Chain ordering of phospholipids in membranes containing cholesterol: What matters?
CChain ordering of phospholipids in membranescontaining cholesterol: What matters?
Fabian Keller and Andreas Heuer ∗ Institute of Physical Chemistry, University of M¨unster, Corrensstraße 28, 48149 M¨unster,Germany
E-mail: [email protected]
Phone: +49 251 83-291771 a r X i v : . [ phy s i c s . b i o - ph ] F e b bstract Cholesterol (CHOL) drives lipid segregation and is thus a key player for the forma-tion of lipid rafts and thus for the ability of a cell to, e.g., enable selective agglomerationof proteins. The lipid segregation is driven by cholesterol’s affinity for saturated lipids,which stands directly in relation to the ability of cholesterol to order the individ-ual phospholipid (PL) acyl chains. In this work, Molecular Dynamics simulations ofDPPC (Dipalmitoylphosphatidylcholine, saturated lipid) and DLiPC (Dilineoylphos-phatidylcholine, unsaturated lipid) mixtures with cholesterol are used to elucidate theunderlying mechanisms of the cholesterol ordering effect. To this end, all enthalpiccontributions, experienced by the PL molecules, are recorded as a function of the PL’sacyl chain order. This involves, the PL-PL, the PL-cholesterol interaction, the inter-action of the PLs with water, and the interleaflet interaction. This systematic analysisallows one to unravel differences of saturated and unsaturated lipids in terms of thedifferent interaction factors. It turns out that cholesterol’s impact on chain orderingstems not only from direct interactions with the PLs but is also indirectly present inthe other energy contributions. Furthermore, the analysis sheds light on the relevanceof the different entropic contributions, related to the degrees of freedom of the acylchain. ntroduction The functionality of Plasma Membranes (PM) of higher eukaryotic cells is controlled bya complex interplay of lipids of varying types, proteins, and other bioactive compounds.Within this interaction network, cholesterol (CHOL) is one of the most important ingredientsexhibiting outstanding features as it is able to tune the mechanical properties and phasebehavior of lipid bilayers. Ranging from concentrations of less than 10 mol% in organellemembranes to concentrations of 20-30 mol% of cholesterol in most of the PM, cholesterolleads to tighter lipid packing, making bilayers less permeable for smaller molecules and thusenhancing the PMs ability to shield the cytosol from the outside world.
The formation of rafts is said to be directly linked to cholesterol’s affinity towards high-melting (saturated) lipids and thus has been well discussed in the literature. The idea thatcholesterol’s effect on bilayer structure is universal and thus independent of composition wasreplaced by the notion that cholesterol’s affinity to a lipid decreases with the lipids unsat-uration and varies with different head groups.
A recent study closer investigated theeffects of cholesterol on unsaturated lipid bilayers, which were assumed to be unaffected bycholesterol by any means. In this study, they indeed found a, though weaker, orderingeffect of cholesterol on unsaturated lipids. Regen et al. used a technique coined nearest-neighbor recognition (NNR), in which pairs of like and unlike molecules are counted andhence a free energy of interaction can be calculated from it. In one approach, they com-pared kinked structures of cholesterol to compare the so-called template effect, where therigid body of cholesterol is said to act as a template for ordering lipid acyl chains and theproposed umbrella model, where PLs act as an umbrella, shielding the cholesterol bodyfrom unfavorable water interactions. Their results point towards the template mecha-nism for the description of cholesterols’ ordering effect. In another study, they comparedkinked and unkinked modifications of PLs to directly identify favorable interactions withsaturated lipids vs unfavorable interactions with unsaturated lipids and via a Monte Carlomodel, derived from NNR results, propose that this affinity is driven mainly by enthalpy3igure 1: DPPC (left) and DLiPC (right) chain order parameter distribution in simulationsvarying in temperature and cholesterol concentration.and not by entropy. The important feature of domain registration is discussed to be highly dependent oncomposition. The degree of the relation of leaflet interdigitation on domain