Insight Into the Dipeptide Self-Assembly Process Using Density

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C: Physical Processes in Nanomaterials and Nanostructures

Insight Into the Dipeptide Self-Assembly Process Using Density Functional Theory Norma Elizabeth Gonzalez-Diaz, Roberto Lopez-Rendon, and Joel Ireta J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b10340 • Publication Date (Web): 10 Jan 2019 Downloaded from http://pubs.acs.org on January 12, 2019

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The Journal of Physical Chemistry

Insight Into the Dipeptide Self-Assembly Process Using Density Functional Theory Norma E. González-Díaz,† Roberto López-Rendón,† and Joel Ireta∗,‡ †Facultad de Ciencias, Universidad Autónoma del Estado de México, Av. Instituto Literario 100, Toluca 50000, Estado de México, México ‡Departamento de Química, División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Iztapalapa, A.P. 55-534, Ciudad de México 09340, México. E-mail: [email protected] Phone: +52 55 5804 6413

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Abstract Hydrophobic dipeptides like L-Ala-L-Val (AV), L-Val-L-Ala (VA), L-Ala-L-Ile (AI), L-Ile-L-Ala (IA), L-Val-L-Val (VV), L-Ile-L-Val (IV) and L-Val-L-Ile (VI), labelled class V-A dipeptides, self-assemble as crystals composed of elongated helical tubes with narrow hydrophobic channels, whereas other hydrophobic dipeptides like L-PheL-Phe (FF), L-Leu-L-Leu (LL), L-Leu-L-Phe (LF), L-Phe-L-Leu (FL) and L-Ile-LLeu (IL), labelled class F-F dipeptides, crystallize as compact helical tubes with wide hydrophilic channels. To elucidate the molecular mechanism driving crystallization of these dipeptides, we use density functional theory for investigating the energetics and structural changes associated to the assembling process of isolated dipeptides into crystals and isolated helical tubes. It is shown that the position in which the side chain branches it is the determining factor driving these dipeptides to form either hydrophobic or hydrophilic channels. Furthermore, the latter also favor the formation of class F-F isolated tubes while disfavor the formation of the class V-A ones, indicating that the two sets of dipeptides follow different self-assembly paths.

Introduction Dipeptides tend to self-assemble into well-ordered structures with interesting chemical and physical properties like piezoelectricity, 1 optical and electronic activity, 2,3 great rigidity 4,5 and notable thermal and chemical stability. 6 These properties make them promising candidates for developing nanodevices for energy storage, drug delivery and electromechanical sensors, among other applications. 7 Moreover, peptides of that size can be considered reductionistic models suitable for investigating the formation of amyloid-like fibers, 8,9 whose presence in certain organs is associated to health disturbances such as Alzheimer’s, Parkinson’s and Huntington’s diseases. 10 It is therefore of great importance to advance our knowledge about the molecular features influencing dipeptide self-assembly. Certain hydrophobic dipeptides tend to crystallize as an assembly of helical tubes 11,12 2


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− in which hydrogen bonding, head (NH+ 3 ) to tail (-COO ) electrostatic attractions and van

der Waals interactions seem to be the primary stabilizing forces. 13–15 The resulting crystals present pores (channels) of diameter between 3 and 10 Å that are either hydrophobic or hydrophilic (Fig. 1). Dipeptides like L-Ala-L-Val (AV), L-Val-L-Ala (VA), L-Ala-L-Ile (AI), L-Ile-L-Ala (IA), L-Val-L-Val (VV), L-Ile-L-Val (IV) and L-Val-L-Ile (VI) labelled class V-A dipeptides, form crystals with hydrophobic channels, 12 whereas L-Phe-L-Phe (FF), L-LeuL-Leu (LL), L-Leu-L-Phe (LF), L-Phe-L-Leu (FL) and L-Ile-L-Leu (IL) labeled class F-F dipeptides, form crystals with hydrophilic channels. 11 Helical tubes forming the class V-A crystals are constituted by six dipeptides per turn in a conformation such that one of the side chains points towards the channel axis, and the other emanates from it (Fig. 1). So, the former side chain forms part of the inner wall of the tube, and the latter contributes to the formation of the inner wall of a neighbor one. Side chains of these dipeptides are thus in a trans conformation with respect to the peptide plane. Helical tubes composing class F-F

Figure 1: Crystal structures of hydrophobic dipeptides. The crystal plane shown is perpendicular to the helical tube axis. a) VA crystal, b) FF crystal. The magnified regions show the peptides constituting the tube wall.

