soluble amyloid oligomers 
 are now thought to be the main toxic 
 species that cause neurodegeneration in alzheimer s and other 
 amyloid diseases .
small assemblies made up of dimers , trimers , and tetramers of the 
 -amyloid peptide ( a ) , as well as larger assemblies such 
 as dodecamers , have been shown to disrupt synaptic activity and cause 
 neuronal cell death .
atomic - level details of the structures of amyloid oligomers are 
 desperately needed in order to understand how the oligomers form and 
 the molecular basis by which they cause neurodegeneration .
the 
 oligomers are polymorphic and dynamic , forming as different 
 species and equilibrating slowly with the monomer and with -amyloid 
 fibrils , which are generally more stable .
while the structures 
 of amyloid oligomers are still largely unknown , a number of approaches 
 have been taken to gain insights into their structures .
-sheet 
 structure and interactions  a common feature of amyloid fibril 
 formation  are generally thought to be important in the structures 
 and interactions of amyloid oligomers .
incorporation of amyloidogenic peptides into larger proteins can 
 control amyloid supramolecular assembly and allow observation of oligomeric 
 assemblies at atomic resolution .
peptide 
 fragments can also serve as chemical models of oligomers ; x - ray crystallographic 
 studies of these peptide fragments have provided insights into the 
 structures of amyloid oligomers .
chemical cross - links 
 within amyloidogenic monomers that stabilize folded -sheet 
 conformations can promote oligomer formation and help prevent fibril 
 formation .
these cross - linked systems are more amenable to study 
 and can provide simpler and more stable chemical models of the unstable 
 oligomers formed by amyloidogenic peptides and proteins . computational 
 models of oligomers have been constructed from atomic - level structures 
 of amyloid fibrils , which are understood far better at atomic resolution 
 than the oligomers .
our laboratory is gaining insights into the 
 structures and interactions 
 of amyloid oligomers by combining fragments of amyloidogenic peptides 
 and proteins with molecular templates to create macrocycles that promote 
 -sheet structure and interactions while blocking amyloid fibril 
 formation .
we recently reported the x - ray 
 crystallographic structures of oligomers of a peptide from -amyloid .
we incorporated the nonapeptide sequence qklvffaed 
 ( a1523 ) into macrocyclic -sheet peptide 1 , with -linked ornithine turn units and a template 
 strand that features an unnatural amino acid , hao . in the solid state ,
the -sheet forms a hydrogen - bonded dimer , which assembles face - to - face 
 to make a cruciform tetramer , which is a key subunit of the lattice . 

the cruciform tetramers assemble into triangular dodecamers , and the 
 triangular dodecamers further assemble into the lattice .
the hydrogen - bonded 
 dimers are antiparallel , and the -strands 
 are fully aligned , with residues 1723 of one of the macrocycles 
 aligned with residues 2317 of the other .
the resulting four - stranded 
 -sheet forms a plane , with the side chains projecting from 
 the upper and lower faces of the plane . residues k16 , v18 , f20 , and e22 of each macrocycle project 
 from one face of the plane ( the vf face ) , and residues 
 q15 , l17 , f19 , a21 , d23 of each macrocycle project from the other face of the plane 
 ( the lfa face ) .
the vf face has the hydrophobic residues 
 v18 and f20 flanked by the polar residues k16 and e22 .
the lfa face has the hydrophobic residues 
 l17 , f19 , and a21 flanked by the 
 polar residues q15 and d23 .
the hydrogen - bonded 
 dimers assemble in a crisscross fashion through hydrophobic interactions 
 between the vf faces to give the cruciform tetramers .
figure 1 illustrates the faces of the macrocycle and the 
 structure of the cruciform tetramer .
cartoon illustrating the lfa and vf faces 
 of macrocyclic -sheet 1 and the cruciform tetramer 
 formed in the solid state .
the 
 vf faces form the inner hydrophobic core of the cruciform tetramer , 
 and the lfa faces form the outer surface . in the current study , we set out to determine how macrocyclic 
 -sheet 
 peptides containing the a1523 nonapeptide 
 assemble in solution .
