Formation and Growth of Oligomers: A Monte Carlo Study of an Amyloid Tau Fragment
[['A century ago , Alois Alzheimer reported dense extracellular deposits and intracellular neuronal aggregates in the brain of a patient suffering from memory loss , focal symptoms , delusions , and hallucinations [1] .', 'The extracellular deposits have been subsequently identified as amyloid plaques composed of an accumulation of β-amyloid peptides , while the intracellular neuronal aggregates are neurofibrillary tangles ( NFTs ) formed by the microtubule-associated protein tau .', "Tau filaments adopt multiple morphologies , among which paired helical filaments ( PHFs ) are the principal constituent of NFTs in the Alzheimer's disease ( AD ) brain , while straight filaments are a minor variant [2] .", 'In electron micrographs , the PHF appears as a twisted double-helical ribbon of subunits that alternate in width between 10–20 nm and has a half-period of 80 nm [3] .', 'The β-amyloid filaments were known a long time ago to exhibit the characteristic “cross-β” structure , a β-sheet rich structure in which the β-strands are aligned perpendicular to the fibril direction and the interstrand hydrogen bonds are parallel to the fibril axis [4] .', 'However , it is only recently that the “cross-β” characteristics of tau filaments from AD brain and from full-length recombinant protein have been conclusively demonstrated [5]–[7] .', 'Protein tau is primarily expressed in neurons , and is involved in microtubule assembly and stabilization [8] , [9] .', 'It is highly soluble and flexible in aqueous solution [10] , belonging to the “intrinsically disordered” proteins .', 'Even when it is bound to the surface of microtubules , tau retains most of its disordered character [11] .', 'In adult human brains , there are six isoforms of tau .', 'Depending on the isoform , three or four repeats constitute the core of the microtubule-binding domain .', 'Coincidently , the second and third repeats in the microtubule-binding domain are also the core of PHFs with the cross-β structure , while the rest of the protein forms the fuzzy coat of PHFs [5] .', 'It has been suggested that the motifs VQIINK ( PHF6* ) in the second repeat and VQIVYK ( PHF6 ) in the third repeat of tau play a key role in the formation of PHF [12] , [13] .', 'By transmission electron microscopy ( TEM ) , it was found that AcPHF6 ( Ac-PHF6-NH2 ) peptides aggregate into straight filaments [14] .', 'Further , X-ray diffraction patterns and electron micrographs were reported for assemblies of some PHF/tau-related peptides , including AcPHF6 and a longer peptide containing both PHF6* and PHF6 [15] .', 'Assemblies of the latter peptide were found to have a twisted fibrillar structure , whereas the data for AcPHF6 were found to be consistent with a tubular assembly with double walls [15] .', 'An X-ray study of PHF6 microcrystals , on the other hand , found a cross-β spine consisting of β-sheet pairs with a “dry steric zipper” organization at the sheet-sheet interface [16] .', 'Recent findings using transgenic mice models have suggested that soluble aggregated tau rather than NFTs might induce neurodegeneration [17]–[19] .', 'The demonstration of toxicity of soluble aggregates has brought up the possibility of using the oligomeric forms as drug targets .', 'Therefore , it is of great importance to understand the initial nucleation and growth process of tau aggregation .', 'While X-ray diffraction , electron micrography , and microcrystallography have provided information on the structural organization of tau filaments , the initial oligomerization process of full-length protein tau or its peptide fragments remains far from being well understood .', 'Computational studies have complemented the experiments to provide insights into amyloid formation .', 'Although a wide range of models [20]–[34] has been employed to simulate amyloid aggregation ( for a recent review , see [35] ) , due to the limitations of currently available computer power , most computational studies were limited to small oligomers , short time-scales , or restrained simulations .', 'An alternative approach , to test the stability of preformed structures , has also been explored [36]–[39] .', 'In this work , we study the aggregation of AcPHF6 by an all-atom protein model with a simplified interaction potential using Monte Carlo ( MC ) simulations .', 'The runs , with up to 36 chains , capture many well known