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Determining Factors for the Unfolding Pathway of Peptides, Peptoids, and Peptidic Foldamers Lalita Uribe, Jürgen Gauss, and Gregor Diezemann J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b06784 • Publication Date (Web): 21 Sep 2016 Downloaded from http://pubs.acs.org on October 1, 2016

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The Journal of Physical Chemistry

Determining Factors for the Unfolding Pathway of Peptides, Peptoids, and Peptidic Foldamers Lalita Uribe,†,‡ Jürgen Gauss,† and Gregor Diezemann∗,† †Institut f¨ ur Physikalische Chemie, Universität Mainz, Duesbergweg 10-14, 55128 Mainz, Germany ‡Graduate School Materials Science in Mainz, Staudinger Weg 9, 55128, Germany E-mail: [email protected] Phone: +49 61313923735. Fax: +49 61313923895

1 ACS Paragon Plus Environment


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Abstract We present a study of the mechanical unfolding pathway of five different oligomers (α-peptide, β-peptide, δ-aromatic-peptides, α/γ-peptides and βpeptoids), adopting stable helix conformations. Using force-probe molecular dynamics, we identify the determining structural factors for the unfolding pathways and reveal the interplay between the hydrogen bond strength and the backbone rigidity in the stabilization of their helix conformations. Based on their behavior we classify the oligomers in four groups and deduce a set of rules for the prediction of the unfolding pathways of small foldamers.

Introduction In recent years, there has been an increasing interest in the synthesis and design of nonnatural folding polymers (so called foldamers), 1–4 as well as in the understanding of their folding process. 5–12 In contrast to bio-polymers, the variety of backbone architectures occurring in foldamers that may give rise to stable folded conformations, is virtually unlimited. Several types of backbones producing a large spectrum of folded motifs have been successfully synthesized (for some recent examples see references 13–17 ) and the list keeps expanding. Furthermore, various studies have been carried out aiming at the design of foldamers with predictable properties and folded conformations. 3,18–20 This effort reflects the awareness of the community for the importance of understanding the influence of the backbone architecture on the secondary conformation adopted by a foldamer. The complete understanding of the folding mechanism of foldamers will further allow to design, prior to synthesis, polymers with a given shape adapted for specific applications.


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In previous studies, 21,22 we have investigated the mechanical unfolding pathways of short α- and β-peptides using force-probe molecular dynamics (FPMD) simulations. Between other relevant findings, we have shown that already short βpeptides (6-18 residues) exhibit a complex mechanical unfolding pathway, which is shaped by both the intrinsic stability of the folded conformation and its interaction with the solvent. However, a more comprehensive understanding of the effect of the backbone architecture on the unfolding pathway is desirable.

Here, we deduce a set of rules for the prediction of the mechanical unfolding pathways of oligomers that adopt helix conformations by comparing and categorizing a set of four foldamers and a biopolymer, that were chosen because of their large range of backbone architectures and helix conformations. For our study, we use FPMD simulations, which allows us to obtain atomistic resolution for the unfolding process at a low computational cost, and to gain detailed information about the oligomers’ conformational landscapes and stability. In this way, we reveal the interplay between the H-bond stability and the backbone rigidity in shaping the oligomers’ energy landscapes and we identify the determining structural factors for the mechanical unfolding pathways.

In the present work we analyze the results of our FPMD simulations in a similar way as in a previous study on a model β-peptide. 21 This comprehensive study led to two fundamental conclusions about the investigation of the unfolding pathway of short oligomers. First, in order to get information about the shape of the unfolding energy landscape, it is necessary to take into account the cooperative character of the unfolding process. We showed that analyzing the results of FPMD simulations in terms of the opening of individual H-bonds does not yield this information. Furthermore, the application of standard models of diffusive



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barier crossing is hampered by the fact that a specific model for the energy profile has to be applied. 23 Additionally, consecutive transitions in multi-well energy landscapes are not independent of each other. 24 This fact has to be taken into account in the analysis requiring more data. Therefore, a quantitative analysis of the results of the FPMD simulations using such models does not unequivocally provide us with reliable information about the energy profile.