we began by using h nmr spectroscopy 
 to study how macrocyclic -sheet peptide 2a folds 
 and oligomerizes in aqueous solution .
the two molecules differ only in that 1 contains 
 a p - bromophenylalanine ( f ) in the template 
 strand , for single anomalous dispersion ( sad ) phasing in x - ray crystallographic 
 structure determination , while 2a contains a tyrosine .
as our studies of macrocyclic -sheet 2a unfolded , we prepared additional homologues ( 2b , 2c , 3 , and 4 ) to interrogate 
 the assembly process .
the following describes these studies and elucidates 
 how the tetramer that forms in solution differs from that which forms 
 in the solid state .
we investigated 
 the folding and assembly of the macrocyclic -sheets in d2o and in h2o 
the h 
 nmr spectrum of macrocyclic -sheet 2a is disperse , 
 with methyl resonances from l17 and a21 unusually 
 upfield ( 0.35 and 0.49 ppm ) , aromatic resonances from f19 unusually upfield ( 6.28 and 6.52 ppm ) , and many of the amino 
 acid -protons unusually downfield ( 5.0 ppm ) .
one of 
 the resonances from one of the hao amino acids ( the h4 resonance 
 of hao1 ) appears unusually downfield at 9.17 ppm .
the upfield 
 shifting of the aromatic and aliphatic resonances is characteristic 
 of the formation of an oligomer with a well - packed hydrophobic core 
 comprising aromatic residues ( hao , phe , etc . ) and aliphatic residues 
 ( leu , ala , etc . ) .
minor additional resonances , associated with a monomer 
 lacking a hydrophobic core are also present , most notably at 0.690.79 
 ppm ( l17 and v18 ) .
figure 2 illustrates the h nmr spectrum of macrocyclic -sheet 2a at 2.0 mm in d2o solution .
h nmr spectra 
 of macrocyclic -sheet peptides 1 , 2a , and 2b at 2.0 mm in d2o at 500 mhz and 
 298 k. noteworthy resonances that reflect 
 important shared features of the folding and assembly of these peptides 
 are labeled and highlighted with dashed lines .
the h nmr spectrum of macrocyclic -sheet 1 is virtually identical to that of macrocyclic -sheet 2a , indicating that both peptides fold and oligomerize in 
 a similar fashion in solution .
the h nmr spectrum of macrocyclic 
 -sheet 1 also exhibits additional minor resonances 
 from l17 and v18 associated with a monomer lacking 
 a hydrophobic core .
these resonances are similar in intensity to those 
 of macrocyclic -sheet 2a , indicating that the 
 oligomers formed by both macrocycles are similar in association constant 
 ( kassoc ) as well as in structure .
h nmr noesy studies establish the formation of hydrogen - bonded 
 dimers that are antiparallel , with the -strands of residues 
 1723 shifted out of alignment by two residues toward the c - termini 
 ( figure 3 ) .
notably , the noesy spectrum in 
 d2o exhibits strong noes between the -protons of 
 l17 and d23 and between the -protons 
 of f19 and a21 ( figure 4 ) .
additional strong noes associated 
 with -sheet folding of the macrocycles occur between the -protons 
 of k16 and y and between the -protons of f20 and k ( figure 4 ) .
other noes characteristic 
 of folding are described in detail in the si , as are additional noes associated with folding and dimerization 
 that are seen in the noesy spectrum in h2o 
macrocyclic -sheet 1 exhibits similar patterns 
 of noes , indicating that it folds and dimerizes in a fashion similar 
 to that of macrocycle 2a ( figure s2 in the si ) .
the shifted structure of the dimers formed 
 by the macrocycles in solution stands in sharp contrast to the aligned 
 structure of macrocycle 1 in the solid state ( figure 3 ) .
cartoons and chemical structures illustrating the hydrogen - bonded 
 dimers formed by macrocyclic -sheet peptide 1 in 
 the solid state ( left ) and by both macrocyclic -sheet peptides 2a and 1 in solution ( right ) .
