Letter pubs.acs.org/JPCL
All-Atom Molecular Dynamics Simulations of Peptide Amphiphile Assemblies That Spontaneously Form Twisted and Helical Ribbon Structures Cheng-Tsung Lai,† Nathaniel L. Rosi,‡ and George C. Schatz*,† †
Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
‡
S Supporting Information *
ABSTRACT: Self-assembly of peptide amphiphiles (PAs) has been an active research area as the assemblies can be programmed into variously shaped nanostructures. Although cylindrical micelles are common structures, gold-binding peptide conjugates can selfassemble into chiral nanofibers with single or double helices. When gold nanoparticles bind to the helices, the resulting chiral nanoparticle assemblies have a collective plasmonic circular dichroism signal that can serve as nanoscale circular polarizers or chiroptical sensors. A better atomic-level understanding of the factors which lead to helical PA assemblies is therefore of significant importance. In this study we show that all-atom molecular dynamics simulations can describe the spontaneous structural transformation from a planar assembly of PAs to a twisted assembly or to a helical ribbon. The twist angle and the helical diameter calculated from the simulations closely match the experimental results, with the oxidation of a single Met residue in each PA leading to a change from bilayer to monolayer assemblies with significantly different ribbon properties. A secondary structure analysis shows how a combination of β-sheet formation near the hydrophobic core of the micelle and PPII structures from proline-rich C-terminus regions favors helix formation. The simulations presented here demonstrate the capability of predicting self-assembly in chiral structures, protocols that can easily be applied to the assembly of other amphiphilic molecules. amyloid β and islet amyloid polypeptide and are linked to neurodegenerative diseases.11 Amyloid fibrils commonly possess a left-handed twist along their main axis, and the twist is attributed to the chirality of peptides contained in the fibril; however, the details whereby peptide chirality leads to twisting are not well-understood. With the idea that high βsheet propensity promotes fibril formation and then chirality of the peptide controls the twist, Rosi and colleagues designed a gold-binding peptide conjugate with the sequence of AYSSGAPPMPPF connected to a C12 aliphatic tail (denoted in this paper as C12-PEPAu).12 Studies demonstrated that the C12PEPAu conjugates self-assemble to left- and right-handed chiral gold nanoparticle (AuNP) double helices using L- and D-amino acids, respectively.12,13 Because chiral AuNP assemblies have a collective plasmonic circular dichroism signal and have the potential to serve as nanoscale circular polarizers or chiroptical sensors, a better understanding of how to control the metrics of the assembled structure is crucial. Twelve different peptide conjugates were therefore further studied, but only a few of the peptide conjugates led to similar twist structures.14 Among these peptide conjugates, the divalent peptide conjugates C18-
M
olecular self-assembly is a promising method for the construction of functional nanostructures. Self-assembly of amphiphilic molecules has become an active research area as these assemblies can be programmed into different structures, such as ribbons, helices, and nanotubes.1−4 Mimicking the natural self-assembly of biomaterials (i.e., amphiphilic lipids and peptides) has been of great interest in the past decade because these types of materials are highly bioprogrammable and are often biocompatible. Studies have successfully demonstrated the use of peptide amphiphile (PA) nanofibers in promoting blood vessel growth, wound healing, and many other applications.5,6 The