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crystals are constituted by six (FF ) or four ( FL, LF, IL and LL) dipeptides per turn in a conformation such that both side chains point outwards the channel axis (Fig. 1); i. e. side chains are in a cis conformation with respect to the peptide plane, and form the outer wall of the tube. The inner wall is formed by the backbone, therefore, the channels become − hydrophilic owing to the presence of -NH, -CO, -NH+ 3 and -COO groups. On the contrary,

the inner wall of the class V-A tubes is composed solely by the side chains of the dipeptides, hence the channels are hydrophobic. Thus, even though class V-A and class F-F dipeptides are hydrophobic, the tube structures in which these crystallize have different characteristics like the hydrophilicity or hydrophobicity of the pores. Therefore these systems are valuable for scrutinizing the features of the side chains that may influence the peptide assembly process and ultimately determine the structure that a peptide adopts. A characteristic of class V-A dipeptides is that their side chains branch at Cβ , except for A, whereas class F-F dipeptides have at least one residue with a side chain branching at Cγ . 12 Here it is shown that such difference in branching crucially influence the crystallization process of these dipeptides. Peptide packing in both kind of crystals illustrates two efficient ways for fulfilling the stringent demand for hydrogen bonding the -NH and -CO backbone groups, and the -NH+ 3 and -COO− ending groups, either by itself or with the help of crystallization solvent. 13 To further our understanding of the peptide self-assembly process it is important to elucidate what molecular features drive the dipeptide self-assembly process to form a specific crystal structure; e. g. why dipeptides of class V-A do not crystallize as those of the class FF, and conversely. Also important to understand is the self-assembly mechanism; i. e. dipeptides first form isolated tubes that later self-assemble forming the porous crystals, or the channels in the crystals result from a self-assembly process of non-tubular aggregates. Self-assembly is a consequence of the interplay among different non-covalent interactions that minimize the free energy of a system. 16 As non-covalent interactions are relatively weak extrinsic factors like temperature, concentration, pH, solvents and co-solvents may control the dipeptide crystal formation. 17,18 Still there must be intrinsic molecular features of a given

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dipeptide driving packing towards the corresponding crystal structure, otherwise dipeptides of class V-A could crystallize as those of the class F-F, and vice versa, situation that has not been observed. In this work we use quantum chemical calculations based on density functional theory (DFT), to assess the energetics and the structural changes associated to the assembling process of dipeptides of classes V-A and F-F as crystals and isolated tubes. Our aim is to get insight into the molecular features that influence the self-assembly of these systems. We show that the conformation in which dipeptides crystallize is connected to the energy difference between the cis and the trans conformation of a given dipeptide, which is lower for F-F dipeptides than for the V-A ones. We discuss that the latter is due to the differences in the branching of the side groups in class F-F and class V-A dipeptides. Moreover, we argue that the latter also provoke that class F-F dipeptides first aggregate forming stable isolated tubes, in agreement with some experimental observations, 18–20 that later self-assemble into the crystal structure, whereas class V-A dipeptides should follow a different assembling path because the formation of isolated tubes will be disfavored. These results thus exemplify how intrinsic molecular features influence peptide self-assembly.

Methodology All calculations presented in this work have been obtained using DFT in its Kohn-Sham formulation and periodic boundary conditions. We have used the Perdew-Burke-Ernzerhof (PBE) approximation to the exchange-correlation functional, 21 plane waves as basis set and the projector augmented waves method 22 as implemented in the VASP code. 23,24 As current approximations to the exchange-correlation functional do not describe appropriately the van der Waals interactions, here we use the Tkatchenko-Scheffler (TS) method 25 to correct the PBE calculations. The combination PBE-TS leads to accurate predictions of structural, energetic, elastic and cohesive properties for various kinds of molecular complexes 26 including peptides in different conformations 27,28 and peptide crystals, 29 where dispersion forces