Systems and Methodology Table 1: Structural information of the five oligomers studied. Oligomer β-peptoid 25

#1 6

H-bonds2 -

Nickname β-peptoid

Solvent CH3 CN

α-peptide

10

6 C=O (i) →H-N(i + 4)

α-Ala10

H2 O

β-peptide 26

8

6 C=O(i) →H-N(i − 2)

β-HAla8

CH3 OH

α/γ-peptide 27 δ-aromatic -peptide 28

9

α/γ-peptide

CHCl3

δ-Chin8

CHCl3

8

4 C=O(i) →H-N(i + 3) 4 C=O(i) →H-N(i − 1) 7 N(i) →H-N(i + 1)

1: Number of residues. 2: Number and types of H-bonds; for example, C=O (i) →H-N(i + 4) denotes a H-bond between the C=O of the residue i and the H-N of the residue (i + 4)

Our study includes an α-peptide, a β-peptide, an α/γ-peptide, a δ-aromaticpeptide, and a β-peptoid, which all have been studied experimentally 25–28 and are known to adopt stable helix conformations. For each type, we chose an oligomer with a chain length short enough to allow for extensive FPMD simulations and long enough to adopt a stable helix conformation. The five oligomers studied are described in Table 1 and their structures are shown in Figure 1.

We performed all FPMD simulations using the GROMACS 4.6.5 program package 29 and the GROMOS 53A6 force field, 30,31 at T = 200 K because at this temperature all the helices are stable and do not unfold spontaneously. Computa-


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Figure 1: Structure of A) β-peptoid, B) α-Ala10 , C) β-HAla8 , D) α/γ-peptide, and E) δ-Chin8



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tional details and force field parameters are given in the supporting information. All FPMD simulations were performed using the force-ramp mode. In this mode, a harmonic potential is applied to a so called pull group (here the N atom of the N-terminus) and a so called reference group (here the C atom of the C-terminus) is kept fixed in space. During the simulation, the harmonic potential attached to the pull group is moved with a constant velocity in the direction of a vector starting at the reference group and pointing towards the pull group. Thus, the oligomer is subject to a force of the form

F = K(V · t − z),

(1)

where z is the displacement of the pull group with respect to its initial position, K is the spring constant of the pulling device (K = 1000 pN/nm in all our simulations), V is the pulling velocity, and t is the time.

From a FPMD trajectory, a force vs extension (FE) curve is calculated which shows the force measured at the spring attached to the pull group as a function of the extension x = V · t + xi . Here, xi is the equilibrium distance between the reference and the pull groups. In detail, when an oligomer is pulled, the force increases due to the stretching of the spring and the molecule. The maxima of the FE curves are rupture events which correspond to large conformational changes, e.g., caused by the opening of an H-bond or a large torsional rotation reflected in large changes in the dihedral angles. When a rupture event occurs the spring relaxes and the force drops, giving rise to rips in the FE curve. Some conformational changes may not lead to a rip in the force, but to a plateau. Here, the spring is practically not stretched because the pulled oligomer unfolds without measurable resistance. Since the results of a single FPMD trajectory depend on the initial velocities 6 ACS Paragon Plus Environment

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and the H-bond rupture is a stochastic process, we performed 100 FPMD simulations for each system in order to obtain statistical significance. For β-HAla8 , α-Ala10 , α/γ-peptide, and δ-Chin8 a loading rate of µ = K × V = 100 pN/ns was used. For the β-peptoid µ = 10 pN/ns was used, because a lower pulling velocity was required to achieve a better resolution of its unfolding pathway. For the α/γ-peptide, 500 simulations with µ = 103 pN/ns were performed to achieve conclusive statistics. A higher velocity was used here to lower the computational cost of the simulations. Finally, we performed for each oligomer 100 simulations with V = 10 nm/ns and 100 simulations with V = 1 nm/ns for the study of the effect of the pulling velocity on the unfolding pathways.

