modular design is used 
 for engineering complex devices in electronics , 
 mechanics , nanotechnology and other fields . recently , biologists have 
 begun to exploit modular parts as a way to build novel synthetic biological 
 systems . many types of parts are required 
 to implement diverse structural , binding and catalytic functions . 
 here , we focus on the -helical coiled coil , which is a protein - interaction 
 domain highly suitable for inclusion in the growing molecular parts 
 toolkit . coiled coils are prevalent in native proteins 
 and are useful interaction motifs due to their capacity to encode 
 complex interaction patterns in a short protein sequence . coiled coils form a rod - like structure composed of -helices 
 that wrap around each other with a superhelical twist . coiled - coil 
 sequences have a characteristic motif commonly referred to as a heptad 
 repeat , denoted as [ abcdefg]n . the a and d positions are 
 dominated by hydrophobic residues , and are found at the core of the 
 structure ; we refer to a and d positions 
 as core positions in this work . in coiled - coil dimers , e and g positions are typically occupied by charged 
 residues and form the boundary between the core and the surface of 
 the coiled coil . the b , c , and f positions are located on the surface and are most often 
 polar or charged . in coiled - coil notation , a prime indicates a residue 
 on an opposing chain . for example , positions e and g are proximal and can form interhelical salt bridges 
 in parallel coiled - coil dimers , whereas e / e and g / g 
 pairs can interact in antiparallel coiled coils . the relationship 
 between coiled - coil sequence and structure is 
 incompletely understood , even after decades of study of native , mutant 
 and de novo - designed coiled coils . this is partly due to the many 
 topologies accessible to coiled - coil sequences . for example , coiled 
 coils can fold into dimers , trimers , tetramers , and even higher - order 
 oligomers . lastly , the orientations ( parallel vs antiparallel ) and axial alignments 
 of the constituent helices can vary . the general 
 problem of predicting detailed coiled - coil structure from sequence 
 has not been solved , although progress has been made developing methods 
 to predict oligomerization state from sequence , and in particular 
 to discriminate parallel dimers from parallel trimers . they 
 have been applied to the design of artificial transcription factors 
 and used to manipulate cell - signaling pathways . they have also been used to build engineered crystals , and to modulate 
 the charge - transfer properties of electronic devices . in many of these studies , modulated 
 the conductance between two monolayers of gold using coiled - coil dimers 
 and showed that parallel and antiparallel coiled coils differentially 
 impacted the electronic properties of the system . coiled coils of 
 different orientations have net molecular dipoles of different magnitude 
 and direction , and can thereby confer different electronic properties . recently , an exciting strategy was developed 
 to design polypeptide 
 polyhedra based around coiled - coil dimers . used a set of parallel and antiparallel dimeric coiled coils as building 
 blocks to engineer a nanoscale single - chain tetrahedron with coiled 
 coils forming each edge . the design strategy 
 involved concatenating a series of 12 sequence segments coding for 
 different coiled - coil helices into a single chain . the artificial 
 protein sequence was designed such that folding of the chain , driven 
 by pairing each coiled - coil helix with its appropriate intrachain 
 partner helix , would generate a prespecified three - dimensional structure . a crucial aspect of the design strategy was the use of coiled - coil 
 components that were orthogonal to one another , i.e. , that had low 
 potential to cross - interact . the designed tetrahedron was based on 
 4 parallel and 2 antiparallel coiled - coil dimers previously reported 
 in the literature . as part of their work , the authors computed the number and type 
 of coiled coils that would be needed to build different polyhedra . for example , of the 6 polyhedra considered by 
 the authors , only an octahedron could be built without using antiparallel 
 dimers . despite the clear benefits of having reagents that allow 
 manipulation 
 of orientation in a molecular assembly , most designed coiled coils 
 adopt a parallel orientation . very few antiparallel coiled - coil dimers 
 have been characterized or designed , and none have been tested for 
 orthogonality . in contrast , dozens of native and synthetic parallel 
 coiled coils have been tested for interactions and orthogonality . there are currently two databases 
 maintained for designed coiled coils , the synzip database , and the pcomp database . currently 96% of the 
 synzip sequences and 63% of the sequences in the pcomp database form parallel dimers . between these two databases , the 
 biophysical properties of only one antiparallel coiled coil ( a heterodimer ) 
 are reported . thus , designing sets of 
 orthogonal antiparallel homodimers would expand the available coiled - coil 
 parts in a meaningful way . because coiled - coil sequences can 
 encode many different structures , 
 negative design to destabilize undesired states is crucial when making 
 peptides intended to assemble into a single topology . several negative design strategies have been used in the 
 past that involve placing charged , beta - branched or polar asparagine 
 residues such that they form unfavorable interactions in undesired 
 states . a recent study relied on all three of these strategies 
 to design a parallel homodimer , homotrimer , and homotetramer . the orientations of the helices were engineered 