registrationis discussed contradictory. While in a recent study the interdigitation is identified as akey driving force for domain registration another work negated any major relevance. In any way, leaflet interdigitation plays a role in ordering lipids. The higher the degreeof unsaturation, the higher the leaflet interdigitation. Additionally, it is reported thatcholesterol decreases leaflet interdigitation. Cholesterol is known to decrease the water permeation by increasing acyl chain order.Even though the permeation is lowered and cholesterol does not have an impact on the PLhead group region, studies have shown that the hydrophobicity of the polar head groupregion is decreased. An early MD work indicates increased hydration of the head region. These findings are strongly related to the aforementioned umbrella model, which relatescholesterol’s ability to order acyl chains and properties at the bilayer-water interface.All these examples show the complex nature of cholesterol’s impact on PL ordering. Inthis work we are taking a systematic look into each of the different sites cholesterol takeseffect on from an energetic point of view. Specifically, we elucidate cholesterol’s effect onPL-PL interactions, PL-water interactions, interleaflet interactions, and, of course, the di-rect PL-cholesterol interaction. Each of these shed light on the interplay between those4ifferent effects. For this purpose, we employed thorough Molecular Dynamics simulationsof binary mixtures of DPPC (Dipalmitoylphosphatidylcholine) and DLiPC (Dilineoylphos-phatidylcholine) with cholesterol, respectively, with concentrations ranging from pure PLsystems to systems containing 30% cholesterol. The choice of a fully saturated (DPPC) anda polyunsaturated (DLiPC) lipid, even though rarely occurring in living organisms, providethe two extreme cases of cholesterol’s mode of action. We expect the behavior of cholesterolto change significantly between these limits. We used the well established CHARMM36force-field, which has proven to very well reproduce lipid membrane properties and, in par-ticular, acyl chain order.
The resulting order parameter distributions for the differentbilayer compositions simulated at different temperatures are shown in figure 1. In accordancewith the expected properties of cholesterol, it shows a distinctively higher ordering effect onDPPC than on DLiPC. Which interactions are needed to correctly describe cholesterol or-dering of saturated and unsaturated lipids? This is the key question that guides the analysisof this work. 5 ethods
Molecular dynamics simulations
The bilayer structures were prepared using the CHARMM-GUI Web-based graphical inter-face. All Molecular dynamics (MD) simulations were conducted using the CHARMM36force-field and Gromacs 2018 MD software package. The systems were equilibrated us-ing the established CHARMM-GUI parameter set. The TIP3P model was used as watermodel. To maintain the temperature the Nos´e-Hoover algorithm was used with a couplingconstant of 1 ps, coupling bilayer and solvent separately. To maintain the pressure at 1 atmthe Parrinello-Rahman barostat was used with a coupling constant of 5 ps and a compress-ibility of 4.5x10 − bar − . Hydrogen bonds were constraint using LINCS. Particle meshEwald electrostatics were used with a cutoff of 1.2 nm. The Lennard-Jones potential wasshifted to zero between 1.0 and 1.2 nm, and a cutoff of 1.2 nm was used. The nonbondedinteraction neighbor list was updated every 20 steps, using a cutoff of 1.2 nm. The tempera-ture ranges, trajectory lengths, and compositions for each bilayer simulation are shown andsummarized in table S1 in the supporting information.
Derivation of measured parameters
All analysis heavily relied on the MDAnalysis package for Python.
All visualizations ofthe simulations were created using VMD The lipid chain order parameter S is defined as S = (cid:104) . θ − . (cid:105) , where θ denotesthe angle between the vector spanned by every second carbon atom in a lipid chain andaverage tilt vector per leaflet. Brackets indicate an average value over both chains and theircarbon vectors. Radial distribution functions (RDF) were calculated using gromacs analysis tools. All RDFs were calculated individually for each leaflet using in-plane distances and were6veraged. For the PL molecules and for CHOL the phosphor and the hydroxyl oxygen atomsrespectively were used as reference positions.