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are expected to be essential. Hydrogen bonding cooperative effects are a key factor to be considered in the aggregation process of polypeptides. It has been shown that these cooperative effects are also well described by the kind of methodologies used in this work. 29–31 Furthermore, below we show that PBE-TS accurately describe the lattice parameters of the investigated crystals. The starting unit cell parameters and dipeptide geometries for the DFT calculations are obtained from the Cambridge Structural Database. 32 The unit cell parameters and all the internal degrees of freedom are fully optimized using a planewave cutoff of 800 eV and the next k-point meshes for sampling the first Brillouin zone: 2×2×2 for AV, VA, AI, IA, VV, IV and VI, 4×1×1 for LL and FL, 1×4×1 for LF and IL, and 1×1×4 for FF. We have corroborated convergence in total energies within 10−3 eV, with respect to the cutoff and the k-point sampling. The fully optimized crystal structures are used for building infinitely long isolated tubes of each of the investigated systems. It has been shown that using infinitely long models hydrogen-bonding cooperative effects are fully taken into account. 30,33 Moreover these kind of models have been successfully applied for investigating the structural and thermodynamic stability of polypeptides in α-helix and β-sheet conformations. 34–36 To build the isolated tubes it is used the same number of dipeptides per unit cell as those in the crystal structure, except for FL and LL because for these systems the crystal structure is comprised of two tubes in antiparallel orientation per unit cell. The geometry of the isolated tubes is fully optimized keeping all the lattice parameters of the unit cells fixed at the values corresponding to the optimized crystal structures, except for those along the perpendicular directions to the tube axis, which are kept fixed at values large enough to avoid lateral tubetube interactions. For the calculations of the isolated tubes two and four k-points along the tube axis are used for the class V-A and class F-F dipeptides, respectively. Isolated dipeptides corresponding to each of the investigated systems are also fully optimized using unit cells with lattice parameters large enough to avoid interactions with the periodic images. For these calculations the Γ-point is used for sampling the Brillouin zone.

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Results The PBE-TS predicted values for the lattice parameters of the class V-A and F-F crystals are in very good agreement with the experimental ones 11,12,37–39 (see Table 1 of the supplementary material). Differences between predicted and experimental longitudinal lattice parameters are small, differ less than 3% (see Fig. 2), and those respect to angular lattice parameters are negligible.

Figure 2: Absolute deviation of the PBE-TS predicted lattice parameters from to the experimental ones (in percentage). The blue columns stand for the a-lattice parameter, the red columns stands for the b-lattice parameter and the green columns for the c-lattice parameter. Therefore, we are confident that the methodology used here adequately describes the investigated systems. It is worth noting that the LL and LF experimental crystal structures include water molecules, therefore these systems are calculated with and without water molecules. The inclusion of water in the calculations change little the predicted lattices parameters (see Table 1 of the supplementary material); e. g. longitudinal lattice parameters change 4%, at most, with respect to the predicted values for the corresponding crystals without water molecules. Moreover, predicted lattice parameters for the hydrated systems differ by 3%, at most, from the experimental ones (Fig. 2). These results indicate that crystallization water molecules do not play a significant role in determining the crystal shapes of these systems. Nevertheless, as it is discussed below, water paves the way for the class F-F dipeptides to crystallize forming tubes with a hydrophilic inner wall, which is in accordance with some experimental observations. 40–42 Thereafter we discuss solely the systems without 7



crystallization water molecules. All dipeptides in the optimized crystal structures are in a zwitterionic state, even in the absence of the crystallization water molecules, i. e. packing is such that dipeptides self-stabilize as zwitterions. A structural feature of these crystals readily comparable is the pitch of the helical tubes. Class F-F helical tubes have a pitch around 5.3 Å, like that of a π-helix, 43 while the pitch of class V-A helical tubes is two times larger, around 10.1 Å; i. e. helical tubes of the class V-A are significantly more elongated than those of the class F-F. As mentioned above class V-A dipeptides are in a trans conformation in the corresponding crystal structure, whereas class F-F dipeptides are in a cis conformation. As a consequence the (φ, ψ) dihedral angles (see Table 2 of the supplementary material) are quite different in these two sets of dipeptides, particularly the φ angle. Comparing these dihedral angle values with the most populated zones in a Ramachandran plot, 44 it is clear that class V-A dipeptides are in a β-sheet like conformation and class F-F dipeptides in a conformation unusual for protein residues, located on the upper left side of the upper right quadrant of the Ramachandran plot (Fig. 3). Next, the geometry of infinitely-long isolated tubes built from the corresponding optimized crystal structures is relaxed keeping the pitch of the helix fixed at the value in the optimized crystal structure. After geometry relaxation it is found that class V-A dipeptides are in the canonical state in the isolated helical tubes (Fig. 4), whereas class F-F dipeptides are as zwitterions (Fig. 5).

