the formation of dimers through edge - to - edge interaction among -sheets is a fundamental mode of protein interaction . homodimers with -sheet dimerization interfaces occur widely in the protein data bank and are often formed from monomers that present an exposed -strand . in these structures , the monomers pair symmetrically through antiparallel -sheet formation ; the topology of -strands does not permit symmetrical pairing through parallel -sheet formation in a protein with only one hydrogen - bonding edge of the -strand exposed . figure 1 illustrates the structures of four such dimers , which were selected from the interchain -sheet ( icbs ) database.(5 ) structures of -sheet dimers : defensin hnp-3 ( upper left , pdb i d 1dfn),(1 ) the -cro repressor ( upper right , pdb i d 1cop),(2 ) interleukin 8 ( lower left , pdb i d 1il8),(3 ) and the ribonuclease h domain of hiv-1 reverse transcriptase ( lower right , pdb i d 1hrh).(4 ) in contrast to the dimers of folded proteins , peptides and unfolded proteins often form aggregates consisting of infinite networks of -sheets . many of these aggregates consist of parallel , in - register -sheets , which can form when both hydrogen - bonding edges of a peptide strand are exposed . further interactions among the faces of the resulting -sheets lead to layered structures in which tightly self - complementing steric zippers  bind together the faces of the paired -sheets.(6 ) we recently reported macrocyclic -sheet peptides that dimerize through antiparallel edge - to - edge interaction among -sheets.(8 ) the macrocyclic peptides ( 1 ) consist of a 54-membered ring comprising a heptapeptide  upper  -strand , two -linked ornithine turn units , and a  lower -strand mimic comprising two  hao  amino acids that mimic a tripeptide -strand and one additional amino acid . the hao units help pre - organize the  upper  -strand while blocking the  lower  edge and preventing the formation of an infinite network . unless stabilized by intermolecular disulfide linkages between the r1 and r7 positions , the structures do not exist as isolated dimers in aqueous solution.(12 ) instead , the dimers ( 11 ) self - assemble through hydrophobic face - to - face interactions to form tetramers , comprising dimers of dimers , or related higher - order assemblies . in this paper , we report the x - ray crystallographic structure of the -sheet dimer of macrocyclic -sheet peptide 1a . this compound is a close homologue of macrocyclic -sheet peptides 1b and 1c , which we described in our original report.(8 ) in homologue 1a , the phenylalanine or tyrosine at the r6 position of 1b or 1c is replaced with 4-bromophenylalanine to facilitate x - ray diffraction studies . the sequence of the heptapeptide strand ( r1r7 ) of these macrocycles is loosely based upon that of the exposed -sheet edge ( ttftytt ) of the redesigned protein g variant nug2 , which crystallizes as a -sheet dimer.(13 ) macrocycle 1a was prepared by synthesis of the corresponding linear peptide on chlorotrityl resin followed by cleavage of the protected linear peptide from the resin , cyclization of the linear peptide in solution , deprotection , and rp - hplc purification.(8 ) crystals were grown by the sitting drop vapor diffusion method from 30% aqueous isopropanol solution with hepes buffer and mgcl2 . x - ray diffraction data were collected with synchrotron radiation using the multi - wavelength anomalous dispersion ( mad ) technique . the incorporation of 4-bromophenylalanine in 1a afforded the opportunity to solve the phase problem by performing a mad experiment , commonly employed in protein crystallography . refinement was performed to 1.35  resolution with the inclusion of 264 molecules of water and six molecules of isopropanol . structural deviation among the dimers is small , with < 0.7  rms deviation among all pairwise comparisons of the dimer coordinates . the largest deviations throughout the structures involve conformations of the 4-bromophenylalanine ( r7 ) and lysine ( r8 ) side chains . two conformations of the r2 tyrosine side chain are observed in one of the 12 monomer units , and two conformations of the r6 tyrosine side chain are observed in another of the 12 monomer units.(14 ) the four - stranded -sheet comprising the dimer exhibits a gentle twist , in a fashion characteristic of protein -sheets.