Effect of Zn 2 + ions on the assembly of amylin oligomers : insight into the molecular mechanisms †

Amylin is an endocrine hormone and is a member of the family of amyloid peptides and proteins that emerge as potential scaffolds by self-assembly processes. Zn ions can bind to amylin peptides to form self-assembled Zn–amylin oligomers. In the current work the binding sites of Zn ions in the selfassembled amylin oligomers at various concentrations of zinc have been investigated. Our results yield two conclusions. First, in the absence of Zn ions polymorphic states (i.e. various classes of amylin oligomers) are obtained, but when Zn ions bind to amylin peptides to form Zn–amylin oligomers, the polymorphism is decreased, i.e. Zn ions bind only to specific classes of amylin. At low concentrations of Zn ions the polymorphism is smaller than at high concentrations. Second, the structural features of the self-assembled amylin oligomers are not affected by the presence of Zn ions. This study proposes new molecular mechanisms of the self-assembly of Zn–amylin oligomers.


Introduction
2][3][4][5] Amyloid assembly is a multistep process, starting from an isolated monomer of amyloid, followed by aggregation into oligomers and fibrils, 6 and it has become the subject of intensive research in soft matter and materials science. 7,8The family of amyloid peptides and amyloid proteins emerge as potential scaffolds and biomaterials for the growth of mammalian cells. 9Spectroscopic and calorimetric approaches have been employed to characterize the stability of aggregated amyloids and elucidate the complex mechanism of fibril polymerization and depolymerization. 10etal ions are used to modulate the in vitro formation of protein nano-objects for creating functional materials. 7,8Metal ions also affect amyloid aggregation, promoting precipitation and fibrillogenesis, and alter the morphology of aggregates. 11ransition metals such as Cu 2+ , Fe 3+ and Zn 2+ are particularly interesting as they are found at high concentrations in the core and periphery of senile amyloid plaque deposits. 124][15] The role of metal ions in other amyloid peptides and proteins with regard to amyloid aggregation is well-documented.][24][25] Amylin, which is also known as human islet amyloid polypeptide (hIAPP), is an endocrine hormone that consists of a 37-residue sequence and is a member of the family of amyloid peptides and proteins.In vitro studies have shown that Cu 2+ ions inhibit the formation of amylin fibrils, 26,27 and prevent the formation of the b-sheet structures of amylin that are identified as oligomers and fibrils. 28Yet, studying the role of Zn 2+ in amylin aggregation is particularly of greater interest than the role of Cu 2+ ions.While Cu 2+ ions do not emerge from the pancreas together with amylin, it is known that amylin and Zn 2+ ions are stored and packed inside the b-cell granules in the pancreatic islets 29,30 and enter the blood stream together. 29In the pathological state of type 2 diabetes (T2D), amylin peptides aggregate to form various fibrillary structures. 31,324][35] It is also known that amylin and Zn 2+ ions have a crucial role in glycemic regulation, but interruption in their delicate balance may cause the aggregation of amylin and thus the progression of T2D. 33,34Therefore, amylin peptides can interact with Zn 2+ ions to form similar amyloid plaque deposits as other amyloids.Yet, the mechanisms and chemistry through which Zn 2+ ions interact with the toxic amylin oligomers are still elusive.
In vitro studies have shown that Zn 2+ ions play a role in promoting amylin aggregation 30,36,37 and it was suggested that Zn 2+ ions bind only to His18 in the amylin monomer. 37,38amamoorthy and coworkers proposed that Zn 2+ ions have a complex effect on amylin aggregation because the Zn 2+ ions have different effects depending on the various stages of amylin aggregation.At an early stage of aggregation (40 min) and at high concentrations of Zn 2+ ions (10 mM), the Zn 2+ ions induce the formation of large sizes of Zn 2+ -amylin aggregates compared with the absence of Zn 2+ ions.However, at an early stage of aggregation (40 min) and at low concentrations of Zn 2+ ions (100 mM), the Zn 2+ ions promote the formation of even larger sizes of Zn 2+ -amylin aggregates than those that are formed at high Zn 2+ concentrations. 39At the later stage of aggregation in which amylin fibrils are formed, the Zn 2+ ions inhibit fibril formation at low concentrations, but the Zn 2+ ions accelerate the formation of fibrils at higher concentrations. 37,39,40espite the extensive work done previously, there are still questions that remain to be solved.How Zn 2+ ions bind to amylin oligomers at the atomic resolution, i.e. what are the coordination binding sites?How Zn 2+ ions affect the structure and stability of amylin oligomers?and what are the possible zinc : amylin ratios in amylin oligomers?This work is the first study that is aimed to address these important questions.