properties of oligomerization .', 'They lead to a multitude of small oligomers rich in β-strand content .', 'We also observe two distinct processes during oligomerization: formation of stable oligomers and emergence of growth capable stable oligomers .', 'Surprisingly , we find that stability of oligomers is not synonymous with their ability to grow .', 'For system sizes permitting the formation of more than one stable oligomer , we find that this type of conformation is more probable than having one large aggregate .', 'Stable oligomers undergo considerable structural reorganization through reptation motion and exchanges of chains with the environment .', 'Growth of stable oligomers is facilitated by a particular kind of ordered structure .', 'New chains do not necessarily attach to a growing oligomer in an ordered manner , so that at every size of the oligomer , there is a slight “barrier” corresponding to a required structural reorganization , before an incremental growth occurs .'], ['Both experimental [40] and computational [21] works suggest that amyloid formation proceeds via a nucleation process .', 'According to the nucleated conformational conversion model [40] , this process shows a two-step behavior: an initial chance association of a sufficient number of monomers to form stable but disordered oligomers , followed by the emergence , through a reorganization process , of ordered oligomers and fibrils .', 'In this article , we begin by studying the first step , i . e . , the formation of stable oligomers .', 'We started with twelve chains of AcPHF6 randomly positioned in the cell , at 308 K . To investigate the concentration dependence , we performed simulations in a number of cubic cells with side lengths of 65 Å , 70 Å , 75 Å , and 80 Å ( see Table 1 ) .', 'These concentrations range from 58 mg/ml ( 73 mM ) to 31 mg/ml ( 40 mM ) , which are typical values in simulations [30] but higher than the experimental concentrations ( 0 . 1–1 . 0 mg/ml [14] ) .', 'To identify aggregates in the simulations , we have used a criterion based on contacts between residues belonging to different chains .', 'Two residues were defined to be in contact if the distance between any pair of heavy atoms of these two residues was less than 4 . 5 Å .', 'Two chains were considered to have a link if they had at least four inter-chain contacts .', 'A set of chains was considered to form a single aggregate , if the graph with those chains as nodes and inter-chain links as edges , was connected .', 'In Figure 1a , we show how the size ( number of chains ) of the biggest aggregate evolved with MC time in representative runs at the highest ( side length 65 Å ) and lowest ( side length 85 Å ) concentrations , respectively ( Figure S1 shows the same for six runs with side length 70 Å ) .', 'In the run at high concentration , aggregation is fast .', 'In contrast , the run at low concentration exhibits a long apparent waiting phase before a large aggregate appears for the first time .', 'In this phase , many meta-stable aggregates with 2–8 chains form and dissolve , without growing into mature stable aggregates .', 'At step 67 ( equivalent to 67×5×107 MC steps ) , a stable aggregate forms for the first time ( see below for its conformation ) , which does not dissolve into smaller aggregates , and the system enters a new , aggregated phase .', 'This behavior is suggestive of a nucleation process , with the nucleation event occurring at step 67 .', 'It is worth stressing that the event observed here is nucleation of oligomer formation which is not the same as nucleation of fibril formation .', 'The formation of a critical nucleus for fibrillization generally involves a reorganization process , which might be the rate-limiting step .', 'Figure 1b shows the evolution of the hydrophobicity energy and the hydrogen bond energy along this ( low concentration ) trajectory .', 'Both these energies ( anti- ) correlate with the size of the largest aggregate .', 'The hydrophobic interaction seems to be the most important driving force in the aggregation process , whereas hydrogen bonding also plays a significant role in defining the geometry of the aggregated structures .', 'The aggregation process optimizes both these interactions .', 'Also shown in Figure 1b is the β-strand content , which is strongly correlated with the hydrogen bond energy .', 'Figure 2 depicts four examples of meta-stable states from the pre-nucleation phase in the