The overlap score is the average overlap integral of groups of lipids based on the Bhat-tacharyya distance defined as BC i ( p, q ) = (cid:80) z ∈ Z (cid:112) p i ( z ) · q i ( z ) where p i ( z ) and q i ( z ) are thenormalized distributions of the bilayer height (z-component) of the positions of the last 3carbon atoms for a lipid group i . In this manner, each PL molecule was assigned a groupof neighboring PLs, with their P atoms located within 1 nm distance of the respective PLmolecule’s P atom. Note that this definition is analogous to the nearest-neighbor N N defi-nition. The BC was then calculated for the z-position distributions of the lipid group andthe lipids within the same radius but in the opposing leaflet. In this definition, a completeoverlap of the last carbons in the PL chains would lead to an overlap score of 1. To relatethe overlap to the order parameter, the order parameter of the host lipid within each groupwas used. Determination of enthalpic contributions
Figure 2: Identification of the different types of interaction for a PL (as CPK): nearest PLneighbors (purple), nearest CHOL neighbors (blue), non-nearest N out neighbors (grey), andthe surrounding water (blue shading). 7e separated the environment of a PL into different contributions to the ordering effectof PL chains, being interactions with its nearest neighbors (N n ), interactions with lipidsof the outer neighboring shells (black region, N out ), the PL interactions with the opposingleaflet (white region) and the interaction with the surrounding water (blue region) (figure2) and calculate the average sum of all interaction energy contributions of a PL with itssurroundings as a function of the PL’s chain order. The interaction functions are averagedover simulations at different temperatures where the bilayers are found in an Ld/Lo state(290 K to 330 K for DLiPC, 330 K to 350 K for DPPC). Each energy is an average withinan order parameter range of 0.1 and its standard deviation in each range lies at roughly90 kJ/mol. The standard deviation is similar in all order parameter ranges, for both DPPCand DLiPC and in all CHOL compositions. Importantly, all averages presented in this workwere determined with a numerical uncertainty of the mean smaller than 1 kJ/mol.8igure 3: Self-energies of DPPC (left) and DLiPC (right) in PL/CHOL mixtures of varyingCHOL concentrations. Here the analysis is restricted to the mutual interactions of atoms ofa single lipid. Results and discussion
PL-PL interaction
We start with the self-energy of a randomly chosen PL with order parameter S, determinedas the average over its two acyl chains. For both PL the self-energy profiles exhibit an overallsimilar shape (figure 3) in the range of order parameters, accessible for both systems. Fur-thermore, even at the highest CHOL concentration no impact of CHOL is visible. Naturally,the interaction of the two acyl-chains dominates the dependence on the order parameter(data not shown). Note that for order parameters smaller than 0.4 the S-dependence is veryweak.When analyzing the interaction of different PL molecules, we distinguish nearest neigh-bor N n interaction from the interaction with outer neighbor shells N out . They are separatedby a distance cutoff taken from the position of the second minimum of the respective ra-dial distribution functions with PL-phosphor and CHOL-hydroxy oxygen atoms as referencepositions (figure S1 and S2).For the N n interaction energy profiles in the pure PL bilayers, we hardly see a differencebetween DPPC and DLiPC in the range of S¡0.5. Furthermore, the dependence on S (figure 4,9igure 4: A) Nearest neighbor N n PL interaction as a function of PL order. B) interactionof a PL with the outer neighbor shell N out . The interaction functions are an average fromsimulations of the respective PL/CHOL mixture for temperatures of 290 to 320 K (DLiPC)and 330 to 350 K (DPPC).A) is very weak. This insensitivity to S reflects the fact that a PL chain is surrounded byPLs with a distribution of order parameters. Qualitatively, this can be expressed as asmearing-out of the self-energy curve. With a higher chain order parameter of DPPC, theinteraction energy increases as is expected for more aligned acyl chains as already visible inthe self-energy curves. Since the acyl chains of DLiPC are disordered, the range of high orderparameters cannot be accessed here. A drastic difference becomes visible when observingthe effect of CHOL: The DPPC interaction is only slightly influenced by the CHOL contentup to a concentration of 20%. This observation sheds additional light on the well-knowncondensing effect, revealing a strong insensitivity of the DPPC-DPPC interaction uponthe integration of CHOL in the membrane. In DPPC, for CHOL concentrations exceeding100%, and in DLiPC for the complete range of CHOL concentrations, a decrease of PL-PLinteraction is visible upon adding CHOL. This is a natural consequence of the decrease ofthe PL-density because here no condensing effect is present.As expected the interaction from the outer neighbor shells N out is much smaller. However,due to its dependence on the order parameter and on the CHOL content, it cannot beneglected for a complete description of the enthalpic contributions in a membrane. TheDPPC-DPPC interaction somewhat depends on the CHOL content even for small CHOLconcentrations. This is in contrast to the N n interaction. Furthermore, the decrease of theinteraction strength with increasing order parameter is opposite to the N n interactions. Theseobservations are a consequence of the fact that interaction beyond the nearest neighborhoodis particularly strong when both interacting lipids have a disordered acyl chain because ofthe increased probability of their encounter. This explains why for low order parametersof the central PL and low CHOL content, implying overall lower order parameters in themembrane, the interaction is strongest. PL-CHOL interaction
