower area than their unsaturated counterparts and can therefore influence stress in the membrane. In simulations, the differential stress induced by phospholipid number asymmetry is therefore compensated by a combination of cholesterol and saturation asymmetries. This leads to the leaflet with higher cholesterol content having lower lipid saturation, as opposed to what would naively be expected from traditional cholesterol preferential partitioning (11,12).

Glycerophospholipids

We then investigate the effect of enforcing the presence of other glycerophospholipids in the membrane, specifically PS and PEp. These are inserted in the cytoplasmic leaflet as described in the materials and methods.

Lipid unsaturation between the two species is very different. PS has similar saturation levels as PC and PE, which is around 4.3 unsaturations per lipid. However, PEp is much more unsaturated at around 4.9 unsaturations per lipid. Saturation contents of individual lipids are only weakly affected by the presence of either PS or PEp with changes on the order of 0.02 unsaturations per lipid (see Fig. S1). Surprisingly, the cholesterol asymmetry is not significantly altered, while the overall unsaturation contents of the cytoplasmic leaflet itself is strongly affected (see Fig. S2). Saturation levels in the exoplasmic leaflet are unaffected. The balance of PE:PC in the cytoplasmic leaflet is altered. Increasing the PS concentration yields a higher PC:PE ratio, while the converse is observed for PEp (see Fig. 2). There is therefore an apparent natural tendency for PEp to replace PE and for PS to replace PC.

Figure 2.

Ratio of PC to PE contents in the cytoplasmic leaflet for bilayers incorporating either PS (A) or PEp (B) in their cytoplasmic leaflet. Color indicates phospholipid number asymmetry. The x axis indicates overall proportion in the cytoplasmic leaflet, including cholesterol. All lipids are free to change their acyl tails. Only PC and PE are free to exchange their headgroups. To see this figure in color, go online.

SM

The effect of SM was then investigated. We ran simulations with three different lipid tails: palmitoyl (16:0), lignoceric acid (24:0), or nervonic acid (24:1, $\omega$-9). Results are similar for all three variants (see supporting material; Fig. S3), and we therefore only show the results for palmitoyl-SM in the main text; other SM molecules are available in the supporting material.

The presence of SM in the exoplasmic leaflet has noticeable two effects. First, as the SM concentration increases, the exoplasmic cholesterol content also increases (Fig. 3 A). Second, glycerolipid saturation is altered. The mean unsaturation in the exoplasmic leaflet increases with SM, while conversely, the unsaturation of the cytoplasmic decreases. This increases the overall glycerolipid unsaturation asymmetry in the membrane (Fig. 3 B; supporting material). While it may be tempting to associate the SM-cholesterol association to strong interactions between these components, the reader should note that SM is highly saturated and therefore possess low area per lipid. Increasing the concentration therefore creates differential tension in the membrane, which, just as in the simple PC/PE case, can be compensated by either cholesterol asymmetry or glycerolipid unsaturation asymmetry.

Figure 3.

Asymmetries observed in SM/PC/PE bilayers as a function of exoplasmic SM contents and number asymmetry. Bilayers incorporate 20% cholesterol. (A) Cholesterol asymmetry and (B) mean PC unsaturation levels. Color indicates phospholipid number asymmetry. The x axis indicates overall proportion of SM in the exoplasmic leaflet, including cholesterol. PC and PE lipids are free to change their acyl tails, whereas SM is constrained to a palmitoyl tail (C16:0). PC and PE are free to exchange their headgroups. To see this figure in color, go online.

Major components

We then consider systems with all simple MARTINI lipids (PC, PE, PCp, PEp, and PS) in a semigrand canonical ensemble while we keep the SM concentration fixed. One may associate this picture as a membrane of loosely regulated glycerolipids while SM is tightly controlled by cells to control membrane properties.

This system yields a complex lipodome, for which we show a typical composition in Fig. 4 A. Glycerolipids in the exoplasmic leaflet are comprised almost exclusively of PC and PCp. The cytoplasmic leaflet is still dominated by PE, likely due to the hydrogen bonding representation in the MARTINI force field. Other components (PS, PC, PCp) comprise only a minor portion of the leaflet (>20% of lipids). Both variants of plasmalogens (PCp, PEp) have similar unsaturation $\left(\approx 4.9-5\right)$, which is higher than their fully esterified counterparts $\left(\approx 4.2-4.5\right)$.

Figure 4.