run at low concentration in Figure 1 .', 'The first example ( Figure 2a ) is a six-stranded , mixed parallel/antiparallel β-sheet with a clear twist , in contact with a random coil .', 'Other β-sheets containing 2–6 strands were also observed .', 'The second example ( Figure 2b ) is a relatively irregular aggregate composed of two small β-sheets with two and three strands , respectively , which are packed against each other .', 'Completely irregular aggregates , without any β-sheet structure , were rare .', 'The third example ( Figure 2c ) is a small β-sandwich consisting of one two-stranded and one four-stranded β-sheet .', 'Finally , the fourth example ( Figure 2d ) is a four-stranded β-sheet with four random coils attached to it .', 'All these four aggregates dissolved later and the system remained in the pre-nucleation stage .', 'According to classical nucleation theory [41] , the critical nucleus is in “unstable equilibrium” .', 'The aggregates containing fewer chains than the critical nucleus dissolve spontaneously , while those larger than the critical nucleus grow spontaneously .', 'The system must overcome a free energy barrier and form a critical nucleus before stable aggregates form .', 'This free energy barrier is low when the concentration is high .', 'Indeed , in our simulations , the length of the pre-nucleation phase showed a strong concentration dependence .', 'This is illustrated by Figure 1a , in which nucleation takes place after about 8 steps for side length 65 Å and after about 67 steps for side length 80 Å .', 'We now illustrate the behavior of the 12-chain system around and after the nucleation step , using the same run as in Figure 2 ( side length 80 Å ) .', 'Figure 3 shows six snapshots from the later part of this run .', 'Once the spontaneous fluctuations result in the formation of a critical nucleus , as at step 67 in this run , the system has reached a point where a stable aggregate may form .', 'The aggregate no longer disperses into smaller pieces or completely dissolves .', 'At the nucleation event at step 67 ( Figure 3a ) , the aggregate consists of two random coils attached to a twisted six-stranded β-sheet .', 'One step later ( Figure 3b ) , a new chain has joined this aggregate by forming a two-stranded β-sheet with one of the two random coils , and the β-sheet has grown to become seven-stranded .', 'Subsequently , the aggregate undergoes reorganization .', 'At step 71 ( Figure 3c ) , there is one large β-sheet composed of eight chains in contact with a small two-stranded β-sheet .', 'The large sheet is concave , which maximizes contacts with the small sheet .', 'The side chains of V1 , I3 , and Y5 are buried at the sheet-sheet interface .', 'From this point on , there is a dynamic equilibrium between the aggregate and individual monomers in “solution” .', 'In other words , an individual chain associates with the aggregate or dissociates from the aggregate from time to time , but the total number of peptides within the aggregate does not change significantly with time .', 'Most of the time , the aggregate contains 10–11 chains ( Figure 1 ) , but not necessarily the same 10–11 chains at different moments .', 'Individual chains attach and detach at the edges of the β-sheets .', 'Occasionally , the size of the aggregate decreases to nine or increases to twelve chains ( Figure 1 ) .', 'During the dynamic equilibrium , conformational reorganization occurs within the aggregate .', 'Typically , the aggregate consists of two twisted β-sheets wrapped around each other .', 'But the number of chains in each sheet is not constant .', 'We even observed , at step 86 ( Figure 3d ) , a single chain in 310-helix conformation in contact with the concave face of a nine-stranded β-sheet .', 'The most common type of aggregate seen in this run is composed of one five-stranded and one six-stranded β-sheet , as at step 91 ( Figure 3e ) .', 'In sandwich structures like this , large changes in the relative orientation of the two β-sheets were observed .', 'For example , in this run , the angle between the two β-sheets changes from 10° to 60° between step 91 ( Figure 3e ) and step 96 ( Figure 3f ) .', 'Smaller β-sheets adjust their relative orientation more easily than larger β-sheets .', 'The local bending and the alignment pattern also vary with time .', 'We observed that the alignment of the edge strands of a β-sheet can change without their detachment from the β-sheet .', 'However , the alignment pattern in the central part of a β-sheet were not seen to change , which is understandable as there are constraints from neighboring strands .', 'Structures resembling those in Figure 3 have been observed in previous simulations of smaller systems , including 6-chain simulations with explicit water for other peptides of the same length as PHF6 [28] .', 'The curved β-sheets seen in Figure 3b–d are reminiscent of the open β-barrels reported by Derreumaux and coworkers [42] , [43] .', 'The structures shown in Figures 2 and 3 , all from a single run , illustrate some general features seen in all our simulations .', 'For example , a vast majority of our observed aggregates are β-sheet rich , and both curved sheets and sandwich-like structures are frequently occurring motifs .', 'However , the details of the structures in Figures 2 and 3 , like the exact alignment of the β-strands , are not statistically representative .', 'To statistically characterize aggregated structures , we carried out an additional set of fifty 12-chain runs , starting from different random initial configurations .', 'For computational convenience , the side length was here set to 70 Å instead of 80 Å .', 'In these runs , the same two phases were seen as in the 80 Å run described above , but the aggregation process was faster .', 'In seven of the fifty runs , the aggregate converted to a stable β-barrel containing 8–12 chains .', 'This type of conformation was not further investigated , because the main focus of the present study is aggregate growth , and a β-barrel is unlikely to grow into a larger aggregate .', 'For sandwich structures , we made a size analysis based on these fifty runs .', 'Here we counted the total number of chains in the aggregate and the difference in number of chains between the two β-sheets after a stable two-sheet aggregate had formed .', 'Figure 4a shows the observed distribution of aggregate size .', 'The peak is at 11 , whereas aggregates with ≤7 chains are quite rare .', 'Note that the distribution depends on the concentration .', 'Figure 4b illustrates the difference in size between the two β-sheets in two-sheet aggregates .', 'Small size differences of 0 or 1 are most common .', 'We note that whenever any collection of objects is randomly divided into two groups , there are more ways of constructing the groups with nearly equal size than of constructing them with a large size difference .', 'Therefore large size differences would be expected to be suppressed entirely due to combinatorial considerations , irrespective of the specific properties of the system .', 'In Figure 4b , the largest size differences involve one very small aggregate , and the observed probabilities are nearly consistent with the random estimate .', 'But the probability of the smallest size differences is enhanced at the expense of the medium size differences of 2 and 3 in Figure 4b , suggesting that size symmetry of sheets in an oligomer is further favored due to interactions .', 'Inspection of the aggregates in Figure 3 shows that the β-strands tend to be arranged so that there are many hydrophobic intra-sheet contacts between them , involving the V1 , I3 and Y5 side chains .', 'A vast majority of the larger aggregates seen in our simulations share this property .', 'In order to maximize the hydrophobic interaction between two adjacent strands in a sheet , the V1 , I3 , and Y5 side chains of both strands must point to the same side of the sheet ( and Q2 , V4 , and K6 to the other ) .', 'This is achieved if the strands are parallel and either in-register or off-register by two residues , or if they are antiparallel and off-register by one or three residues .', 'Obviously , this property depends on sequence .', 'For example , if the peptide has an alternating hydrophobic/hydrophilic pattern but an odd number of residues , both parallel and antiparallel in-register arrangements will maximize the hydrophobic interactions .', 'Figure 5a illustrates the strand organization and the orientation of the side chains for the largest of the two β-sheets in Figure 3e .', 'The strand organization is such that all V1 , I3 , and Y5 side chains point to the same direction .', 'In our simulated aggregates , there were two dominating β-strand arrangements , illustrated by Figure 5a , namely parallel in-register and antiparallel out-of-register by one residue .', 'These arrangements lead to different hydrogen bond patterns .', 