Due to computer time requirements the pulling velocities and force constants used in this study, although standard for FPMD simulations, 32 are significantly larger than the ones used in single-molecule force spectroscopy (SMFS). Because of the large differences in the parameters’ scales, it is not guaranteed that FPMD samples the same unfolding pathways as SMFS does. However, for two of the systems studied here in ref. 22 we have performed ”quasi-static” simulations and calculated the potentials of mean force (PMFs). The comparison of the PMFs and FPMD simulations showed that both methods predict the same results in terms of number of energy barriers. This is a strong hint towards the fact that the unfolding pathway of these systems does not strongly depend on the pulling parameters.

Results and discussion Due to fundamental differences in the unfolding dynamics of the five studied oligomers, they were classified into four groups. Each is discussed in the following



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sections, to emphasize the relevant backbone features that give rise to a given unfolding pathway.

The β-peptoid - Simultaneous unfolding of all turns The β-peptoid was designed to adopt a helix (Figure 2A,2B) conformation mainly stabilized by the stiffness of the Cα -C-N-Cβ -dihedral-angles, which was achieved by attaching large and rigid substituents to the backbone N atoms. 25 The lack of intra-molecular H-bonds in the helix formed by the β-peptoid makes its unfolding pathway fundamentally different from the other systems studied, as will be evidenced below. In Figure 3, we show a typical FE curve obtained for the β-peptoid (black), and its so called dynamic strength (DS, an average over 100 FE curves (red)).

The sample FE curve and the DS show a similar behavior:

for small extensions, an almost constant force in the interval ∼ 2.0 - 2.3 nm is found (see inset in Figure 3). Here, several conformational changes take place at a low constant force without generating a rip in the force. This suggests that the energy barrier associated with this event is practically negligible. In contrast, a second rupture event occurs around 4.5 nm at a force of ∼ 2000 pN, which indicates a high energy barrier associated with this process. Both hypotheses are confirmed by the calculation of the PMF, shown in the supporting information.

To investigate the fraction of conformational space accessed by the β-peptoid during its unfolding, we calculated a fraction of native contacts (for details, see the supporting information) vs extension curve for each of the 100 simulations. An average over these 100 fraction of native contacts vs extension curves (ANC) is shown in Figure 4. The two-step decay in the ANC agrees with the two rup8 ACS Paragon Plus Environment

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Figure 2: Schematic representation of the conformations adopted by the βpeptoid during its unfolding. A) and B) Helix conformation. C) Intermediate state conformation. D) Unfolded conformation. The black dashed lines represent H-bonds.

Figure 3: Black: typical FE curve for β-peptoid using K = 1000 pN/nm and V = 0.01 nm/ns at T = 200 K. Red: Average of 100 FE curves for β-peptoid, so called dynamic strength. Inset: zoom of the small force region. 3000 2500 force / pN

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2000 1500 1000 500 0

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 extension / nm

ture events found in the FE curve and the DS. The FPMD simulations show that during the first rupture event all turns of the helix (Figure 2A,B) unfold simultaneously, through the rotation of several backbone bonds, except the NCO bonds, leading to the conformation shown in Figure 2C. In the intermediate state conformation, H-bonds between the carbonyl groups and the H atoms of 9 ACS Paragon Plus Environment


the aromatic rings are formed. In the second rupture event, the N-CO bonds rotate, giving rise to the fully unfolded conformation (see Figure 2D). The almost constant regime between the two decays in the ANC indicates a highly stable intermediate (Figure 2C). The high stability of the intermediate is a consequence of the stiffness of the Cα -C-N-Cβ -dihedral angles.

Figure 4: ANC for the β-peptoid using K = 1000 pN/nm and V = 0.01 nm/ns at T = 200 K. fraction of native contacts

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1.0 0.8 0.6 0.4 0.2 0.0

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 extension / nm

To understand the way the β-peptoid unfolds in the FPMD simulations, it is sufficient to consider the stiffness of the backbone dihedral angles. Most of the β-peptoid’s backbone bonds can easily rotate, except the N-CO bonds, this rotation is hindered by the large aromatic substituents at the N atoms. Therefore, when the β-peptoid’s helix is pulled, in a first step all backbone bonds (except the N-CO bonds) rotate simultaneously, and in a second step the N-CO bonds rotate.