 by placing lysines at all e positions and glutamates 
 at all g positions , which leads to electrostatic 
 attraction in parallel assemblies but repulsion in antiparallel states . oligomerization states were specified by the differential placement 
 of beta - branched residues in core a and d heptad positions , a strategy first discovered by harbury et al . , 
 and by the use of asparagine residues to specify dimer formation , 
 which was originally reported by lumb and kim . including charged residues in core a or d positions has also been observed to destabilize nondimer 
 states . designing sets of orthogonal 
 coiled - coil homodimers presents additional 
 challenges related to encoding interaction specificity . this is due 
 to the increased number of undesired , off - target states associated 
 with forming hetero - oligomeric species . the number of possible hetero 
 species increases dramatically as the number of designed orthogonal 
 coiled coils grows , such that three orthogonal antiparallel homodimers 
 have the potential to form six possible off - target parallel or antiparallel 
 heterodimers ; other undesired structures are also possible . to design 
 sets of orthogonal antiparallel coiled - coil dimers , we therefore turned 
 to computational methods to keep track of the numerous desired and 
 undesired structures in this design problem . despite the many 
 successes of structure - based approaches for modeling 
 and designing protein the computational costs of modeling each structure can be large , 
 and current optimization functions used with structure - based models 
 do not provide efficient routines for optimizing one set of states 
 while simultaneously destabilizing many off - target states . the multistate 
 design framework classy addresses these issues by carrying out design 
 in protein sequence space , without the need to explicitly model all 
 protein structures . by using a transformation of 
 structure - based models to sequence - based models , classy addresses 
 both the search and scoring problems of multistate design , and the 
 method has previously been applied to design parallel coiled coils 
 specific for binding to a target in preference to closely related 
 off - target proteins . this paper describes our work applying classy in conjunction 
 with 
 the dfire statistical potential to the 
 de novo design of sets of coiled coils consisting of three orthogonal 
 antiparallel homodimers . we designed two sets of three proteins , and 
 used biophysical techniques to determine the oligomerization state , 
 helix orientation and thermal stability of structures formed by the 
 designed sequences . some designed peptides formed trimers or higher - order 
 assemblies , but we identified 3 peptides ( aph2 , aph3 , and aph4 ) that 
 formed orthogonal antiparallel homodimers . in addition , we showed 
 that these proteins homodimerize in preference to binding to aph , 
 a previously reported antiparallel homodimer . thus , we provide evidence for four sequences that preferentially 
 form antiparallel homodimers that can be used for protein engineering 
 applications . as described 
 in detail below , side chains were modeled on idealized coiled - coil 
 backbones using rosetta and scored using difire * , a modified version 
 of the dfire statistical potential . to construct libraries of parallel 
 and antiparallel backbones , a set of 214 canonical coiled coils ( i.e. , 
 left - handed coiled coils with uninterrupted heptad registers , abcdefg ) with 2 helices each longer then 20 residues were 
 culled from the cc+ database as of august 18 , 2010 . within the parallel and antiparallel sets , seven geometrical parameters 
 defined by crick to describe a coiled coil were fit to each structure 
 using the cccp structure fitter . this set of 
 backbones was then filtered to give 25 parallel and 23 antiparallel 
 backbones with parameters within one standard deviation of the average 
 value for each parameter . idealized 
 versions of these 48 structures were generated using the cccp structure 
 generator . coiled - coil sequences to be 
 scored were modeled on each idealized backbone using the fixed - backbone 
 packing protocol of rosetta 3.2 . the 
 soft - potential flag and expansion of the first and second dihedral 
 angles of the rotamer library were used , along with the side - chain 
 minimization flag . all surface heptad positions ( b , c , and f ) were modeled as alanine . structures were scored using a modified version of dfire , a distance - dependent 
 pairwise statistical potential based on the distance - scaled , finite 
 ideal - gas reference state . the cutoff distance , rcut , was set to 5.8  , and interatomic 
 energies were evaluated only between residues on opposite helices 
 in the coiled coil . we refer to this modified version of dfire as 
 dfire*. dfire * outperforms dfire on certain interaction prediction 
 tests for parallel coiled coils ( v. potapov , personal communication ) . the lowest dfire * energy for each sequence over all 25 parallel or 
 23 antiparallel backbones was used as the parallel or antiparallel 
 energy , respectively . two cluster - expanded 
 functions based on dfire * were derived to score the propensity of 
 sequences to form antiparallel and parallel coiled coils . for an outline 
 of the protocol , see figure s1 , and for 
 an in - depth discussion of performing cluster - expansion calculations 
 using clever 1.0 see negron et al . in 
 the present application , the cluster - expanded models express energy 
 as a sum of terms corresponding to weights for single amino acids 
 at a , d , e , and g heptad positions and pairs of amino acids at these positions . 