interconversion between different nanostructures upon external stimulus also demonstrates the potential application of PA assemblies in drug delivery and as artificial muscles.7 Although molecular self-assembly is a promising method for the construction of nanostructures, precise control of nanoparticle superstructure remains challenging. The self-assembled nanostructures arise from the interplay of many different driving forces, including hydrogen bonds, π−π stacking, and hydrophobic and electrostatic interactions, from both solute and solvent. This complexity of interactions makes the a priori prediction of assembly morphology difficult. On the basis of many PA self-assembly studies, β-sheet formation is found to play a pivotal role in determining nanofiber structure.3,8−10 High β-sheet propensity is found in protein aggregates such as © XXXX American Chemical Society
Received: March 28, 2017 Accepted: April 28, 2017 Published: April 28, 2017 2170
DOI: 10.1021/acs.jpclett.7b00745 J. Phys. Chem. Lett. 2017, 8, 2170−2174
Letter
The Journal of Physical Chemistry Letters (PEPAu)2 exhibit twisted nanofibers with a pitch of ∼184 nm for ∼9 nm width and thickness. Also, a recent study shows that the oxidation of the Met residue on this C18-(PEPAuM‑ox)2 conjugate leads to a single helix twist instead of double helices,15 thus revealing extreme sensitivity to residue composition. Understanding the mechanism whereby PAs assemble into helical structures is of importance in advancing research in this field. However, because the assembled structures are disordered, it is difficult to determine information at the atomic level from experiments. An alternative is to use computational modeling to provide atomic detail structure and energetic information for interpreting the experimental data. To date, most theoretical or computational studies of peptide assembly have considered cylindrical or globular structures.16−19 Only a few studies have tried to model chiral structural properties, and these have used coarse-grained molecular dynamics (MD) or Monte Carlo simulations that have a limited ability to describe chirality.20−22 Motivated by the experimental studies that demonstrate that C18-(PEPAu)2 conjugates can lead to twisted or helical ribbon structures, in this study we used all-atom MD simulations (detailed protocols are listed in the Supporting Information) to model the spontaneous process whereby a planar bilayer or monolayer assembly of PAs transforms to a twisted structure or into a helical ribbon. We first simulated the spontaneous twisting of a bilayer C18(PEP)2 assembly. Because it is inappropriate to impose periodic boundary conditions to simulate an infinite twisted ribbon structure, it is necessary to simulate a finite raft instead and then to infer the twist angle per unit length from the truncated ribbon that results. The bilayer setup is shown in Figure 1. The initial dimensions of the bilayer raft are about 9, 22, and 13 nm in the X, Y, and Z directions, respectively, where Y corresponds to the fiber (ribbon) growing axis. We chose the X dimension
of our initial raft so that the resulting ribbon (after equilibration) has the same thickness as in the experiment.14 In this setup, the 22 nm length accounts for ∼1/8 of a complete turn here considering the experimental pitch value of 184 nm. We performed 200 ns all-atom MD simulations, and a left-hand twisted structure was observed (Figure 2A). Note that the
Figure 2. Twisted ribbon structure. (A) A twisted ribbon is formed after 200 ns. (B) Determination of twist angle. The centers of mass of the residues at the edges (highlighted in color) and aliphatic tails are chosen for the dihedral angle measurement. Plot on the right shows twist angle versus time during the MD simulation.