both hydrogen - bonded 
 dimers are antiparallel : in the solid - state dimer , residues 1723 
 of one of the macrocycles align with residues 2317 of the 
 other ; in the solution - state dimers , these -strands are shifted 
 out of alignment by two residues toward the c - termini .
key noes associated 
 with solution - state dimerization and folding of 2a are 
 shown with red and blue arrows . selected expansions of the noesy spectrum of macrocyclic -sheet 
 peptide 2a at 8.0 mm in d2o at 500 mhz and 
 300.5 k. key intermolecular interstrand noes associated with dimerization 
 are highlighted in red ; key intramolecular interstrand noes associated 
 with folding are highlighted in blue . at low concentrations ( e.g. ,  0.1 mm ) , the monomer 
 predominates 
 in the h nmr spectrum of macrocyclic -sheet 2a .
the methyl resonances from l17 and v18 of the monomer are prominent at 0.690.79 ppm , and the methyl 
 resonances from l17 and a21 of the oligomer 
 at 0.35 and 0.49 ppm are small . as the concentration of 2a
is increased , the relative intensities of the resonances 
 from the oligomer increase and the relative intensities of the resonances 
 from the monomer decrease ( figure 5 and figure 
 s3 in the si ) . at 0.2 mm ,
the resonances of the monomer and oligomer are roughly 
 equal in intensity . at high concentrations 
 ( e.g. , 8.0 mm ) , the resonances of the monomer are barely visible . 
 the strong concentration dependence of the monomer 
dimer equilibrium , 
 but rather reflects cooperative association in which the dimers are 
 a subunit of a higher - order oligomer  in this case a tetramer 
 consisting of a dimer of dimers .
expansions of the h nmr spectra 
 of macrocyclic -sheet 
 peptide 2a at various concentrations in d2o at 500 mhz and 298 k. noteworthy characteristic resonances of the 
 monomer and the oligomer are labeled and highlighted with dashed lines .
the noesy spectrum of macrocyclic 
 -sheet 2a shows additional crosspeaks that are 
 consistent with a tetramer 
 in which two hydrogen - bonded dimers form a sandwich - like assembly . 

notably , the noesy spectrum in d2o exhibits noes between 
 hao2 and threonine and between hao2 and hao1 that only make sense as interlayer noes between the hydrogen - bonded 
 dimers .
specifically , the methoxy group of hao2 gives noes 
 with the methyl group of threonine , and the h3 and h4 protons of hao2 give noes with the h3 and h4 protons of hao1 .
figure 6 illustrates these interlayer noe crosspeaks in the noesy 
 spectrum ; figure 7 illustrates the sandwich - like 
 assembly consistent with these noes .
figure 
 s4 and table s1 ( si ) provide additional 
 data . selected expansions of the noesy spectrum of macrocyclic -sheet 
 peptide 2a at 8.0 mm in d2o at 500 mhz and 
 300.5 k. key interlayer noes associated with tetramerization
illustration of the tetramer formed as a sandwich - like 
 assembly 
 of two hydrogen - bonded dimers of macrocyclic -sheet peptide 2a in aqueous solution .
macrocyclic 
 -sheet peptide 1 forms a similar sandwich - like 
 tetramer in solution .
the four threonines of the tetramer point toward the interior 
 of 
 the sandwich - like assembly , as do all of the residues on the lfa faces 
 of the -sheets ( q15 , l17 , f19 , a21 , and d23 ) . the magnetic anisotropy from 
 the packed aromatic groups of the resulting hydrophobic core shift 
 the methyl resonances of l17 and a21 upfield . 