The observed high energy barrier for the second unfolding event is consistent with a previous molecular dynamics (MD) study by Lausern et al. 25 at T = 300 K. There, the β-peptoid was found to adopt a large number of partially folded conformations, but being capable to return to the helix. However, Lausern et al. did not observe a complete unfolding, proving that even at T = 300 K it is 10 ACS Paragon Plus Environment

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unlikely to overcome the high energy barrier predicted by our FPMD simulations between the intermediate and the fully unfolded conformation.

α-Ala10 and β-HAla8 - Unfolding from the termini to the center In contrast to the β-peptoid, in the other oligomers, there is an extra factor affecting the helix stability: intra-molecular H-bonds. The helices adopted by α-Ala10 and β-HAla8 are shown in Figure 5 and typical FE curves are displayed in Figure 6. In both FE curves, several rupture events can be identified and all Figure 5: Schematic representation of the helix conformations adopted by: right: α-helix of α-Ala10 and left: 14-Helix of β-HAla8 . The colored lines represent the H-bonds that stabilize the helix conformations.

of them correspond to the opening of at least one H-bond. The DSs and average H-bond distance vs. extension curves (AHDCs) were calculated from the 100 FPMD simulations of β-HAla8 and α-Ala10 (Figure 7). The AHDCs show how the H-bond distances evolve with the increase of the extension. 11 ACS Paragon Plus Environment


Figure 6: Typical FE curve using K = 1000 pN/nm and V = 0.1 nm/ns at T = 200 K. Each colored line mark the opening of one of the H-bonds of each oligomer. The color code corresponds to the one shown in Figure 5. Left β-HAla8 and right α-Ala10 . 500

force / pN

400 300

1 2 3 4 5 6

200 100 0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

400 350 300 250 200 150 100 50 0

1 2 3 4 5 6

2.0

2.5

3.0

3.5

4.0

extension / nm

Figure 7: Top: DSs using K = 1000 pN/nm and V = 0.1 nm/ns at T = 200 K. Bottom: AHDCs (the H-bond distance is defined as the O-H distance). The black horizontal lines mark the threshold (0.3 nm) used to decide that a H-bond was opened. Left β-HAla8 and right α-Ala10 . 350 300 force / pN

250 200 150 100 50 0 H-bond distance / nm

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1.0 0.8 0.6

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1 2 3 4 5 6

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Three rupture events are observed in β-HAla8 DS. The last two rupture events are clearly distinguishable, but the first rupture event only appears as a shoulder of the first maximum. By comparing the extension at which the rupture events appear in the DS and the extension at which the H-bonds open in the AHDC, we found that the average unfolding pathway of β-HAla8 consists of three steps: i) breaking of the N-terminus H-bond, ii) breaking of the outermost H-bonds (2, 5 and 6), and iii) breaking of the innermost H-bonds (3 and 4). The opening of an H-bond in β-HAla8 ’s unfolding is only accompanied by the rotation of a Cα -CO bond. This behavior agrees with a previous MD study by Keller et al., 33 in which the Cβ -Cα -CO-N-dihedral angle was shown to be the only flexible one in β-peptides’ backbone.

Analogously to β-HAla8 , we find that the unfolding pathway of α-Ala10 consists of two steps: i) breaking of the outermost H-bonds (1,5, and 6) and ii) breaking of the inner H-bonds (2, 3 and 4). During the α-Ala10 unfolding a H-bond opening is accompanied by the rotation of a Cα -CO and a Cα -N bond, which shows the reduced stiffness of α-Ala10 ’s backbone in comparison to βHAla8 ’s backbone, also reflected in the less pronounced maxima in α-Ala10 ’s DS (see Figure 7). These results are considerably different from those found in our previous study of α-Ala10 at T = 240 K, 22 where the helix was found not to be stable enough to observe any rupture events in the DS.

β-HAla8 and α-Ala10 preferred unfolding pathway is similar, starts at the termini and propagates to the center. To identify which backbone features of α-Ala10 and β-HAla8 trigger the preference for such a pathway, it is useful to understand which backbone features make other pathways improbable. This analysis is focused on β-HAla8 , because all arguments also apply to α-Ala10 . A first alternative



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pathway would be a cooperative simultaneous unfolding of all turns, similar to the unfolding of the β-peptoid. Since this would imply the synchronized opening of all H-bonds, which requires a large amount of energy, this is highly improbable under our simulation conditions.

