Structure Formation in Langmuir Peptide Films As Revealed from

Article pubs.acs.org/Langmuir

Structure Formation in Langmuir Peptide Films As Revealed from Coarse-Grained Molecular Dynamics Simulations Volker Knecht,† Günter Reiter,†,‡ Helmut Schlaad,§ and Renate Reiter*,†,‡ †

Freiburg Centre for Interactive Materials and Bioinspired Technologies (FIT), 79110 Freiburg, Germany Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany § Institute of Chemistry, University of Potsdam, Karl-Liebknecht-Str. 24-25, 14476 Potsdam, Germany ‡

ABSTRACT: Molecular dynamics simulations in conjunction with the Martini coarse-grained model have been used to investigate the (nonequilibrium) behavior of helical 22-residue poly(γ-benzyl-L-glutamate) (PBLG) peptides at the water/vapor interface. Preformed PBLG mono- or bilayers homogeneously covering the water surface laterally collapse in tens of nanoseconds, exposing significant proportions of empty water surface. This behavior was also observed in recent AFM experiments at similar areas per monomer, where a complete coverage had been assumed in earlier work. In the simulations, depending on the area per monomer, either elongated clusters or fibrils form, whose heights (together with the portion of empty water surface) increase over time. Peptides tend to align with respect to the fiber axis or with the major principal axis of the cluster, respectively. The aspect ratio of the cluster observed is 1.7 and, hence, comparable to though somewhat smaller than the aspect ratio of the peptides in α-helical conformation, which is 2.2. The heights of the fibrils is 3 nm after 20 ns and increases to 4.5 nm if the relaxation time is increased by 2 orders of magnitude, in agreement with the experiment. Aggregates with heights of about 3 or 4.5 nm are found to correspond to local bi- or trilayer structures, respectively.

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INTRODUCTION Peptides and proteins frequently form nanofibrils which might aggregate further to form macrofibers, networks, or other assemblies like spherulites or plaques.1,2 This hierarchical construction principle is observed in numerous biological systems and renders a wide range of extraordinary material properties possible as for example the extreme load bearing capacity of certain collagen assemblies3 or the extreme toughness and tensile strength of spider silk.4 In the case of amyloid fibrils, however, assembly might result in the formation of tractable plaques that cannot disassemble and which are considered to play a role in neurodegenerative diseases2 and are known to have outstanding mechanical properties. The few selected examples give a glimpse on the diversity of aggregated states of fibrous proteins and some associated properties which result from the hierarchical self-assembly of their peptide building blocks. One might argue that this diversity is due to sequence specific interactions and the fact that amino acid sequences, even within one protein family as e.g. collagens, show differences. On the other hand, quite a number of systems with less structural complexity like chitin,5 polymers,6 or homopeptides7 form fibrils of comparable dimensions. This naturally leads to the question of general principles driving the process of fiber formation and related aggregation. The presented study aims at contributing to this topic through molecular dynamic simulations of Langmuir films of poly(γbenzyl-L-glutamate) (PBLG). Langmuir films offer a suitable platform because the investigated system is confined to a © XXXX American Chemical Society

reduced space with an excellent control over the surface density. In many organic solvents this polypeptide forms helical rods and shows a multifaceted phase diagram which includes liquid crystalline (LC) phases. Numerous theoretical and experimental investigations were carried out8 (see also ref 9 and references therein), and in addition to well-defined phases the formation of fibers, which form a network, has been observed.10,11 Their occurrence was attributed to gel phases which typically emerge when the system is quenched. Attracted by the potential to form thin films with LC-like phases, on one hand, and biological membranes due to the peptidic nature of the molecule, on the other hand, Langmuir films of PBLG were already investigated some decades ago.12−14 One important question in that context was to find out if the helical structure of the peptide denatures when it is spread from a helix forming solvent onto the air water interface. Directly probing the conformation on the air−water interface with spectroscopic measurements was, however, not possible at that time because it needs methods like infrared reflection− absorption spectroscopy (IRRAS) which evolved in the late 1980s. Therefore, polarized infrared spectra were measured on built-up films of 50−100 layers transferred to germanium plates13,14 or on collapsed macro fibers of about 20 μm diameter that can be directly picked up from the water Received: April 28, 2017 Revised: June 6, 2017 Published: June 8, 2017 A

DOI: 10.1021/acs.langmuir.7b01455 Langmuir XXXX, XXX, XXX−XXX

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Langmuir surface.12 In all cases the helical structure was clearly identified. Loeb et al.15 investigated the molecular conformations of poly(γ-methyl-L-glutamate) (having shorter side chains than PBLG) under helicogenic and nonhelicogenic solvent conditions. Depending on the solvent used, the limiting area in the isotherm shifted and the characteristics of the curves changed simultaneously. This finding was attributed to the existence of two conformational states of the molecule on the water surface: α-helices and extended β-chains. Multiple internal reflection IR measurements on monolayers, transferred to solid substrates under the respective solvent conditions, confirmed these two states. It is also worth mentioning that the α-helical conformation of PBLG was also detected when submonolayers were prepared through drop-casting of highly diluted helicogenic solutions on a solid substrate.16 This finding rebuts the concern that transferring a monolayer to a substrate might induce helix formation. Taking all studies mentioned above into account, we suppose that PBLG molecules, which were spread onto the air−water interface out of a helicogenic solvent, consist of helices. The molecular dynamics simulations of the presented study are based on this strongly supported assumption. Furthermore, newer monolayer studies of PBLG using Brewster angle and scanning probe microscopy showed that the molecules have a strong tendency to aggregate laterally even without the application of external pressure17−20 which motivated us to choose this system to investigate the aggregation with computational tools. The simulations were performed under conditions to match a previously performed experimental study of Langmuir films of PBLG.21 In that previous work, Chandran et al.21 used atomic force microscopy (AFM) to study the morphology of Langmuir films of 22-residue PBLG peptides formed at the air/water interface and transferred to a solid substrate. The peptides are insoluble in water and widely accepted to adopt α-helical conformation in helicogenic solvent.14,15,22 The film structures were analyzed for increasing area densities. At the largest area per monomer (i.e., area per residue) considered, Am = 0.24 nm2, the film consisted of slightly elongated molecular clusters with a typical length of 25 ± 1 nm and a height of 2.5 ± 0.4 nm. At constant rate compression, the surface pressure steeply increased until it reached a plateau-like region at 0.185 nm2 ≥ Am ≥ 0.127 nm2. Here, the film consisted of fibers with a typical width of 25 nm and heights in the range h = 3.5 ± 1.5 nm. Depending on the compression protocol, this film was either (i) decorated with patches of material squeezed out during continuous compression, (ii) coexisting with coarsened fibers with a height of 8 ± 1 nm and a typical width of 50 nm, or (iii) coexisting with continuous layers forming stripe-shaped domains (parallel to the fibrils) with widths of up to 600 nm. Fractions of up to f = 50% of the surface were found to be empty, i.e., not occupied by peptide material. This observation was in contrast to earlier reports on PBLG where a complete coverage was claimed when reaching the plateau pressure.17,18 It should be mentioned that these studies have merely assumed homogeneous coverage in numerical calculations17 or used comparably low spatial resolution like Brewster angle microscopy.18 In order to understand Langmuir films formed by rod-like polymers at a molecular level, we have used molecular (MD) dynamics to study 22-residue PBLG peptides at the air/water interface. Previous MD studies yielded insights into the orientational order of the α-helical backbone of PBLG peptides,23 on PBLG peptides in nonaqueous solvents24,25 or