thus , the structure of this solution - state tetramer , 
 in which the lfa faces make up the hydrophobic core , differs markedly 
 from the structure of the solid - state tetramer , in which the vf faces 
 make up the hydrophobic core . in the solid - state structure ,
the lfa 
 faces are on the exterior of the tetramer and the vf faces are on 
 the interior ; in the solution - state structure , the vf faces are on 
 the exterior and the lfa faces are on the interior . to 
 probe the assembly of the tetramer , we studied macrocyclic -sheet 
 peptide 3 .
macrocyclic -sheet 3 is 
 a homologue of 2a with a lysine in place of the threonine 
 in the template strand . at 1.0 mm essentially no tetramer
is observed 
 in the h nmr spectrum of 3 ( figure 8) . as the concentration
is increased to 2.0 and 
 4.0 mm , resonances for the tetramer appear ; at 8.0 mm the tetramer 
 predominates .
the tetramerization is far weaker than that of macrocyclic 
 -sheet 2a , in which the tetramer is observed at 
 0.1 mm and predominates at 0.3 mm .
expansions of the h nmr spectra 
 of macrocyclic -sheet 
 peptide 3 at various concentrations in d2o 
 at 500 mhz and 298 k. noteworthy characteristic resonances of the 
 monomer and the oligomer are labeled and highlighted with dashed lines .
addition of salt ( nacl ) augments 
 tetramer formation , suggesting 
 that intermolecular ionic repulsion is partially responsible for the 
 diminished tetramerization of macrocyclic -sheet 3 .
without nacl , macrocylic -sheet 3 is 46% tetramerized 
 at 4.0 mm ; with 25 mm nacl , it is 70% tetramerized ; with 150 mm nacl , 
 it is 80% tetramerized ( figure s6 and table s3 in the si ) .
the loss of 
 hydrophobic interactions between the methyl group of threonine and 
 the methoxy group of hao2 may also contribute to the diminished 
 stability of the tetramer of macrocyclic -sheet 3 .
diffusion - ordered spectroscopy ( dosy ) nmr studies support 
 the formation 
 of a tetrameric species .
measurement of the 
 dosy spectrum of macrocyclic -sheet peptide 2a in d2o at 2.0 mm and 8.0 mm and 298 k gave a diffusion 
 coefficient of 10.0  10 cm / s 
 and 10.1  10 cm / s , respectively , 
 for the oligomer .
the diffusion coefficient does 
 not vary from 2.0 mm to 8.0 mm , suggesting the presence of a single 
 oligomerization state .
measurement 
 of the dosy spectrum of macrocyclic -sheet peptide 3 in d2o at 2.0 mm and 298 k gave a diffusion coefficient 
 of 16.4  10 cm / s for the corresponding 
 monomer .
consistent with tetramer formation , the diffusion coefficient 
 of the oligomer of macrocyclic -sheet peptide 2a is 0.61 times that of the monomer of macrocyclic -sheet peptide 3 . to further study the assembly of the tetramer , we mutated residues 
 on the lfa and vf faces to examine how the hydrophobic residues on 
 each face control tetramer formation .
we created two double mutants 
 of 2a , in which either the hydrophobic residues v18 and f20 or the hydrophobic residues f19 and a21 were rendered more hydrophilic by hydroxylation . 
 in double mutant 2b , v18 was replaced with 
 threonine and f20 was replaced with tyrosine ( v18t , f20y ) . in double mutant 2c , f19 was replaced with tyrosine and a21 was replaced with 
 serine ( f19y , a21s ) .
the h nmr spectrum of the v18t , f20y double mutant 2b is strikingly similar to that of 
 macrocyclic -sheet 2a ( figure 2 ) , indicating that 2a and 2b fold 
 and oligomerize in a similar fashion in aqueous solution .
the methyl 
 resonances from l17 and a21 appear unusually 
 upfield , the aromatic resonances from f19 also appear unusually 
 upfield , and many of the amino acid -protons appear unusually 
 downfield .
the h nmr spectra of both compounds reflect 
 similar monomer  oligomer equilibria . at 0.1 mm ,
the monomer 
 predominates and only small resonances from the tetramer are present ; 
 at 1.0 mm , the resonances from the tetramer predominate and only small 
 resonances from the monomer are present .
thus , v18t , f20y double mutation does not substantially alter the equilibrium 
 constant for tetramer formation .
the h nmr spectrum 
 of the f19y , a21s double mutant 2c differs markedly from those of 2a and 2b ( figure s7 in the si ) .
the methyl resonances 
 from l17 do not appear 
 unusually upfield and the amino acid -protons do not appear 
 unusually downfield .
these observations indicate that f19y , a21s double mutation disrupts the formation of the tetramer . 