A second alternative unfolding pathway could start with the opening at one terminus followed by the propagation of the unfolding to the opposite terminus. This would require that the opening of the H-bonds at one terminus is more favorable than the opening at the other terminus. Given that all H-bonds in β-HAla8 ’s helix are equally strong, the opening of the H-bonds at one of termini is not more favorable. Therefore, this case is also not probable.

Finally, all unfolding pathways in which the H-bonds in the center are the first to open can also be ruled out by studying the H-bond pattern in β-HAla8 helix. The opening of H-bond 3 would require the rotation of one of the two Cα CO bonds marked cyan and pink in Figure 5. The rotation of the cyan Cα -CO bond would at least induce the opening of H-bond 2. On the other hand, the rotation of the pink Cα -CO bond would require the opening of H-bond 4 and 6. Therefore, due to β-HAla8 ’s H-bond pattern the opening of a central H-bond implies the opening of at least one other H-bond, requiring more energy than the opening of an outer H-bond. Consequently, in 100 FPMD simulations, not a single trajectory in which a inner H-bond opened before the outer H-bonds was observed.

Therefore, there are two backbone features, the presence of equally strong Hbonds and the H-bond pattern, that triggers β-HAla8 and α-Ala10 preference for an unfolding pathway consisting in the opening of the termini H-bonds, followed


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by the opening of the adjacent H-bonds, and ending with the opening of the innermost H-bonds. We observed the same unfolding pathway for β-peptides with chain lengths ranging from 6 to 18 residues in an earlier study. 22

α/γ-peptide - Unfolding from one terminus to the other Using an analysis analogous to β-HAla8 and α-Ala10 , two equally probable unfolding pathways were found for the α/γ-peptide, Figure 8, each of them consisting of four steps.

The DSs and AHDCs for both pathways are shown in Figure 9.

Figure 8: Schematic representation of the 12/10-helix adopted by the α/γpeptide. 27 The colored lines represent H-bonds. The H-bonds 1, 3, 5, and 7 are of the type (i + 3) and the H-bonds 2, 4, 6, and 8 are of the type (i − 1).

The first two steps are the same in the two pathways: i) opening of H-bonds 8 and 7, and ii) opening of H-bonds 6 and 5. In one pathway, the last two steps are: iii) opening of H-bonds 4 and 3, and iv) opening of H-bonds 2 and 1. In the other pathway the order of the last steps is inverted. The DS for the first 15 ACS Paragon Plus Environment


Figure 9: Top: DSs for the two equally probable unfolding pathways of α/γpeptide using K = 1000 pN/nm and V = 1 m/s at T = 200 K. Bottom: AHDCs for the DS in black and the DS in red, respectively. The black horizontal lines mark the threshold (0.3 nm) used to decide when a H-bond is opened. 500 force / pN

400 300 200 100 0 0.9 H-bond distance / nm

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pathway shows four rupture events (see black curve in Figure 9), but in the DS for the second pathway there are only three clearly resolved maxima (see red curve in Figure 9). However, it is possible that the maximum located around 3.2 nm, which is quite broad, actually consists of two overlapping maxima.

In both pathways, the α/γ-peptide unfolds one turn at a time through the opening of pairs of H-bonds belonging to a single monomer (see Figure 9). Each pair consists of two H-bonds of a different nature: a C=O(i) →H-N(i − 1) (in short (i − 1)) H-bond and a C=O(i) →H-N(i + 3) (in short (i + 3)) H-bond. The opening of both H-bonds is accompanied with the rotation of a Cα -Cβ bond, the only flexible backbone bond of the γ-amino-acids that constitutes the α/γpeptide. An analogous behavior for a similar type of peptidic foldamer has been 16 ACS Paragon Plus Environment

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observed by Balamurugan et al. 12

The two types of H-bonds in α/γ-peptide’s helix are not equally strong. Whereas the (i − 1) H-bonds form rings of 10 atoms, the (i + 3) H-bonds form rings of 12 atoms. Due to their higher geometrical constraints, H-bonds forming smaller rings are expected to have a lower stability. Fisher et al. 27 found, studying the NMR-spectra of α-valine/trans-EtACHA peptides with varying chain lengths, that H-bonding is more favorable for H-bonds forming larger rings.

