Amyloid β-peptides 1–40 and 1–42 form oligomers with mixed β-sheets

Aβ40 and Aβ42 co-aggregate and form oligomers with mixed β-sheets as revealed by isotope-edited infrared spectroscopy.


Introduction
Alzheimer's diseasethe most common form of dementiais associated with the deposition of amyloid brils in the human brain. These consist mainly of $40 residue-long proteolytic fragments of the b-amyloid precursor protein. The main variants of these amyloid-b (Ab) peptides are 40 (Ab 40 ) and 42 (Ab 42 ) residues long. Although more of the shorter alloform Ab 40 is generated, the longer alloform Ab 42 dominates in the Ab deposits in the human brain. 1 The Ab 42 : Ab 40 ratio is enhanced in some familial Alzheimer diseases, which likely causes the early onset of these diseases 2-5 due to increased toxicity from Ab 42 6 and less protection by Ab 40 . 5,7,8 However, the situation is more complex than indicated by this simplistic explanation: a relatively small increase in the Ab 42 : Ab 40 ratio causes a dramatic increase in toxicity 6 and mixing two weakly toxic alloforms can generate high toxicity. 9 Thus, the properties of Ab mixtures, including their toxicity, cannot simply be extrapolated from the properties of the pure peptides 6,9,10 and a recent review concludes that studies of Ab mixtures "will be crucial in understanding the toxic effects of Ab". 11 One of the most fundamental aspects in this context is whether or not different Ab alloforms co-aggregate and form common structures. In a wider perspective, cross-reactivity of Ab with other amyloidogenic proteins 12-14 may link neurodegenerate diseases that are so far considered to be different.
Co-incubation of Ab 40 and Ab 42 or cross-seeding leads to coaggregation (cross-reactivity) in early aggregates, 15,16 modies aggregation kinetics, 6,7,10,17-24 aggregate type distribution, 6,10,22,23 and may enable the formation of mixed brils, 22,25,26 although the latter has been disputed recently. 16 Most of the current evidence for co-aggregation in Ab oligomers is indirect because either larger aggregates, 10,[16][17][18][19]22 or monomeric peptides 7,10 have been observed. Direct evidence for mixing in Ab oligomers has been obtained, 15 but using bulky labels attached to Ab, which may affect aggregation properties. To the best of our knowledge there has not been a study that directly investigates the extent of mixture of Ab 40 and Ab 42 in Ab oligomers with chemically unmodied peptides and that investigates the molecular architecture of mixed aggregates. This is in spite of the suggested importance of oligomers 27,28 and of the Ab 42 : Ab 40 ratio 2,6 for the severity of Alzheimer's disease.
To reveal whether and to what extent Ab 40 and Ab 42 form mixed aggregates, we used here isotope-edited infrared (IR) spectroscopy. The main present use of this method is to determine the local conformation of polypeptides. [29][30][31] It has also been applied to separate the spectral contributions of different components in a complex 32,33 but only rarely to detect mixing of two polypeptides 34,35 or of two protein domains 36 in a common secondary structure. Our work uses the latter approach, provides a computational simulation of the effect, introduces the methodology to determine the randomness of mixing and discusses the sensitivity of the method for this property. We focus on the amide I vibration of the peptide backbone, which is sensitive to secondary structure and to further structural properties like the extension of b-sheets, their twist, the strength of hydrogen bonding, and the relative arrangement of adjacent strands. [37][38][39][40][41] Our results directly demonstrate co-aggregation of Ab 40 and Ab 42 in oligomeric aggregates. These aggregates are well structured and seem to contain a large proportion of antiparallel b-sheets. Advantageously, the results were obtained with chemically unmodied peptides, without addition of reporter compounds, and in aqueous solution.