embedded in block copolymers,26,27 and on other peptides at water surfaces.28−39 In the present work we show that PBLG peptides spread at a water surface form clusters or fibrils with empty surface area in between depending on the area per monomer. Monolayers that cover the total surface homogeneously are never observed, but fractions of bilayer structures undergoing transitions to trilayers are witnessed.

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EXPERIMENTAL SECTION

MD simulations of PBLG peptides at the air/water interface (with air modeled by vapor) were conducted using the Martini coarse-grained (CG) model for biomolecular systems40,41 using the GROMACS simulation suite.42 In the Martini model,40,41 on average, four heavy atoms (e.g., four water molecules) are mapped into a single CG bead. An exception is rings like benzyl rings where the mapping is two or three to one. Covalent interactions are modeled using bond, angle, and dihedral potentials. Noncovalent interactions present in our systems are treated using Lennard-Jones potentials V(r) = 4ϵ[(σ/r)12 − (σ/r)6], where r denotes the corresponding interparticle distance, ϵ the depth of the energy well, and σ the distance at which V vanishes. For normal particles σ = 0.47 nm, while for ring particles σ = 0.43 nm. The parameter ϵ encodes the polarity of the corresponding chemical groups and is chosen such as to mimic the experimentally known partitioning of small compounds between water and various organic phases. PBLG peptides were modeled in α-helical conformation. In the Martini model, parameters were available for standard amino acids but not for γ-benzyl-L-glutamate. In this work, parameters for γ-benzyl-Lglutamate were derived using the parameters for glutamate and phenylalanine from the Martini model version 2.141 as a template. In addition, the framework for the parametrization of helical peptides in this version of the Martini model was employed. The model for PBGL thus derived is described in the next section. Intermolecular Interactions for PBLG. The mapping of atomic groups onto coarse-grained beads for the PBLG peptides is shown in Figure 1a. The backbone of each residue was treated as a single bead

Figure 1. Coarse-grained (CG) model for PBLG peptide based on Martini force field.40,41 Shown are (a) the mapping of atomic groups to CG beads (magenta and orange circles) and the names of the beads as well as (b) a single γ-benzyl-L-glutamate residue and (c) a single PBLG22 peptide in CG representation. and denoted as BAS. The backbones of the four N-terminal residues not involved in intramolecular hydrogen bonds (thus each containing a free NH group) were described as particles of type Nd (modeling hydrogen donors). The backbones of the four C-terminal residues not involved in intramolecular hydrogen bonds (thus each containing a free CO group) were treated as particles of type Na (modeling hydrogen bond acceptors). The backbones of the inner residues (whose NH and CO groups are hydrogen bonded to other residues) were modeled as particles of type N0. The termini were modeled uncharged.43 The acetic acid moieties of the side chains (−CH2− COO−) were described using a single bead with zero charge and denoted as SID. Two versions were employed, modeling it as either particle type P3 (free acetic acid) or Na (building block C−O−CO, as in methyl formate).40 The benzyl ring was treated as three SC4 B


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Langmuir Table 1. Simulations Conducteda Sim

np

nw

nx

ny

nz

a (nm)

b (nm)

c (nm)

Am (nm2)

t (ns)

teq (ns)

1P 1N 4p Sc S M L wX

1 1 4 72 144 288 576 0

4130 4130 17604 34488 30816 124272 505152 944

1 1 2 12 12 24 48

1 1 2 6 6 6 6

1 1 1 1 2 2 2

7.9 7.9 15.9 23.8 23.8 47.6 95.3 5.0

7.9 7.9 15.9 22.6 22.6 22.6 22.6 5.0

23.8 23.8 23.8 23.8 23.8 32.2 49.1 5.0

2.86 2.86 2.86 0.34 0.17 0.17 0.17

1000 1000 1000 639 2000 426 153 1000

15 90 520 1500 400 113 0

Given are the name of the simulation, “Sim”, the corresponding number of PBLG22 peptides, np, the number of water beads, nw, the (initial) box dimension in the x (a), y (b), and z direction (c), the area per monomer, Am (given by the box area in the xy plane divided by the total number of amino acid residues), the time scale considered, t, as well as the time period skipped for equilibration when determining averaged quantities, teq. If not stated otherwise, the systems consisted of a water slab parallel to the xy plane containing either a single peptide initially placed in water (“1P” and “1N”), or multiple peptides placed at the water/vapor interface. In the latter systems, nx × ny × nz arrays of peptides were placed next to the water phase with peptides pointing in the y direction. The acetic acid moiety was treated as particle type Na, except for simulation 1P where it was described using the particle type P3. Simulations wX considered bulk water with a single particle of type X = Na, Nd, N0, or SC4, to determine the corresponding rdfs with water. a

