We have used the time variation of the area per lipid as an indicator of the equilibration of the bilayer and its average value to assess the adequacy of the simulation methodology (Anézo et al. 2003; Kandt et al. 2007). The time traces of the area per molecule for the system POPC/POPG/Chol/Arb corresponding to the z+ and z− leaflets are shown in Fig. S1A and S1C, respectively. As expected, no significant changes were found in the general bilayer properties in this diluted system, i.e., system having 128 lipid molecules and only 1 molecule of Arb. The data show that phospholipids and cholesterol were equilibrated early on the course of the simulation, either at the z+ or at the z− bilayer leaflets, indicating that the system reached a steady state after 1500 ps of simulation. The time traces of the molecular area for the system POPC/POPG/Chol/Arp and corresponding to the z+ and z− leaflets are shown in Fig. S1B and S1D, respectively. As commented above, no significant changes were found in the general properties in this diluted system, and the phospholipid and cholesterol molecules were equilibrated at both leaflets early on the course of the simulation time. In this case, the system reached a steady state after 2000 ps of simulation. At the end of both simulations, one system containing Arb and the other containing Arp, the mean area of POPC, POPG, and Chol were 58–60, 59–62, and 27–33 A2, respectively, in agreement with previously reported data (Zhuang et al. 2014).
In contrast, the molecular area of either Arb or Arp were different from those of the phospholipids and cholesterol and at the same time, and they differed from each other (Fig. S1A and S1B). Furthermore, the molecular area of both Arb and Arp presented a great variation along the whole simulation time in each membrane model system. This variation in molecular area should be due to differences in membrane location, molecule orientation, or both. Apart from that, comparing the molecular areas of Arb (Fig. S1A) and Arp (Fig. S1B), it is possible to see that Arb variation was greater than the Arp one. Whereas the molecular area of Arb along the whole simulation time oscillated between 30 and 105 A2, i.e., a difference of about 75 A2, the molecular area of Arp oscillated between 60 and 110 A2, i.e., a difference of about 50 A2. The area histograms for Arb and Arp for the last 2 ps of the simulation are shown in Fig. S1E and S1F, respectively. The mean area of Arb was found to be about 65–70 A2, whereas the mean area of Arp was about 80 A2. The area dispersion was lower for Arb, about 30 A2, than for Arp, about 45 A2.
The time variation of the center-of-mass for both Arb and Arp molecules compared with the z+ phosphate atoms center-of-mass are shown in Fig. 2a, b, respectively. Arb equilibrated to a position similar to that found at the end of the simulation in about 40 ns, although there was a noticeable dispersion in the center-of-mass variation of the molecule along the whole simulation time. It had a minimum of about 4 Å and a maximum of about 17 Å, i.e., a variation of about 12 Å (Fig. 2a). The time needed by Arp to reach a quasi-equilibrium position was significantly lower than Arb, since it was reached at about 2 ns (Fig. 2b). The center-of-mass dispersion of Arb was also significantly lower than Arb, since along the whole simulation time it varied from about 8–17 Å. The histograms corresponding to the Arb and Arp center-of-mass for the last 2 ps of the simulation are shown in Fig. 2c, d, respectively. There was a small difference in the final location of the center-of-mass of both molecules, since that pertaining to Arb was located at about 10–11 Å from the center of the bilayer, whereas that corresponding to Arp was located at about 12.5–13.5 Å. The center-of-mass dispersion was larger for Arb, about 6 Å, than for Arp, about 3.5 Å. In a similarly way to the behavior of the area versus time trend commented above, membrane thickness, measured as the average distance between the center-of-mass of the phosphate atoms of opposite leaflets, was held relatively constant after 12 and 20 ns for the systems POPC/POPG/Chol/Arb and POPC/POPG/Chol/Arp, respectively (Fig. 2e, f). These data would indicate again a rapid equilibration of both systems.