One may expect that the PL-CHOL interaction is essential to understand the different impactof CHOL on the ordering of both lipids. The results for the DPPC-CHOL and DLiPC-CHOL N n interactions are shown in figure 5, A. Naturally, for higher CHOL concentrationa stronger interaction is observed. This can be expressed even more quantitatively. It turnsout that after normalization by the actual number of surrounding CHOL-molecules (for agiven order parameter) the interaction energy per PL-CHOL pair does no longer dependon the number of surrounding CHOL-molecules (inset of figure 5). Stated differently, thePL-CHOL interaction is simply additive even for larger concentrations where a PL with,e.g., an order parameter around 0.5 is surrounded by approx. 2 CHOL-molecules.Closer inspection shows that the DPPC-CHOL and DLiPC-CHOL N n interactions, bothin absolute and relative terms, are very similar for order parameters up to 0.5 (figure 5, A).11igure 5: A) Nearest neighbor N N and B) outer neighbor N out PL-CHOL interaction asa function of PL order. The interaction functions are an average from simulations of therespective PL/CHOL mixture for temperatures of 290 to 320 K (DLiPC) and 330 to 350 K(DPPC).Thus, for disordered chains the PL-CHOL interaction gives rise to an increase of PL order,in particular for higher CHOL concentrations. This is directly related to the linear increasein the average order parameters of the system.For high order parameters the DPPC-CHOL and DLiPC-CHOL interactions seem todiffer. Only the DPPC-CHOL N n interaction strength exhibits a maximum (energy mini-mum) which is found at S=0.7. This implies the presence of an optimum configuration ofa saturated acyl chain, adapting to CHOL’s rigid body. This observation also reflects theunique ability of CHOL to inhibit gel formation for DPPC and supports the idea by Regenet al. that the CHOL body acts as a template for chain ordering and that any change ofits structure will lead to a drastically different ordering capability. Interestingly, when con-12igure 6: Interaction of PLs with lipids of the opposing leaflet as a function of the PL chainorder parameter. The insets show the relation between a lipids overlap score, defined as thecorrelation of the position distributions of the last three carbon atoms, with its chain orderparameter for DPPC and DLiPC bilayers.sidering the interaction energy, normalized by the number of CHOL-neighbors, also DLiPCapproaches such a maximum so that in analogy to DPPC there also exists an optimum in-teraction motif. Of course, due to the presence of double bonds in the acyl chains, orderparameters significantly beyond that maximum cannot be explored.In contrast to the PL-PL interaction, the PL-CHOL N out interaction has only a very smallcontribution to the overall energy of chain ordering (figure 5, B) which is in accordance withthe discussion above. Interleaflet interaction
Domain registration requires an interaction between the opposing leaflets of a bilayer. Herewe investigate the interdependence of interleaflet interaction and the degree of leaflet inter-calation and discuss possible additional factors that influence interleaflet interactions. Upto order parameters of approx. 0.5, both, DPPC and DLiPC interleaflet interaction energiesincrease with S (figure 6). Interestingly though, the DPPC interleaflet interaction strengthdecreases at high order parameters whereas no reversal is observed for DLiPC. Changes inDLiPC order generally have a significantly stronger effect on the interaction than is the casefor DPPC. In both cases, the addition of CHOL reduces the interleaflet interaction at a given13rder parameter.To understand the underlying sources of changed interaction we calculated the averageoverlap score of the PLs as a function of the PLs order parameter (insets of figure 6); seeMethods. Lin et al. found that the higher the lipid unsaturation, the higher the leafletinterdigitation, and, indeed, we find that the overall interdigitation is higher for DLiPC.While chain ordering of DPPC leads to a decrease in DPPC chain intercalation, the DLiPCintercalation even weakly increases with increasing DLiPC order parameter. In accordancewith the work of Maibaum, the overlap score decreases for both lipids with increasing CHOLconcentration. To clarify the major differences between both PL, in the SI (figure S4) we show the inter-leaflet energy as a function of both overlap score and chain order parameter. For DLiPC theinteraction strength increases both with overlap score (for fixed order parameter) and withorder parameter (for fixed interaction strength). As, additionally, the average overlap scoreincreases with chain order parameter, the S-dependence of DLiPC can be easily understoodas a superposition of the direct chain order effect and the indirect overlap effect (overlapscore increasing with chain order parameter). For DPPC the situation is more complex. Asalso shown in figure S4 the interleaflet interaction is again increasing with overlap score (forfixed order parameter) and order parameter (for fixed overlap score), although here the ef-fect of order parameter is somewhat weaker than for DLiPC. Now two opposing effects haveto be taken into account for DPPC. For an increasing order parameter, on the one hand,there is a direct increase of the interleaflet interaction strength. On the other hand, due tothe decrease of the overlap score with order parameter, the interaction strength decreasesindirectly. The first effect dominates at small S, the second effect at large S.As again shown in figure S4 the addition of CHOL decreases the interleaflet interactionstrength even for fixed order parameter and fixed overlap score. This observation, reflectingsome complex impact of CHOL on the different interaction terms, naturally explains thedependence on the CHOL concentration for DPPC and DLiPC in figure 6.14igure 7: Average number of water molecules around PL phosphor atoms as a function ofthe PL chain order parameter.The influence of leaflet intercalation on domain registration is discussed contradictory byShinoda et al. and Cheng et al.