Figure 10: Schematic representation of the rotation of the Cα -Cβ bond (green) within the 8th residue of the α/γ-peptide. The red and blue dashed lines represent the (i − 1) H-bond and the (i + 3) H-bond, respectively

The unfolding pathway of the α/γ-peptide can be explained by taking into account the relative stability of α/γ-peptide’s H-bonds. In the case of the Cterminus, the outermost H-bond is the weaker one (H-bond 8), in comparison in the N-terminus the outermost is the stronger one (H-bond 1). Consequently, the unfolding starts at the C-terminus with the breaking of H-bond 8 accompanied by a large rotation of the Cα -Cβ bond in the 8th residue (see Figure 10), which destabilizes the adjacent (i + 3) H-bond (H-bond 7) and generates it to open. The almost simultaneous opening of pairs of (i − 1) and (i + 3) H-bonds continues following the path of the weaker H-bond.



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δ-Chin8 - Pulling velocity dependence A schematic representation of the helix adopted byδ-Chin8 is given in Figure 11 and the DS and ANC are shown in Figure 12. Figure 11: Schematic representation of the helix conformation adopted by δChin8 , 28 the substituents of the aromatic rings are not shown for simplicity. The colored lines represent H-bonds.

By comparing the DS and the ANC, we find that the unfolding pathway of δ-Chin8 consist of four steps: i) opening of the N-terminus H-bond (H-bond 1), ii) opening of H-bonds 2 and 7, iii) opening of H-bonds 3 and 4, and iv) opening of the H-bonds 5 and 6. δ-Chin8 has six different types of backbone bonds. Four of these bonds cannot rotate, because they either belong to an aromatic ring or are peptide bonds. Therefore, δ-Chin8 has only two types of backbone bonds that may rotate. From these, only the backbone Cα -CO bonds rotate during δ-Chin8 ’s unfolding. This reflects the high stiffness of δ-Chin8 ’s backbone and is in agreement with Abramyan et al. 11 meta-dynamics study. These authors found that during the handedness inversion of a series of δ-Chinn (n = 4-6) the only bonds that rotate are the Cα CO bonds.


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force / pN

Figure 12: Top: DS and bottom: AHDC for δ-Chin8 using K = 1000 pN/nm and V = 0.1 m/s at T = 200 K. The black horizontal lines mark the threshold (0.25 nm) used to decide when a H-bond is opened.

H-bond distance / nm

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1 2 3 4 5 6 7

0.20 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 extension / nm

It is expected that δ-Chin8 ’s unfolding pathway is similar to the one of β-HAla8 and α-Ala10 , since all δ-Chin8 ’s H-bonds have the same strength. However, δChin8 ’s helix has an extremely stiff backbone, a large N to C asymmetry, and a particular H-bond pattern. In contrast to all the other studied H-bonded helices, the H-bonds in δ-Chin8 ’s helix are not aligned parallel to the helix axis, but they are almost perpendicular it (see Figure 11). Given that the pulling direction is practically aligned along the helix axis, δ-Chin8 ’s H-bonds are the only ones that are not parallel to the pulling direction. Remarkably, the relative orientation of the H-bonds with respect to the pulling direction seems not to produce any appreciable effect in the unfolding pathway. Hence, the role of the H-bonds is mainly to restrain the rotation of bonds and in this sense is similar to the role of



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Figure 13: δ-Chin8 . A) Schematic representation of the rotation of the Cα -CO (green) between the N-terminus residue and the 2nd residue. The group in blue is the one that rotates. B) Schematic representation of the rotation of the Cα -CO (green) between the 7th residue and the C-terminus residue. The group in red is the one that rotates. The black dashed lines represent H-bonds.

