Modeling the Self-Assembly of Peptide Amphiphiles into Fibers Using

We have studied the self-assembly of peptide amphiphiles (PAs) into a cylindrical micelle fiber starting from a homogeneous mixture of PAs in water us...
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Modeling the Self-Assembly of Peptide Amphiphiles into Fibers Using Coarse-Grained Molecular Dynamics One-Sun Lee, Vince Cho, and George C. Schatz* Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3113, United States S Supporting Information *

ABSTRACT: We have studied the self-assembly of peptide amphiphiles (PAs) into a cylindrical micelle fiber starting from a homogeneous mixture of PAs in water using coarse-grained molecular dynamics simulations. Nine independent 16 μs runs all show spontaneous fiber formation in which the PA molecules first form spherical micelles, and then micelles form a three-dimensional network via van der Waals interactions. As the hydrophobic core belonging to the different micelles merge, the three-dimensional network disappears and a fiber having a diameter of ∼80 Å appears. In agreement with atomistic simulation results, water molecules are excluded from the hydrophobic core and penetrate to ∼15 Å away from the axis of fiber. About 66% of the surface of fiber is covered with the IKVAV epitope, and ∼92% of the epitope is exposed to water molecules. KEYWORDS: Peptide amphiphile, self-assembly, molecular dynamics simulation, coarse-grained model, micelle, fiber

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modeling because the self-assembly process involves a microsecond time scale, so instead the assembly was seeded starting from a structure that is roughly similar to the final micelle. To study the process of PA self-assembly and the structure of the resulting fibers, many different kinds of theoretical investigations have been performed. Schatz, Ratner, and colleagues used theories that range from simple bead and packing models to restricted atomistic calculations on clusters of PA molecules to study self-assembly.16−21 A different approach was used by de la Cruz and co-workers, who developed a simplified coarse-grained (CG) model to study the influence of hydrogen-bond formation on the self-assembly of PAs.22 This model, which did not include electrostatic interactions, found that the interplay between hydrophobic interactions and the network of hydrogen bonds results in the formation of fiberlike assemblies. However in none of these earlier studies was the complete process of the self-assembly of PA into fibers starting from a homogeneous mixture reported. In this paper, we model the self-assembly process leading to fiber formation for the IKVAV epitope bearing PA starting from a homogeneous mixture using a CG MD simulation approach based on the MARTINI force-field.23,24 MARTINI is a general force field for peptides and other molecules that has often been used to describe self-assembly in the context of lipids, but this application to PAs starting from homogeneous conditions is new. We have performed nine independent simulations for 16 μs and observed spontaneous fiber formation in all of the

peptide amphiphile (PA) is an amphiphilic molecule that consists of a hydrophobic alkyl chain that is attached to a peptide. Upon appropriate adjustment of pH and salt concentration, the PAs self-assemble into various morphologies depending on choice of residues and alkane, as has been extensively studied.1−8 In particular, Stupp and co-workers have reported PAs that self-assemble into cylindrical micelle fibers and aggregates of such fibers.9−11 A portion of a β-sheet forming sequence is intentionally inserted into these PAs, and it is believed that most of the PAs adopt β-sheet secondary structure in this region, thus driving assembly into cylindrical micelles fibers as opposed to spherical or planar structures. Biofunctionality of the fibers is achieved by choosing a domain of the PA to be a bioactive sequence that serves as the epitope for stimulating biological activity. The laminin-1 sequence IleLys-Val-Ala-Val (IKVAV) that is known to promote neurite sprouting is an example of a possible epitope, and IKVAVbearing PAs have been shown to promote regeneration of both motor and sensory nerves in a mouse model of spinal cord injury.11−13 Recently, we have suggested a molecular dynamics (MD) protocol for simulating PA self-assembly that leads to the formation of a cylindrical fiber shape at the atomistic level.14,15 This type of MD simulation provides a complete picture of the possible secondary structures present in the fiber, making it possible to determine the role of the secondary structure in determining fiber properties. Using PAs with the amino acid sequence SLSLAAAEIKVAV, we found that β-sheets are scattered in the resulting fiber with an average population of ∼14%. However, the process of self-assembly of PAs from a homogeneous mixture was not possible with our atomistic © XXXX American Chemical Society