Results and discussion
Ab hetero-oligomers with mixed isotope composition Monomeric, recombinant peptides prepared at alkaline pH in 2 H 2 O were brought to p 2 H 7.4 and their IR spectra measured against a buffer spectrum aer 20 min of incubation as described in ESI. † The preparation led to small-sized oligomers and additional larger aggregates for Ab 42 and Ab 42 -rich mixtures with Ab 40 when analyzed by gel electrophoresis aer photoinduced crosslinking (see Fig. S5 of ESI †).
The IR absorbance and second derivative spectra of unlabeled and 13 C, 15 N-labeled Ab 40 and Ab 42 show the typical features of oligomers that are commonly assigned to antiparallel b-sheets (see Fig. S1 to S3 and discussion in ESI †). To test whether Ab 40 and Ab 42 become incorporated into the same oligomers, unlabeled Ab 42 was mixed with an equimolar concentration of uniformly 13 C, 15 N-labeled Ab 40 at alkaline p 2 H and incubated at p 2 H 7.4. In a further experiment, labeled and unlabeled peptides were exchanged. The second derivative spectra of the 1 : 1 mixtures are shown in Fig. 1A and B (solid lines). Negative bands in these spectra correspond to component bands in the absorbance spectra. Also shown in Fig. 1A and B are calculated spectra (dashed lines) obtained by averaging the individual oligomer spectra shown in Fig. S1 and S2 † (for the corresponding absorbance spectra see Fig. S3 †). The calculated spectra are expected when unlabeled and labeled peptides do not mix, but rather give rise to distinct all-unlabeled and all-labeled oligomers. The positions of the main bands in these spectra are the same as in the individual oligomer spectra. In contrast, the real mixture spectra exhibit shis of all main bands and a loss in intensity of the 12 C-band (near 1625 cm À1 ). This clearly indicates that the backbones of Ab 40 and Ab 42 interact in the oligomers and that this interaction inuences the vibrational coupling that determines the band position of the b-sheet band.

Band shis upon isotopic dilution
To discuss further the structural basis of the Ab 42 :Ab 40 mixing effect, panels C and D of Fig. 1 show spectra recorded for a number of different Ab 42 : Ab 40 ratios, where one of the peptides was labeled. They reveal gradual upshis of the main 12 C-and 13 C-b-sheet bands (near 1625 and 1580 cm À1 , respectively) and a downshi of the minor b-sheet band (near 1680 cm À1 ) upon isotopic dilution. Such band shis upon isotopic dilution have been observed previously. 34,36,[42][43][44][45][46] We chose the 13 C-band for further evaluation, because it can be detected even at low 13 C : 12 C-ratio in second derivative spectra. The position of this band is plotted in Fig. 2 and reects the continuous downshi of the band upon 13 C-enrichment. The different end points of the curves (when only labeled peptide is present) reect the different structures of the pure oligomers (see Fig. S2 †).
We explain the observed 13 C-band shi by the formation of b-sheets with mixed isotopic composition, i.e. sheets that consist of 12 C-and 13 C-strands. For the experiments shown in Fig. 1C and D, this means that the sheets contain strands from Ab 40 and Ab 42 . This interpretation will be tested in the following sections by calculations and control experiments.

