Arrangements of β-sheet Conformations
PG-1 dimers in a β-sheet motif were used in the all-atom simulations. In our simulations, PG-1 dimers in two different β-sheet arrangements, antiparallel (turn-next-to-tail) and parallel (turn-next-to-turn) β-sheets in an NCCN packing mode, were considered [18]. Fig. 1 shows topological diagrams for the PG-1 dimers in the (a) antiparallel and (b) parallel β-sheet arrangements. In the NCCN packing mode, the intermolecular interface for both dimers is located in-between the C-terminal strands of the planar β-sheet. Since the experimental crystal structure of the PG-1 dimer is currently unavailable, the simulation used the β-sheets of the PG-1 dimer that were initially assembled from the β-hairpins with two different conformational origins: (i) the β-hairpin resolved by NMR spectroscopy [3] (A1 & P1 β-sheets; A stands for antiparallel, P for parallel), and (ii) the pre-relaxed β-hairpin in the lipid bilayer environment [22] (A2 & P2 β-sheets). Although the topological diagram suggests that there are six possible intramolecular backbone hydrogen bonds (H-bond) between the β-strands within each β-hairpin monomer and also six possible intermolecular backbone H-bonds between the β-hairpin monomers [15, 18], in our simulations the initially assembled PG-1 dimers have a smaller number of the backbone H-bonds than in the topology diagram. For the A1 and P1 β-sheets, five intramolecular and four intermolecular backbone H-bonds were initially observed. However, for the A2 and P2 β-sheets, five intramolecular and two intermolecular backbone H-bonds were initially counted. The smaller number of the intermolecular backbone H-bonds in the A2 and P2 β-sheets are the outcome of the cross β-stranded structure of the pre-relaxed β-hairpin in the lipid bilayer [22], preventing maximal contracts of the intermolecular backbone H-bonds between the C-terminal strands from each monomer. Although, in our simulations the A2 and P2 β-sheets have fewer intermolecular backbone H-bonds than the A1 and P1 β-sheets, the dimer interface for the A2 and P2 β-sheets is held tightly by two intermolecular backbone H-bonds between two cysteine residues. These residues have lower fluctuations due to the disulfide bond. The different numbers of intermolecular backbone H-bonds observed for the different β-sheets reflect the fact that the β-sheet dimer can be at different locations, e.g. dimer formation in bulk or on/in the membrane.
Dimeric β-sheet conformations at different environments
Figure 2(a) illustrates the time-dependent fractions of intermolecular (red lines) and intramolecular (light and dark blue lines for each β-hairpin monomer) backbone hydrogen bonds (H-bonds), QH-bond, for the antiparallel (A1 & A2) and parallel (P1 & P2) β-sheets of PG-1 dimer at the amphipathic interface of the lipid bilayer. We calculated the fraction using QH-bond = NH-bond/, where NH-bond is the number of the intermolecular and intramolecular backbone H-bonds that are monitored during the simulations, and is the maximum possible number of the backbone H-bonds as described in the topological diagram of Fig. 1. It can be seen from the figure that the dimer interface in the antiparallel β-sheets (A1 & A2) is more stable than that in the parallel β-sheets (P1 & P2), since for the antiparallel β-sheets, the fluctuations of the red lines that represent the formation of the intermolecular backbone H-bonds are less than those corresponding to the parallel β-sheets. However, the large fluctuations in the formation of the intermolecular backbone H-bonds observed in the parallel β-sheets are closely related to the β-sheet activity on the lipid bilayer. All the β-sheets appear stable with the backbone H-bonds fluctuating near initial values.
In the bulk water environment, the β-sheets structures of PG-1 dimer are less stable, since in Fig. 2(b) large fluctuations in the QH-bond lines are observed. To compare the dimeric behavior between the water and on the lipid, the β-sheets used in the water simulation are the same (A1 and P1) as those used in the lipid simulation. Although the PG-1 dimers in water exhibit a partially ordered or slightly collapsed β-sheet conformation compared to the β-sheet conformations on the lipid bilayer, two intermolecular backbone H-bonds between two cysteine residues at the C-terminal strands from each monomer retain strongly the dimer interface. The formation of PG-1 dimer in water implies that the PG-1 dimer can exist in many different environments and acts as a seed in the formation of ordered aggregates in a proper environment.