Received: July 5, 2012 Revised: August 22, 2012

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simulations. During the early stage of the self-assembly, the hydrophobic tails aggregate and spherical micelles are formed. The peptides are exposed to the surface of micelles, and micelles form a three-dimensional network with the neighboring micelles. As the micelles aggregate, the hydrophobic tails belonging to different micelles merge and the interaction between neighboring micelles diminishes. As the micelles merge through tail−tail interactions, a cylindrical fiber forms. The diameter of the fiber is ∼80 Å, and the length is infinite given the periodic boundary conditions that are used. Water molecules are excluded from the hydrophobic core of the fiber, and the IKVAV epitope is exposed to the surface of fiber. About 66% of the surface of fiber is covered with the epitope, and ∼92% of the epitope is exposed to water. Our analysis will include comparisons with our earlier atomistic force field results as a calibration of the quality of the MARTINI results. Methods. CG Model. The peptide sequence chosen for each PA is Ser-Leu-Ser-Leu-Ala-Ala-Ala-Glu-Ile-Lys-Val-Ala-Val; see Figure 1A for a detailed structure. A CG model of the PA is built based on the MARTINI force field (Figure 1B).23,24 The MARTINI CG model was developed for the simulations of lipids, proteins, and carbohydrates.23−26 This uses a four-to-one mapping in which four atoms and associated hydrogens are represented by one CG bead. Water and ions are treated explicitly at the same level of coarse-graining. Bond, angle, and dihedral energy functions are used for the intramolecular bonded interactions, whereas Lennard-Jones (LJ) and Coulomb functions are used for the intermolecular nonbonded interactions. The LJ interaction is divided into ten levels, and the range of the interaction strength is from 2.0 to 5.6 kJ/mol. The levels of the LJ interaction between two different CG beads are summarized in Supporting Information Tables S1 and S2, and the parameters for bond and angle functions are listed in Figure S1, Tables S3 and S4 (Supporting Information). Details of the CG PA model are shown in Table 1. One of the important differences between the atomistic model and the MARTINI CG model is that the secondary structure of a peptide needs to be provided externally to the MARTINI force field and is fixed during the simulation.24 Choosing this secondary structure is therefore a required component of the modeling. According to our previous atomistic simulations of PA fibers (for a sequence that is identical to that being considered for CG work), we found that there is a distribution of PA secondary structures even though the peptide sequences of all molecules are the same.14 Indeed, 40 ns atomistic simulations show that most PAs adopt a random coil structure, but some PAs also show helical or sheet structures. Therefore, we decided to develop a CG model in which three representative secondary structures are used, as described in Table 1 and Figure 1C. A 25/15/60 ratio of secondary structures is found to reproduce the atomistic simulations. But note that these ratios are only determined to ∼5% accuracy as the ratios fluctuate with time as illustrated in Supporting Information Figure S2. In the optimized ratio of PA molecules, the system is composed of 35 PA1 (25%), 21 PA2 (15%), and 84 PA3 (60%) with the total number of PAs in the simulation being 140. The mixture of three different CG PA models reproduces well the distribution of the secondary structure of PA obtained from atomistic simulation even though some disagreement between two models is also observed (Figure 1C). Precise agreement between the CG model and the atomistic model is not necessary because the secondary structure of PA fluctuates with

Figure 1. Schematic structure of (A) Atomistic and (B) CG model of PA molecule. See Table 1 for the detailed information on each bead of the CG model. Color representation of CG model of amino acids is shown (adapted from the work of Monticelli et al24). (C) The distribution of secondary structure of the PAs along the peptide sequence. Twenty-five percent of PA1, 15% of PA2, and 60% of PA3 see Table 1) are mixed to reproduce the secondary structure distribution obtained from the atomistic simulation reported by Lee et al.14 The distributions obtained from atomistic simulation are shown in dotted lines for comparison. The distribution of α-helix is not included in the CG model, and it is not applicable in the CG model.

time as noted above. Also we performed simulations of a system composed of 140 PA3 without PA1 and PA2 to test the effect of the PA secondary structure on self-assembly, and found that the secondary structure does not significantly affect the morphology of the self-assembled structure (as further described in Results and Discussion). However having the correct secondary structures is important to describing the interaction of the fibers with other molecules, so we prefer to incorporate the secondary structure modeling into our overall method even though it does require a short atomistic calculation as input. Since the total charge of each PA molecule is −1, we added 140 sodium CG ions to electrically neutralize the system (0.24 mol/kg). A total of 8127 CG water was added, and 0.1 mol B