'With a parallel in-register arrangement , each pair of adjacent strands is connected by five hydrogen bonds ( see Figure 5a ) .', 'If two strands are antiparallel and off-register by one residue , there will be either four or six hydrogen bonds connecting them .', 'The arrangement can be repeated so that there are six hydrogen bonds between all pairs of adjacent strands ( see Figure 5a ) , with successive strands shifting in the same direction .', 'Another possibility is that the third chain is in the same relation to the second as the second is to the first , which leads to a zig-zag pattern with successive strands shifting in opposite direction , as in Figure 5b .', 'The drawback of this organization is that there are only four hydrogen bonds between the second and the third strand .', 'We observed this pattern in our simulations , but with a relatively low frequency .', 'The organization to the right in Figure 5a , which maximizes the number of hydrogen bonds , was more common .', 'Unlike both these organizations , the parallel organization , to the left in Figure 5a , is in-register , which may be advantageous in large sheets .', 'In fact , we found that the fraction of parallel over antiparallel β-sheet structure increased with aggregate size , as will be discussed below .', 'Having observed the formation of stable oligomers in the 12-chain runs , we increased the system size to 24 chains to study oligomer growth .', 'For this system size , we performed a set of 72 unseeded and 35 seeded runs ( see Table 1 ) , at the same temperature as before ( 308 K ) .', 'The side length was 95 Å , corresponding to a concentration of 36 . 7 mg/ml .', 'In our unseeded 24-chain runs , the same two phases were observed as in the 12-chain runs: an initial waiting phase with only small aggregates , followed by a phase with large aggregates in dynamic equilibrium with small aggregates and free monomers .', 'The waiting phase was often short , due to the relatively high concentration .', 'In the aggregated phase , there was in some runs one dominating aggregate , typically with 16–20 chains .', 'These big aggregates were invariably composed of two stacked β-sheets , as in Figure 6a .', 'In a majority of the runs , there were two , rather than one , major aggregates , each with typically 8–10 chains .', 'These aggregates were similar to those observed in our 12-chain runs .', 'Some of them were of the barrel type .', 'In total , we saw 15 stable β-barrels in our 72 unseeded 24-chain runs .', 'As in the 12-chain case , these aggregates , which are unlikely to grow into larger aggregates , will not be further analyzed in this work .', 'To get a quantitative picture of the aggregation behavior of the 24-chain system , we determined the sizes of the largest and next-largest aggregates for each conformation in our unseeded runs , which we denote by x and y , respectively .', 'Figure 7 shows minus the logarithm of the histogram of x and y .', 'The most populated region corresponds to two aggregates of similar size , 8–10 chains .', 'In addition , there is a weak local minimum at large x and low y , corresponding to configurations with one dominating aggregate .', 'However , the minimum corresponding to two distinct similar size aggregates is much deeper .', 'If the growth of an arbitrary stable oligomer had been easy , upon the formation of the first such oligomer , the remaining free monomers would have rapidly associated with that , leading to one big aggregate .', 'But in Figure 7 we see that the probability of two similar-size aggregates is significantly larger .', 'This indicates that further growth is not fast compared to the formation of a new nucleus .', 'Instead , at a size of ∼10 chains , it seems that the aggregation process reaches a stage at which conformational reorganization is required before further growth .', 'Our 35 seeded 24-chain simulations further elucidate this point .', 'These runs were started from initial conformations prepared by taking aggregates from the 12-chain runs and adding random coils .', 'Despite the presence of a template , a large aggregate ( with >15 chains ) appeared in only 15 of these runs .', 'In 17 of the remaining runs , the free monomers instead assembled into a second aggregate , thus leading to a state with two distinct aggregates of similar size .', 'In the remaining 3 runs , the newly added chains stayed in the pre-nucleation phase .', 'Even when a stable seed is