The detailed secondary structures for the β-sheet conformations are investigated. Fig. 3 shows the contour maps, representing the distributions of backbone dihedral angles of φ and ψ for the residues in the β-strands. In Fig. 3(a) the contour maps for the β-sheets on the lipid bilayer suggest that the PG-1 dimers preserve the β-sheet structure during the simulation, since the contour lines encompass a high population at the region that represents the β-sheet characteristics. In Fig. 3(b) the contour maps for the β-sheets in water suggest that the PG-1 dimers also preserve the β-sheet structure during the simulation. But the wide distributions of φ and ψ angles suggest that the β-sheets in water are flexible, leading to a slightly collapsed or partially folded β-sheet conformation.
The orientation of the PG-1 β-sheet on the lipid bilayer is monitored by calculating the angle between the backbone carbonyl bond, C=O, and the normal to the bilayer surface. Only the backbone carbonyl bonds located in residues that form the β-strands (residues 4 to 8 and 13 to 17 of each β-hairpin) are considered in the calculation. The probability distribution for the angle of the C=O vector relative to the membrane normal is shown in Fig. 4(a). At the starting point, the PG-1 β-sheet is in contact with the lipid bilayer, with the β-sheet plane parallel to the bilayer surface. For a perfect planar β-sheet, the distribution curve might be located at a right angle, since all C=O vectors should lie on the membrane surface. However, the peaks in the distribution curve located at many places indicate that the PG-1 β-sheets are not perfectly planar. That is, the β-sheet plane is slightly bent or lies with an oblique angle to the bilayer surface.
For an α-helical peptide, the peptide orientation in the lipid bilayer can be measured experimentally by polarized ATR-FTIR spectroscopy [23, 24], and computationally by a calculation of the peptide order parameter [25, 26]. We calculate the order parameter for the PG-1 β-sheets on the lipid bilayer, with the same method as that used in the recent simulations [25, 26]. The peptide order parameter can be defined by
(1)
where θ
ij
is the angle between two vectors of the backbone carbonyl bonds, C=O, in the i and j residues, and N is the total number of the vector pairs. In the calculation, only the C=O bonds located in β-strands (residues 4 to 8 and 13 to 17 of each β-hairpin) are considered. Fig. 4(b) shows the probability distribution of the peptide order parameter, SC=O, over the 20 ns trajectories. For the A1 and P1 β-sheets, where the initial β-hairpin monomer structure is from NMR [3], the initial values of SC=O are 0.75 and 0.77, respectively. These values are much smaller for the A2 and P2 β-sheets, where the initial β-hairpin monomer structure is from our previous simulation [22], which are 0.27 and 0.35, respectively. However, these initial values of the peptide order parameter are not preserved for the β-sheets with the same monomer origin during the simulations. The distributions of SC=O reveal that for the antiparallel β-sheets (A1 & A2), the distribution curves are located around SC=O = 0.3, while the curves are found around SC=O = 0.2 for the parallel β-sheets (P1 & P2). Both parallel β-sheets have smaller values of the peptide order parameter, indicating that the values of the peptide order parameter strongly depend on the β-sheet topology.
Interactions of PG-1 β-sheets with Lipids
The interaction energy between the PG-1 β-sheets and lipids is calculated in order to understand the dominant forces that stabilize the β-sheet structure. Fig. 5 shows the averaged interaction energies of the PG-1 β-sheets with the lipid (light gray bars) for the different β-sheet conformations. The figure also presents the averaged interaction energies between the Arg residues and lipid (dark gray bars). The interaction energy is calculated every 10 ps and averaged over the 20 ns simulations for each monomer separately. For the antiparallel β-sheets (A1 & A2), the strength of the interaction energy of each monomer with the lipid is similar. However, for the parallel β-sheets (P1 & P2), at least one monomer interacts with the lipid more strongly than the other. The strong interaction reflects the strong electrostatic interaction of the Arg residues with the lipid headgroups. For the P1 β-sheet, the terminal Arg residues of the monomer whose apolar surface faces the bilayer surface closely contact the lipid, while for the P2 β-sheet the loop Arg residues of the monomer whose apolar surface faces the bulk region interact strongly with lipid. These strong Arg-lipid interactions observed in the parallel PG-1 β-sheet are closely related to the bending or tilting of the β-sheet, ultimately causing the membrane thinning and disruption.
Fig. 6 shows the averaged lipid accessible surface area for the PG-1 β-sheets in different arrangements (light gray bars). The lipid accessible surface area is calculated every 10 ps and averaged over the 20 ns simulations for each monomer separately. The figure also presents the averaged lipid accessible surface areas for the Arg residues (dark gray bars). As expected, the lipid accessible surface area is strongly correlated with the interaction energy of the PG-1 β-sheets as seen in Fig. 5. Larger lipid accessible surface area yields larger interaction energy. This is also true for the Arg residues, especially for the parallel PG-1 β-sheets, suggesting that the Arg side chains in parallel β-sheets are indeed located at the deep amphipathic interface, perturbing the polar lipid heads in the lipid bilayer.