Calculated amide I spectra of antiparallel b-sheets with mixed isotope composition
To support our explanation for the shi of the 13 C-band upon isotopic dilution we discuss now spectrum calculations that simulate the above experiments. The aim was to reproduce the effects of isotopic dilution in a qualitative way.
Details of the calculations are provided in ESI. † In brief, amide I spectra were calculated using coupling constants from density functional theory for nearest neighbor interactions and from transition dipole coupling for other interactions. Diagonal and non-diagonal elements of the mass-normalized force constant matrix considered the carbon isotope of the respective amide group(s). Spectra were calculated from 3000 sheets with a statistical distribution of 12 C-and 13 C-strands at a given 13 C : 12 C ratio. Errors in calculated band positions were obtained by repeating the calculations 20-times.
Antiparallel b-sheets of different sizes generated qualitatively similar spectra. As an example, Fig. 3 shows results obtained with a sheet of 6 strands and 10 residues (9 complete amide groups) per strand. The main 12 C-band near 1622 cm À1 loses intensity already at low 13 C : 12 C-ratios whereas the 13 C-band is observed for all ratios. It shis gradually down with increasing 13 C : 12 C-ratios as observed in the experiments. These simulations show that the experimental result can be explained by mixing strands with different carbon isotopes in the same bsheet. This conclusion is independent from the molecular  Calculated amide I spectra for an antiparallel b-sheet with 6 strands and 10 residues per strand (9 complete amide groups). The blue and red spectra were calculated for entirely unlabeled and labeled sheets, respectively. The gray spectra were calculated for different molar fractions of 13 C-peptides, as used in the experiments (0.1, 0.25, 0.5, 0.75, 0.9). Each simulated spectrum is the average of the spectra from 60 000 sheets with a statistical distribution of labeled and unlabeled strands at a given 13 C : 12 C-ratio. 13 C-enrichment gradually shifts the 13 C-band from 1603.5 to 1586.2 cm À1 . The 12 C band position for the completely unlabeled sheet is 1622.2 cm À1 . architecture of the b-sheets as qualitatively similar results were obtained for parallel sheets (see Fig. S7 †).
While the band positions of the completely labeled and unlabeled 6-stranded sheet are in reasonable agreement with the experimental values, the 13 C-band shi between 10% and 100% 13 C content is calculated to be larger than experimentally observed (17 cm À1 versus 9-12 cm À1 observed in the four mixing experiments shown in Fig. 2). The calculated shi is smaller for a parallel b-sheet of the same size (14 cm À1 ) but these calculations fail to reproduce the high wavenumber band that is clearly observed in the experimental spectra (compare Fig. 1 and S7 †). The discrepancy is not due to our use of ideal b-sheet structures for the calculations, as similar or larger shis were obtained for a 6-stranded antiparallel sheet from a streptavidin mutant (20 cm À1 ) and in a calculation for an ideal antiparallel sheet in which the vibrational coupling constants were varied statistically to simulate structural disorder (17 cm À1 ).
The likely reason for the discrepancy between the experimental and the calculated 13 C-band shi is the internal structure of the oligomers as the shi is sensitive to the number of adjacent strands that contain the same carbon isotope. 36,46 When this number is one, the calculated 13 C-band shi (between 10% and 100% 13 C content) was 24 cm À1 for large parallel sheets. 36,46 When this number is two, the shi decreased to 18 cm À1 . The shi decreased further when the number of adjacent strands with the same carbon isotope was increased to three or four. We conrmed this trend in our own calculations with 6-stranded sheets that were composed of building blocks of two adjacent b-strands with the same carbon isotope. The shi was now reduced to 10 cm À1 , which compares favorably to the 9-12 cm À1 shi in the four mixing experiments shown in Fig. 2. Therefore a plausible explanation of our results is that each peptide contributes two or more adjacent strands to the oligomers. Our shis are smaller than those calculated by Moran et al. because we use sheets with a much smaller number of strands.