The latter is likely connected to

the hydrogen bonds formed by the end groups of the dipeptides. Inspecting the geometry of the isolated tubes it is found that each oxygen of the -COO− ending group of the class F-F dipeptides is forming at least one hydrogen bond (Fig. 5). However, the oxygen of the carbonyl group at the -COOH ending group of the class V-A dipeptides it is not hydrogen bonded (Fig. 4), which disfavor the zwitterionic state stabilization, as it has been shown in other peptide crystals. 29 Comparing the conformations of dipeptides in the crystals and in the isolated tubes it is found that these are quite similar; averaged (φ, ψ) angles of dipeptides in the isolated tubes differ by ∼12◦ , at most, from those of dipeptides in the

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Figure 3: The φ and ψ dihedral angles of the dipeptides in the crystal structures (squares), isolated tubes (triangles) and isolated dipeptides (circles). The close squares, triangles and circles stand for the class V-A dipeptides. The open squares, triangles and circles stand for the class F-F dipeptides. The depicted φ and ψ values of dipeptides in crystals and tubes are the average over all the dipeptides in the unit cell.

Figure 4: Relaxed geometry of class V-A isolated tubes. Side chains are omitted for clarity. The magnified region shows the hydrogen bonds (dotted lines) formed by the dipeptides constituting the tube. Notice that dipeptides are in a canonical state. 9



Figure 5: Relaxed geometry of class F-F isolated tubes. Side chains are omitted for clarity. The magnified region shows the hydrogen bonds (dotted lines) formed by the dipeptides constituting the tube. Notice that dipeptides are in a zwitterionic state. crystals (Fig. 3 and Table 2 of the supplementary informatiom). Optimizing the geometry of isolated dipeptides from the crystal structures, it is found that these prefer to be canonical, as expected, owing to the absence of solvent in the calculations. Moreover, the relaxed geometry of the isolated dipeptides is also quite similar to that in the crystals and isolated tubes (Fig.

3), the dihedral angles differ by ∼18◦ , at most. Thus, the packing process

alter little the dipeptide geometry except for the proton transferred for transforming the canonical state to the zwitterionic one. It is important to mention that in the process of relaxing the geometry of the isolated dipeptides, different orientations of the -COOH ending groups are sampled. The (φ, ψ) values of the isolated dipeptides reported in Table 2 of the supplementary material and depicted in Fig. 3, correspond to the conformation in which the -COOH orientation, measured with the dihedral angle O-C-C-N (labelled ψ’) where the O atom is the one belonging to the carbonyl group in -COOH, is the optimal. In Table 2 of the supplementary material the ψ’ values are also reported. Clearly the optimal orientation

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of the -COOH group in class V-A dipeptides differ from the one in class F-F dipeptides, which is another structural distinction between these two sets of dipeptides. Association energies of crystals and isolated tubes (Fig. 6), i. e. differences between total energies per dipeptide of dipeptides in crystals/tubes and those of the corresponding isolated dipeptides, are calculated considering isolated tubes/dipeptides rigid and fully relaxed. Taking isolated tubes and dipeptides as rigid means that their geometries are the ones at the relaxed crystals. Analyzing the total association energies for the crystals, obtained with the

Figure 6: Association energies (∆Eassoc ), in kcal mol−1 , of crystals (squares) and isolated tubes (dots) composed with class V-A dipeptides (these to the left of the vertical dashed line) or class F-F dipeptides (these to the right of the vertical dashed line). Calculations are done using the rigid (solid lines) and the fully relaxed (dotted lines) approaches. rigid model, it is found that these are slightly larger for the class F-F crystals than for the class V-A ones. The former association energies vary between -120 and -130 kcal/mol and the latter between -110 and -120 kcal/mol. However, the isolated-tube association energies also estimated with the rigid model are significantly different between the two sets of systems (Fig. 6). Those for class F-F tubes are two times larger, at least, than those for the class V-A ones. Indeed, association energies for class F-F isolated tubes are around 90% of the corresponding total association energies, whereas those for class V-A tubes solely amount to 40%, at most. Association energies obtained considering the fully relaxed systems follow the same trend that those obtained with the rigid model (Fig. 6), except that the former are significantly lower in absolute values. Such behavior is primarily due to the difference in the state of the isolated dipeptide used for calculating the association energies, for the relaxed 11



cases such dipeptide state is canonical and for the rigid ones zwitterionic. To further our analysis, it is estimated the energy connected to the assembly process of tubes into crystals, which is calculated as the difference between crystal association energies and isolated-tube association energies (Fig. 7). Assembly energies for class V-A systems are about 60% of