The former found a high influence of leaflet intercalationsimulating different asymmetric SM/DOPC/CHOL bilayer compositions, while the latterfound no influence of leaflet intercalation in POPC/DSPC/CHOL bilayers. It is reasonableto assume that the presence of domain registration goes along with a strong interleafletinteraction which, naturally, will depend on the local composition. In the SM/DOPC/CHOLsetup a clear phase separation is visible with regions enriched in the unsaturated DOPC anddepleted of CHOL. As concluded from our results, those regions exhibit a strong interleafletinteraction, as all three factors apply here (inherent disorder of chains of DOPC, increasedintercalation and depletion of CHOL). On the other hand, the POPC/DSPC/CHOL systemshould show a more or less homogenous lateral distribution and thus, even though there isan overlap, should have a significantly weaker interleaflet interaction than is the case for theregions enriched in DOPC.
PL-water interaction
The effect of CHOL on the bilayer water interfacial structure has been widely discussed andcan be conflated to the so-called umbrella model, proposing an unfavorable interaction ofwater with the CHOL body and, accordingly, the PL head groups acting as an umbrella to15igure 8: Interaction of a PL with water as a function of the PLs chain order parameter.The inset shows the ratio of water interaction and the respective average number of watermolecules, thus constituting a PL-water pair energy.shield CHOL from water. In this manner, increased CHOL concentration should lead to anincrease in the interaction of PLs with water. Furthermore, as discussed in the introduction,CHOL influences the PL head group hydration. We first looked at the effect of order parameter and CHOL content on the hydration of thePL head group region (figure 7). A neighbor cutoff was determined from the position of thefirst minimum of the PL-OH2 RDFs (figure S3). Surprisingly, both for DPPC and DLiPCthe number of neighboring water molecules around the PL phosphor atom increases withorder, though the hydration of the head group region is larger for DLiPC. Cholesterol hasan opposite, albeit weak, effect on the two lipid types: While for DPPC the average numberof water neighbors decreases with increasing CHOL content, it increases for DLiPC. Thischange of the number of water molecules with CHOL concentration is stronger for DPPCand, consequently, the trend is visible in the water interaction energies as well (figure 8).To distinguish between the effects of the merely increased number of water molecules thatinteract with the PL and an optimization of a water-PL interaction configuration, we calcu-lated the energy gain per water molecule in the first neighbor shell around the PL phosphoratoms (inset of figure 8). Remarkably, the energy contribution per water molecule no longerdepends on the order of the PL nor on the CHOL concentration.Thus, the dependence of the water interaction on lipid chain order parameter and CHOL16igure 9: Sum of all interaction components E P L − P L , E P L − CHOL , E interleaflet , E water and E self as a function of PL chain order parameter and CHOL concentration. The insets showthe respective energy gain by changing the PL’s chain order parameter from a disordered(S=0.3) to a more ordered state (S=0.5).concentration is solely a consequence of the slightly varying degree of hydration. We, there-fore, found no evidence for a mechanistic effect of CHOL on the lipid water interaction asproposed by the umbrella model and agree with the literature in that CHOL does not affectthe PL head group region, measured by the lipid interaction profile. Chain entropy
Now we are in the position to estimate the overall enthalpic energy contribution for a ran-domly chosen PL by summing up all contributions, discussed so far. The result is shown infigure 9. We obtain two remarkable results. First, the results for DPPC and DLiPC hardlydiffer in the order parameter range between 0.3 and 0.5. This statement holds for the depen-dence on the order parameter as well as on the CHOL content. Note that individual energycontributions so far showed much larger differences between the saturated and the unsat-urated lipids. For example, the interleaflet interaction showed very different dependencieson the order parameter for both lipids, whereas, e.g., the PL-CHOL interaction displayeda much larger dependence on CHOL concentration. Thus, we may conclude that there is asignificant canceling effect.In figure 1 we showed that CHOL has an ordering effect on DPPC roughly twice as17igure 