particles (ring-type particles) denoted as SI1, SI2, and SI3 and forming a triangle with bonds of fixed lengths 0.27 nm using constraints. Intramolecular Interactions for PBLG. Flexible harmonic bonds were added (i) between the backbone and the acetic acid moiety of the side chain, with an equilibrium distance of 0.40 nm and a force constant of 5000 kJ mol−1 nm−2, and (ii) between SID and SI1, with an equilibrium distance of 0.31 nm and a force constant of 7500 kJ mol−1 nm−2. Each of the angles formed by the CG bead triplets SID− SI1−SI2 and SID−SI1−SI3 was subjected to an angle potential with an equilibrium angle of 150° and a force constant of 50 kJ mol−1 deg−1. The dihedral angle defined by the bead quadruple SID−SI2−SI3−SI1 was subjected to an improper dihedral with an equilibrium angle of 0° and a force constant of 50 kJ mol−1 deg−1 to prevent back-flipping of the benzyl ring. Following the framework of the Martini model for proteins,41 harmonic bonds between backbone beads of adjacent residues, angles formed by three consecutive residues specific for αhelical conformations, and dihedral angles formed by four consecutive residues and stabilizing α-helical conformations were employed. Initial Peptide Configuration. The initial configuration of peptides was obtained by first modeling a phenylalanine22 peptide in an α-helical conformation using DAFT,44 then placing an acetic acid moiety between the backbone and the benzyl ring, and finally relaxing the potential energy of the peptide in vacuum to a local minimum using steepest descent. Systems Simulated. The peptide/water/vapor systems simulated under periodic boundary conditions are summarized in Table 1. The simulation boxes were chosen rectangular. Most systems consisted of a water slab parallel to the xy-plane containing either a single peptide initially placed in water (“1P” and “1N”) or multiple peptides placed at the water/vapor interface at three different areas per monomer. In the latter systems, two- or three-dimensional arrays of peptides were placed next to the water phase with peptides pointing in the y direction and homogeneously covering the complete interface. For box dimensions in the x and the y direction below 24 nm (simulations 1P, 1N, 4p, Sc, and S), the thickness of the water slab was chosen as 7 nm. For systems with 2- or 4-fold larger box dimensions in the x direction (simulations M and L), the thickness of the water slab was increased to 14 or 28 nm, respectively, to ensure stability of the water slab. The acetic acid moiety of the side chain was treated as particle type Na, except for simulation 1P where it was described using the particle type P3. Simulations of a single particle of type X = Na, Nd, N0, or SC4 in bulk water were performed in order to determine the corresponding radial distribution functions with water. Time Scales. In coarse-grained models, effects of degrees of freedom not simulated explicitly on the kinetics of the system are often mimicked by introducing friction and random forces. This is not done in the Martini model. Here, the absence of such forces, together with

the interaction potentials, which are smoother than atomistic potentials, accelerate the dynamics such that the effective time scales are larger than the nominal time scales. In simulations using the Martini model, time scales are usually given as effective time scales obtained from matching lipid diffusion to experimental values. The effective time scale thus given is the nominal time scale multiplied by 4. In the present work, though, we do not compare absolute time scales between simulations and experiments. Therefore, time scales are given in terms of the nominal time scales. Simulation Protocol. Each system was first relaxed to a local energy minimum using steepest descent. Subsequently, systems were simulated via solving the equations of motion and coupling to a heat bath. Water slabs in vacuum were simulated using fixed volume (fixed box dimensions in all directions). In simulations of bulk water an isotropic pressure of 1 bar, an average pressure of 1 bar in the x and the y direction was maintained, using a Berendsen barostat45 with a relaxation time of 30 ps. The time step for integrating the equations of motion employed was 30 fs. The neighbor list was updated every ten steps, using a neighbor list cutoff of 1.3 nm. Lennard-Jones potentials were switched between 0.9 and 1.2 nm. A temperature of 300 K was maintained via separately coupling water and peptides to a heat bath using a Berendsen thermostat45 with a relaxation time of 1 ps. The protocol chosen corresponds to standard settings for the Martini model, except for the neighbor list cutoff which was chosen larger than the usual value of 1.2 nm in order to reduce numerical noise. Particle positions were saved after time intervals 300−900 ps for further analysis. Specifically, the time intervals used were 900 or 600 ps for system L or M, respectively, and 300 ps otherwise. Analyses. In simulations of a single peptide, the center of mass (CoM) of the peptide relative to the CoM of the water slab was determined. Peptide aggregation in system 4p was monitored via determining the number of peptides in a cluster. Here, two peptides are considered to belong to the same cluster if there is a sequence of peptides, 1, 2, ..., n where each pair (i, i + 1) shows a minimal distance below rc = 0.65 nm. Peptide−Water Contacts. The number of contacts between water and peptide or water and benzyl rings was inferred. Here, two CG beads were considered in contact if their distance was below a cutoff rc. The value of rc was chosen from the solute−water radial distribution functions (rdfs) for simulations of single particles in bulk water, considering all particle types involved in the peptide model. The first local minimum of the rdfs of all particles was 0.71 nm, which was, hence, chosen as the value of rc. Helix Orientations. Putative kinks in helices were inferred from vectors connecting backbone beads of suitable residues. Considering the vector u pointing from residue 11 to residue 1, and the vector v pointing from residue 12 to residue 22, the angle between u and v, β̅ = C