 as in grigroyan et al . , only pairs of positions within the same or 
 adjoining heptads were considered . the training data consisted of dfire * energies for a central two - heptad 
 unit within a six - heptad structure , calculated using the scoring protocol 
 described in the previous section for 30  000 sequences . another 
 8000 sequences , nonoverlapping with the training set , were generated 
 in the same way to be used as a test set . training sequences were 
 42 residues ( six heptads ) long and composed of a repeating two - heptad 
 unit . training sequences were generated randomly but with heptad - specific 
 single - residue frequencies matching those of known coiled - coil dimers 
 ( both parallel and antiparallel ) . once determined , cluster expansion ( ce ) weights 
 can be used to score antiparallel and parallel coiled - coil dimers 
 of arbitrary length . examples of 
 parallel and antiparallel 
 coiled coils were obtained from the filtered cc+ set and further filtered 
 to exclude those shorter than 28 residues and those that contained 
 non - natural amino acids . for certain sequences , three residues at 
 the terminal ends of the two chains were removed so that the two chains 
 fully overlapped in both the parallel and antiparallel orientations ; 
 i.e. , the coiled coils that were modeled were blunt - ended in both 
 orientations . the final orientation test set contained 30 antiparallel 
 complexes ( composed of 285 heptads ) and 48 parallel complexes 
 ( composed of 547 heptads ) . pdb ids with chain and residue 
 numbers for the orientation test set are given in table s2 . a detailed 
 description of how 
 integer linear programming ( ilp ) can be applied as part of the classy 
 multistate design method is given in negron et al . in this work , the objective function for ilp was the total 
 energy ( e ) , given by the sum of the energies 
 of three antiparallel homodimers ( e = e + e + e ) . all energies were obtained from either the 
 antiparallel or parallel cluster - expanded models . the ilp solver of 
 the ibm ilog cplex optimizer was used to minimize this objective function 
 under a set of constraints . the constraints 
 included energy gaps to off - target dimer states ( see figure 2a , b ) , as well as constraints 
 on the number of polar residues allowed at a and d heptad positions ( maximum of 2 charged residues at a , and 1 lys residue at d per design sequence ) . a constraint was included on the energy gap between every antiparallel 
 homodimer and every off - target state ( of those types considered in 
 the calculation ) that the constituent peptide could participate in . e >  , where e represents the energy of a single off - target 
 state , of which there were several as shown in figure 2 . e represents 
 the energy of a single antiparallel homodimer , i.e. , e , e , or e.  is a user - defined specificity gap , and different 
 values of  were used as shown in figure 2c , d . a solution , consisting of three sequences , was obtained for 
 each . two sets of design calculations were done , one including 
 glutamate as an option at a positions ( sequence space 
 1 ) and one not allowing glutamate ( sequence space 2 ) . one solution 
 was chosen manually for experimental testing from each calculation , 
 based on predicted stabilities and specificities . synthetic 
 genes encoding computationally designed coiled - coil sequences , and 
 control sequences , were constructed by pcr amplification from two 
 258-base pair oligonucleotides and one 157-base pair oligonucleotide 
 ( gblocks ) purchased from integrated dna technologies . low - frequency e. coli codons selected 
 by dnaworks were manually switched with synonymous high - frequency 
 codons . following amplification with primers to provide appropriate 
 vector overlap , gibson cloning ( new england biolabs ) was used to clone 
 synthetic genes into pentr vectors . the products of the gibson reactions 
 were then recombined into pmal ( new england biolabs ) destination vectors 
 using lr clonase ii ( invitrogen ) in 2.5 l reactions . pmal encodes 
 mbp followed by a tev protease cleavage site ( not used ) , a gateway 
 linker region , and a c - terminal his6 tag . the lr clonase 
 ii reaction inserted the synthetic gene between the gateway linker 
 region and the c - terminal his6 site . the pmal vectors were 
 transformed into bl21 ( de3 ) cells ( agilent ) . bl21 cells were grown 