the h nmr spectrum of macrocyclic -sheet 2c shows some minor broadened resonances at 2.0 mm , which 
 diminish at lower concentrations , suggesting that some weaker nonspecific 
 self - association may persist when tetramer formation is disrupted .
the dramatic differences between macrocyclic -sheets 2b and 2c further demonstrate the importance 
 of hydrophobic interactions of the lfa face of the macrocycle in tetramer 
 formation .
when the lfa face is hydroxylated , tetramer formation is 
 disrupted , but when the vf face is hydroxylated , tetramer formation 
 is not affected . to probe 
 the role of hydrogen bonding in tetramer formation
, we blocked the 
 hydrogen - bonding edge of the macrocycle by n - methylation . 

macrocyclic -sheet 4 is a homologue of macrocyclic 
 -sheet 2a with n - methylphenylalanine 
 in place of phenylalanine at position 20 .
the f20f mutation is designed to block 
 formation of the hydrogen - bonded dimer and thus the assembly of a 
 tetramer comprising a dimer of hydrogen - bonded dimers .
the h nmr spectrum of macrocyclic -sheet 4 also differs 
 markedly from those of 2a and 2b ( figure 
 s7 in the si ) .
the methyl resonances from 
 l17 and a21 do not appear unusually upfield 
 and the amino acid -protons do not appear unusually downfield . 

the disruption of tetramer formation by n - methylation 
 demonstrates that hydrogen bonding is also essential for tetramer 
 formation .
dosy nmr studies 
 of macrocyclic -sheets 14 suggest that 1 , 2a , and 2b are tetrameric at millimolar concentrations , while 2c , 3 , and 4 are monomeric . as mentioned above , the oligomeric 2a exhibits a diffusion coefficient of 10.0  10 cm / s in d2o at 298 k , while 
 monomeric 3 exhibits a diffusion coefficient of 16.4 
  10 cm / s .
the ratio of these 
 diffusion coefficients  about 0.6  is consistent with 
 tetramer formation .
macrocyclic 
 -sheets 1 and 2b exhibit diffusion 
 coefficients similar to that of 2a , while macrocyclic 
 -sheets 2c and 4 exhibit diffusion 
 coefficients similar to that of 3 ( table 1 ) .
diffusion coefficient 
 measured at 
 8.0 mm . to corroborate the 
 dosy studies , we performed analytical ultracentrifugation ( auc ) sedimentation 
 velocity studies on macrocyclic -sheet 2b .
the auc studies are best performed in nonzero ionic strength to 
 avoid nonideality resulting from charge interactions between the large 
 cationic molecules .
thus , we performed auc sedimentation velocity 
 studies in the presence of salt , using 0.10 , 0.30 , and 0.66 mm solutions 
 of macrocycle 2b in h2o containing 25 mm nacl 
 at 293 k. the sedimentation velocity data fit well to a reversible 
 monomer  tetramer equilibrium with slow exchange on the time 
 scale of the experiment ( hours ) .
the tetramer predominated at all 
 three concentrations , with the greatest fraction of monomer present 
 at 0.10 mm .
analysis of the data from the 0.10 mm experiment gave 
 a good fit to a monomer  tetramer equilibrium with a 2.14 kda 
 monomer and a 8.55 kda tetramer and a kassoc of 1.93  10 m. ( for details see the si . ) the magnetic anisotropy of 
 the diastereotopic -protons of the -linked ornithine 
 turn units in the h nmr spectra reflect that the tetramers 
 of 1a , 2a , and 2b form well - folded 
 -sheets , while the monomers of 2c , 3 , and 4 are only partially folded . in a well - folded 
 macrocyclic -sheet ,
the difference in the chemical shifts (  ) 
 of the diastereotopic pro - s and pro - r -protons of the -linked ornithine turn units ( orn ) is about 0.6 ppm in aqueous solution .