(15 ) x - ray crystallographic structure of the dimer of 1a . cartoon ( a ) and atomic ( b ) representations of a representative dimer ; overlay of the six dimers in the asymmetric unit ( c ) . polar contacts corresponding to main - chain hydrogen bonds are shown as magenta dashes in panel b ; polar contacts corresponding to side - chain hydrogen bonds are shown as yellow dashes in panel b. each dimer exhibits intra- and intermolecular hydrogen bonding characteristic of antiparallel -sheets . a network of hydrogen bonds runs among the four peptide main chains comprising the dimer and is shown as magenta dashes in figure 2b . the hydrogen bonds have no distances ( 2.83.0  ) and geometries typical of -sheets . all hydrogen - bond donors and acceptors of the  inner  two peptide main chains are satisfied , with the exception of the -amino group of the ornithine residue , which forms hydrogen bonds with solvent water molecules . outer  two peptide main chains ( those containing the hao amino acids ) form hydrogen bonds with the  inner  two peptide main chains . the outer edges of the hao - containing peptide chains are solvent exposed . ordered water molecules ( not shown in figure 2 ) form hydrogen bonds with the exposed backbone oxygens and nitrogens on these edges . three hydrogen bonds are formed between the threonine and serine side chains at the dimer interface and are shown as yellow dashes in figure 2b . hydrogen - bond donors and acceptors on the threonine and serine side chains also interact with bulk solvent ( which accounts for 59% of the crystal volume ) , as do those on the tyrosine and lysine side chains . the trimers of dimers are virtually identical in structure and have minimal contact within the lattice.(16 ) figure 3 illustrates the structure of one of the two trimers . in each trimer , the r3 and r5 phenylalanine and tyrosine side chains point inward to create a loose hydrophobic core of the trimer . the r1 and r7 serine and threonine side chains also point inward and create hydrophilic caps to the core . the r2 , r4 , r6 , and r8 tyrosine , threonine , 4-bromophenylalanine , and lysine side chains point outward . an unusual feature of this barrel - like structure is the large volume of the cavity at center of the barrel ( 1033 ).(17 ) x - ray crystallographic structure of the trimer of dimers of 1a . the asymmetric unit contains two trimers of dimers , which are virtually identical in structure . the interface between each dimer within the trimer is stabilized by aromatic edge - to - face interactions of the r3 phenylalanine and r5 tyrosine side chains and van der waals contacts with the hao moieties . the sum of the area buried by both surfaces in this interface is 820  , and the shape complementarity correlation sc of the interface is 0.817.(18 ) the instability afforded by the creation of a void in the center of the barrel - like structure appears to be compensated by the amount of surface area buried by interfaces between the dimers and the high degree of surface complementarity . the controlled self - assembly of designed peptides , proteins , and peptide analogues has emerged as a major theme in the broadly defined areas of supramolecular chemistry and foldamers . the development of strategies that permit the creation of biomimetic and bio - inspired structures that fold and self - assemble like proteins permits the rational design of synthetic assemblies that function like the biomolecular assemblies in living organisms . in cases of rigid , conformationally constrained peptides for which the solid and solution - state structures are not expected to differ appreciably , x - ray crystallography provides a method of structure determination that is complementary to solution - state nmr spectroscopy.(19 ) the x - ray crystallographic structure of macrocyclic -sheet peptide 1a provides direct insight into the structures of the peptidomimetic -linked ornithine and hao building blocks that our laboratory has developed and used extensively in the creation of compounds that mimic the structures and interactions of -sheets . the -linked ornithine adopts a conformation that resembles a hydrogen - bonded -turn , in which the ornithine takes the place of the i+1 and i+2 residues ( figure 4 ) . the ornithine side chain adopts a well - defined conformation that resembles the chair conformer of a cyclohexane ring . in this conformation , the ornithine pro - s -hydrogen and -hydrogen are in contact and occupy the positions that would be occupied by carbons in the cyclohexane ring . x - ray crystallographic structures of the -linked ornithine turn and hao units of 1a . the hao amino acid building block adopts a conformation that resembles a tripeptide in a -strand conformation ( figure 4 ) : the hydrazine and aromatic carboxamide groups occupy the position of the first amino acid of the tripeptide ; the aromatic ring occupies the position of the second amino acid ; and the oxalic and aromatic amino groups occupy the position of the third amino acid.(9 ) one edge of the hao unit presents an alternating array of hydrogen - bond donor and acceptor groups in the same pattern as that of a tripeptide -strand , while the other edge does not present this hydrogen - bonding pattern and is blocked by intramolecular hydrogen bonding and the aromatic ring . the blocking created by these features is reminiscent of the negative design that occurs in natural -sheet proteins and prevents uncontrolled edge - to - edge interactions.(22 ) the macrocyclic structure formed by 1a is similar to that of the -defensin peptides.(23 ) these cyclooctadecapeptides form hydrogen - bonded cyclic -sheet structures that are reinforced by three disulfide bridges between the non - hydrogen - bonded residues of the macrocycles . figure 5 illustrates the structures of the monomer subunit of macrocyclic -sheet peptide 1a and the potent anti - hiv -defensin retrocyclin-2 . in both structures , the postulated barrel - like structure of these trimers is similar to the structure of the trimers of dimers observed for macrocyclic -sheet peptide 1a ( figure 3).