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Langmuir arccos(uv/|u∥v|), and, hence, the kink angle, β = 180° − β̅, were inferred, where β = 0 for a perfectly straight helix. The orientation of peptides with respect to the x, y, and z axis was evaluated considering the vector u pointing from residue 1 to residue 22. The angle with the i axis (with i = x, y, z), αi, was inferred from αi = arccos(uêi/|u|), where êi denotes the unit vector pointing in the direction of the i axis. Volume per Peptide. The volume per peptide, vp, inferred from the dimensions of a single peptide was estimated from v1 = πr2L, where 2r = 1.5 nm is the thickness of the peptide as inferred from the FWHM of the density profile for a single peptide at water/vapor interface, and L is given by the helix length per residue of 0.15 nm times the number of residues (22), yielding L = 3.3 nm and v1 = 5.8 nm3. The effective volume of a single peptide in an aggregate is related to the number of peptides per unit volume in the aggregate, ρ = 1/vp, assuming hexagonal packing, which leads to 1/vp = η/v1 with the packing density η = 0.9069 ≈ 0.91 (hexagonal packing in a plane). On the other hand, vp was estimated from the height (h) and width of the fibrils (wf) observed in our simulations, considering the corresponding number of peptides in the system, N, according to

vp =

hwf Lf N

(1)

(2)

Figure 2. Adsorption of single PBLG22 peptide at the water surface. (a) Time evolutions of the center of mass (CoM) positions of a single peptide in a water slab relative to the center of mass of the water slab normal to the water/vapor interface, zp (simulations 1P and 1N in Table 1). Here, the acetic acid moieties of the side chains were treated as particles of either type P3 (“1P”, green curve) or Na (“1N”, red curve). (b) Mass density of peptide (red curve) and water (blue curve) along the z axis in simulation 1N, averaged over times t > 15 ns. (c) Number of peptide−water contacts versus |zp| in simulation 1N. (d) Distribution of helix kink (blue curve) and angle between helix and the xy plane (green curve) in simulation 1N for times t > 15 ns.

RESULTS Adsorption of a Single Peptide at the Water Surface. Experimentally, PBLG22 is insoluble in water, which is a prerequisite for studying it at the air/water interface at welldefined areas per monomer. Hence, it must be ensured that PBLG22 is also insoluble in simulation. This was validated by performing simulations of a single peptide in a water slab, where the peptide was initially placed in the center of the water slab. Two force field versions were employed. Here, the acetic acid moieties of the side chains of the peptide were modeled either using the particle type P3 which corresponds to free acetic acid (Table 1, simulation “1P”) or particle type Na (see Table 1, simulation “1N”). The particle type Na models building blocks containing hydrogen bond acceptors which are less polar than free acetic acid.40 Figure 2a reveals that in simulation 1P the peptide undergoes reversible adsorption/desorption events, indicating that the peptide is soluble. In contrast, in simulation 1N, the peptide is irreversibly adsorbed after 15 ns and, thus, appears insoluble. Therefore, modeling the acetic acid moieties of the side chains as particles of type Na yields a more realistic behavior. Hence, further on, only results and simulations obtained using this force field version will be reported. Figure 2b shows that the peptide, though adsorbed at the interface, is deeply immersed in the water phase (and not on top of the water phase), like a swimmer in water. This is reflected in the number of contacts between the peptide and water. Figure 2c shows that the number of peptide−water contacts is 500 ± 20 (average ± standard deviation) when the peptide resides in the bulk. When the peptide is adsorbed at the interface, the average number of contacts is decreased by ≈20%

to ≈420 and strongly fluctuates with a standard deviation of 100. Figure 2d shows that the helix is mostly straight, though, nevertheless, a small population of kinked conformations is observed. The figure also reveals that the peptide is overall parallel to the water surface. Figure 2b shows the mass density profile of the peptide along the z axis. The full width at halfmaximum (FWHM) of the curve is h = 1.5 nm. Taken together, the data for the peptide conformation, helix orientation, and the FWHM of the density profile suggest that h = 1.5 nm is the thickness of a single PBLG22 helix. This is also in line with the dimensions of the hexagonal lattice formed by dry PBLG determined experimentally.9,46 With a length of 0.15 nm per residue and thus a total length of L = 3.3 nm, each helical peptide thus exhibits an aspect ratio of L/h = 2.2. Formation of Dimers. To investigate the interaction of an ensemble of peptides at the water/vapor interface, four peptides, initially spatially separated from each other, were placed at a water surface. Figure 3a shows that within 16.5 ns two dimers form which remain separate from each other. Figure 3b reveals that (after 47 ns) one of the dimers diffuses across the water slab and subsequently (after 87 ns) adsorbs at the opposite surface of the water slab. Figure 3c shows the average densities of peptides and water along the z axis. Again, the peptides reside at the water surface but remain deeply immersed in the water phase. The FWHM of the density profile for the peptides is 1.6 nm, similar to the value for a single peptide. This suggests that the peptides in a dimer at the water surface are next to (and not on top of) each other. Favorable intermolecular interactions between the peptides could compete with intramolecular interactions and thus

where Lf denotes the dimension of the box in the direction of the fibril. Equation 1 was also used to derive an expression to calculate the volume per peptide in experiment as follows. The area per monomer, Am, is given by Am = A/nrN, where nr denotes the number of residues per peptide and A the total surface area. The latter obeys A = wrLf, where wr is the repeat length (periodicity). Via equation 1, wf and wr are expressed in terms of the fraction of free water surface, f, which yields

vp = hnA m (1 − f )

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Langmuir

Formation of Cluster. Experimentally, PBLG22 peptides at a water surface at an area per monomer of 0.24 nm2 form elongated clusters. To study this process, a simulation was conducted at an area per monomer of 0.36 nm2. As shown in Figure 4a,e, the peptides pointing in the y direction were arranged in a regular array, homogeneously covering the interface as a monolayer that percolates in the x and the y direction. After 2.4 ns (Figure 4b,f), peptide-free water surface has emerged, the peptides form a network, and percolation is lost in the x direction, i.e., normal to the initial orientation of the peptides. The contraction of the layer in the lateral direction goes along with a thickening of the layer, as expected, as the total volume of the peptide layer should remain constant. After 147 ns (Figure 4c,g), percolation is lost in the y direction, and after 520 ns (Figure 4d,h), an elongated cluster has formed. The height of the cluster is about 3 times larger than the height of the initial monolayer. Formation of Fibrils. Experimentally, it was observed that PBLG22 at areas per monomer between 0.185 and 0.127 nm2 forms fibrillar structures.21 To investigate this process at a molecular level, a system containing 144 peptides was simulated at an area per monomer of 0.17 nm2. The peptides were initially placed as a regular three-dimensional array of molecules at a water surface, forming a bilayer, with peptides pointing in the y direction (Figure 4i,m). At t = 3 ns (Figure 4j,n), free space has emerged. At t = 19.2 ns (Figure 4o,k), percolation is lost in the x direction. At t = 690 ns (Figure 4l,p), the aggregate still percolates in the y direction, corresponding to a fiber. Percolation in the x direction may be facilitated compared to percolation in the y direction because the box is somewhat less extended in the y compared to the x direction, though the difference is only 5%. Another reason may be that the peptides