The orientation of both Arb and Arp in the membrane was studied considering the angle formed by the vector joining ring carbons 9 and 16 of Arb/Arp with the membrane z-axis (Fig. 3, scheme). There was a great deviation in angle for Arb along the simulation time, since the highest observed angle was about 175° and the lowest one was about 2° (Fig. 3a). This is in contrast with the angle variation observed for Arp, where the angle values ranged from a minimum value of about 39° and a maximum of 135° (Fig. 3b). At the end of the simulation, the dispersion was a bit lower for Arb than for Arp (Fig. 3c). For the last 2 ns, Arb presented an average angle of about 155–160° ± 20°, whereas Arp presented an average angle of about 80° ± 20° (Fig. 3c), indicating a significant difference in molecular orientation between Arb and Arp in the membrane (see below).
We have analyzed a different but related parameter concerning the molecular orientation of both Arb and Arp in the membrane, i.e., the difference between the z-axis values of carbon 16 and nitrogen 27 (Fig. 3, scheme). If the difference is 0 Å, the molecule lies nearly parallel to the membrane, if the difference approximates to 12 Å, the molecule lies nearly perpendicular to the membrane. As observed in Fig. 3d, there was a great variation in this parameter along the whole range of the simulation for Arb, ranging from 0 Å (lowest value, parallel to the membrane) to near 11.9 Å (largest value, perpendicular to the membrane). For the last 2 ns, Arb presented an average difference distance of about 10.5–11 ± 1 Å (Fig. 3f). In this way and for the last 2 ns of simulation, Arb was nearly perpendicular to the plane of the membrane. For Arp, the variation for this parameter (Fig. 3e) was lower along the whole range of the simulation than that observed for Arb, since varied from 0 Å (parallel) to near 9.7 Å (nearly perpendicular). However, Arp presented an average difference distance for the last 2 ns of about 3.5–4 ± 3.5 Å (Fig. 3f), indicating that Arp was laid in a near parallel orientation to the membrane plane for the last 2 ns. It should be taken into account that Arb/Arp have two rings and a relatively rigid structure. Furthermore, the molecule does not completely span the leaflet of the bilayer.
Another parameter we have studied which can give us a useful information about the global structure of both Arb/Arp is the distance between the farthest atoms of the molecule, i.e., nitrogen 27 and carbon 16 (Fig. 3, scheme). If the difference tends to be 0 Å, there is a twist in the molecule so that both ends tend to be next to each other; on the other way, if the difference tends to be about 12 Å, the molecule is in a complete extended configuration. As observed in Fig. 3g, the average distance between atoms 16 and 27 of Arb varied from about 9 Å to about 12 Å along the whole simulation time, whereas for Arp (Fig. 3h) the average distance between these atoms varied from about 8 Å to about 11 Å. For the last 2 ns of the simulation, the two ends of Arb presented a distance of about 11 ± 1 Å, whereas it was about 9.75 ± 1 Å for Arp (Fig. 3i). These data show us that Arb presented a nearly extended conformation, whereas Arp presented a small kink, which slightly approached the two ends of the molecule.
Mass density profiles for the model systems composed of POPC/POPG/Chol/Arb and POPC/POPG/Chol/Arp are shown in Fig. 4a, b, respectively. As seen in Fig. 4a, Arb is located at a lower depth than the phosphate groups of both phospholipids, POPC and POPG, reaching as low as the center of the bilayer, where the cholesterol tail is located. However, Arp, being located at a lower depth than the phosphate groups of both phospholipids, has a membrane depth similar to that of the OH group of cholesterol (Fig. 4b). The mass density profile of the phospholipid phosphate atoms in both systems was rather symmetric. In the case of the POPC/POPG/Chol/Arb system, the half bandwidths were about 5.7 and 5.9 Å for the z+ and z− leaflets, respectively. For the POPC/POPG/Chol/Arp system, the half bandwidths were of about 5.8 and 5.2 Å for the z+ and z− leaflets, respectively. However, there were significant differences in the mass density profile of the phosphate atoms in both systems for each type of phospholipid, i.e., POPC and POPG. For the POPC/POPG/Chol/Arb system (Fig. 4c), the maximum of the POPC phosphate atoms mass density was found at 21.47 and 20.98 Å for the z+ and z− leaflets, respectively, whereas for the POPG phosphate atoms they were 20.93 and 20.48 Å, respectively. The difference between the POPC and POPG maxima were therefore 0.54 and 0.5 Å for the z+ and z− leaflets, respectively. For the POPC/POPG/Chol/Arp system (Fig. 4d), the maximum of the POPC phosphate atoms mass density was found at 21.38 and 21.17 Å for the z+ and z− leaflets, respectively, whereas for the POPG phosphate atoms they were 20.05 and 20.52 Å, respectively. The difference between the POPC and POPG maxima were therefore 1.33 and 0.65 Å for the z+ and z− leaflets, respectively. This data would imply the existence of differences in the location of the phosphate atoms depending on phospholipid type. Furthermore, the location and/or orientation of Arp in the bilayer induced a larger distortion on the phosphate atoms of the phospholipids than Arb. This can be easily observed on the of the Arb/Arp mass density profile expansion shown on Fig. 4e. The Arb mass density profile is a broad one, with a half bandwidth of about 9.35 Å, whereas the mass density profile half bandwidth of Arp is about 6.4 Å. This data show us that the orientation of Arp in the membrane is nearly parallel to the membrane z-axis, whereas Arp tends to be perpendicular to it. This difference in molecule location and orientation in the membrane is the cause of the different effects commented above.