Properties of bilayers incorporating many types of lipids. (A) Representative lipid composition for $\delta =0$ as a function of unsaturation levels (indicated by color). Red (blue) bars denote exoplasmic (cytoplasmic) lipids. Note that exoplasmic SM and overall cholesterol compositions are constrained. (B) Enrichment of exoplasmic PC as a function of unsaturation levels and phospholipid number asymmetry for a membrane incorporating 240 SM lipids. Color indicates phospholipid number asymmetry. Lipids with less than three unsaturations typically represent less than 0.5% of the overall population levels and are therefore not shown here. In this simulation, phospholipids are free to change acyl tails, whereas SM molecules always have a palmityol tail. Phospholipids are free to exchange headgroups. To see this figure in color, go online.

While their general behavior is similar to previous numerical experiments, the saturation levels of PC molecules is more complex than in the absence of PCp. On the exoplasmic leaflet, the saturation change of PC with SM is much weaker. However, increases of SM affect the PC:PCp ratio (see supporting material), leading to an overall increase of glycerophospholipid saturation. Cytoplasmic saturation levels of glycerophospholipids change much more rapidly with SM (see supporting material), resulting in a similar overall saturation asymmetry as in absence of PCp; when viewed as a function of lipid unsaturation number, the ratio between the two leaflets appears as a monotonic, almost linear trend (see Figs. 4 B and S4 for corresponding PC data, as well as S5 for PE data).

Discussion

The lipid compositions obtained from our model are surprisingly similar to biological ones given its simplicity. While PE is overrepresented in the cytoplasmic leaflet, levels of PC, PS, and PEp are similar to each other, as in experiments (7). Additionally, plasmalogen lipids are less saturated than fully esterified lipids (7). This suggests that the model emulates well some of the biological processes. These simulations suffer from the same problem as in vivo measurements in that they cannot be easily compared with synthetic asymmetric membranes due to the large number of components and the presence of regulation.

An additional asymmetry, in the saturation levels of PC, also arises naturally as a consequence of other imposed asymmetries; here, it arises from both exoplasmic SM levels and phospholipid number asymmetry. It is not clear whether both these mechanisms operate through the same principle; in theory, they could both drive differential tension in the bilayer, which in turn would drive saturation asymmetry. In biological environments, asymmetries may also be influenced by other factors, such as membrane-associated proteins. Measuring general trends in lipidomics, e.g., PC saturation asymmetry versus SM levels, across multiple cell types may help establish which asymmetries are enforced by cells and which are natural results of others. Plasmalogen asymmetry, visible in Fig. 4 and in experimental lipodomes (7), is similarly understudied due to the lack of detailed lipodomes for cell types other than erythrocytes.

We also want to address limitations of the MARTINI force field on the results observed here. MARTINI is often cited to possess interactions between tails of differing saturation that are too weak (14). This is part of a series of contentious points (15,16,17), which we will not address directly. We did observe that strengthening interactions, by creating a so-called “high-$\chi$” force field with strong repulsion between saturated and unsaturated beads, caused the regulation processes become stronger (8). We therefore assume that effects seen here are a baseline.

Beyond the question of interaction strength in the coarse-grain force field lies the question of coarse-grained resolution. To explore this in our results, we want to single out plasmalogens. These lipids are always less saturated than their esterified counterparts. In the MARTINI force field, this arises from a single bead modification of the glycerol region. What puzzles us is that headgroups (PC versus PE versus PS) have nearly no influence on the saturation contents of their acyl chains, whereas the linker (ester versus ether) does. If changing the ester to an ether affects acyl tails due to changes in polarity, one would expect that any changes to the water structure near the lipid head would also influence acyl tails, in particular if a charged group (PS) is introduced. Whether this is a real effect or an artifact stemming from either our usage of usual nonpolarizable water or the force field itself is still elusive to us. Using a detailed force field (e.g., united atom) to further address the question is computationally impractical (see (10)), and we will therefore leave this question for future studies.

In the absence of SM, cholesterol is naturally pulled toward the cytoplasmic side. It is not clear whether this stems from intrinsic curvature (as discussed in (12)) or preferred lipid order (as discussed in (11)). In fact, the difference in lipid order seen in (11) could arise from subtle curvature effects. However, the asymmetries observed, around 48:52, are very mild. Adding PS or PEp does alter this value in a measurable, but quantitatively insignificant, way. This may appear surprising given that one PS has been linked to cholesterol asymmetry (18) and that two PEp tends to be more unsaturated than PE. However, overall membrane saturation changes upon the addition of PEp or PS are small, and cholesterol asymmetry is small even in the PC/PE system, whose lipids should have very different spontaneous curvatures (9). This therefore further supports the hypothesis that the link between PS and cholesterol asymmetry in vivo is related to interactions with proteins (19,20).