present , an independent new aggregate thus forms in about half of our runs , which suggests that the time scale for the conformational reorganization required for further growth is comparable to that of the formation of a new stable aggregate of about 10 chains .', 'Figure 6b gives an example of a large aggregate from a seeded simulation .', 'After the first large aggregate had appeared in this run , the system spent the rest of the run in a phase of dynamic equilibrium , with only small fluctuations in aggregate size .', 'Figure 6b shows a randomly chosen snapshot from this phase .', 'This aggregate shares several common features with that from the unseeded simulation shown in Figure 6a .', 'Both aggregates are composed of two large β-sheets that are twisted and wrap around each other .', 'The overall twist is 8 . 8° and 6 . 3° for the two sheets in Figure 6a , and 12 . 0° and 13 . 9° for those in Figure 6b ( see Methods ) .', 'In both structures , parallel strand pairs are either in-register or out-of-register by two residues , while antiparallel pairs are off-register by one residue , as discussed in connection with Figure 5 .', 'In addition to being twisted , the strands are also bent , which helps to make better side-chain contacts .', 'Twisting , bending , strand alignment and side-chain packing are all important factors influencing the final conformation .', 'Based on our 72 unseeded 24-chain runs , we performed a statistical analysis of some important properties of the aggregated structures .', 'Of particular interest is the β-sheet organization , which in most of our simulated aggregates is mixed parallel/antiparallel ( see Figures 2 , 3 , and 6 ) but is known to be parallel in AcPHF6 fibrils [14] .', 'In our 72 runs , we counted parallel and antiparallel pairs of adjacent strands for all aggregates of a given size .', 'Figure 8 shows the fractions of parallel and antiparallel β-sheet structure , as obtained this way , against aggregate size .', 'For small sizes , there is a clear statistical preference for the antiparallel organization .', 'However , the fraction of parallel structure increases steadily with aggregate size .', 'In aggregates with more than 18 chains , the parallel organization is more common than the antiparallel one .', 'Using the same runs , we also analyzed the relative orientation of the two β-sheets in sandwich structures .', 'For all two-sheet structures with 5–7 chains in each sheet , the angle between the two sheets was determined ( see Methods ) .', 'Figure 9a shows the calculated distribution of this angle .', 'The distribution exhibits a broad peak in the region 5°–35° .', 'Relative orientations in the range 45°–90° occur but are rare .', 'Finally , we also calculated the overall twist for all β-sheets in two-sheet aggregates with at least five strands in each ( see Methods ) .', 'The two edge strands of a sheet were not included in the analysis , because we found that those strands often were more twisted than the rest of the sheet .', 'Figure 9b shows the observed distribution of the average twist angle .', 'Its maximum is near 11° .', 'The shape of the distribution is asymmetric , with a shoulder near 0° .', 'It is worth pointing out that the runs presented in this article are of limited length .', 'In any given run , it is most likely that some important free-energy minima were not sampled , due to high free-energy barriers .', 'Our findings are , however , based on a set of many independent simulations .', 'We feel confident that major trends seen , like the increase in the fraction of parallel β-sheet structure with aggregate size , are statistically robust .', 'We also did seventy-two 36-chain simulations ( see Table 1 ) , seeded with minimum energy conformations from our 72 unseeded 24-chain runs , to which 12 random coils were added .', 'In many of these runs , the formation of a new independent aggregate with ∼10 chains was observed , whereas the one or two major aggregates present initially grew by only one or a few chains .', 'In a few runs , significant growth was observed for one of the pre-existing seeds .', 'The behavior of the 36-chain system thus supports the picture emerging from the 24-chain runs .', 'New independent aggregates large enough to be long-lived form relatively easily in our simulations , but that an aggregate reaches this size does not mean that further growth is fast .', 'Most aggregates seem to require conformational reorganization