Figure 7: Energy associated to the assembling of class V-A isolated tubes (systems to the left of the vertical dashed line) and class F-F isolated tubes (systems to the right of the vertical dashed line) into crystals (∆Eassem ), in kcal mol−1 . Calculations are done using the rigid (solid line) and fully relaxed (dotted line) approaches. the corresponding crystal association energies, whereas those for the class FF ones amount solely to ∼10% of the corresponding crystal association energies. Assembly energies calculated with the rigid and relaxed models differ significantly for the class V-A systems. The latter is primarily due to the difference in the state of the dipeptides in the isolated tubes, which is zwitterionic in the first case and canonical in the second one. Assembly energies for the class F-F systems calculated either with the rigid or the fully relaxed models are almost the same (Fig. 7), due to the fact that the zwitterionic state of the dipeptides is already formed in the isolated dipeptides. This result indicates that geometry relaxation effects upon packing tubes into crystals are negligible for the class F-F dipeptides. In order to pinpoint why dipeptides of the class F-F self-assemble in a cis conformation and those of the class V-A in a trans one, but not the another way around, the conformation of the former dipeptides is swapped with that of the latter ones; i. e. the (φ,ψ, ψ’) dihedral angles of a given isolated dipeptide of the class F-F are set to the averaged (φ, ψ, ψ’) values obtained from the class V-A isolated dipeptides, and vice versa. Then its geometry is fully 12


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relaxed to the closest minimum. The dihedral angles of the new set of optimized dipeptides (labelled as swapped) are depicted in Fig. 8 together with the original values. These values

Figure 8: φ and ψ dihedral angles for the class V-A dipeptides (squares) and the class F-F dipeptides (circles). The close squares and circles stands for the isolated dipeptides from the crystals (unchanged dipeptides). Open squares and circles stand for the swapped dipeptides. The arrows indicate the correspondence between the unchanged and the swapped dipeptides. are also listed in Table 2 of the supplementary material. According to these values optimized swapped isolated dipeptides of the class V-A are in a cis conformation, and the optimized swapped isolated dipeptides of the class F-F in a trans conformation (Fig. 8). Comparing the total energies of the isolated dipeptides in cis and trans conformations, it is found that the trans conformation is lower in energy than the cis one (Fig. 9). For class V-A dipeptides the trans conformation is around 4 or 5 kcal/mol more stable than the cis one. For the class F-F dipeptides the energetic difference between cis and trans is slightly smaller, it amounts to 2 or 3 kcal/mol. Thus both set of isolated dipeptides prefer to be in a trans conformation, nevertheless the class F-F ones crystallize in a cis conformation (Fig. 9).

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Figure 9: Energy difference, in kcal mol−1 , between the cis and the trans conformations for the class V-A (blue bars) and class F-F (green bars) isolated dipeptides. The trans conformation is considered as the reference system.

Discussion Considering that the assembly process does not alter significantly the geometry of the dipeptides, then one may expect that at experimental conditions the majority of the class V-A dipeptides in solution, before crystallizing, are in a trans conformation whereas the class F-F dipeptides in the cis one. However, according to our results both sets of dipeptides prefer the trans conformation in isolation. This implies that at experimental conditions externar factors like solvent or temperature revert the cis-trans energetic ordering of the class F-F dipeptides, likely due to the low energetic difference between these two conformations for such dipeptides. It seems that the latter effect does not revert the energetic ordering the class V-A dipeptides owing to a larger energetic difference between the cis and the trans conformations. Such energetic differences between the cis and the trans conformations could be connected to the branching of the side chains i. e. class F-F dipeptides are formed by at least one residue with a side chain branching at Cγ , whereas V-A dipeptides are formed by residues branching at Cβ . This difference makes the carbon atoms bonded to Cβ to be closer to the Cα backbone in class V-A dipeptides than in the class F-F ones. Measuring these distances in the geometry optimized cis dipeptides, it is found that at least two distances are ∼ 2.53 Å in the class V-A dipeptides. However, in the class F-F dipeptides these distances are slightly larger, about 2.57 Å. Therefore, class V-A dipeptides in cis conformations are 14