values substantially lower than 
 0.6 ppm reflect the formation of partially folded macrocyclic -sheet 
 structures . at 2.0 mm and 298 k in d2o , the tetramers of 1 , 2a , and 2b exhibit large magnetic 
 anisotropies , while the monomers of 2c , 3 , and 4 exhibit smaller magnetic anisotropies ( table 2 ) .
to further 
 investigate the folding and oligomerization of macrocylic 
 -sheet 2a , we compared the h nmr chemical 
 shifts of the -protons of the 2a tetramer to those 
 of acyclic control peptide 5 .
peptide 5 contains the a1523 nonapeptide and two -linked ornithine turn units but 
 lacks the lower template strand .
the -proton resonances of 
 a1523 in the 2a tetramer appear 
 0.041.04 ppm downfield of those of acyclic control , with an 
 average downfield shifting of 0.66 ppm ( figures 9 and s8 in the si ) .
the large downfield 
 shifting of the -protons suggests the formation of a well - folded 
 -sheet structure .
downfield 
 shifting of the h nmr -proton resonances 
 of the 2a tetramer and the 3 monomer , relative 
 to acyclic control 5 .
the h nmr spectrum 
 of 2a was recorded at 8.0 mm in d2o at 500 
 mhz and 300.5 k. the h nmr spectra of 3 and 5 were recorded at 2.0 and 1.2 mm , respectively , in d2o at 500 mhz and 298 k. in contrast , the -proton resonances of the monomer 
 of 2a are not nearly as far downfield shifted . although 
 it is 
 not feasible to identify all of the -proton resonances of the 
 monomer of 2a because the tetramer predominates even 
 at submillimolar concentrations , it is possible to do so in the close 
 homologue 3 , which is largely monomeric at low millimolar 
 concentrations .
the -proton resonances of a1523 in the 3 monomer show far less downfield shifting , 
 with an average of only 0.13 ppm ( figures 9 and s8 in the si ) .
the smaller downfield 
 shifting of the -protons of the monomers of 2a and 3 reflects the formation of -sheet structures 
 that are only partially folded .
although 
 the individual peptide monomer units are only partially folded , the 
 tetramers that form exhibit secondary , tertiary , and quaternary structure 
 reminiscent of proteins .
the unusually well - defined structures of 
 the tetramers are reflected in the strong noes observed and in the 
 large magnetic anisotropies of the l17 , f19 , 
 and a21 side chains and many of the -protons in 
 the h nmr spectra . to gain further insight into 
 the structure of the tetramers formed 
 by the macrocyclic -sheets in aqueous solution
, we used the 
 x - ray crystallographic structure of the tetramer of macrocyclic -sheet 1 to create a model of the solution - state tetramer of macrocyclic 
 -sheet 2a .
we generated the initial coordinates 
 for the model in pymol by ( 1 ) changing the p - bromophenylalanine 
 of 1 to tyrosine , ( 2 ) shifting the crystallographic dimers 
 out of alignment by two residues toward the c - termini , ( 3 ) moving 
 the dimers to pack through the lfa faces instead of the vf faces , 
 ( 4 ) selecting appropriate rotamers of f20 , and ( 5 ) orienting 
 the dimers to approximately match the observed interlayer noes between 
 the methoxy group of hao2 and the methyl group of threonine . 

we then generated a minimum - energy structure ( local minimum ) of the 
 tetramer in macromodel with the maestro user interface using the mmffs 
 force field with gb / sa water solvation , minimizing first with distance 
 constraints to match the observed noes between -protons ( figure 3 ) and between the layers of the -sheets ( figures 6 and 7 ) and then without 
 constraints .
the tetramer consists of a dimer of hydrogen - bonded 
 dimers and is essentially symmetrical , consisting of four roughly 
 symmetrical monomers arranged in roughly d2 symmetry .
f19 , and a21 of the dimers pack tightly to form a hydrophobic core within the 
 tetramer ( figure 10b and c ) .
the methyl group 
 of a21 sits over the phenyl group of f19 in 
 the opposing layer of the sandwich - like structure , consistent with 
 the observed upfield shifting of the methyl resonance of a21 in the h nmr spectrum .