before they can grow , which prevents rapid growth .', 'A detailed analysis of our 36-chain runs is beyond the scope of the present work and will be presented in a forthcoming publication .'], ['As of now , the nucleation event in the oligomerization process is difficult or impossible to examine using experimental approaches .', 'Light and neutron scattering techniques are capable of revealing the shape of micelles of Aβ , but these aggregates are larger than the critical nucleus [44] .', 'Computer simulations offer unique opportunities to observe and analyze early aggregation events at the molecular level .', 'In our 12-chain simulations of AcPHF6 peptides from random initial conformations , two distinct phases can be identified: an early phase with only smaller aggregates , followed by a phase characterized by the presence of a large aggregate .', 'This behavior suggests that the formation of stable oligomers occurs through a nucleation process .', 'In a simple nucleation process , an embryo of the new phase will grow spontaneously once it has reached a certain critical size .', 'By contrast , when proteins/peptides aggregate , the size of the embryo is not the only relevant parameter; the ability of the critical embryo to grow depends also upon its conformation .', 'Our run at low concentration in Figure 1 illustrates this .', 'Here the nucleation event occurred after 67 steps .', 'Some aggregates of comparable size appeared before step 67 , but these aggregates dissolved into smaller aggregates and/or monomers .', 'The pre-nucleation behavior of our system resembles what has been seen in several previous studies of small systems with 2–9 chains .', 'These studies found many different meta-stable aggregates with various forms of β-sheet structure , and suggest that the barrier for converting from one of these aggregates to another is low [26] , [37] , [45]–[48] .', 'The aggregate observed at the nucleation stage in the run discussed above ( step 67 ) is composed of a twisted six-stranded β-sheet and two attached random coils ( Figure 3a ) .', 'A striking feature of this β-sheet is that the V1 , I3 , and Y5 side chains point in the same direction in all strands .', 'The aggregates from the pre-nucleation phase ( see Figure 2 ) do not have this property .', 'In the proposed dry steric zipper model for PHF6 fibrils , based on X-ray microcrystallography , the β-sheet pair adopts a face-to-face stacking arrangement in which the side chains of V1 , I3 , and Y5 nestle between sheets [16] .', 'The V1 , I3 , and Y5 side chains pointing to the same side of a β-sheet might very well be a prerequisite for its participation in a stable double-layered structure .', 'Even a single strand with the V1 , I3 , and Y5 side chains pointing to the opposite side of the β-sheet could mean that the entropy loss upon formation of the aggregate cannot be compensated by an enthalpy reduction from intermolecular interactions .', 'The second component of this aggregate ( Figure 3a ) is the two random coils that are in contact with the β-sheet .', 'One of the random coils is attached to the V1–I3–Y5 side of the sheet , solely by side-chain interactions , while the other is attached to an edge of the sheet .', 'This kind of arrangement has been observed in previous simulations for Aβ16–22 [45] , Aβ11–25 [49] , and the GNNQQNY segment of yeast prion protein Sup35 [31] , [50] .', 'The attachment of random coils to a β-sheet might help to stabilize the sheet through side-chain interactions .', 'In the aggregated phase , after the nucleation event , we observed different kinds of β-sheet rich aggregates .', 'A common type of conformation was the β-sandwich .', 'In these aggregates , the two sheets tended to be of similar size ( Figure 4 ) , and V1 , I3 and Y5 side chains were typically found at the sheet-sheet interface ( see Figure 3c , 3e , and 3f ) , as in the dry steric zipper arrangement [16] .', 'An interesting question is how ordered early oligomers are .', 'Nguyen and Hall employed a coarse-grained protein representation and discontinuous molecular dynamics to simulate amyloid aggregation for a system of 96 polyalanine peptides ( Ac-KA14K-NH2 ) .', 'As a first step , preceding fibrillization , the chains were found to form irregular aggregates , which then converted into small β-sheets [21] .', 'In our simulations , very few completely disordered aggregates were found .', 'In part , this may be due to the short