Explanation of the band shis upon isotopic dilution
The reason for the spectral shis can be found in the decreased coupling between neighboring oscillators in a b-sheet with mixed isotope composition compared to an all-unlabeled or alllabeled sheet. This is shown schematically in Fig. 4 using an ideal anti-parallel b-sheet to illustrate the principle. In a b-sheet composed entirely of either unlabeled or labeled strands, such as the one shown in the top panel, the local amide I 0 oscillations of individual peptide groups (dashed ellipses) couple strongly because (1) they have a similar vibrational frequency, (2) the main component of their transition dipole moments is oriented in the same direction and (3) they are close in space. This delocalizes the vibrations over up to 12 strands 47 (solid ellipse). The strongest coupling of a particular amide group in an antiparallel b-sheet is with the two hydrogen bonded amide groups in the adjacent strands and with the diagonally opposed amide group in one of the adjacent strands. 37,48 Intrastrand coupling between nearest neighbors is smaller but still signicant. Nevertheless and to simplify the illustration, only the strongest interaction is considered in Fig. 4. Coupling affects band positions and leads to a downshi in case of the main b-sheet band. This is shown in the set of spectra on the right side of the top panel of Fig. 4. Stronger coupling leads to a larger downshi, which increases with sheet atness and number of incorporated strands (usually up to 10 strands) [37][38][39][40] and is, among others, the reason for the downshied absorption of b-sheets in amorphous aggregates compared to those in soluble proteins. The above discussion indicates that IR spectroscopy is sensitive to structural variations in b-sheets that occur within a length scale of 10-12 strands.
In the case of an isotopically mixed b-sheet (bottom panel of Fig. 4), where fully unlabeled and fully labeled strands alternate randomly, the difference in the intrinsic vibrational frequencies of the amide oscillators makes that unlabeled (blue ellipses) and labeled (red ellipses) oscillators couple only weakly. Therefore, the vibration is less delocalized over the span of the sheet and more localized on the individual strands. The net effect is that the vibrational frequencies of both unlabeled and labeled oscillators are closer to those of the uncoupled, hydrogen-bonded amide carbonyls ($1645 cm À1 for 12 C]O, and $1600 cm À1 for 13 C]O), and the corresponding b-sheet absorption bands shi to higher wavenumbers compared to a fully unlabeled or fully labeled sheet.
The opposite phenomenon occurs for the high wavenumber band of anti-parallel b-sheets, which experiences a downshi In the sheet, carbon, nitrogen and oxygen atoms are shown in gray, blue and red, respectively. The dashed ellipses denote individual amide I oscillators, they are blue for 12 C-amides and red for 13 C-amides. The solid ellipse denotes a delocalized vibration due to coupling of the indicated individual oscillators. The dashed and solid spectra on the side show the main b-sheet absorption band before and after coupling is established (top), as well as before and after it is partially broken (bottom) for the main 12 C-(blue) and the main 13 C-band (red).
upon loss of coupling. The smaller magnitude of the shi, together with the moderate intensity of this band, makes it less useful in the study of amyloid-b oligomers compared to the main b-sheet band.

Control: Ab homo-oligomers with mixed isotope composition
If the 13 C-band shi indicates isotopically mixed b-sheets, then similar shis must be observed when labeled and unlabeled versions of the same peptide are mixed in homo-oligomers. In such experiments, labeled and unlabeled peptides form randomly mixed b-sheets because they are chemically identical. Our experiments with homo-oligomers of varying isotope composition resulted in similar 13 C-band shis, which are included as gray lines in Fig. 2. The results with homooligomers support our interpretation that Ab 42 :Ab 40 heterooligomers form mixed b-sheets.

Evidence for random mixing in hetero-oligomers
The 13 C-band shis of the homo-oligomers shown in Fig. 2 serve as reference curves for random mixing. They superimpose well with the curves for Ab 42 :Ab 40 mixtures indicating that these two peptides form common b-sheets which contain a random or close to random mixture of Ab 40 and Ab 42 strands.
In our experiments, Ab 42 :Ab 40 oligomers of different sizes are formed (see ESI †), which might have different mixing preferences. The limiting cases are randomly mixed Ab 42 :Ab 40 oligomers on the one hand and chemically homogeneous aggregates, i.e. pure Ab 42 or pure Ab 40 oligomers, on the other hand. Intermediate cases are also conceivable. When one of the two Ab alloforms is labeled, such different kinds of oligomers will have different 13 C-band positions for a given isotope ratio according to the calculations shown in Fig. S8. † The 13 C-band position will be lower for the aggregates with higher purity than for aggregates with a statistical Ab 42 :Ab 40 composition. Experimentally, these different band positions will be difficult to distinguish because the bands are likely to overlap. The overlap will lead to a single broad 13 C-band that is downshied with respect to that for randomly mixed aggregates at all isotope ratios. This is not observed. Instead, 13 C-band positions for the heterogeneous Ab 42 :Ab 40 mixtures (black curves in Fig. 2) superimpose well on those for homogeneous oligomers, which have a statistical distribution of labeled and unlabeled strands (gray curves in Fig. 2). Therefore none of the dominant oligomers in our Ab 42 :Ab 40 samples deviates enough from the random mixing case to produce a detectable effect.