the large substituents in the β-peptoid. The N to C asymmetry refers to the fact that the sequence of backbone atoms in a peptide-like oligomer is inverted when seen from the C-terminus compared to a view from the N-terminus. The N to C asymmetry is larger for δ-Chin8 than for β-HAla8 and α-Ala10 , because each δ-Chin8 ’s monomer has six backbone atoms, whereas each β-HAla8 ’s and α-Ala10 ’s monomer has four and three backbone atoms, respectively. A consequence of the N to C asymmetry is that the rotation of the Cα -CO bond in the N-terminus and in the C-terminus is not equivalent. When the N-terminus’s Cα -CO bond rotates, only the aromatic ring and its substituents (shown in blue in Figure 13A) rotate with it. In contrast, when the C-terminus’s Cα -CO bond rotates, the whole C-terminus residue and the CO group of the 7th residue (shown in red in Figure 13B) rotate with it. Assuming that the rotation


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of a larger group requires more energy, the N-terminus rotation is favored against the C-terminus rotation. Therefore, the N-terminus H-bond is the first one to open.

Once the N-terminus H-bond is opened there is no further effect of the asymmetry, because the fragments that rotate when any other of the H-bonds open are equally large. Thus, it is expected that the unfolding will continue from the termini to the center, as for β-HAla8 and α-Ala10 . The second unfolding event, in which H-bonds 2 and 7 open, fulfills this expectation. However, the third unfolding event, in which H-bonds 3 and 4 open, contradicts this expectation. An analysis of the conformations adopted by δ-Chin8 during the FPMD simulations revealed that after the opening of H-bond 7 a second effect of the asymmetry appears. We found that when any of the H-bonds opens (except H-bond 7) the rotation around the Cα -CO bond shifts the Cβ -Cα -CO-N-dihedral angle from 150◦ to 100◦ (i.e., a 50◦ rotation), as shown in Figure 13A. In contrast, when H-bond 7 opens, the rotation around the Cα -CO bond shifts the Cβ -Cα -CO-Ndihedral angle from 150◦ to 50◦ (i.e., a 100◦ rotation), as shown in Figure 13B. This large rotation generates a conformation in which the opening of the H-bond 6 is disfavored. Therefore, after the opening of H-bond 7 the unfolding can only proceed from the N-terminus side. This second asymmetry effect is the reason why δ-Chin8 does not unfold from the termini to the center. We mention that we also performed FPMD simulations with the pull group and the reference group interchanged and found identical results, cf. the supporting information.

The effect of the N to C asymmetry on δ-Chin8 ’s unfolding pathway was further investigated by performing 100 FPMD simulations with V = 10 nm/ns and 100 simulations with V = 1 nm/ns. Remarkably, at these velocities the first effect



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of the N to C asymmetry is also observed, i.e., the N-terminus is always the first one to open. However, the second effect of the asymmetry is only observed at the smaller velocity (V = 1 nm/ns). For V = 10 nm/ns, due to the absence of the second effect of the asymmetry the unfolding happens from the termini to the center, similarly to β-HAla8 and α-Ala10 .

At high pulling velocities the second effect of the asymmetry is not observed any more, because the behavior of the rotation of the Cα -CO bonds changes. At V = 10 nm/ns, the sequential opening of H-bonds occurs faster and does not allow the system to reach the conformation in which the Cβ -Cα -CO-N-dihedral in the C-terminus takes a value of 50◦ (Figure 13B). Thus, at this pulling velocity, the opening of H-bond 6 is not hindered by the opening of H-bond 7.

We also evaluated the effect of the pulling velocity in the unfolding pathway of the other four oligomers; the same parameters as for δ-Chin8 were used. The unfolding pathway of none of the four oligomers was found to be modified by the increase of the pulling velocity. Therefore, δ-Chin8 is a special case in which the unfolding pathway does depend on the pulling velocity. This dependence is a consequence of the extra factor that affects δ-Chin8 ’s unfolding. While for βHAla8 , α-Ala10 , and the α/γ-peptide considering the backbone stiffness and the H-bond stability is enough, for δ-Chin8 it is also necessary to consider the effect of the N to C asymmetry, which depends on the pulling velocity.