10: Estimation of the acyl chain entropy derived from the total sum of all enthalpicenergy contributions and the order parameter distributions in the simulations for DPPC andDLiPC at two CHOL concentrations (left) and the difference between between the respectiveestimate for DPPC and DLiPC in bilayer composition from 0% to 30% CHOL.strong as on DLiPC, with DPPC exhibiting overall higher order parameter values thanDLiPC. Indeed, the energy gain for a transition from a disordered to a (more) ordered state(S=0.3 to S=0.5) increases linearly with CHOL concentration. However, the energy gain forthe two PL types is very similar so that the impact of CHOL on PL order cannot solely beunderstood via its effect on the enthalpy gain.For a complete description of the system also entropic effects have to be taken intoaccount. An estimate Z(S) for the entropic contribution can be derived from the totalinteraction function H tot (S) and the order parameter distribution p(S) in the simulations viathe relation Z ( S ) ∝ p ( S ) · exp βH ( S ) where β is the inverse product of the molar gas constantR and the temperature T. Similar to the interaction enthalpy functions, the functions Z(S)were averaged over temperatures of 290 K to 330 K for DLiPC, 330 K to 350 K for DPPCand, for better comparability, were shifted to zero at S=0.35, which roughly lies in the orderparameter region of the pure PL bilayers in the disordered phase (DPPC S=0.35, DLiPCS=0.25) (figure 10, left).Naturally, one observes that high order parameters are strongly disfavored. When com-paring first the case without CHOL, the DLiPC entropy curve displays a somewhat strongerdependence on the order parameter. Of course, the difference would be even stronger foreven higher values of S due to the strong reduction or absence of chain configurations withvery high order parameters. 18igure 11: Average order parameter in a bilayer simulation at 330 K (dashed) as a functionof CHOL concentration in DPPC (brown) and DLiPC (blue) and (left) the recalculated av-erage order parameter at the respective CHOL concentrations from the interaction functions H tot ( S ) and Z ( S ) of the pure PL bilayer (solid) and (right) the recalculated average orderparameter when the combinations Z P L ( S ) with H P L ( S ) are exchanged between DPPC andDLiPC. The colour refers to the choice of the enthalpy function.Since Z(S) mainly reflects the degrees of freedom of the PL acyl chains, no significantdependence on the CHOL content is expected. To quantify the residual dependence on CHOLcontent, we have determined the differences ∆ RT ln Z ( S ) by comparing the entropy functionswith those at zero CHOL content (figure 10, right). In the case of DPPC the differencesare very small (∆ RT ln Z ( S ) changes less than ± . Z ( S )does not change upon adding CHOL; see figure 11, left. In the case of DPPC the agreementwith the actual average order parameter values is very good. Thus, as already mentioned justbefore, the weak dependence of entropy on the CHOL concentration is negligible. However,in the case of DLiPC the calculation leads to an overestimation of CHOL’s ordering effect.Thus, a prerequisite of the smaller dependence of the average order parameter on CHOLconcentration for DLiPC as compared to DPPC is partly embedded in the dependence ofthe entropy on the CHOL content.In a similar way one can check whether the difference of H tot ( S ) between DPPC and19igure 12: Contributions of the total interaction enthalpy gain for ordering the respectiveacyl chains from S=0.3 to S=0.5. The dashed line separates contributions that are readilyincluded in a lattice model (left), from the ones that typically are not included (right).DLiPC or the difference of Z ( S ) are more relevant. For this purpose, we combine theenthalpy function of one PL with the entropy function of the other PL and vice versa. Ifthe enthalpy profiles are similar, the resulting calculated average order parameters shouldbe mainly determined by the choice of Z ( S ) and vice versa. Interestingly, it turns out thatthe predictions for the mixed combinations lie between the simulated data and, on average,are quite similar. Thus, we have to conclude that the differences between DPPC and DLPCare embedded in the enthalpy and the entropy to approx. equal parts. Implications for bilayer models
The importance of nearest neighbor interactions to describe the lateral range of influence hasbeen discussed in various simplistic models of lipid bilayers, strongly supporting the notionthat lipids in a bilayer are only influenced by their nearest neighbors.