the pro - s methyl 
 group of l17 sits over the aromatic ring of hao2 in the opposing layer , consistent with the pronounced upfield shifting 
 of one of the methyl resonances of l17 in the h nmr spectrum .
the methyl group of the threonine is close to the 
 methoxy group of hao2 , and hao1 is close to 
 hao2 , consistent with the observed noes between these groups 
 ( figure 10d and figure 6 ) .
model of macrocyclic -sheet peptide 2a as a 
 tetramer , based on the noe cross peaks of 2a and the 
 x - ray crystallographic structure of 1 . ( a )
the hydrogen - bonded dimers are antiparallel 
 and shifted out of alignment by two residues toward the c - termini . 

residues l17 , f19 , and a21 of the 
 hydrophobic core are shown ( the lfa face ) .
( d ) detail of the contacts between threonine , hao1 , and 
 hao2 , which give rise to the interlayer noe crosspeaks 
 that are shown in figure 6 .
the solution - state tetramers formed by macrocyclic 
 -sheets 1 , 2a , and 2b differ from the solid - state 
 tetramer observed for macrocyclic -sheet 1 in 
 three notable ways : although both tetramers comprise antiparallel 
 -sheet dimers , the solution - state dimers are out of register , 
 shifted out of alignment by two residues toward the c - termini , while 
 the solid - state dimers are in register , with all residues aligned 
 ( figure 11 ) .
the solution - state dimers are 
 sandwiched through the lfa faces , while the solid - state dimers are 
 sandwiched through the vf faces ( figure 12 ) . 
 the two solution - state dimers that form the tetramer are nearly parallel 
 to each other , while the two solid - state dimers are nearly orthogonal ; 
 the former are oriented at roughly 15 , while the latter are 
 oriented at roughly 83 ( figure 12 ) .
model 
 of macrocyclic -sheet peptide 2a and 
 the x - ray crystallographic structure of 1 as dimers . 

( a ) x - ray crystallographic structure of hydrogen - bonded dimers of 1 that are antiparallel and fully aligned . ( b ) solution - state 
 structure of hydrogen - bonded dimers of 2a that are antiparallel 
 and shifted out of alignment by two residues toward the c - termini .
model of macrocyclic -sheet peptide 2a and 
 the x - ray crystallographic structure of 1 as tetramers . 

( a ) top view of the x - ray crystallographic structure of 1 as a tetramer .
residues v18 and f20 of the 
 hydrophobic core are shown ( the vf face ) .
( b ) top view of solution - state 
 structure of 2a as a tetramer .
residues l17 , f19 , and a21 of the hydrophobic core are 
 shown ( the lfa face ) .
the differences between the solution - state tetramer and the 
 solid - state 
 tetramer may reflect the need to maximize hydrophobic contacts in 
 aqueous solution .
the lfa face of the dimer presents six 
 hydrophobic residues from a1523 , while the 
 vf face presents only four ( figure 12 ) .
hydrophobic contact is maximized in the aqueous 
 tetramer through contact between these six residues .
the bulky hydrophobic 
 side chains of l17 and f19 pack well with the 
 small hydrophobic side chain of a21 in the opposing dimer 
 of the tetramer . in the solid state ,
the tetramer is part of a lattice 
 in which there are additional intermolecular contacts .
the tetramers 
 are in contact with other tetramers , as well as with water and organic 
 cocrystallants , and these contacts likely help stabilize the tetramer . 

differences in ph and protonation state may also be important in the 
 differences between the solution - state and solid - state tetramers .
the differing morphology of the solution - state and solid - state 
 tetramers is significant , because it may provide a glimpse into some 
 of the structural bases for polymorphism among a oligomers 
 in alzheimer s disease .
polymorphism has previously been observed 
 at atomic resolution in a fibrils , but not in oligomers . because little is known about the structures of amyloid oligomers , 
 little is known about the structural bases of oligomer polymorphism . 