To address these issues, we applied our previous amylin oligomers, 41 which were derived from the structural ssNMR models 31 and from the crystal structural models. 32We have shown that there are four different amylin oligomers that are derived from the experimental studies that vary by the orientation of the residues along the sequence of the b-arch structure of amylin oligomers.Herein, we present a first study that investigates the specific binding sites in the various amylin oligomers, considering His18 as a potential residue that binds Zn 2+ ions, as previously proposed by ssNMR. 39,40In order to provide insight into the effect of Zn 2+ ions on the structure and the stability of amylin oligomers, we compare the structural characterization of Zn 2+ -amylin oligomers versus our previous amylin oligomers (in the absence of Zn 2+ ions).Finally, we examine various Zn 2+ : amylin ratios, which have been proposed by experimental studies. 39,40Our molecular dynamics (MD) simulations revealed that Zn 2+ ions selectively bind to specific classes of amylin oligomers thus reducing the polymorphism, but within these classes of Zn 2+ -amylin oligomers, polymorphic states were characterized due to the various concentrations of Zn 2+ ions.

Molecular dynamics (MD) simulations protocol
We constructed various models of Zn 2+ -amylin octamers with different Zn 2+ : amylin ratios by using Accelerys Discovery Studio software. 42Since the His18 residues in all constructed models bind Zn 2+ ions, all His18 residues were deprotonated.MD simulations of the solvated models were performed in the NPT ensemble using the NAMD package 43 with the CHARMM27 force field. 44,45The models were energy minimized and explicitly solvated in a TIP3P water box 46,47 with a minimum distance of 15 Å from each edge of the box.Each water molecule within 2.5 Å of the models was removed.Counter ions were added at random locations to neutralize the models' charge.The Langevin piston method 43,48,49 with a decay period of 100 fs and a damping time of 50 fs was used to maintain a constant pressure of 1 atm.A temperature of 330 K was controlled using a Langevin thermostat with a damping coefficient of 10 ps À1 . 43The short-range van der Waals interactions were calculated using the switching function, with a twin range cut-off of 10.0 and 12.0 Å. Long-range electrostatic interactions were calculated using the particle mesh Ewald method with a cutoff of 12.0 Å. 48,50 The equations of motion were integrated using the leapfrog integrator with a step of 1 fs.The solvated systems were energy minimized for 2000 conjugated gradient steps, where the hydrogen bonding distance between the b-sheets in each oligomer was fixed in the range 2.2-2.5 Å.The counter ions and water molecules were allowed to move.The hydrogen atoms were constrained to the equilibrium bond using the SHAKE algorithm. 51The minimized solvated systems were energy minimized for 5000 additional conjugate gradient steps and 20 000 heating steps at 250 K, with all atoms being allowed to move.Then, the system was heated from 250 to 330 K for 300 ps and equilibrated at 330 K for 300 ps.All simulations were run for 50 ns at 330 K.These conditions were applied to all of the Zn 2+ -amylin octamers.The temperature of 330 K (which is higher that room/body temperature) has been chosen in order to investigate the stability of the Zn 2+ -amylin oligomers.Obviously, Zn 2+ -amylin oligomers that are stable at this temperature will be stable also at lower temperatures.The timescale of 50 ns has been examined for all simulated Zn 2+ -amylin octamers to ensure that this timescale is sufficient for these systems (see the Results and discussion section).