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slightly less stable than the class F-F ones owing to larger repulsive effects. As a consequence of the structure adopted by these dipeptides at experimental conditions, the helical tubes that can be formed are structurally different, which in turn may define its assembling path. Certainly more robust methods, like multiscale modeling, 45 are necessary to simulate the solvation of dipeptides. Thus one may fully prove that class F-F dipeptides indeed adopt a cis conformation, and the V-A dipeptides a trans one, in solution at experimental conditions. Nevertheless, our results together with experimental observations are still valuable as a guide to advance plausible assembly paths as it is discussed next. In aqueous solution peptides tend to be zwitterions if the pH is close to neutrality. Therefore, one could suggest that among the plausible assembly paths, those in which dipeptides are kept in the zwitterionic state are more favorable. These assembly paths will involve solely a desolvation process of the charged and polar groups as dipeptide geometrical changes are minimal upon assembling. Actually, experimental studies of the thermodynamics of the assembly of the FF dipeptide display the characteristics of a desolvation process. 46 According to our results assembling dipeptides into isolated tubes favors the zwitterionic state for the F-F dipeptides but disfavors that for the V-A ones. Although in the presence of aqueous solvent V-A dipeptides could also keep the zwitterionic state upon assembling into tubes, as the carbonyl group of the C term will be exposed to the solvent, such assembling process will be energetically not so favored because the hydrogen bonding network along the backbone of the V-A dipeptides is not formed (see Fig. 4). Hence, a plausible self-assembly path for the F-F dipeptides is first the formation of isolated tubes, which is in agreement with some experimental findings, 18–20 that later self-assemble into crystals. Such path preserves the zwitterionic state and favors the formation of backbone -NH· · ·OC- hydrogen bonds as the class F-F dipeptides assemble into isolated tubes. The latter self-assembly path, however, may no be the one followed by the class V-A dipeptides, mainly because it is not favored the formation of backbone -NH· · ·OChydrogen bonds as the class V-A dipeptides are self-assembly into the isolated tubes. Likely there are another ways of starting the clustering the V-A dipeptides in such a way that the

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formation of backbone -NH· · ·OC- hydrogen bonds is favored and the zwitterionic state is preserved, either by the solvent or by the contact with neighbor peptides. Further investigations are thus required to shed light into the self assembling mechanism that follows the V-A dipeptides.

Conclusions In conclusion we show using quantum chemical calculations based on DFT, that the structural differences of crystals composed of class V-A and class F-F dipeptides are connected to intrinsic features of its constituting units. Particularly to their side chain branching, which makes the cis disposition of the side chains respect to the peptide plane a plausible conformation for the class F-F dipeptides, but the trans conformation for the V-A ones at experimental conditions. Therefore, class V-A dipeptides crystallize in a trans conformation and class F-F in a cis one. Due to the conformations adopted by the dipeptides the class F-F forms compact helical tubes in which dipeptides are in a zwitterionic state, whereas class V-A dipeptides forms elongated helical tubes in which dipeptides are in a canonical state. Based on these results we conclude that dipeptides of the class F-F first aggregate as stable isolated tubes that later self-assemble into crystals, while class V-A dipeptides should follow a different self-assembly path. We are confident that these results further our understanding of the self-assembling process of peptides.

Acknowledgement N.-E. G. acknowledges CONACYT for the scholarship granted. Authors gratefully acknowledge the computing time granted by LANCAD and CONACYT on the supercomputer Yoltla at the LSVP at UAM-Iztapalapa.

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Supporting Information Available The PBE-TS predicted and experimental lattice parameters of the investigated crystals. The values for the dihedral angles φ, ψ and ψ’ for the dipeptides in the crystal structures, isolated tubes, and isolated and swapped dipeptides.

This material is available free of charge via

the Internet at http://pubs.acs.org/.

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Insight Into the Dipeptide Self-Assembly Process Using Density

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