aliphatic tail region has contracted significantly because of exposure to water, which gives the raft a characteristic V-profile around the periphery. The overall dimensions in the X and Y directions are similar to the initial values. The Z direction, which corresponds to the width of the raft perpendicular to the ribbon axis, has shrunk to ∼9 nm. Note that we also simulated cases with smaller thickness and found that the fiber loses stability and becomes vulnerable to breakage (Figure S1); therefore, 9 nm is apparently the smallest stable thickness. To calculate the twist angle, we determined the dihedral angle from center of mass of residues at the edges of the ribbon and aliphatic tails (Figure 2B). From the twist angle calculation, we found the ribbon left-hand twists by ∼30−50° after 100 ns (Figure 2B). Taking the average of the two independent simulations after 100 ns, the twist angle in our simulation is ∼40° or ∼2°/nm. As mentioned earlier, the pitch of the nanofiber observed in the experiments is 184 nm, which means ∼2°/nm rotation along the growing axis. Our simulation results have therefore closely replicated the experimental value. We also measured the twist angle between the divalent linkers and aliphatic tails and observed a 20−40° twist, indicating that twist is mainly associated with the aliphatic tail region (Figure S2). This explains why varying the aliphatic tail length changes the
Figure 1. PEP conjugates and the model of bilayer self-assembly ribbon structure used in our simulations. (A) PEP conjugate structure. (B) Bilayer ribbon raft model used in this study. Aliphatic tail, divalent region, and peptides are colored in red, yellow, and blue, respectively. 2171
DOI: 10.1021/acs.jpclett.7b00745 J. Phys. Chem. Lett. 2017, 8, 2170−2174
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The Journal of Physical Chemistry Letters
axis (Figure 4). This kind of orientation of β-sheets is a cross-β geometry that is commonly found in amyloid aggregates.11,25,26 The radial distribution function (RDF) of Tyr residues, the most bulky residue in the peptide, shows two peaks at 4.9 and 9.0 Å (Figure S5). Based on these data, a crystalline packing model of the C18-(PEPAu)2 conjugates like that in Figure S6 is possible. In this model, the distance between β-strands along the main axis is 4.9 Å, while the distance between β-sheets is 9.0 Å. The larger distance between β-sheets is used to accommodate peptide side chains, which are extended perpendicularly to the main axis. Recent experimental results demonstrate that oxidation of the Met residue in the C18-(PEPAu)2 conjugate [denoted as C18(PEPAuM‑ox)2] makes the conjugates self-assemble into a helical ribbon instead of a twisted ribbon.15 The vertical thickness of this ribbon is ∼4 nm, which is about half that of the bilayer ribbon described above. This suggests that the helical ribbon is made of monolayer of C18-(PEPAuM‑ox)2 conjugates, which means that Met oxidation destabilizes the bilayer structure relative to a monolayer structure. A commonly accepted model for the formation of a nanotube from PAs is that they initially self-assemble into a planar monolayer structure and subsequently transform into a twisted structure.7 As the twisting increases over time, a helical ribbon structure is formed (Figure S7). Finally, the gaps between the helical ribbon are sealed, turning it into a nanotube. In other words, helical ribbons are thought to be intermediates in the self-assembly of PA nanotubes. We hypothesized that a supertwisted monolayer of the C18-(PEPAuM‑ox)2 conjugate assemble will transform to a helical assembly. To test our hypothesis, we made a 66° twist monolayer C18-(PEPAuM‑ox)2 assembly, corresponding to a roughly 1.5 fold twist compared to the bilayer case (Figure S8). We performed a 100 ns simulation and found that the supertwisted ribbon gradually forms a helical ribbon. Figure 5A
twist angle that results in different pitch values.14 Next, we considered whether a C18-(PEPAu)2 conjugate bilayer assembly with ∼45° twist angle in our truncated case is in a stable state. In other words, does a twisted C18-(PEPAu)2 conjugate assembly with the same twist angle maintain this twist angle for a long time? To study this, we made a twisted bilayer ribbon containing the experimental twist angle (45° left-hand twist based on the size we simulated). Simulations starting with this structure (Figure 3) for 100 ns showed that the twist angle was maintained at 55° ± 5°, which indicates that the twisted structure is stable.
Figure 3. Simulation starting from a twisted ribbon. The twist angle maintains a 55° ± 5° angle in the 100 ns simulation.
The secondary structure of the peptides has a huge impact on the nanofiber’s structure. For example, both experimental results and computational simulations have demonstrated a higher propensity for β-strands to promote amyloid aggregation.23,24 We examined the secondary structure of our simulation results and found that the first four residues (AYSS) mostly exhibit a β-sheet conformation, while the proline-rich C-terminus (PPMPPF) presents a left-turn polyproline II (PPII) structure (Figure 4). A detailed secondary
Figure 4. Overall structure of bilayer PEP conjugate assemblies. βsheet structure is colored in yellow. Figure 5. Helical structure of monolayer PEPox conjugate assembly. (A) Snapshots at different time points. (B) Representative points used in radius calculation.