Control: Ab hetero-oligomers from unlabeled peptides
While the isotope effect evident in Fig. 1 and 2 reveals mixing of Ab 40 and Ab 42 , it masks band shis due to structural differences between the homo-oligomers and the hetero-oligomers. Therefore we repeated the experiment with unlabeled peptides. When unlabeled Ab 40 and Ab 42 were mixed, both the band position of the main b-sheet and that of the broad band near 1645 cm À1 shied in a nearly linear fashion between the extreme values of the pure compounds. This is shown in panels A and B of Fig. 5. Please note that this series of experiments is completely independent from the ones shown in Fig. 1. Therefore the band positions of the pure compounds are slightly different. The band position of the Ab 42 spectrum in Fig. 5 (1624.8 cm À1 ) is the lowest measured for six independent samples (average 1625.5 AE 0.4 cm À1 ). The band position for Ab 40 (1622.2 cm À1 ) in Fig. 5 is very close to the average of 1622.3 AE 0.1 cm À1 determined for three samples.
Concomitant with the shiing band positions, the broad band near 1645 cm À1 intensies as the Ab 40 content increases (see also Fig. S1 †). This may indicate that there is more random coil structure in the Ab 40 oligomers. However, intensities in second derivative should be compared with care as they also depend on the band width. Therefore we sought conrmation for the above interpretation in the respective absorbance spectra and found it conrmed: the absorbance spectrum of Ab 40 , but not that of Ab 42 , shows a pronounced shoulder near 1640 cm À1 that can be assigned to random coil structures as band near 1625 cm À1 in the second derivative spectra. (C) Integrated absorbance near 1645 cm À1 divided by the integrated absorbance near 1625 cm À1 . Integration in the ranges 1650-1640 cm À1 and 1630-1620 cm À1 was done with method E of the Bruker OPUS software with respect to a baseline drawn between the averaged absorbance in the 1700-1695 cm À1 and in the 1610-1605 cm À1 range.
shown in Fig. S3. † In the mixtures, the absorbance in the 1650-1640 cm À1 region increases relative to that in the 1630-1620 cm À1 region as the Ab 40 content increases (panel C of Fig. 5).
As the curves in Fig. 5 are nearly linear, they indicate a gradual transition between the spectra of the pure oligomers and thus a gradual shi between the backbone structures of Ab 42 oligomers and of Ab 40 oligomers as the peptide composition of the oligomers changes. This result has several implications: (i) As a control experiment it indicates that the backbone structures of the mixed aggregates are similar to those of the pure oligomers. The shi of the main b-sheet band (panel B) is much smaller than the 13 C-band shi in Fig. 5. Therefore, a conformational effect can be excluded as an explanation for the 13 C-band shi. Note also that the shis in Fig. 5 depend on the Ab 42 : Ab 40 ratio, whereas those in Fig. 1 and 2 depend on the 13 C : 12 C-ratio. In the latter experiments, increasing the Ab 40 content leads to a downshi of the 13 C-band when Ab 40 is labeled, but to an upshi when it is not labeled.
(ii) From a methodological perspective, Fig. 5 demonstrates that mixing can only be detected with the help of isotope labels ( Fig. 1) because the curves in Fig. 5 are close to those expected for the case when Ab 40 and Ab 42 do not mix.
(iii) Regarding the biological system, Fig. 5 shows that none of the peptides forces the backbone structures of its pure oligomers on the mixed aggregates when the two peptides coaggregate from a mixture of monomers. Otherwise, the curves in Fig. 5 should be more curved.