We have also studied the effect of the presence of both Arb and Arp molecules on the hydrocarbon chain order for the phospholipid acyl chains (Figure S2). With that aim, we have obtained the deuterium order parameter, –S
CD, for the saturated and unsaturated hydrocarbon acyl chains of both POPC and POPG phospholipids in the POPC/POPG/Chol/Arb and POPC/POPG/Chol/Arp systems. When there is full order along the normal bilayer, –S
CD has a value of 0.5, but when there is full order along the bilayer plane, –S
CD has a value of −0.25 (Tieleman et al. 1997). An isotropic orientation is given by a –S
CD value of 0.
The average –S
CD values of the sn-1 and sn-2 acyl chains of POPC for the POPC/POPG/Chol/Arb system are relatively similar in both leaflets, z+ and z− (Fig. S2A and S2B, respectively), in agreement with the profiles observed earlier for experimental and simulated data (Bockmann et al. 2003; Klauda et al. 2010; Tsai et al. 2015). The same can be said for the average –S
CD values of the sn-1 of POPG in the same system (Fig. S2E). However, small but significant differences could be observed for the –S
CD values of the sn-2 of POPG when comparing leaflets z+ and z− (Fig. S2F), indicating that Arb modifies the order parameter of the hydrocarbon chains in the leaflet it resides. Since there is only one molecule of Arb per system, we have also calculated the –S
CD values of the hydrocarbon acyl chains of POPC and POPG molecules that are within 7 Å of the molecule of Arb. The presence of Arb gives place to minor differences in the –S
CD values, particularly on carbons 5–10 of the sn-1 chain of POPC (Fig. S2A), 10–14 of the sn-1 chain of POPG (Fig. S2E), and 12–16 of the sn-2 chain of POPG (Fig. S2F).
Similarly to what has been said for the –S
CD values of POPC in the POPC/POPG/Chol/Arb system, the average –S
CD values of the sn-1 and sn-2 acyl chains of POPC in the POPC/POPG/Chol/Arp system were relatively similar in both leaflets, z+ and z− (Fig. S2C and S2D, respectively). The –S
CD values of the sn-1 and sn-2 acyl chains of POPC molecules that are within 7 Å of the molecule of Arb are similar to the global –S
CD values (Fig. S2C and S2D). There were no significant differences between the –S
CD values of POPG in the POPC/POPG/Chol/Arp system of both leaflets z+ and z−, either in the sn-1 chain or in the sn-2 one (Fig. S2G and S2H). However, differences in the –S
CD values of POPG within 7 Å of the molecule of Arp could be observed, more apparent on the sn-1 chain than on the sn-2 one. As observed in Fig. S2G, carbons 3–13 of the sn-1 chain have greatly reduced –S
CD values when compared to the global –S
CD values, indicating the specific interaction of Arp with the sn-1 chain of POPG. Although some differences were observed for the sn-2 chain of POPG, these were not as significant as those observed for the sn-1 chain (compare Fig. 3g, h).