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Table 1. Sequence, Charge, Secondary Structure, and the Type of Coarse-Grained Bead of PAs Used in Simulationsa PA 1 name T1 T2 T3 T4 Sb1 Ss1 Lb2 Ls2 Sb3 Ss3 Lb4 Ls4 Ab5 Ab6 Ab7 Eb8 Es8 Ib9 Is9 Kb10 Ks10a Ks10b Vb11 Vs11 Ab12 Vb13 Vs13 a

amino acid

Ser Leu Ser Leu Ala Ala Ala Glu Ile Lys

Val Ala Val

charge

CG type

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 −1 0 0 0 0 +1 0 0 0 −1 0

C1 C1 C1 Na P5 P1 Nda AC1 Nda P1 Nda AC1 N0 N0 N0 Nda Qa Nda AC1 Nda C3 Qd Nda AC2 P4 Qa AC2

PA 2

secondary structure

CG type C1 C1 C1 Na P5 P1 Nda AC1 Nda P1 Nda AC1 N0 N0 N0 Nda Qa Nda AC1 Nda C3 Qd Nda AC2 N0 Qa AC2

C E E E T T T T E

E E C C

PA 3

secondary structure

C T T T E E E E T

T T T C

CG type C1 C1 C1 Na P5 P1 P5 AC1 P5 P1 P5 AC1 P4 P4 P4 P5 Qa P5 AC1 P5 C3 Qd P5 AC2 P4 Qa AC2

secondary structure

C C C C C C C C C

C C C C

For the secondary structure of peptide, E is for sheet, T is for turn, and C is for random coil.

micelle is 30−50. During this micellization, the hydrophobic tails aggregate inside the micelle, whereas peptides are exposed to the surface of the micelle. The micelles have close contacts with the neighboring micelles via van der Waals interaction. During the 0.1−0.5 μs time interval (snapshots shown in the second row of Figure 2), the micelles grow and aggregate to form a three-dimensional network. At ∼1 μs, the tails belonging to different neighboring micelles merge and the threedimensional network is replaced by a single PA fiber (snapshots shown in the third row of Figure 3). Therefore, we conclude that the PA molecules form spherical micelles first, which then transform into fibers. The sphere-to-cylinder transition of self-assembled structures has been reported for many different self-assembly problems.32−37 Winnik and co-workers have reported the transition of spherical micelles to elongated, high aspect ratio structures of various block copolymers, and suggested that crystallization of the core polymer is the main driving force for the formation of the cylindrical morphology.38−40 Marrink and co-worker reported the sphere-to-rod transition of nonionic surfactant micelles in aqueous solution using CG MD simulations with the MARTINI force field.37 They found that surfactant molecules self-assemble into spherical micelles with Nagg < 80, whereas surfactant molecules form an elongated worm-like structure with Nagg > 100. The calculations show that all 140 PA molecules belong to the same fiber after ∼10 μs. The density of PAs in the fiber is 14 PA/nm along the fiber axis and the diameter of fiber is ∼80 Å. These numbers are comparable to results obtained in our previous simulation at the atomistic level14 (density of 19.2 PA/

fraction of the CG water model has been replaced with the “antifreezing” model to avoid the freezing effect that sometimes occurs with the MARTINI model.23 The total PA concentration is 26 wt %. Simulation Parameters. All simulations were performed with the GROMACS simulation package (version 3.5.1) with a time step of 25 fs in the NPT ensemble.27 The pressure and temperature are maintained at 1 bar and 330 K, respectively, by means of the Berendsen method.28 Bond lengths in aromatic amino acid side chains and the backbone-side chain bonds for Val and Ile were constrained with the LINCS algorithm29 to avoid numerical instabilities arising from fast fluctuations. The neighbor list was updated every 10 steps using a neighbor list cutoff of rcut = 1.2 nm. When interpreting the simulation results with the MARTINI model, a standard conversion factor of 4 is used to specify the speedup in the CG diffusion dynamics compared to real water due to smoothing of the potential energy landscape.30,31 In the remainder of this paper, we will use an effective time rather than the actual simulation time unless specifically stated. We performed nine independent simulations and the total simulation time for each run is 16 μs. Coordinates were saved every 5 ns for the trajectory analysis, and no coordinates were constrained during the simulation. Results and Discussion. We observed the spontaneous self-assembly of PAs into a fiber in all of nine 16 μs CG MD simulations, one of which is shown in Figure 2. In the first row of Figure 2, snapshots in the early stage (0−0.04 μs) of PA selfassembly are shown. In this stage, the hydrophobic tails aggregate to form roughly spherical micelles. The aggregation number (Nagg) of PA molecules that participate in a typical C

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Figure 2. Process of PA fiber formation from a homogeneous mixture. Hydrophobic tails are shown in red and peptides in gray. Snapshots from t = 0 to 0.04 μs (first row) show the early stage of self-aggregation. Snapshots from t = 0.1 to 0.5 μs are in the second row; whereas snapshots from t = 1 to 16 μs are in the third row. Beads for water and ions are not shown for clarity. Green dotted lines represent periodic boundaries. The discontinuity of the hydrophobic core inside the fiber is indicated by a green arrow for the snapshot taken at 16 μs.