Analysis details
We examined the structural stability of the studied models by following the changes in the number of hydrogen bonds between b-strands, with the hydrogen bond cut-off being set to 2.5 Å.We further computed the root-mean square deviations (RMSDs), root-mean square fluctuations (RMSFs) and monitored the change in the inter-sheet distance (Ca backbonebackbone distance) in the core domain of all of the simulated Zn 2+ -amylin octamers.We estimated the core domain, as we previously estimated for amylin oligomers. 41In all the simulated Zn 2+ -amylin octamers that are based on model A2, the core domain was defined as the distance between residue 12 and residue 30.In all the simulated Zn 2+ -amylin octamers that are based on model A3, the distance between residue 12 and residue 29 was defined as the core domain.Finally, we estimated the average number of water molecules around each side-chain Cb carbon within 4 Å for each simulated Zn 2+amylin octamer.
This journal is © the Owner Societies 2016

Generalized born method with molecular volume (GBMV)
To obtain the relative conformational energies of the previous simulated amylin octamers 41 and the current simulated Zn 2+amylin octamers, the trajectories of the last 5 ns of each simulated Zn 2+ -amylin octamer were first extracted from the explicit MD simulation excluding the water molecules.The solvation energies of all systems were calculated using the GBMV. 52,53In the GBMV calculations, the dielectric constant of water was set to 80.The hydrophobic solvent-accessible surface area (SASA) term factor was set to 0.00592 kcal mol À1 Å À2 .Each conformer was minimized using 1000 cycles, and the conformational energy was evaluated by grid-based GBMV.
A total of 1500 conformations (500 conformations for each of the 3 previous conformers 41 ) were used to construct the energy landscape of the simulated amylin octamer that are based on model A2 (models M2, M2D and M5) and to evaluate the conformer probabilities by using Monte Carlo (MC) simulations.Similarly, a total of 1500 conformations were used: 500 conformations for each of the 2 examined conformers of the simulated Zn 2+ -amylin octamers that are based on model A2 with the Zn 2+ : amylin ratio of 1 : 2 (models R1 and R2) and one examined conformer simulated Zn 2+ -amylin octamer that is based on model A3 with the Zn 2+ : amylin ratio of 1 : 2 (model S1).Finally, we used 1000 conformations, 500 conformations for each of the 2 examined conformers: one for the simulated Zn 2+ -amylin octamer that is based on model A2 with the Zn 2+ : amylin ratio of 1 : 4 (model R3) and the second for the simulated Zn 2+ -amylin octamer that is based on model A3 with the Zn 2+ : amylin ratio of 1 : 4 (model S3).
In the first step, one conformation of conformer i and one conformation of conformer j were randomly selected.Then, the Boltzmann factor was computed as e À(Ej À Ei)/KT , where E i and E j are the conformational energies evaluated using the GBMV calculations for conformations i and j, respectively, K is the Boltzmann constant and T is the absolute temperature (298 K used here).If the value of the Boltzmann factor was larger than the random number, then the move from conformation i to conformation j was allowed.After 1 million steps, the conformations 'visited' for each conformer were counted.

Results and discussion
Zn 2+ ions selectively bind to specific classes of amylin oligomers It has been shown by Ramamoorthy's group that Zn 2+ ions in amylin solution lead to the formation of oligomers and fibrils. 37,39herefore, the Zn 2+ ions induce the formation of the cross-b structure of amylin and thus our initial constructed models here are based on the amylin oligomers and fibril-like structures with their self-assembled cross-b structure.Previously, 41 we generated eight various molecular structural amylin cross-b octamers of single-and double-layer conformations applying models A1-A4 as 'building blocks' from Tycko's 31 and Eiesnberg's 32 coordinates (Fig. 1).These four models share the same sequence of 37 residues of amylin, but they differ in the orientations of the residues both along the backbone of the two b-strands and the U-turn of the b-arch structure of amylin.A particular difference that is related to this study is the location of His18 in the U-turn domain of amylin.In models A1 and A4, His18 is located inside the core domain, while in models A2 and A3 His18 is located outside the core domain (Fig. 1).