Figure 3. Dimerization of PBLG22 peptides (simulation 4p in Table 1). Shown are (a, b) the time evolutions of (a) the average number of peptides in a cluster and (b) the centers of mass of individual peptides relative to the center of the water slab in the z direction, as well as (c) the mass densities of peptides (red curve) and water (blue curve) along the z axis and (d) the distribution of helix kink angles ((c, d) both averaged over times t > 90 ns).

perturb the conformations of the peptides. Indeed, Figure 3d shows that in the dimers the population of kinked peptides is increased, and the distribution of their kink angles is broadened compared to monomers (Figure 2d), indicating that dimerization induces disorder in terms of peptide conformation.

Figure 4. Cluster and fibril formation by PBLG22 peptides at water surface. Shown are snapshots of simulations at (a−h) 0.34 nm2 per monomer or (i−x) 0.17 nm2 per monomer for systems containing (a−h) 72, (i−p) 144, (q−t) 288, or (u−x) 576 peptides. Configurations at times (a, e, i, m, q, u) 0, (b, f) 2.4 ns, (c, g) 147 ns, (d, h) 520 ns, (j, n) 3 ns, (k, o) 19 ns, (l, p) 690 ns, (r) 600 ps, (s) 3.9 ns, (t) 400 ns, (v) 900 ps, (w) 1.8 ns, and (p) 113.4 ns are depicted. The peptides are viewed (a−d, i−l, q−x) from the vapor phase or (e−h, m−p) parallel to the water/vapor interface (with the vapor phase residing above the peptide layer). The representation of the peptide is similar to that chosen in Figure 1. The water is not shown. The snapshots were prepared using VMD.47 E


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Langmuir initially pointed in the y direction, in agreement with the previous assumption that the aspect ratio of 2 of the helical peptides, though relatively small, may induce the anisotropy and directionality of the aggregates.21 The height of the fibril is about 50% larger than the height of the bilayer from which the simulation was started (compare Figure 4p and Figure 4m). To study broader fibrils, the system was replicated once (Figure 4q) or 3 times in the x direction (Figure 4u). In both cases, empty space emerges at an early stage (Figure 4r,v), percolation is lost in the x direction (Figure 4s,w), and the peptides finally form fibrils in the y direction (Figure 4t,x). Figure 5 shows that during the formation of the cluster (Figure 5a) and the fibrils (Figure 5b) the number of benzyl−

Figure 7a shows the distribution of peptides in the cluster along the long (green curve) and the short principal axis of the cluster (red curve). The corresponding FWHM values are wx = 7.5 nm and wy = 13 nm. The cluster thus exhibits an aspect ratio of wy/wx = 1.7, which is comparable to, though somewhat lower than, the aspect ratio 2.2 of individual peptides. The distributions of peptides in the fibrils along the x axis (i.e., normal to the fibril axis and parallel to the water surface) are shown in Figure 7b. The FWHM for the fibril formed by 144 peptides (blue curve) is wf = 9.1 nm, corresponding to the width of the fibril. Hence, the lateral extensions of this fibril and the cluster are only about half of those observed experimentally (where typical diameters of clusters and fibril widths of 25 nm were detected).21 The lateral dimensions of the aggregates in our simulations are limited by the respective total number of peptides considered. Increasing the number of peptides to 288 yields a fibril of width wf = 23.3 nm (FWHM of red curve in Figure 7b), which is similar to the typical experimental fiber width of 25 nm.21 Increasing the number of peptides by another factor of 2, on the other hand, yields a fibril of width wf = 53.5 nm (FWHM of green curve in Figure 7b). Fibers of the same width, arising from fiber coarsening, are also observed experimentally after stepwise compression.21 That all peptides in the system assemble into a single layer may be understood from the tendency of the system to minimize the length of the boundary between peptide-covered and peptide-free water surface at thermodynamic equilibrium. The experimental observation that peptides do not form a single layer but separate into fibrils could be explained from kinetic trapping of nonequilibrium structures. That in our simulations thermodynamic equilibrium appears to be reached much faster than in experiment could potentially arise form poor time scale matching between experiment and simulations. It cannot be excluded, though, that the difference in the system’s behavior in experiment and simulation also partially arises from the difference in initial conditions and system sizes considered. First, the simulations start from highly ordered initial configurations, while the experiments presumably involve much more disordered transient structures. Second, the systems studied experimentally are much larger, allowing for higher order structures like networks and domains with different fibril orientations. These orientations probably result from dewetting and also the material flow in an anisotropic geometry. In experiment, domains of submicrometer size in which the peptides instead of fibrils form continuous layers are observed after isobaric compression and relaxation times exceeding those employed in continuous or stepwise compression.21 This supports the idea that the thermodynamically stable state of the Langmuir peptide film is a continuous layer, whereas the fibrillar structures arise from kinetic trapping of metastable states. Height of Aggregates and Bilayer-to-Trilayer Transformation. As summarized in Table 2, the heights of clusters observed experimentally were h = 2.5 ± 0.5 nm, and the same value of h = 2.5 ± 0.5 nm for fibrils at an area per monomer of Am = 0.185 nm2 was witnessed after continuous compression. However, h = 4.5 ± 0.5 nm at Am = 0.127 nm2 was measured after stepwise compression.21 As the fibril heights reported referred to two different areas per monomer and two different preparation protocols, the effect of the preparation protocol alone is not clear and shall therefore be addressed in the following.