MD simulation is not identical with that obtained from the atomistic model. The peptides are exposed to the fiber surface and the hydrophobic tails are aggregated inside the fiber, but the hydrophobic core exhibits some discontinuities along the fiber, as indicated by a green arrow in Figure 2. The discontinuity of the hydrophobic tail is found in all of nine simulations, but presumably a longer simulation would lead to a continuous cylindrical shape of the hydrophobic core. Since a simulation longer than 16 μs is impractical even with the CG model, we performed CG MD simulations at a higher temperature (500 K) to allow the system to access a relaxed configuration. In these 500 K simulations, we observed selfassembly of the PA into a fiber with a continuous hydrophobic core. However, except for the hydrophobic core, the structural properties of the fiber obtained in these simulations are identical with those of the fibers obtained at 330 K. Note that even at 330 K, every tail of the 140 PA molecules is aggregated inside the fiber and not exposed to the aqueous environment after ∼2 μs of simulations. Water molecules are excluded from the hydrophobic core of the fiber as PA molecules self-assemble. The distribution of water molecules during the last 2 μs of the simulation is shown in Figure 3 (blue line). Water molecules can penetrate to ∼15 Å away from the axis of the fiber, and are not observed even in the region where the tail binds to the peptide. The tails are self-

Figure 3. Normalized distribution of tail and water inside the selfassembled fiber during the last 2 μs of the simulation. Schematic representation of the radius of the cylindrical shape of self-assembled PA is shown in the inset. The distribution is multiplied by 4, which is the coarse-graining scaling factor of the MARTINI force field.

nm and diameter of ∼88 Å) and also in the experiments (diameter of 80−100 Å that varies with the number of amino acids41). Note that the length of fiber in our simulations is infinite because of the periodic boundary conditions. Since the diameters of the beads in the MARTINI force field used in this study are all identical, the fiber density obtained from the CG D

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assembled inside the fiber and approximately two-thirds of tails reside within ∼10 Å away from the axis of the fiber (red dotted line in Figure 3) because of favorable tail−tail van der Waals interaction. The tail distribution quickly drops after 10 Å. This is consistent with our previous atomistic simulations. This also compares well with the conclusions of Tovar et al. that infer that the peptide region is well solvated.42 As the hydrophobic tails aggregate inside the fiber, most IKVAV epitopes are exposed to the surface of the fiber (Figure 4). We calculated the solvent accessible surface area (SASA) of

Figure 5. (A) Snapshots of the PA fiber at 16 μs. PA1 is shown in blue, PA2 in green, PA3 in yellow, and the tails of all sequences are in red. (See Table 1 for the detailed information.) PA1 and PA2 aggregate together and form a domain, whereas PA3 independently forms another domain. Beads for water and ions are not shown for clarity. (B) Peptide secondary structure of a PA fiber obtained from atomistic simulations is presented for comparison. The turn is in green, β-sheet is in yellow, helix is in purple, random coil is in gray, and the tail is in red. Adapted from the work in ref 14. Periodic boundary conditions are represented by dotted lines.

Figure 4. Snapshots of the top and side views of the fiber taken at 16 μs of simulation. Beads for the IKVAV epitope are shown in blue, whereas other parts are in gray. Most epitopes are on the fiber surface. According to SASA calculation, ∼66% of the surface of fiber is covered with the IKVAV epitope.