Control: Ab 42 and S100A9
The ability of Ab 42 and Ab 40 to form mixed oligomers has the natural consequence that they mutually inuence their aggregation properties. In contrast, other interaction partners may affect aggregation without integrating into the backbone structure of the Ab aggregates. In the following we will show that isotope-edited IR spectroscopy can distinguish between these two cases and thus provides information that is complementary to that obtained from other aggregation assays.
As an example for the second case, we chose the brainexpressed, pro-inammatory calcium binding protein S100A9, which is also called migration inhibitory factor-related protein 14 (MRP14) or calgranulin B. It forms amyloids on its own and is known to interact with Ab, which enhances the amyloidogenicity of both. 49,50 In this case the interaction proceeds via transient hydrophobic contacts involving side chains, 49,50 rather than via direct interaction between backbone segments of the two proteins.
The IR absorption spectrum of S100A9 in the amide I 0 region is shown in black in panels A and C of Fig. 6. It exhibits three main components. A strong, sharp band at 1650 cm À1 originates from a-helices, the dominant secondary structure in the protein. The minor band at 1631 cm À1 , usually assigned to bsheet structures, rather originates from solvent-exposed and highly hydrated stretches of a-helices as there are no b-sheets in this protein. 51 The band at 1675 cm À1 originates from turns.
The spectrum of the mixture with unlabeled Ab 42 oligomers is shown as blue spectrum in panel B together with a calculated spectrum of the 1 : 1 mixture (average spectrum of the pure components, dashed spectrum). The two spectra are virtually superimposable, with all the main features of the Ab 42 oligomer spectrum being preserved. A small ($1 cm À1 ) downshi of the main b-sheet band can be observed (arrowhead 1) and is likely due to accelerated aggregation in the presence of S100A9. This interpretation is based on the observation that the position of this band downshis with increased aggregation time. 52 The same experiment was performed with labeled Ab 42 oligomers, as shown in panels C and D. Again, the calculated (dashed) and experimental (solid red) spectra of the 1 : 1 mixture are virtually superimposable and a small downshi of Fig. 6 Oligomer formation by unlabeled and labeled Ab 42 in the presence of S100A9. Panels (A), (B) and (C), (D) refer to experiments performed using unlabeled and labeled Ab 42 , respectively. S100A9 is unlabeled in both experiments. Panels (A) and (C) show spectra of the pure components and panels (B) and (D) spectra of the 1 : 1 mixtures (w/w). "Experiment" refers to the experimental spectrum and "Average" to the average spectrum of the pure components, which is the expected mixture spectrum in the absence of structural changes. the main b-sheet band of labeled Ab 42 oligomers can be observed (arrowhead 2). In contrast to the Ab 40 and Ab 42 mixtures, no upshi of the main 13 C-b-sheet band occurs when S100A9 is added to Ab 42 . This indicates that the upshi observed for Ab 40 :Ab 42 mixtures is not induced by transient, hydrophobic interactions between side chains as they occur between S100A9 and Ab.

Conclusions
Our experiments and control experiments clearly demonstrate that Ab 40 and Ab 42 form mixed oligomers, when they are mixed as monomers before aggregation is initiated. Mixing occurs on the level of secondary structure, where the Ab 40 backbone is in direct interaction with the Ab 42 backbone in the b-sheets of the oligomers. Mixing of Ab 40 and Ab 42 strands in the b-sheets is random or close to random. This structural information was inferred from band shis in the IR spectrum, when one of the peptides was 13 C-labeled. The different carbon isotopes in the mixed sheets disrupt the interstrand vibrational coupling, which leads to an upshi of the main b-sheet band. This conclusion is also supported by our spectrum calculations, which reproduce the shis observed in the experiments. The best agreement between calculations and experiments is obtained when we assume that each peptide contributes two adjacent strands to the oligomers.
The backbone structures of mixed Ab 42 :Ab 40 oligomers are intermediate between those of the pure aggregates. There is no indication that one of the alloforms forces its preferred structure on the other alloform when they are mixed as monomers. This conclusion is based on band shis observed for mixtures of unlabeled peptides, which depend linearly on the composition of the aggregates.
The random or close to random mixing of Ab 40 and Ab 42 in the b-sheets of oligomers occurs in spite of their different propensities to aggregate 6,10,16,21,23 and the different oligomer structures that they adopt 23 (see also Fig. S1 †). Our ndings are in line with previous more qualitative conclusions using chemically modied peptides 15 or peptides attached to a support 10 and with conclusions drawn indirectly from the observation of bril formation. 16 Our work adds information on the extent of mixing and on the structural architecture of mixed oligomers. It strengthens the view that heterogeneous oligomers are relevant for Alzheimer's disease. In addition, it highlights the necessity to consider them in the amyloid eld in general, since similar mixed oligomers may assemble under many other amyloidogenic conditions in several diseases.

Conflicts of interest
There are no conicts to declare.