Membrane Disruption Effects by PG-1 β-sheets
In our previous study of the PG-1 monomer on the lipid bilayers [22], we have shown that the PG-1 β-hairpin indeed induced the thinning effect in the lipid bilayer containing anionic lipids, while no thinning effect was observed for the pure lipid bilayer composed of POPC. To observe a similar effect induced by the PG-1 dimer, the degree of flatness or roughness of the bilayer surface plane is monitored during the simulations. We introduce the plane order parameter of the bilayer surface, SPOP, which calculates the angle between the positional vector connecting two adjacent phosphate atoms and the plane of the bilayer surface,
(2)
where rij is the distance between two phosphate atoms, and and are the height of the phosphate atoms along the bilayer normal at the i th and j th residue, respectively. The notation <i,j> means that the sum is restricted to adjacent pairs of phosphate atoms. The plane order parameter SPOP can measure the flatness or roughness of the bilayer surface, indicating that for SPOP < 1 the bilayer surface is a perfect smooth plane, while for SPOP < 1 the bilayer surface is bent or contains many troughs. Fig. 7 shows the averaged plane order parameter, <SPOP >, at the top leaflet (solid bars) and at the bottom leaflet (gray bars) of the lipid bilayer during the simulations. The PG-1 β-sheet is located at the top leaflet of the lipid bilayer. As expected, the bilayer surface at the top leaflet is rougher than the bottom leaflet of the lipid bilayer, since the top leaflet contains the β-sheet. Note however that the bilayer surface at the top leaflet containing the parallel β-sheets (P1 & P2) is rougher than that at the same leaflet containing the antiparallel β-sheets (A1 & A2). This suggests that the parallel β-sheets are very active and more strongly interact with the lipid bilayer, with the activity closely related to the bilayer disruption.
The disruption of the lipid bilayer reflects disordering of lipid molecules around the PG-1 β-sheets. The average positions of lipid groups may illustrate how lipids are distributed in the bilayer in response to the dimer invasion. Fig. 8 shows the position probability distribution functions (P) for five different component groups of POPC, water, and salts as a function of the distance from the POPC lipid bilayer center. The POPC headgroup is divided into four subunits, choline (PChol, black lines), phosphate (PPO4, red lines), glycerol (PGlyc, green lines), and carbonyl (PCarb, yellow lines). The tail group involves two fatty acids with terminal methyl (PCH3, blue lines). The PG-1 β-sheet is located at the top leaflet of the lipid bilayer (positive z area), while the bottom leaflet of the lipid bilayer (negative z area) contains lipids only. For the antiparallel β-sheets (A1 & A2), the symmetric distributions of the lipid headgroups at both sides of the bilayer indicate that there are no disturbances in the lipid arrangement induced by the β-sheets. However, for the parallel β-sheets (P1 & P2), the asymmetric distributions of the lipid headgroups indicate that there are great disturbances in the lipid arrangement, especially at the top leaflet of the lipid bilayer. This is consistent with the result presented in Fig. 7 that the bilayer surface containing the parallel β-sheet is very rough, resulting from the disordered lipid headgroups. This leads to the bilayer disruption. In the distributions of salts, the probability for finding chloride ions is very high near the bilayer surface at the top leaflet, since the PG-1 β-sheet contains many positive charges.
To investigate the average structure in the interior of the bilayer, the deuterium order parameter, SCD, was calculated using
(3)
where θ is the angle between the C-H bond vector and the membrane normal, and the angular brackets indicate averaging over time and over lipids. Fig. 9 shows the order parameters for the oleoyl (left column) and palmitoyl (right) chains for the lipid bilayers composed of POPC for the antiparallel β-sheets (A1 (solid circles) & A2 (open circles)) and the parallel β-sheets (P1 (solid triangles) & P2 (open triangles)). Lipids at the top leaflet (peptide-containing, upper panel) and the bottom leaflet (lower) of the lipid bilayer are considered separately. The bars represent the standard deviation errors. At the top leaflet, the order parameters for the lipids with the antiparallel β-sheets are slightly higher than those for the lipids with the parallel β-sheets. At the bottom leaflet, however, the order parameters for the lipids are similar. Lower order parameters for the lipids containing the parallel β-sheets indicate that the lipids have significantly disordered tails, causing the disruption of the lipid bilayer.