 in liquid lb cultures ( 1 l ) at 37 c to an od600 of 
 0.40.6 . protein expression was then induced with 1 
 mm iptg for 4.55.5 h. cells were pelleted , resuspended , and 
 then lysed by sonication . mbp - fused proteins were purified from the 
 supernatant using ninta ( qiagen ) column purification under native 
 conditions . the elution buffer contained 0.3 m imidazole , 20 mm tris 
 base , and 0.5 m nacl at a ph of 7.91 . the approximate sizes of mbp - fused 
 proteins were confirmed using protein gels with size ladders . a second set of constructs was made by amplifying from gblocks 
 using primers encoding a cysteine either at the n - terminal or c - terminal 
 end , as well as flanking bamhi / xhoi restriction sites . the genes were cloned by means of the bamhi / xhoi restriction sites into a modified 
 version of the pdest17 vector . this vector encodes an n - terminal his6 tag as well as a geskeykkgsgs linker shown to improve the 
 solubility of recombinant proteins . cysteine - containing 
 constructs were expressed in rp3098 cells grown , induced and lysed 
 as described above for bl21 . however , these proteins were purified 
 from the supernatant using ninta ( qiagen ) under denaturing conditions . 
 the elution buffer consisted of 60% acetonitrile ( hplc - grade ) and 
 0.1% trifluoroacetic acid ( tfa ) . ni - affinity purification was followed 
 by reverse - phase hplc with a water / acetonitrile gradient in the presence 
 of 0.1% tfa . concentrations of all constructs were determined using the edelhoch 
 method , measuring uv absorbance of aromatic residues at 280 nm in 
 6 m guanidinium chloride . proteins were dialyzed with three changes of reference buffer ( 40 
 mm tris base , 150 mm nacl , ph 7.91 ) over the course of 24 h. sedimentation 
 equilibrium runs were performed with a beckman xl - i analytical ultracentrifuge 
 using an an-50 ti rotor at 20 c . constructs fused to 
 mbp were spun at concentrations ranging from 4 to 40 m at 10  200 , 
 16  300 and 20  400 rpm . these spins were monitored either 
 using uv absorbance at 280 nm , or with interference optics when multiple 
 mbp constructs were mixed . for protein constructs containing cysteine , 
 1 mm tcep was added to the reference buffer prior to dialysis . these 
 constructs were spun at concentrations of 20 and 40 m at 28  000 , 
 35  000 and 42  000 rpm and monitored using interference 
 optics . for each speed , equilibrium was confirmed by negligible differences 
 between the sample distributions in the cells over sequential scans . data sets for each construct were globally fit to a model for a single 
 ideal species using the program sedphat . values for v - bar , solvent density , and viscosity were obtained from 
 sednterp . cysteine - containing 
 proteins in varying states of oxidation / reduction ( depending on construct ) 
 were placed in a redox buffer ( 500 m reduced glutathione , 250 
 m oxidized glutathione , 40 mm tris base , 150 mm nacl , ph 7.91 ) 
 at 20 m of each protein at room temperature . redox reactions 
 were quenched at different time points using a drop of 6 m hydrochloric 
 acid . the products of the reactions were then run on an analytical 
 vydac c18 reverse - phase column with absorbance monitored 
 at 220 nm using a linear water / acetonitrile gradient containing 0.1% 
 tfa . equilibrium was confirmed by monitoring changes in hplc profiles 
 as a function of time . retention times for the reduced proteins and 
 for the oxidized states for each of the 6 cysteine - containing proteins 
 were assigned by hplc analysis of the constructs in tbs ( 40 mm tris 
 base , 150 mm nacl , ph 7.91 ) alone , in tbs with tcep added for an incubation 
 time of 30 min ( to generate the fully reduced species ) , or in tbs 
 solution left exposed to air and stirring overnight ( to generate the 
 fully oxidized species ) . glutathione adduct peaks were assigned by 
 the appearance , following incubation in redox buffer , of a peak with 
 a retention time not consistent with the reduced or oxidized states 
 of each of the six individual protein constructs . antiparallel peaks 
 were assigned by monitoring the appearance of a peak that was only 
 observed after mixing two constructs that encoded the same coiled 
 coil , but with cysteine residues at opposing ends . cd spectra and 
 thermal - denaturation curves were measured on an aviv 400 cd spectrometer . peptides were equilibrated in pbs buffer ( 137 mm nacl , 2.7 mm kcl , 