(23d ) comparison of the x - ray crystallographic structure of the monomer subunit of 1a ( upper ) to an nmr structure of the -defensin retrocyclin-2 ( lower , pdb i d 2atg ) . macrocycle 1a comprises 12 amino acids , in contrast to the 18 of the -defensin , because each hao amino acid takes the place of three -amino acids and each -linked ornithine takes the place of the two central amino acids of the -turns . the hao amino acids help reinforce a folded -sheet structure in 1a , like the disulfide bridges help reinforce a -sheet structure in the -defensins . interactions between the electron - rich tyrosines at the r2 and r6 positions of 1a and the electron - deficient oxalic groups may contribute to this stabilization . the -linked ornithine units are particularly effective in forming -hairpin structures and may also contribute to the stabilization.(10 ) the dimers formed by macrocyclic -sheet 1a resemble the dimers of many proteins , such as defensin hnp-3,(1 ) the -cro repressor,(2 ) interleukin 8,(3 ) and the ribonuclease h domain of hiv-1 reverse transcriptase,(4 ) which are shown in figure 1 . the dimerization interfaces of all of these structures comprise a hydrogen - bonded antiparallel -sheet in which each monomer contributes a -strand . this fundamental form of biomolecular recognition has also been observed in other designed peptides and proteins.(24 ) x - ray crystallography is excellent for observing -sheet dimers , because the high concentration in the solid state and additional crystal packing forces help stabilize the dimers . in aqueous solution , hydrophobic interactions between molecules can reinforce the hydrogen bonds and provide an important mechanism for stabilizing the dimers . the additional hydrophobic buttressing of the helices in interleukin 8 , for example , stabilizes the dimer in aqueous solution.(3 ) self - assembly through hydrophobic face - to - face interactions stabilizes the dimers of artificial -sheets 1 in aqueous solution.(8 ) covalent bonds provided by disulfide linkages can also stabilize the dimers . the x - ray crystallographic structure of macrocyclic -sheet 1a provides deeper insights into the solution - phase structures of macrocycles 1.(8 ) macrocycle 1d , for example is a double mutant of 1a ( r2 = rser , r6 = rthr ) that forms dimers of dimers in aqueous solution . the association state of these tetramers was established through extensive analytical ultracentrifugation and pulsed field gradient ( pfg ) nmr diffusion studies . macrocycles 1b and 1c were also determined to be dimers of dimers , albeit less rigorously , through pfg nmr diffusion studies alone . nmr studies also show that macrocycles 1ac are largely folded in the monomeric state , while macrocycle 1d is largely unfolded . interactions between the aromatic residues at the r2 and r6 positions and the two hao amino acid units observed in the x - ray crystallographic structure of 1a ( figure 2 ) may explain the greater propensities of macrocycles 1ac to fold . we used the x - ray crystallographic structure of the trimer of dimers formed by 1a to create a molecular model of the dimer of dimers of 1d . to do this , we simply removed one dimer unit from the trimer of dimers ( figure 3 ) and moved the dimers together in a face - to - face fashion to form a -sheet sandwich . we minimized the resulting structure using macromodel v6.5 with the mmff force field and gb / sa water solvation and mutated residues 2 and 6 to alanine and then to serine and threonine , reminimizing after each mutation . the model is based on the x - ray crystallographic structure of the trimer of dimers of 1a ( figure 3 ) and the known propensity of 1d to form a dimer of dimers in aqueous solution . in the dimer of dimers of macrocyclic -sheet peptide 1d modeled in figure 6 , much of the interdimer contact arises from the phenylalanine and tyrosine residues in the central peptide strands . the surface area buried by the dimerdimer interface in this model is smaller than that buried by each dimerdimer contact in the trimer of dimers of macrocyclic -sheet peptide 1a shown in figure 3 ( 460 vs 820  ) , and the shape complementarity correlation sc of the interface is lower ( 0.554 vs 0.817 ) . the observed polymorphism of these macrocyclic -sheet peptides likely reflects differences in the environments in which the samples were studied rather than their differences in sequence . the high ( 75 mm ) concentration of 1a in the solid state may favor the trimer of dimers , while the lower concentrations ( 10 mm ) at which 1bd have been studied in solution may favor the dimer of dimers . the salts and isopropanol used for the crystallization may also favor the trimer of dimers . the observed polymorphism of macrocyclic -sheet peptides 1 is reminiscent of the polymorphism of alzheimer s -amyloid fibrils reported by tycko and co - workers.