much of what is currently known about amyloid oligomer polymorphism 
 focuses on differences in reactivity toward oligomer - specific antibodies 
 or differences in size and shape that can be observed by electron 
 microscopy , atomic - force microscopy , gel electrophoresis , or mass 
 spectrometry .
the contrasting structures of the solution - state and solid - state tetramers 
 described here demonstrate subtle differences among oligomers that 
 can be observed at atomic resolution .
differing 
 alignment of the -strands within the -sheets also gives 
 rise to unique structures .
while not seen in the two types of tetramers 
 here , both parallel and antiparallel -sheet structures may 
 also be possible .
macrocyclic -sheet 
 peptides containing the a1523 nonapeptide 
 exhibit rich supramolecular 
 chemistry , forming tetramers with well - defined structures in aqueous 
 solution and in the solid state .
the 
 solution - state and solid - state tetramers exhibit noteworthy polymorphism , 
 differing in the alignment of the monomers within the hydrogen - bonded 
 dimers , the faces of the hydrogen - bonded dimers involved in tetramer 
 formation , and the rotational orientation of the hydrogen - bonded dimers 
 within the tetramers ( figure 13 ) . both hydrogen 
 bonding and hydrophobic interactions are important in tetramer formation . 

residues l17 , f19 , and a21 are critical 
 in the formation of the hydrophobic core of the tetramers in solution , 
 and the size complementarity of the small a21 residue and 
 large l17 and f19 residues may play a special 
 role in their stability .
cartoon illustrating the structure of the solid - state 
 tetramer 
 of macrocyclic -sheet 1 ( top ) , and the solution - state 
 tetramer of macrocyclic -sheets 1 and 2a ( bottom ) .
the vf faces form the inner hydrophobic core of the solid - state 
 tetramer of 1 , and the lfa faces form the outer surface . 

the lfa faces form the inner hydrophobic core of the solution - state 
 tetramer of 1 and 2a , and the vf faces form 
 the outer surface .
the supramolecular assembly 
 of amyloidogenic peptides to form soluble 
 oligomers is almost impossible to study at atomic resolution with 
 natural full - length amyloidogenic peptides , because the oligomers 
 that form are heterogeneous in size and morphology and because the 
 oligomers are dynamic and can ultimately form insoluble amyloid .
chemical 
 model systems that limit uncontrolled supramolecular assembly and 
 contain important segments of the amyloidogenic peptides can help 
 identify modes in which the peptides interact .
we anticipate that 
 chemical model systems based on macrocyclic peptides will prove widely 
 useful in elucidating the supramolecular assembly and oligomer formation 
 of other amyloidogenic peptides .
 this 
 contribution reports solution - phase structural studies of 
 oligomers of a family of peptides derived from the -amyloid 
 peptide ( a ) . 
 we had previously reported the x - ray crystallographic 
 structures of the oligomers and oligomer assemblies formed in the 
 solid state by a macrocyclic -sheet peptide containing the 
 a1523 nonapeptide . in the current study , 
 we set out to determine its assembly in aqueous solution . in the solid 
 state 
 , macrocyclic -sheet peptide 1 assembles 
 to form hydrogen - bonded dimers that further assemble in a sandwich - like 
 fashion to form tetramers through hydrophobic interactions between 
 the faces bearing v18 and f20 . 
 in aqueous solution , 
 macrocyclic -sheet peptide 1 and homologue 2a form hydrogen - bonded dimers that assemble to form tetramers 
 through hydrophobic interactions between the faces bearing l17 , f19 , and a21 . in the solid state , 
 the hydrogen - bonded 
 dimers are antiparallel , and the -strands are fully aligned , 
 with residues 1723 of one of the macrocycles aligned with 
 residues 2317 of the other . in solution , residues 1723 
 of the hydrogen - bonded dimers are shifted out of alignment by two 
 residues toward the c - termini . 
 the two hydrogen - bonded dimers are 
 nearly orthogonal in the solid state , while in solution the dimers 
 are only slightly rotated . 
 the differing morphology of the solution - state 
 and solid - state tetramers is significant , because it may provide a 
 glimpse into some of the structural bases for polymorphism among a 
 oligomers in alzheimer s disease . 
Introduction
Results
Discussion
Conclusion