 10 mm na2hpo4 , 2 mm kh2po4 , ph 7.4 ) containing 1 mm of dithiothreitol ( dtt ) at 25 c 
 for at least 1.5 h prior to measurement . measurements were made in 
 a 1 mm quartz cuvette at a protein concentration of 20 m using 
 the n - terminal cysteine - containing constructs . , three wavelength scans were measured 
 and then averaged . for each wavelength scan , data were collected from 
 190 to 280 nm , in 1 nm steps , averaging for 5 s at each wavelength . thermal denaturation curves were generated by monitoring 222 using a 30 s averaging time , 3 min equilibration time , 
 and temperature increments of 2.5 c from 0 to 98 c . melting 
 temperatures , tm , were obtained by fitting 
 the change of the cd signal over the change in temperature . the fractional helicity of each design was estimated by 
 substituting the experimentally measured 222 into 
 the equation ( 222  3000)/(36  000 
  3000 ) . computational 
 design of orthogonal antiparallel homodimers requires 
 an energy function capable of scoring antiparallel vs parallel dimers . 
 to assess whether our design energy function could predict helix orientation 
 for coiled - coil dimers of known structure we created a 
 database of 30 antiparallel and 48 parallel dimer structures based 
 on the cc+ database of testa et al . ; we 
 refer to this database as the orientation test set ( see materials and methods ) . the orientation test set in this study 
 differed from that used by apgar et al . due to its higher stringency 
 on length , 28 residues vs 18 residues this more stringent cutoff has the effect of 
 removing examples of short coiled - coil sequences embedded in large 
 structures , for which the helix orientation is less likely to be determined 
 by the sequence of the coiled - coil region alone . furthermore , sequence 
 features of antiparallel coiled coils in the pdb are a function of 
 their lengths ; e.g. , shorter coiled coils have a 16% higher frequency 
 of hydrophobic residues at the g position ( table s4 ) . a modified version of dfire , 
 dfire * , which includes only interchain energy terms , was used for 
 scoring . the orientation test - set sequences were modeled in both parallel 
 and antiparallel orientations using rosetta and scored using dfire * , 
 as described in the materials and methods . the dfire * energy gap between the antiparallel and parallel state 
 for each sequence is plotted in figure 1a . we report energies in arbitrary units ( au ) , as we have no information 
 at this time about how predicted energies from this procedure correlate 
 with experimental free energies . the ability of dfire * to predict 
 orientation preference on the test set was measured using the area 
 under the curve ( auc ) when plotting the fraction of parallel test - set 
 sequences predicted correctly vs the fraction of antiparallel sequences 
 predicted correctly , as a function of the score cutoff used to discriminate 
 parallel from antiparallel sequences . as seen in figure 1b , dfire * predicts orientation preference in this test with 
 an auc value of 0.91 ( random predictions would result in an auc of 
 0.5 ) . predicting coiled - coil orientation preference and testing cluster - expanded 
 dfire*. ( a ) eap and ep are the antiparallel ( ap ) and parallel ( p ) dfire * energies 
 for each orientation test set coiled coil . antiparallel or parallel 
 coiled coils ( according to pdb structure ) are plotted with red crosses 
 or black diamonds , respectively . min_gap 
 was used to remove examples with small dfire * orientation preferences 
 ( see text ) ; shading indicates increasing min_gap from the line of 
 optimal separation . ( b ) the fraction of antiparallel sequences predicted 
 correctly vs the fraction of parallel sequences predicted correctly , 
 as the cutoff value for eap ep was changed , is plotted for dfire * and the 
 ce model of dfire*. curves for data sets with different values of 
 min_gap are shown for the ce model of dfire*. ( c , d ) dfire * energies 
 vs the ce model of dfire * energies for randomly generated dimer - like 
 test structures in the antiparallel ( c ) and parallel ( d ) states . cluster expansion ( ce ) 
 is a computational method for generating a sequence - based scoring 
 function that approximates energies calculated using structure - based 
 techniques . once generated , a ce model eliminates the need for computationally 
 costly structure building in protein design . two ce models were built 