(25 ) the x - ray crystallographic structure of 1a provides with unparalleled confidence the structures of the dimers formed by macrocyclic -sheets 1 . the structure reveals in detail the peptidomimetic templates , the folded monomers , and the -sheet dimers and corroborates the understanding of these units that had been developed through extensive solution - phase studies . this cross - validation goes both ways , validating solution - phase structures that had previously only been inferred while establishing that the crystalline state does not appreciably distort the structure of the macrocycle . x - ray crystallography also reveals a mode of higher - order self - assembly of the dimers that had not been anticipated from solution - phase studies of the closely related homologues . both the anticipated dimers of dimers and the crystallographically observed trimer of dimers share in common the buttressing of the hydrogen - bonded dimers through additional hydrophobic interactions . the artificial -sheet dimers elucidated by this study are similar in structure to those formed by naturally occurring -sheet proteins . we anticipate using insights provided from this study to better design molecules that interact through -sheet formation to control -sheet interactions between proteins and to inhibit the -sheet interactions associated with peptide and protein aggregation . macrocyclic -sheet peptide 1a was synthesized and purified as described previously for macrocyclic -sheet peptides 1bd.(8 ) crystals of 1a were grown with an aldrich basic crystallography kit by the sitting drop vapor diffusion method at 25 c . 0.4  0.4  0.4 mm ) grew from aqueous solution with 0.2 m mgcl2 , 0.1 m hepes ph 7.5 buffer , and 30% isopropanol in space group p212121 with cell dimensions a = 64.05  , b = 64.19  , c = 64.25  ,  =  =  = 90 , and 12 molecules of 1a in the asymmetric unit ( au ) . to avoid rapid evaporation of the mother liquor during crystal collection , drops were opened at 277 k. crystals were soaked in well solution containing 30% glycerol as a cryoprotectant and flash - frozen at 100 k in liquid n2 prior to data collection . x - ray diffraction data were collected using three wavelengths at the stanford synchrotron radiation laboratory ( ssrl ) beamline 9 - 2 on a mar325 ccd detector . a second crystal was used to collect a high - resolution data set at beamline 7 - 1 on an adsc quantum315 ccd detector . data were collected at 100 k. indexing , integration , and scaling were performed with the program hkl2000.(26 ) all 12 bromine atoms in the au were located using the program solve.(27 ) the resulting mad phases had a mean figure of merit of 0.68 . clear , continuous electron density was observed for all 12 cyclic peptides in the au . the density was improved using one round of density modification and solvent flipping in cns.(28 ) model building was performed with the graphics program coot.(29 ) geometric restraints for the hao amino acid were generated by the prodrg server.(30 ) the model was refined to 1.35  using the maximum likelihood algorithm within refmac5 in the ccp4 program suite.(31 ) multiple rounds of model building and refinement followed . the addition of water and six well - defined isopropanol molecules improved the rwork and rfree to 0.150 and 0.157 , respectively . all the amino acid residues in the structure lay within the favored -sheet region of the ramachandran plot .
this paper describes the x - ray crystallographic structure of a designed cyclic -sheet peptide that forms a well - defined hydrogen - bonded dimer that mimics -sheet dimers formed by proteins . 
 the 54-membered ring macrocyclic peptide ( 1a ) contains molecular template and turn units that induce -sheet structure in a heptapeptide strand that forms the dimerization interface . 
 the x - ray crystallographic structure reveals the structures of the two  hao  amino acids that help template the -sheet structure and the two -linked ornithine turn units that link the hao - containing template to the heptapeptide -strand . 
 the hao amino acids adopt a conformation that resembles a tripeptide in a -strand conformation , with one edge of the hao unit presenting an alternating array of hydrogen - bond donor and acceptor groups in the same pattern as that of a tripeptide -strand . 
 the -linked ornithines adopt a conformation that resembles a hydrogen - bonded -turn , in which the ornithine takes the place of the i+1 and i+2 residues . 
 the dimers formed by macrocyclic -sheet 1a resemble the dimers of many proteins , such as defensin hnp-3 , the -cro repressor , interleukin 8 , and the ribonuclease h domain of hiv-1 reverse transcriptase . 
 the dimers of 1a self - assemble in the solid state into a barrel - shaped trimer of dimers in which the three dimers are arranged in a triangular fashion . molecular modeling in which one of the three dimers is removed and the remaining two dimers 
 are aligned face - to - face provides a model of the dimers of dimers of closely related macrocyclic -sheet peptides that were observed in solution .