The question ariseswhether this influence or lack thereof can effectively be observed in the interaction functionsand how this observation deviates between the examined lipid types.In this work, all energetic contributions of ordering PL chains can generally be distin-guished between lateral, nearest-neighbor interactions, and the remaining interactions. Inlattice models of bilayers typically the latter energetic contributions are discarded. Theycould be included through an additional ”effective” entropic contribution if the energies do20ot depend on the CHOL concentration. To quantify the residual dependence on that con-centration we display the energetic contributions for ordering from S=0.3 to S=0.5 for thedifferent CHOL concentrations separately, distinguishing between the nearest-neighbor andnon-nearest-neighbor components (figure 12).It turns out that the dependence of all non-nearest-neighbor interactions on CHOL con-centration is weak, only the PL-PL non-nearest-neighbor interaction exhibits a dependenceon CHOL concentration. When comparing the extreme cases of 0% and 30% CHOL, thesevalues vary at most by about 2.5 kJ/mol as compared to the (interpolated) value at 15%CHOL concentration for both types of PL. A scenario, where the maximum error might occuris, e.g., the modeling of lipid rafts where the CHOL concentration may spatially vary betweena very low and a very high value. However, since the maximum error is even smaller thanRT, models based on nearest-neighbor interaction should be able to reproduce the propertiesof CHOL-containing membranes.The remaining challenge is to incorporate a chain entropy function that effectively takesinto account the dependence on CHOL content. Since the chain entropy function character-izes a very local property of a chain, it is likely that one may take into account the numberof neighboring CHOL molecules to specify the entropy. Work along this line is in progress.21 onclusion
In this work, we have derived the different contributions to the total interaction energyof cholesterol ordering of DPPC or DLiPC to understand the differing affinity cholesterolexhibits, as well as the underlying mechanism of cholesterol’s unique ordering capability.Having studied the prototype lipids DPPC and DLiPC as proxies for saturated and unsat-urated lipids, we believe that our results provide important new insight for the interplay ofthe different enthalpy contributions of membranes containing cholesterol and phospholipids.A key observation is the maximum in interaction strength of the PL-CHOL interaction as afunction of the order parameter which is a cornerstone for understanding the simultaneouseffect of cholesterol to increase the order in the disordered phase and to fluidify the gel state.Furthermore, we could, e.g., rationalize why inherently disordered lipids display a strongerinteraction between the bilayer leaflets or show that cholesterol only weakly influences thebilayer-water interaction, independent of the lipid type. This is relevant for the discussionof the umbrella model.The results of this present work also serve as a valuable basis for the construction of alattice model, taking into account the diverse effects of cholesterol. In light of this basis, weconclude that it is possible to formulate a bilayer lattice model based on enthalpic informationnot extending the nearest neighbors. Due to the lack of significant dependence on cholesterolconcentration, the impact of the PL-interaction with water and the opposite leaflet can bedirectly taken into account by the use of an effective entropy function, as used, e.g., in. This model may help to better rationalize the impact of local interaction properties on themesoscopic phase behavior of lipid mixtures.22 cknowledgement
The authors thank Prof. Roland Wedlich-S¨oldner for helpful discussions and the DeutscheForschungsgemeinschaft (DFG) for funding via SFB 1348.23 upporting Information Available
Table S1: Parameters of the MD simulations.
System Temperatures (K) Lengths (ns) > > >
500 360 40DPPC/CHOL20% 330-350 >
800 280 70DPPC/CHOL30% 330-350 >
500 252 108DLiPC/CHOL10% 290-330 >
900 306 34DLiPC/CHOL20% 290-330 >
600 256 64DLiPC/CHOL30% 290-330 >
500 238 102Figure S1: Radial distribution functions for lateral distances between P atoms. The RDFswere calculated individually for each leaflet and averaged.1igure S2: Radial distribution functions for lateral distances between P and O atoms. TheRDFs were calculated individually for each leaflet and averaged.Figure S3: Radial distribution functions for distances between P and O atoms of surroundingwater. 2igure S4: Interleaflet interaction as a function of both, the lipids overlap and its chain orderparameter in respective bilayer DPPC/CHOL and DLiPC/CHOL mixtures from 0% to 30%CHOL.
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