We first examined the binding site of Zn 2+ ions in amylin oligomers that are based on these four models A1-A4 for singleand double-layer conformations.The Zn 2+ ions were interacted with His18, since it was suggested that Zn 2+ ions bind to His18 in the amylin monomer. 37,38We constructed various conformations with the Zn 2+ : amylin ratio of 1 : 2 models Q1, Q2, T1 and T2 (Fig. 2) and R1, R2, S1 and S2 (Fig. 3).Table 1 summarizes these various conformations of Zn 2+ -amylin oligomers.The single-and the double-layer conformations that were constructed from models A1 (models Q1 and Q2) and A4 (models T1 and T2), in which His18 is located in the core domain, illustrated unstable Zn 2+ -amylin oligomers.During minimization, the Zn 2+ ions escaped upon interaction with His18.We suggest that the steric effects inside the core domain in the b-arch domain of the amylin oligomers do not allow Zn 2+ ions to interact with His18 residues (Fig. S1, ESI †).We therefore propose that Zn 2+ ions do not bind to amylin oligomers that are based on models A1 and A4 and thus decrease the polymorphism, which is strongly reflected in the aggregation of amylin with the absence of Zn 2+ ions, as we previously demonstrated for amylin oligomers. 41n models A2 and A3 His18 is located outside the core domain of the b-arch.The single-and the double-layer conformations of models R1 and R2, which are based on model A2, and the single-layer conformation model S1, which is based on model A3, demonstrated that during minimization and MD simulations the Zn 2+ ions were not escaped from the binding site.Surprisingly, in the double-layer conformation model S2, which is based on model A3, the Zn 2+ ions escaped from the binding site after 5 ns of simulations (Fig. S2, ESI †).Finally, for the Zn 2+ : amylin ratio of 1 : 4, only single-layer conformation model R3 is based on model A2 and single-layer conformation model S3 is allowed to bind Zn 2+ ions within this ratio.Table 1 summarizes these two conformations of Zn 2+ -amylin oligomers with the ratio of 1 : 4. We therefore focused our simulations and Fig. 1 Representation of the molecular models of the fibril-like structures of amylin that differ in the orientations of the residues along the b-arch and the turn domain.The models were extracted from experimental studies 31,32 and from our previous work. 41Residue colors: Arg11, red; His18, blue; Asn19, purple; and Asn31, green.
analysis only on models R1, R2 and S1 for the Zn 2+ : amylin ratio of 1 : 2 and R3 and S3 for the ratio of 1 : 4.

Examining the variety of Zn 2+ coordination modes in amylin oligomers
In numerous biological systems Zn 2+ ions bind to ligands, such as amino acids and water molecules.Since it is known that Zn 2+ ions bind His18 in the amylin monomer, 37 it is great of interest to investigate the Zn 2+ : amylin ratio in Zn 2+ -amylin oligomers.To examine the possible Zn 2+ : amylin ratio in Zn 2+amylin oligomers, we constructed various Zn 2+ : amylin ratios of octamers that are based on models A2 and A3.There is a diversity of coordination modes of Zn 2+ ions in proteins.It has been suggested that Zn 2+ ions can bind to 4-6 amino acids or/and water molecules in proteins. 545][56] Previously Ramamoorthy's group suggested that Zn 2+ ions bind to 3, 4 and 6 helical amylin monomeric structure in His18. 39,40Yet, Ramammorthy's group also suggested that Zn 2+ ions induce the formation of amylin fibrils, i.e. cross-b structures of amylin.Therefore, the coordination mode of Zn 2+ ions in the self-assembled cross-b structure of amylin oligomers is still unknown.To address this issue, we examined various Zn 2+ : amylin ratios of 1 : 1 (Fig. S3, ESI †), 1 : 2 (models R1, R2 and S1) and 1 : 4 (models R3 and S3).The ratio of 1 : 3 has not been examined here and ongoing work is performed in our group to examine this ratio.Finally, the ratio of 1 : 6 may be applicable to be examined for the six helical monomeric structures of amylin, 39,40 but this ratio cannot be applicable in the cross-b structure of amylin oligomers that are studied here.
We examined the Zn 2+ : amylin ratio of 1 : 1 for both single and double-layer conformations that are based on models A2 and A3.Not surprisingly, the Zn 2+ ions were escaped from the binding site, probably due to the electrostatic repulsions between the Zn 2+ ions (Fig. S3, ESI †).Furthermore, it is more likely that the Zn 2+ : protein ratio or the Zn 2+ : amylin ratio of 1 : 1 is not possible when the Zn 2+ ion binds to only one residue, such as His18 in amylin, and our simulations provided support to this hypothesis.