Figure 5. Time evolution of the number of benzyl−benzyl contacts per PBLG22 peptide during (a) cluster formation at 0.34 nm2 per monomer or (b) fibril formation at 0.17 nm2 per monomer for systems containing 144 (blue curve), 288 (red curve), or 576 peptides (green curve).

benzyl contacts per peptide, NBB, steadily increases over time. Fibril formation leads to higher values for NBB due to higher ratios of bulk versus boundary peptides. The NBB values for fibril formation are very similar, though the values for the two larger systems are slightly above those for the smallest system, again due to (somewhat) higher ratios of bulk versus boundary peptides. Figure 6 visualizes the morphology of the cluster and the fibrils in terms of the numbers of particles per unit volume for the peptides and the water in two spatial dimensions, averaging over the third dimension and over time. As during the simulations not only individual molecules but also the whole clusters and fibrils show significant diffusion, the analysis of the morphology of the cluster and the fibrils required to remove the translational and (for the clusters) rotational diffusion of the aggregates. To this aim, for each configuration, the respective cluster or fibril was centered in the simulation box. Clusters in addition were rotated such that their longest principal axis in the xy plane pointed into the y direction. The height of the cluster and the fibrils, i.e., their dimension normal to the water surface, is in the range 3−5 nm, in agreement with experiment.21 It should be emphasized that the AFM height measurements imply an experimental error which does not allow for unambiguously distinguishing between mono- and bilayer on a local, subnanometric scale. Therefore, the high resolution of MD simulations is necessary to obtain a better understanding of the system’s behavior. The fibrils are immersed in the water, slightly bulged out toward the vapor, and their surface is separated from the vapor via a thin water film (Figure 6f,i,k). The narrowest fibril is observed to be curved toward the vapor (Figure 6e,f), while the wider fibrils are rather flat (Figure 6h−k). F


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the range 1−6) involved a finite waiting time of 1000 s after each step and an additional waiting time of 500 s close to Am = 0.209 nm2.21 For n = 6, this summed up to a time period of t2 = 6500 s, which corresponds to the longest relaxation period employed. To study the effect of the relaxation period on the values from our simulations, we determined h considering two different relaxation periods t1 and t2. The absolute time scales employed in the simulations were much shorter than those used in the experiments. As noted above, this may be due to poor time scale matching between experiments and simulations. It cannot be excluded that the difference in the absolute time scales also partially arises from the difference in system size and initial configurations. The snapshots in Figure 4e−h,m−p already indicate in a qualitative manner that the height of the aggregates increases with time. In the following, this trend will be investigated more quantitatively. The short relaxation period, t1, was chosen as t1 = 20 ns. At this time, the topology of the fibrils (finite width) was established for all the three systems considered (see Figure 4g,k,o). In order to determine the corresponding fibril height, h, the peptide density along the z axis was analyzed via averaging from t1 to 30 ns, and from the respective FWHM, h was inferred. The long relaxation period was chosen as t2 = 1.5 μs, assessed for the smallest system only. The corresponding peptide density along the x axis was determined via averaging from t2 to 2 μs.

Table 2. Geometries of PBLG22 Fibrils in Simulations and Experiments as a Function of the Relaxation Period Considereda method MD(S) MD(M) MD(L) MD(S) exp21 exp21

Am (nm2) 0.17 0.17 0.17 0.17 0.185 0.127

t (s) −8

2 × 10 2 × 10−8 2 × 10−8 1.5 × 10−6 73 6500

h (nm)

f (%)

vp (nm3)

2.7 3.1 3.0 4.7 2.5 ± 0.5 4.5 ± 0.5

33 37 36 61 30 ± 2 48 ± 2

6.7 7.3 7.2 6.8 7±2 7±2

a

Given are the average area per monomer, Am, the heights of the fibrils, h, the fraction of peptide-free water surface, f, and the volume per peptide, vp. The data for h and f for the simulations were obtained from the FWHM of the corresponding peptide densities along the z and the x axis, respectively, considering two different relaxation periods, t1 = 20 ns and t2 = 1.5 μs, averaging over the time periods t1− 30 ns and t2−2 μs.

The two types of protocols employed in the experiments differed in the corresponding relaxation times, t1 for continuous and t2 for stepwise compression, with t2 > t1.21 In the experiments, continuous compression was conducted using a constant compression rate to change the area per monomer per unit time with r = 0.10 nm2/min. Hence, the time t1 to change the area per monomer from Am,0 to Am,1 was t1 = 73 s, which corresponds to the short time period employed. On the other hand, compressing the monolayer in n steps (with n chosen in

Figure 6. Morphology of clusters and fibrils of PBLG22 peptides. Two-dimensional distributions of (a−c, d−e, g−h, j) peptides or (f, i, k) water (a− c) in cluster at 0.34 nm2 per monomer or (d−k) in fibrils at 0.17 nm2 per monomer for systems containing (d−f) 144, (g−i) 288, or (j−k) 576 peptides averaged over time, skipping the equilibration periods specified in Table 1, are shown. G


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of finite size (see Figure 4c). Averaging over the time period t1−160 ns, the peptide density profile along the z axis was determined (not shown), yielding h = 3.6 nm. The value of h is comparable to, though somewhat larger than, the experimental value. The height of the cluster found suggests that the peptides form a bilayer. A bilayer is also suggested from the corresponding distribution of backbone along the z axis which shows two peaks (Figure 7c, black dashed line). Figure 7c also shows the distributions of peptide, backbone, and water along the z axis for the cluster averaged over the time period t2−639 ns with t2 = 520 ns. The FWHM of the peptide profile yields h = 4.4 nm (see also Table 3). The height of the Table 3. Heights of PBLG22 Cluster(s), h, in MD Simulations and in Experiments at the Areas per Monomer (Am) Specifieda method

Am (nm)

h (nm)

teq (ns)

tfinal (ns)

MD MD exp21

0.34 0.34 0.24

4.4 3.6 2−3

520 150

639 160

a

The values for h from the simulations were taken as the FWHM of the corresponding peptide densities along the z axis, averaging over two different time periods teq−tfinal.

