Figure 1.
Overview of the simulation and analysis procedure.
Starting from a peptide monomer, we constructed candidate β-sheet bilayer patterns. Molecular dynamics (MD) simulation of both the monomer and bilayers were performed first in implicit solvent to relax the initial structures then in explicit water for accurate trajectory generation. The first 1.1 ns of the explicit water simulation was the heating and equilibration phase. The remaining production run at 300 K lasting 2 to 6 ns was used to calculate ΔGbind via a generalized Born (GB) solvation model [52] and normal mode analysis (NMA) [53]. The long preparatory runs in the implicit solvent and the 1-ns equilibration in explicit water drove most bilayer patterns into fairly stable states, so that the profile of ΔGbind did not vary greatly throughout the production run, which was more prominent for native-like structures (cf., Figs. S1 and S4–S8).
Table 1.
Summary of simulated configurations.
Figure 2.
Ten possible β-sheet bilayer patterns of parallel β-sheets.
(A) GNNQQNY and (B) NNQQ. The filament axis is vertical, and top/bottom layers are represented by dark/light arrows, where each arrow represents a single peptide. Top left in (A): A side view of a single GNNQQNY peptide with even-/odd-numbered side chains in yellow/red, which defines Front/Back faces of the parallel β-sheet. Bottom right in (A): relaxation of BBA1 after MD (axial view; cf. Fig. 5).
Figure 3.
Peptide registry in a single β-sheet considered in this study.
Parallel in-register (Preg) pattern maximizes the number of backbone hydrogen bonds (green lines) in (A) and (B). There are comparable numbers of backbone hydrogen bonds in the anti-parallel β-sheets shown in (C) and (D). Color codes are the same as in Fig. 2.
Figure 4.
Nine possible configurations of anti-parallel β-sheets.
Depending on the number of amino acids, there were distinct sets; (A) VEALYL and STVIIE, and (B) KLVFFAE. Arrows and color codes are the same as in Fig. 2.
Figure 5.
Conformations of candidate bilayer patterns of GNNQQNY after MD (axial view).
Snapshots at 2 ns of the production run was used to draw each figure. Color scheme is the same as in Fig. 2.
Figure 6.
Integrity of β-sheet bilayer patterns during the production run.
(A) Distance between β-sheets in a bilayer. (B) RMSD of Cα atoms from the first snapshot. Within the simulation time, no filament except for FBA2 dissociated. The distance between β-sheets was defined by the distance between the least-squares-fit plane spanned by Cα atoms in one layer and the center of mass of Cα atoms in the other layer.
Figure 7.
Free energy profiles of parallel β-sheets (GNNQQNY and NNQQ).
(A) Open/solid circle: calculation based on MD with/without PBC in the filament axis. The exposed edge in the case without PBC elevates the overall energy level. (B) In the case when the inter-peptide distance d was adjusted, we used the CPT dynamics to maintain a constant pressure while the axial length of the simulation box fluctuated. Error bars in all graphs denote standard deviations. Values of individual energy terms are in Tables 2 and S2.
Figure 8.
Comparison between PDB structures (transparent tube) and native-like candidates (wireframe).
Snapshots at 2 ns of the production run were used to compare with x-ray crystallographic coordinates. (A) GNNQQNY, (B) VEALYL, and (C) NNQQ.
Table 2.
Decomposition of of GNNQQNY bilayers.
Figure 9.
Free energy profile of anti-parallel β-sheets.
(A) VEALYL, (B) KLVFFAE, and (C) STVIIE. Values of individual energy terms are in Tables S3–S5.
Figure 10.
Most stable anti-parallel β-sheet bilayer configurations of Aβ(16−22) (KLVFFAE) and STVIIE.
Figure 11.
Free energy change accompanying the native bilayer formation.
The y-axis is in units of kcal/mol. (A) BBA1 of GNNQQNY, (B) FFA1 (d = 4.92Å) of NNQQ, (C) AinvP2 of VEALYL, (D) AregFF (anti-parallel, black), Ainv2P2 (anti-parallel, blue), and FFA1 (parallel, red) of KLVFFAE at pH 7, (E) Areg2FF of STVIIE, and (F) Ainv1A of KLVFFAE at pH 2. Circle: ΔEvdW, triangle: ΔGhp, square: ΔEintra, and inverse-triangle: ΔEelec + ΔGscreen.
Figure 12.
Per-residue contribution to ΔGNB.
(A) BBA1 of GNNQQNY (open square and open inverted triangle) and GNNAQNY (solid square and solid inverted triangle), where data for black square and red inverted triangle are based on the monomer energy calculated from the standard procedure in Fig. 1, and by the REMD simulation, respectively. Blue solid circle: the average B-factor of each residue in the 1YJP structure. Compared to Q4, A4 has higher ΔGNB relative to other residues. The inset shows the cross section of the Q4A filament after the simulation, indicating a well-formed steric zipper interface. (B) FBA1 (d = 4.85Å) of NNQQ. Square (circle) represents each residue in the upper (lower) layer of β-sheet and N1 is marked in the picture to distinguish the direction of peptides. (C) AregFF of KLVFFAE.