As seen in Fig. 3, we also examined the Zn 2+ : amylin ratio of 1 : 2 both for single-and double layer conformations that are based on models A2 (models R1 and R2) and A3 (model S1).Our simulations suggest that each Zn 2+ ion binds to two Ne atoms (each of two His18 residues of two amylin monomers) in these models, and four O atoms of water molecules complete the coordination mode to six coordination by forming an octahedral molecular geometry (Fig. S4 and Table S1, ESI †).Interestingly, the ratio of Zn 2+ : Ab of 1 : 2 has also been illustrated by Fig. 3 Single-and double-layer constructed models of the Zn 2+ -amylin oligomer in which the amylin peptides are composed of A2 (models R1 and R2) and A3 (models S1 and S2).The Zn 2+ : amylin ratio is 1 : 2, i.e. each Zn 2+ ion binds two His18 of two peptides.Residue colors: Arg11, red; His18, blue; Asn19, purple; and Asn31, green.
Miller et al. for Zn 2+ -Ab oligomers; however, the completion of coordination with water molecules has not been studied for these oligomers. 25As noted in the previous section, surprisingly, in the double-layer conformation model S2, which is based on model A3, the Zn 2+ ions escaped from the binding site after 5 ns of the simulations (Fig. S2, ESI †).Finally, we examined the Zn 2+ : amylin ratio of 1 : 4 for models that are based on model A2 (model R3) and model A4 (model S3).In each one of models R3 and S3, two single-layer conformations were joined together by Zn 2+ ions (Fig. 4).These two models, R3 and S3, exhibited stable Zn 2+ -amylin oligomers.Each Zn 2+ ion in these two models binds to Ne atoms (each of four His18 residues of four amylin monomers) and two water molecules (Fig. S5 and Table S2, ESI †).The Zn 2+ : Ab ratio of 1 : 4 has also been shown by Miller et al. for Zn 2+ -Ab oligomers, but the completion of the coordination with water molecules has not been shown. 25It should be noted that the ratio of 1 : 4 cannot allow the formation of double-layer conformations of Zn 2+ -amylin oligomers in the well-organized cross-b structure.

Polymorphic states of Zn 2+ -amylin oligomers depend on the concentration of Zn 2+ ions
We have previously shown that amylin oligomers exhibit polymorphic states, i.e. there are several conformations of amylin oligomers with similar energies and similar populations. 41t was previously suggested that Zn 2+ ions increase the polymorphism in Ab oligomers. 25,57Herein, we showed that because Zn 2+ ions cannot bind to all polymorphic amylin oligomers, the Zn 2+ ions decrease polymorphism in amylin oligomers.Yet, within the structures of Zn 2+ -amylin oligomers, it is of great interest to examine whether binding Zn 2+ ions to amylin oligomers may also lead to polymorphism.To investigate this issue, we estimated the conformational energies of Zn 2+ -amylin oligomer models with the Zn 2+ : amylin ratio of 1 : 2, which are based on model A2: models R1, R2 and the model that is based on A3: model S1.We further estimated the conformational energies of Zn 2+ -amylin oligomer models with the Zn 2+ : amylin ratio of 1 : 4 for the model that is based on A2 (model R3) and models that are based on A3 (model S3).The values of the averaged conformational energies are listed in Table S3 (ESI †).Finally, we estimated the relative conformational energies values of the equivalent amylin oligomers: models M2, M2d and M5 from our previous study. 41The values of the averaged conformational energies are also listed in Table S3 (ESI †).
The averaged conformational energies and the distribution of the last 500 conformations for these models are in seen in Fig. 5.One can see that with the absence of Zn 2+ ions the energy difference between amylin oligomers that are based on model A2 (model M2 and M2d) and the amylin oligomer that is based on model A3 (model M5) is in the range of 200-320 kcal mol À1 .However, these are not the only models of amylin oligomers, as we previously shown, amylin oligomers are polymorphic and there are at least 12 different amylin oligomers. 41When adding Zn 2+ ions with the Zn 2+ : amylin ratio of 1 : 4, the energy difference between the models that are based on model A2 (model R3) and the model that is based on model A3 (model S3) is B250 kcal mol À1 .Therefore, we suggest that adding relatively low concentrations of Zn 2+ ions decrease polymorphism and yield a relatively high preference of one model over the other model.In this case, model R3 is highly preferred over model S3.However, at higher concentrations, i.e. in the Zn 2+ : amylin ratio of 1 : 2, the energy difference between the models that are based Fig. 4 Constructed models of the Zn 2+ -amylin oligomer in which the amylin peptides are composed of A2 (model R3) and A3 (model S3).The Zn 2+ : amylin ratio is 1 : 4, i.e. each Zn 2+ ion binds four His18 of four peptides.Residue colors: Arg11, red; His18, blue; Asn19, purple; and Asn31, green.