structure analysis based on φ/ψ angle measurements confirmed that the first four residues have high β-sheet propensity, while the proline-rich C-terminus has a high propensity for the φ/ψ angles to be −75°/150°, which is a PPII structure (Figure S3). The nonbonded interaction energy between peptides demonstrates that the first four residues (AYSS) have the strongest interaction, followed by the first two residues (PM) in the Ctermini PPII region (Figure S4), confirming that β-sheet formation is very important to maintaining the structure. We next measured the orientation of the β-sheets and found that the β-sheet plane is mostly parallel to the fibril axis, with the individual β-strand directions mostly perpendicular to the fiber
shows trajectory snapshots at 10, 50, and 100 ns. The monolayer gradually bends toward the aliphatic tail side, corresponding to aggregation of the aliphatic tail of the PAs in order to prevent direct contact with water molecules. In addition, the smaller volume of the tail region compared to the peptide region also drives bending toward the aliphatic tail side. To determine the helical radius associated with the structures in Figure 5, we used a least-squares fitting approach and found the 2172
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The Journal of Physical Chemistry Letters radius of the helical ribbon is 9.9 ± 1.5 nm, which is very close to the experimental value of 10.2 ± 0.8 nm.15 Note that we also did simulations for an initial untwisted structure and found that the resulting assembly is twisted and bent (Figure S9). However, the conformation after 100 ns in this calculation is similar to what is in Figure 5 after 10 ns, indicating that imposing an initial twist accelerates helical ribbon formation. Next, we examined the secondary structure of the monolayer C18-(PEPAuM‑ox)2 conjugate. φ/ψ angle measurements show similar β-sheet and PPII propensities compared to the above bilayer C18-(PEPAu)2 system (Figures S10 and S3). The RDF of Tyr residues reveals two peaks at 4.9 and 6.0 Å, suggesting the packing of β-sheets in the monolayer assembly is tighter than that of the bilayer C18-(PEPAu)2 assembly (Figure S11). Because the conjugates are packed tighter, the orientations of β-strand and β-sheet do not have a clear direction like the bilayer twisted assembly described above. Nonbonded interaction energies between peptides support this viewpoint as the interactions between nearby residues (off-diagonal) are stronger than in the bilayer case (Figures S12 and S4). In conclusion, our simulation results show that a bilayer C18(PEPAu)2 conjugate assembly that is 9 nm in width and thickness forms a twisted assembly structure with a twist angle per unit length of ∼2°/nm. On the other hand, C18(PEPAuM‑ox)2 PAs form a supertwisted monolayer assembly that evolves into a helical assembly. Starting from untwisted initial structures, the twisted or helical assemblies form in ∼100 ns. Both the twist angle and the helical diameter are comparable to experimental values, which indicates that the all-atom force field used is adequate for describing these structures. Detailed structural analyses show that the first four residues and Cterminus proline-rich region form β-sheet and PPII conformations, respectively. The strongest nonbonded interaction between peptides is found to be the β-sheet region. The simulation protocols presented here provide an important missing capability in the modeling and predicting of the selfassembly in chiral structures, protocols that can easily be applied to the assembly of other amphiphilic molecules and which are relevant to the bottom-up fabrication of chiral metamaterials and photonic structures.
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ABBREVIATIONS
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REFERENCES
CG, coarse-grained; AuNP, gold nanoparticle; MD, molecular dynamics; PA, peptide amphiphile; PPII, polyproline II; RDF, radial distribution function
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.7b00745.
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Letter
Additional figures and computational details (PDF)
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Cheng-Tsung Lai: 0000-0002-1192-2815 George C. Schatz: 0000-0001-5837-4740 Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We are grateful for financial support from the Air Force Office of Scientific Research (FA9550-11-1-0275). C.-T.L. and G.C.S. were supported by NSF Grant CHE-1465045. 2173
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