Figure 7. One-dimensional distributions of PBLG22 peptides in cluster and fibrils. Shown are the distribution of peptide (a) along the long (c = y) and the short principal axis of the cluster in the xy plane (c = x) as well as (b) along the x axis for fibrils (0.17 nm2 per monomer) for the systems containing 144 (blue curve), 288 (red curve), or 576 peptides (green curve). Furthermore, (c, d) the distributions of peptide (red), backbone (black solid line), acetic acid moieties of the side chains (green), benzyl rings (brown), and water (blue) along the z axis (normal to water surface) (c) at 0.34 nm2 per monomer and (d) 0.17 nm2 per monomer for the system containing 144 peptides are presented. The data were obtained via averaging over time, skipping the equilibration periods specified in Table 1. For comparison, the distributions of backbone from averaging over earlier time periods (150−160 ns for the cluster in (c) and 20−30 ns for the fibril in (d), black dashed lines) are also shown.

cluster found suggests that the peptides form a trilayer, also suggested from the distribution of backbone along the z axis which shows three peaks (Figure 7c, black curve). The comparison of the (cluster and) fibril heights observed in our simulations and in experiment suggests that the main factor governing also the experimental values is the relaxation period (rather than the area per monomer). The comparison of the fibril heights observed in our simulations and in experiment, as well as the structural insights from our trajectories, suggests that during relaxation at a given area per monomer in experiment, the fibrils undergo transformations from bi- to trilayer structures. Peptide-Free Water Surface. The fraction of peptide-free water surface observed experimentally was f = 32 ± 2% at the relaxation period t1 and an area per monomer of Am,1 = 0.185 nm2 and f = 48 ± 2% after the relaxation period t2 at Am,1 = 0.127 nm2 (see Table 2).21 From the simulations, the free water surface was determined via w f=1− f wr (3)

The heights of the fibrils for the short relaxation period observed in the simulations were 2.7−3.1 nm (Table 2), in good agreement with the value for the short relaxation period in experiment (h = 2.5 ± 0.5 nm). Considering the thickness of a single helix of 1.5 nm, the height of the fibrils found suggests that the peptides form a bilayer. A bilayer structure is also indicated from corresponding distributions of backbone along the z axis which exhibit two peaks, as shown in Figure 7d (black dashed line) for the smallest system considered. The height of the fibril for this system after the long relaxation period was 4.7 nm, in good agreement with the data after the long relaxation period (though, at a lower area per monomer) in experiment. The value for h suggests a trilayer structure, as also seen in the corresponding distribution of backbone along the z axis, which exhibits three peaks (Figure 7d (black solid line)). Hence, during relaxation, the fibril has transformed from a bi- to trilayer. The fact that trilayer formation in MD simulations is already observed at areas per monomer smaller than those for which the increased heights of h = 4.5 ± 0.5 nm were reported for the experiments highlights the importance of relaxational effects over crowding effects. A similar bi- to trilayer transformation is seen for the cluster (Figure 7c). The short relaxation period was t1 = 150 ns. Within this time, the initially infinite layer has just turned into a cluster

where wr denotes the width of the simulation box (periodicity) and wf the width of the fibrils. The latter was taken as the FWHM of the densities of the peptide along the x axis in Figure 7b, considering two different relaxation periods t1 and t2 as in the previous section. As (i) the height of the fibrils at a given relaxation period is independent of the area per monomer, Am, and, thus, independent of the periodicity, wr, and as (ii) the volume per peptide should be conserved, the free space, f, is expected to depend both on the relaxation period and on Am. This is indeed also observed in simulations, as shown in Table 2. The free space for the different systems after the short relaxation period at Am = 0.17 nm2 in our simulations ( f = 33− 36%) is similar to the free space observed experimentally after a short relaxation period at a similar area per monomer of Am = 0.185 nm2. The free space after the long relaxation period, f = 61%, is larger than the experimentally determined free space f = H


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MD and AFM studies reveal similar structural units of the film may indicate that the transfer of the film does not significantly change the structure of the film. In the coarse-grained model employed here, the conformation of the peptides is restrained to be helical. For peptides adsorbed at the water surface this assumed conformation is in accordance with experimental evidence. Restraining the conformation is necessary as the coarse-grained model is not predictive in terms of the secondary structure of peptides and without restraining the secondary structure the peptide might adopt coil conformations in the simulations. Another limitation of the Martini model is that it strongly underestimates the surface tension of water40 which should decrease the apparent surface activity of a hydrophobic peptide. On the other hand, while on a microsecond time scale in our model an isolated PBLG peptide is irreversibly adsorbed at the water surface, one out of two dimers is observed to leave the surface and cross the water slab, being adsorbed at the opposite water surface. We note, though, that this leaving of the surface is a stochastic process, and the number of events (zero per microsecond for the isolated peptide and one per two microseconds for the dimer) is too low to reveal a statistically significant difference in the surface activities of PBLG between the isolated and the dimeric state. We note, though, that this crossing of the water slab by a peptide dimer is observed for dilute conditions which are difficult to probe experimentally. Hence, it is not clear whether the slight solubility of the dimer is realistic or not. At the experimentally more relevant higher area densities at which clusters or fibrils form, though, the peptides appear to be stabilized at the water surface. For these conditions, our simulations provide better statistics in terms of the stability of the surface-adsorbed state of peptides. Here, analysis of the time-averaged densities reveals that none of the peptides crosses the water slab during the simulations. The Martini model represents a coarse-grained description of biomolecular systems, treating groups of on average four nonhydrogen atoms as a single bead, and describing aromatic groups by just three beads. Such a coarse-grained description is not necessarily accurate in terms of absolute surface activities of PBLG peptides. Nevertheless, besides a single crossing of the water slab by a peptide dimer at dilute conditions, the peptides appear essentially insoluble in water in our simulations, as a prerequisite of a reliable model for Langmuir films formed by such peptides. In addition, the good agreement of the heights of PBLG aggregates and the fraction of free space coexisting with fibrils suggests that the treatment employed here captures the main features of Langmuir PBLG films. Admittedly, due to the semiquantitative nature of the model employed, it is not clear whether all details of the predictions like the observation that the given peptides reside below the water surface are realistic or not. The degree of immersion is expected to depend on the relative magnitude of the surface tension of the peptide and the interfacial tension between the peptide and the water, none of which are known for the model employed.