on model A2 (models R1 and R2) and the model that is based on A3 (model S1) is B100 kcal mol À1 .Thus, at high concentrations of Zn 2+ ions, the polymorphic states are increased compared with low concentration of Zn 2+ ions, and models that are based on both A2 and A3 are preferred.Obviously, the polymorphism in such a case is relatively low compared with the case with the absence of Zn 2+ ions.
Previously, it was suggested by Miller et al. 58 that Ab oligomers present polymorphic states and that metal ions increase the polymorphism, as previously shown for Zn 2+ -Ab 1-42 oligomers. 25Interestingly, we found that in amylin the Zn 2+ ions may decrease or increase the polymorphism within the classes of amylin oligomers due to the concentrations of Zn 2+ , i.e., due to the Zn 2+ : amylin ratio.

Zn 2+ ions do not change the structural features of amylin oligomers
A previous study by Ramamoorthy's group has shown that both in the absence and in the presence of Zn 2+ ions, amylin peptides are self-assembled into fibrillar structures, i.e. forming cross-b structures, and that the structural features are similar. 39To investigate the structural features of our simulated Zn 2+ -amylin oligomer models, we first examined whether the fibril-like structures are well-packed (Fig. S6, ESI †).We further estimated the percentage of hydrogen bonds along the cross-b structure that are retained throughout the MD simulations (Fig. S7, ESI †).Finally, we computed the root-mean square deviations (RMSDs) (Fig. S8, ESI †).These analyses show that all simulated models are well-packed with cross-b fibrillar structures, as suggested by the experimental observation. 39Furthermore, the RMSD analyses show that all simulated models were structurally converged in the last 10 ns of the simulations.
To focus in more detail on the structural stability, we performed analysis of the secondary structure of the simulated amylin oligomers.According to dihedral angles c and j analysis, the secondary structure of the Zn 2+ -amylin oligomers is similar to our previous equivalent amylin oligomers (Fig. 6).As seen in the secondary structure of the studied models, the two b-strand domains (residues 8-17 and residues 26-37) retained the stability, similarly to the equivalent amylin oligomer models that we previously studied. 41Therefore, we propose that the Zn 2+ ions do not change the formation of stable cross-b structures of amylin, as previously suggested by experimental observations. 39 2+ ions affect the turn domains of specific classes of amylin oligomers As noted above, the Zn 2+ ions that bind to amylin oligomers in models that are based on models A2 and A3 in this study for both the ratios of Zn 2+ : amylin of 1 : 2 and 1 : 4 have no significant effect on the secondary structure of the turn domain (Fig. 6).The secondary structure of the Zn 2+ -amylin oligomers demonstrates a similar secondary structure to the equivalent amylin oligomers.
Since the Zn 2+ ions bind to His18 that is located in the turn domain of the b-arch of the self-assembled amylin, it is important to examine whether the Zn 2+ ions affect the morphologies of this domain.To examine the fluctuations of the simulated amylin oligomers (M2, M2d and M5) and the equivalent simulated Zn 2+ -amylin oligomers, we computed the root-mean square fluctuations (RMSFs) for each residue of the amylin oligomers (Fig. 7).We previously have shown that the turn domain of all amylin oligomer models fluctuates relatively more than the two b-strands domains. 41   Herein, one can see a similar scenario for both ratios of Zn 2+ : amylin of 1 : 2 and 1 : 4 (Fig. 7).In models that are based on model A2 (models R1, R2 and R3), the turn domain fluctuates less compared with the turn domain in models that are based on model A3 (models S1 and S3).