length of our peptide , which leads to a high propensity for it to be in an extended state .', 'Another factor influencing the aggregation into either ordered or amorphous species is the hydrophobicity of the sequence .', 'Indeed , a recent study by Cheon et al . [30] found amorphous aggregates for the more hydrophobic Aβ16–22 peptide but only ordered aggregates for the less hydrophobic Aβ25–35 peptide .', 'Our results suggest that AcPHF6 behaves like Aβ25–35 rather than like Aβ16–22 in this respect .', 'The large aggregates seen in our study also differ from the aggregates seen in the polyalanine simulations of Nguyen and Hall [21] .', 'One difference is that the β-sheets lacked twist in the polyalanine study .', 'Another , possibly related , difference is that Nguyen and Hall saw multiple-sheet stacking , whereas our aggregates were sandwich structures with only two stacked β-sheets .', 'The relation between sheet stacking pattern and sheet twist was studied in recent simulations [37] .', 'β-sheets in the Protein Data Bank ( PDB ) are generally twisted .', 'A recent study analyzed β-sheet twist in PDB structures in terms of adjacent pairs of residues on neighboring β-strands [51] .', 'The average twist angle was found to be 17°±7° for parallel β-sheets , 15°±10° for non-hydrogen bonded residue pairs in antiparallel β-sheets , and 8°±8° for hydrogen bonded residue pairs in antiparallel β-sheets [51] .', 'The distribution of sheet twist angle presented in Figure 9b is in line wi
['Introduction', 'Results', 'Discussion', 'Methods']
["Small oligomers formed early in the process of amyloid fibril formation may be the major toxic species in Alzheimer's disease .", 'We investigate the early stages of amyloid aggregation for the tau fragment AcPHF6 ( Ac-VQIVYK-NH2 ) using an implicit solvent all-atom model and extensive Monte Carlo simulations of 12 , 24 , and 36 chains .', 'A variety of small metastable aggregates form and dissolve until an aggregate of a critical size and conformation arises .', 'However , the stable oligomers , which are β-sheet-rich and feature many hydrophobic contacts , are not always growth-ready .', 'The simulations indicate instead that these supercritical oligomers spend a lengthy period in equilibrium in which considerable reorganization takes place accompanied by exchange of chains with the solution .', 'Growth competence of the stable oligomers correlates with the alignment of the strands in the β-sheets .', 'The larger aggregates seen in our simulations are all composed of two twisted β-sheets , packed against each other with hydrophobic side chains at the sheet–sheet interface .', 'These β-sandwiches show similarities with the proposed steric zipper structure for PHF6 fibrils but have a mixed parallel/antiparallel β-strand organization as opposed to the parallel organization found in experiments on fibrils .', 'Interestingly , we find that the fraction of parallel β-sheet structure increases with aggregate size .', 'We speculate that the reorganization of the β-sheets into parallel ones is an important rate-limiting step in the formation of PHF6 fibrils .']
["It is believed that the self association of certain protein molecules into aggregated structures , known as amyloid fibrils , plays an important role in a variety of human diseases , such as Alzheimer's disease and Parkinson's disease .", 'Although the ability to form such amyloid fibrils is a common property for proteins , the process leading to these fibrils is incompletely understood .', 'The early stages of the process involve small transient heterogeneous structures made of a few protein chains and are especially difficult to characterize .', "Here we use atomic-level simulations to explore the early part of the aggregation process for a fibril-forming fragment of the protein tau associated with Alzheimer's disease .", 'We find that a multitude of small aggregates , rich in sheetlike structures , form through a nucleation process .', 'Interestingly , a statistically preferred type of aggregate , consisting of two tightly packed sheets , emerges with increasing aggregate size .', 'Growth of these larger aggregates seems to be a slow process that correlates with the emergence of more uniformly ordered sheets .', 'We speculate that reorganization of the protein chains leading to that ordered arrangement is an important bottleneck to amyloid fibril formation for this peptide .']
['biophysics/theory and simulation']