48 ± 2% after the long relaxation period at a smaller area per monomer, Am = 0.127 nm2. A quantitative relation between peptide-free surface (f), area per monomer (Am), and fibril height (h) is obtained when considering that any change in Am or h should conserve the volume per peptide, vp. This leads to f = 1 − vp/hnAm. Hence, as a consistency check, corresponding values for vp at different conditions were computed based on the fibril geometries observed in experiment and in simulation, considering the area per monomer (experiment) or the number of peptides present (simulations), and compared to the volume per peptide inferred from the dimensions of a single peptide. As detailed in Table 2, the volumes per peptide from the fibril geometries in our simulations at different conditions (system size and length of relaxation period) as well as in experiment (length of relaxation period) are in the range 6.7−7.3 nm3, thus fairly constant and reasonably close to (though slightly larger than) the value expected from the dimensions of a single peptide, vp = 6.4 nm3. Peptide Orientations. Figure 8a,c (blue curves) demonstrates that in the cluster and in the smallest fibril the peptides overall form straight helices. In the fibril, though, a small population of configurations is observed in which the peptides adopt a collapsed state with kink angles around 150°. In the cluster and in the fibril, the helices show a tendency to point in the direction of the longest principal axis (cluster) and along the fibril axis, though this alignment is more pronounced for the fibril than for the cluster. For the cluster, the distribution of angles of helices with the shorter principal axis parallel to the water surface, as well as that of the angle with the surface normal, are close to random distributions of angles.

Figure 8. Distribution of (a) helix kink angles and (b) the angles of helices with the y (red), x (green), and z axis (cyan), compared to a random distribution of angles (sin x, brown), in the PBLG22 cluster containing 72 peptides as well as (c) distribution of helix kink angles (blue) and angles of helices with the y axis (red) in the fibril containing 144 peptides.

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DISCUSSION In our work we compare the structural properties of Langmuir PBLG films at the water surface probed in situ via MD simulations and Langmuir PBLG films transferred to a solid substrate studied via AFM.21 As the MD simulations and the AFM experiments investigate Langmuir PBLG films on two different substrates the two studies complement each other. A priori, it is not clear whether the structural properites of Langmuir PBLG films at the two substrates are the same. That

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CONCLUSIONS Molecular dynamics simulations in conjunction with a coarsegrained model have been used to investigate the (nonequilibrium) behavior of helical 22-residue poly(γ-benzyl-Lglutamate) (PBLG) peptides at a water/vapor interface (vapor modeling air). In the model employed, a single peptide placed I


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the Universities of the State of Baden-Württemberg, Germany, within the framework program bwHPC. This work has been supported by the Deutsche Forschungsgemeinschaft through the SFB/TRR 141 “Biological Design and Integrative Structures”.

in the center of a water slab is spontaneously adsorbed at one of the two vapor/water interfaces. Peptides placed at a water surface separately from each other spontaneously dimerize. To study larger aggregates in the present work, 72 peptides at a water surface at 0.34 nm2 per monomer were simulated. The peptides were initially arranged as a monolayer homogeneously covering the surface, with helix axes parallel to the surface and to each other. Here, the peptides were observed to form an elongated cluster on a submicrosecond time scale, with a height of 3.6 nm in the time period 150−160 ns and a height of 4.4 nm after 500 ns. The aspect ratio of the cluster observed is 1.7 and, thus, comparable to (though somewhat smaller than) the aspect ratio 2.2 of individual peptides derived from the known dimensions of the α-helix. At 0.17 nm2 per monomer, ≈140−580 peptides were initially arranged as a bilayer homogeneously covering the surface, with helix axes again parallel to the surface and to each other. After a few tens of nanoseconds, significant peptide-free water surface emerged. In this time period, the height of the fibers was in the range 2.7−3.1 nm, and the fraction of peptide-free surface in the range 33−36%. After 1.5 μs assessed for the smallest system, the corresponding fiber exhibited a height of 4.7 nm and ≈60% of the water surface is peptide-free. The formation of PBLG clusters or fibrils at the areas per monomer given as well as the time-dependent heights and fractions of peptide-free water surface after relaxation periods differing by 2 orders of magnitude are in good agreement with recent experimental data.21 The peptide helices are seen to preferentially point (i) into the direction of the major axis in the case of the cluster and (ii) into the direction of the fiber axis in the case of fibrils. Aggregates (clusters or fibrils) with heights around 3 nm were observed to correspond to peptide bilayers, and aggregates with heights of ≈4.5 nm to correspond to trilayers. The plateau region of surface pressure−area per monomer isotherms of PBLG at a water−air interface is often interpreted as a mono- to bilayer transition.14,17 AFM studies show that a second layer consisting of material islands forms upon continuous compression, while no out-of-plane layer is seen upon stepwise or isobaric compression.21 The first layer consists of fibrillar structures which (upon isobaric compression) coexists with domains in which the peptides form a continuous layer. Our work shows that this first layer itself is in fact not a monolayer, but consists of patches of bi- or even trilayers, depending on the relaxation period, not only at small areas per monomer where fibrils form but also at larger ones where only clusters exist.

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REFERENCES

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; phone +49 (0) 761 203-5863. ORCID

Volker Knecht: 0000-0001-6008-1744 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank S. Chandran and B. Heck for useful discussions. Furthermore, we acknowledge the use of the computing resources provided by the computational resource bwUniCluster funded by the Ministry of Science, Research and Arts and J


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