Interestingly, these fluctuations more likely affect the intersheet distance (Ca backbone-backbone distance) in the core domain of amylin oligomers.The inter-sheet distances of models R1 and R3 demonstrate relatively smaller values than those of models S1 and S3 (Fig. S6, ESI †).Indeed, one can see from Fig. 7 that the fluctuations of residues in the N-terminal domain of model S1 are relatively large compared to those of model R1.Therefore, it indicates that the cross-b structures of models R1 and R3 are well packed compared to those of models S1 and S3.
Finally, the turn domains in models that are based on model A2 are more solvated than models that are based on model A3 for both ratios of Zn 2+ : amylin of 1 : 2 and 1 : 4 (Fig. S9, ESI †).One can see that the turn domain of model S1 is more solvated than that of model R1 (and R2) and the turn domain of model S3 is more solvated than that of model R3.Interestingly, the solvation of the turn domain is in accordance with the fluctuation of the turn domain (Fig. 7).When the turn domain fluctuates more, it is more exposed to solvent and therefore it is more solvated.

Conclusions
Amylin aggregation is associated with b-cell death in T2D.The role of Zn 2+ in T2D is controversial.It is known that patients with T2D have zinc deficiency in b-cells. 59One of the fundamental questions is what is the effect of zinc deficiency in b-cell granules on the development of T2D, such as on the aggregation of amylin.Previously, it was suggested that amylin and Zn 2+ ions have a crucial role in glycemic regulation, but interruption in their delicate balance may cause aggregation of amylin and thus the progression of T2D. 33,34It has been suggested that Zn 2+ ions interact with amylin peptides and lead to the self-assembly of amylin peptides into fibrillar structures, via the oligomeric toxic species. 39In this study we investigated the interactions of the Zn 2+ ions within the amylin peptides at the atomic resolution in the toxic oligomeric states of amylin.Specifically, we investigated the effect of these interactions on the self-assembly of amylin.Our results led to two main conclusions.First, while polymorphic states were obtained in the absence of Zn 2+ ions, i.e. various classes of amylin oligomers were present, 41 in the absence of Zn 2+ ions only specific classes of amylin oligomers were obtained.We therefore suggest that Zn 2+ ions decrease amylin polymorphism.Yet, the level of polymorphic states depends on the concentration of the Zn 2+ ions.Fig. 8 illustrates the various mechanisms proposed for the formation of amylin oligomers at different concentrations of Zn 2+ ions.At high concentrations of Zn 2+ ions, various polymorphic states of Zn 2+ -amylin oligomers are obtained, while at low concentrations of Zn 2+ ions there is high preference for one Zn 2+ -amylin oligomer.Second, Zn 2+ ions do not affect the structural features of the self-assembly of amylin, as previously shown by experimental measurements. 39Yet, in several classes of amylin oligomers there are slight fluctuations in the turn domain of amylin, due to the interactions with the Zn 2+ ions.1][62][63][64] It was also proposed that at an early stage of amylin oligomerization in solution, amylin forms interactions between His18 and Tyr37, i.e. interactions between the turn domain (in which His18 is located and can bind Zn 2+ ions) and the C-terminal of amylin (residue Tyr37). 38We therefore suggest that interactions of the Zn 2+ ions can affect the initiation of the process of amylin aggregation.Herein, we have shown that stable Zn 2+ -amylin oligomers were less solvated, and thus more prone to aggregate.Yet, future experimental work is needed to approve this interesting finding from our simulations.
Specifically, the turn domain of model M2 (which are based on model A2) illustrated relatively less fluctuations than that of model M5 (which is based on model A3) (Fig. S7, ESI †).

Fig. 6
Fig.6The secondary structure along the sequence of amylin of the simulated models of the simulated models amylin oligomers M2, M5 and M5d (obtained from our previous study), simulated models of Zn 2+ -amylin oligomers with the Zn 2+ : amylin ratio of 1 : 2 -models R1, R2, and S1 and simulated models of Zn 2+ -amylin oligomers with the Zn 2+ : amylin ratio of 1 : 4 -models R3 and S3.The arrows illustrate the b-strand structure.

Table 1
A detailed description of the various constructed models of Zn 2+ -amylin oligomers