the fiber using a probe radius of 2.64 Å (= σ/2 × 21/6 for the MARTINI model, where σ is the collision diameter of the Lennard-Jones potential) during the last 2 μs of the simulation, and found that ∼66% of the surface of the fiber is covered with the IKVAV epitope. We also calculated the ratio of epitopes that are exposed to water molecules with the cutoff distance of 9.4 Å (= 2 × σ). According to this calculation, about 92% of the epitope is exposed to water, whereas the ratio is 73% for nonepitope peptide (SLSLAAAE). Since the purpose of the IKVAV design is neurite growth, the PA provides an efficient structure for exposing this sequence. We also investigated the effect of mixing PA molecules with different secondary structures. Two snapshots from the CG MD simulations taken from opposite directions of the fiber at 16 μs are shown in Figure 5A. The hydrophobic core of the fiber is shown in red, while PA1 is blue, PA2 is green, and PA3 is yellow. We observed that PA1 and PA2 form domains together whereas PA3 independently forms another domain. The main difference between PA1, PA2, and PA3 is the backbone secondary structure (Figure 1), which as noted previously is assigned before the simulation based on secondary

structure information obtained from our previous simulation of self-assembled PAs at the atomistic level. PA1 and PA2 contain β-sheet and the turn structures whereas PA3 contains only random coil structure (Table 1). The CG β-sheet model which is shown in yellow in Supporting Information Figure S3 is seen to be similar to the β-sheet shown in Figure 5B of the atomistic model. The length of the CG β-sheet is 2−3 nm along the fiber, which is comparable with that from the atomistic model.14 The van der Waals interaction is represented by LennardJones potential functions in the MARTINI force field.23 The LJ interaction is divided into ten levels, and the range of the interaction strength is from 2.0 to 5.6 kJ/mol. The strength of LJ interaction between PA1−PA1 (or PA2−PA2), PA3−PA1 (or PA3−PA2), and PA3−PA3 is 3.5−4.5 kJ/mol, 3.5−5.0 kJ/ mol, and 4.5−5.6 kJ/mol, respectively (Tables S1 and S2 in Supporting Information). Since the PA3−PA3 interaction has the highest LJ interaction, PA3 molecules tend to self-assemble E

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ACKNOWLEDGMENTS This research was supported by National Science Foundation (Grant CHE-1147335), by AFOSR MURI Grant FA9550-11-10275, and by the DOE NERC EFRC (DE-SC0000989).

side by side compared to PA1 or PA2 even though PA1, PA2, and PA3 self-assemble together and form a fiber. Therefore, we can conclude that the strong PA3−PA3 interaction is the driving force for the domain formation. To test the effect of the secondary structure of the PA on the morphology of the self-assembled structure, we also performed MD simulations for a system composed of 140 PA3 molecules. Even though this system does not contain any PAs with β-sheet structure, we observed spontaneous fiber formation. According to an analysis of the secondary structure using circular dichroism spectroscopy, the β-sheet population in the selfassembled PA fibers is ∼25 ± 20%,43 so it is clear that we need to include a distribution of secondary structures in the simulation to match the observations. However, β-sheet formation is apparently not a necessary condition for selfassembly. Recently, Khan et al. found that a glucogen-like peptide 1-mimetic PA self-assembles into fibers that contain 97% α-helix and 0% β-sheet,44 which clearly shows that the assembly can occur for a range of secondary structures. In general, there are many experimental conditions that influence morphology of the self-assembled structures, including concentration, temperature, and solvent,34,39,45 so the variations with secondary structure studied here are just one component of this complex story. In conclusion, we have performed nine independent CG MD simulations of a homogeneous mixture of 140 PA molecules solvated in an aqueous environment for 16 μs using the MARTINI force field and observed the self-assembly process of PA molecules that leads into a fiber. The PA molecules selfassemble into micelles during the early stage of the selfassembly (0−0.05 μs), where each micelle is composed of 30− 50 PA molecules. The hydrophobic tails are aggregated inside each micelle and the peptides that are exposed on the micelle surface form a three-dimensional network with neighboring micelles via van der Waals interactions. Subsequently the tails belonging to the different micelles merge, and the PA molecules form a fiber. Water molecules are excluded from the hydrophobic core of the fiber, and ∼66% of the surface of the fiber is covered with the IKVAV epitope whereas ∼92% of the epitope is exposed to aqueous environment. PA molecules with different secondary structures form different domains according to the different van der Waals interactions. The process of the self-assembly and the structural properties of the PAs reported in this paper will be useful for further design of PA molecules with improved functions.

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ASSOCIATED CONTENT

S Supporting Information *

Potential functions of the MARTINI force field, distribution of secondary structure of PA, domain formation in the selfassembled fibrous structure, Tables S1−S4, and Figures S1−S3. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: (847) 4915657. Fax: (847) 491-7713. Notes

The authors declare no competing financial interest. F

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