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Rules for the prediction of the unfolding pathway of oligomers adopting a helix conformation Based on the results conducted from our simulations we propose the following rules for the prediction of the mechanical unfolding pathway of an oligomer. As input only basic properties like the presence and type of H-bonds, the backbone’s stiffness, the H-bond pattern, and the N to C asymmetry are considered. These rules describe the unfolding pathway of an oligomer from its helix conformation to a fully unfolded conformation, i.e., a conformation in which the oligomers is fully stretched. 1. The turns of helices without intra-molecular H-bonds (as the β-peptoid) will unfold simultaneously. The number of intermediate states in the unfolding pathway of such a helices may be tuned by changing the number of stiff backbone’s dihedral angles, e.g., a helix with several different types of stiff dihedral angles could have more than one stable intermediate state. 2. A helix with only one type of H-bonds (as α-Ala10 and β-HAla8 ) will unfold from the termini to the center, independently of the backbone flexibility. However, the backbone flexibility does determine the overall stability of the helix and intermediate states, as shown by us in our previous study of α-Ala10 and β-HAla8 . 22 3. Helices with different types of H-bonds (as the α/γ-peptide) will unfold following the path of the weaker H-bond. A further tuning of their pathway could be accomplished by modifying the rigidity of their backbone.



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4. The unfolding pathway of a helix with a stiff backbone and large N to C asymmetry (as δ-Chin8 ) may depend on the pulling velocity. The effect of a large N to C asymmetry is highly dependent on the systems and may be difficult to predict. We believe that these rules should hold quite generally for the various classes of oligomers, but of course more detailed studies are required to demonstrate this.

Conclusions We studied the unfolding pathway of four foldamers and one α-peptide, that adopt helix conformations, using FPMD simulations. For all the studied oligomers, we found that the unfolding takes place in a cooperative manner, i.e., several Hbonds open or backbone bonds rotate at the same time. However, we found that each helix’s backbone architecture influences the unfolding pathway in a different way and that for helices with intra-molecular H-bonds there is an interplay between the H-bond stability and the backbone rigidity in shaping their energy landscapes. Remarkably, the role of H-bonds in the unfolding pathway is found similar to the role of large substituents, because both features of the backbone architecture mainly act to stiffen the backbone’s dihedral angles. However, following the opening of the H-bonds during the unfolding pathway remains an ideal indicator of conformational changes.

From the five studied oligomers four different unfolding pathways were identified. The first pathway, exhibited by the β-peptoid, consists in the simultaneous unfolding of all the turns of the helix. In the second pathway, exhibited by βHAla8 and α-Ala10 , the unfolding starts at the termini and propagates to the center of the helix. In the third pathway, exhibited by the α/γ-peptide, the un24 ACS Paragon Plus Environment

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folding starts at one terminus and propagates to the other terminus. Finally, the fourth pathway, exhibit by δ-Chin8 , depends on the pulling velocity. At high velocities the unfolding starts at the termini and propagates to the center of the helix and at low velocities the unfolding starts at one terminus and propagated to the other terminus.

Based on the observations made about the different pathways, we proposed a series of rules for the prediction of the unfolding pathway of oligomers adopting helix conformations. These rules can be extended by studying the effect of external parameters, such as solvent and temperature, in the unfolding pathway of foldamers. Of course, there are many open questions such as the relation of the mechanical unfolding pathway to thermal unfolding. In addition, more simulations with a broader variation of the pulling parameters will be performed in order to extract the kinetic rates of all relevant conformational transitions. We additionally plan to study more systems in order to further substantiate our conclusions.

Supporting Information Available The Supporting Information is available on the ACS Publications website. It contains details of MD-simulations, FE-curves, PMFs, fractions of native contacts and force field parameters used.

Acknowledgments Financial support by the DFG via the TRR146 and grant No. DI693/3-1 and by the MAINZ graduate school of excellence via a fellowship to L.U. is gratefully acknowledged. 25 ACS Paragon Plus Environment


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Figure 14: TOC

FPMD simula-ons: different pathways pull

β-‐peptoid

1

1

consecu-ve α/γ-‐pep-de one step

3

3

termini to center β-‐alanine

2

2


Determining Factors for the Unfolding Pathway of ... - ACS Publications

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