The addition of SM to the exoplasmic leaflet is particularly interesting as it results in increased cholesterol contents in the upper leaflet. The presence of SM can drive the cholesterol asymmetry significantly further than observed in PC/PE bilayers. Including effects arising from phospholipid number asymmetry, we observe up ratios of up to 65:35. Significant cholesterol excess on the cytoplasmic side therefore requires a combination of low SM concentration and strong phospholipid number asymmetry. Number asymmetries larger than those imposed here $\left(\pm 5\%\right)$ typically lead to mechanical failures of the bilayer during simulations and are thus unlikely to arise under normal circumstances. Whether higher cholesterol concentrations affect the range of mechanically stable number asymmetries has not been thoroughly explored. Cholesterol distribution in cells is contentious, and experimentally reported values range from 90:10 to 10:90 depending on the technique used and the cell type (3). On the modeling side, this value is typically much milder (11,12) and in line with our reported values. While it has been conjectured that the large asymmetries experimentally reported may be attributable to systematic biases of the measurement techniques, the reader should be aware that emerging experimental evidence points at very large phospholipid number asymmetry in cells $\left(\delta \approx -30\%\right)$, which could stabilize such large cholesterol asymmetries (21). Cells can also potentially dynamically alter this asymmetry by altering the SM concentration or the phospholipid number asymmetry to respond to environmental conditions.

We note that these results are independent of the SM tail chosen, including for long C24:0 chains. This is in opposition to results of (22), where authors have observed that C24:0 SM tended to push cholesterol away. Their work has given rise to some controversy, as there are potential issues with the experiments (3) and simulations (23). In fact, the opposite trend was observed in (23), with C24:0 SM pulling more cholesterol than C18:0 SM.

Beyond cholesterol asymmetry, increasing SM levels also creates an additional asymmetry in PC saturation levels. This can be rationalized in terms of a Le Chatelier principle: SM is highly saturated, and the two leaflets want to adopt a similar order parameter. This requires the cytoplasmic leaflet to saturate and other species of the exoplasmic leaflet to desaturate. This asymmetry, which was shown in (7), is therefore a natural consequence of the high saturation “contrast” between glycerophospholipids and SM. This offers a simple explanation without the need to resort to remodeling cycles. The picture is slightly more complex in the presence of plasmalogens. Increasing SM content results in an increase of the ether:ester linkage ratio, which suppresses the desaturation of the exoplasmic lipids and reinforces saturation of the cytoplasmic leaflet. However, there still exists an induced saturation asymmetry.

Various factors may cause further deviations from our results. For instance, lipid distributions may vary between cell types. There are other lipids, for instance glycolipids, that we have not considered and may play a role. Other “unregulated” components, such as proteins, can influence membrane asymmetry. For proteins, this can arise due to the particular shape of the transmembrane domain, which is also asymmetric (7), but also through nonequilibrium processes, for instance if protein activity is linked to the lipid environment. The trends observed here, or their absence, can therefore be used to delineate passive from active processes.

Divergences between lipid ensembles observed here and in lipodomic studies such as (7) may be attributable to the equal-binding approximation (see (8)), which oversimplifies the underlying fatty acid regulation mechanisms. We also note that membrane-associated proteins show preferences for specific lipid environments, which may alter chemical potential values (24).

Conclusions

These results highlight an important fact about lipid bilayer: some asymmetries naturally arise as a response to other asymmetries. Here, we show this for PC saturation asymmetry arising as a result of SM concentration and phospholipid number asymmetry. However, the converse may also be true: a PC saturation asymmetry could induce some SM concentration asymmetry. It may therefore be impossible in some cases to distinguish between cause and effect. However, we find that induced asymmetries are generally weak. Similarly, the highest cholesterol asymmetry observed is 65:35, which requires a combination of number asymmetry and high SM contents. Beyond this, some asymmetries may be reinforcing each other. For example, proteins that localize in the plasma membrane tend to exhibit asymmetric transmembrane domains, which have been implicated in protein sorting (25). However, inserting such proteins in a regulated bilayer will naturally cause it to become asymmetric. The asymmetry that drives protein sorting would therefore be responsible, at least partially, for its own existence.

Software

We make use of the MARTINI force-field (9), the HOOMD-Blue molecular dynamics engine (v2.9.3) (26,27,28), the hoobas molecular builder (29) and the semi-grand canonical ensemble package (10). Images are rendered using ovito (30). Analysis is done using in-house software.

Editor: Michael F. Brown.