 to approximate dfire * energies for antiparallel and parallel coiled - coil 
 dimers , as described in the materials and methods , and the models were used to score 8000 test sequences ( figure 1c , d ) . both models showed good correlation with dfire * , r = 0.90 , indicating that the approximation 
 of structure - based modeling with a sequence - based function introduced 
 relatively little error within the sequence space explored . we benchmarked the orientation prediction performance of the ce dfire * 
 models using the orientation test set . every pair of sequences in 
 the set was scored with the antiparallel ce model and the parallel 
 ce model . the energy difference between the two ce models was used 
 to predict the orientation preference of each sequence . the auc value 
 using the ce approximation of dfire * was 0.84 ( figure 1b ) , demonstrating that the faster , yet more approximate model 
 gave reduced performance , as expected . however , the auc value significantly 
 improved as coiled coils with small energy gaps were removed from 
 the orientation test set . for 44 coiled coils with the largest predicted 
 differences in ce energy between parallel and antiparallel orientation 
 ( greater than 0.4047 ) , the prediction performance ( 0.93 ) was similar 
 to the performance of dfire * on the entire orientation test set . for 
 20 examples with predicted energy gaps greater than 0.8094 , prediction 
 performance was perfect . this information was used to set energy gap 
 requirements for off - target states during the sequence - design stage 
 of classy . classy is a protein - design method that uses integer 
 linear programming ( ilp ) to optimize a protein sequence using a ce 
 scoring function . importantly , the method allows a user to impose 
 numerous constraints on the designed sequence . these can include constraints 
 on sequence composition or properties ( e.g. , total charge ) . in multistate 
 design , it is convenient to impose a constraint on the energy of a 
 designed sequence adopting an undesired structure , to disfavor formation 
 of that structure . in our application , the antiparallel and 
 parallel ce models were combined with ilp to do classy design of six - heptad 
 antiparallel homodimers . designed antiparallel coiled coil aph is 
 also six heptads long , and a four - heptad variant of aph had low thermal 
 stability . on the basis of this , we reasoned 
 that six heptads should provide ample space to include specificity 
 elements while maintaining a folded structure . only residues at a , d , e , and g positions were designed ; these residues are thought to be most critical 
 for interaction specificity . the b , c , and f surface positions were 
 taken from aph , which is one of the few characterized antiparallel 
 homodimers reported in the literature . the surface of aph mainly consists 
 of patterned glutamine and alanine residues at b and c positions , and lysine residues at f positions . this surface design has been used for both parallel and antiparallel 
 coiled coils , and is thought to play a minimal role in interaction 
 specificity . we used the ce model of 
 dfire * to design the globally best - scoring 
 antiparallel homodimer in a sequence space without cysteine , proline , 
 or glycine and found that the designed sequence was highly charged 
 and contained no hydrophobic residues in any heptad position . this 
 peptide would not be expected to fold into a coiled - coil structure . the unrealistic design sequence is not inconsistent with the good 
 performance of dfire * and the ce model of dfire * on the orientation 
 prediction test above . in the orientation test , in contrast , without constraints 
 on sequence composition , optimization using the ce model of dfire * 
 had the freedom to build a sequence entirely from charged pairs that 
 have highly favorable ce weights . the 20 most favorable weights in 
 the ce dfire * model are all core - to - edge ( i.e. , a or d to e or g ) , or core - to - core charge we therefore imposed constraints 
 on the number of polar residues allowed at core heptad positions ( see materials and methods ) and restricted the design 
 calculations to subsets of sequence space , as described below . two separate sequence spaces , sequence space 1 and sequence space 
 2 , were chosen to search for antiparallel homodimer sequences ( figure 2a , b ) . both sequence spaces included residues known 
 to influence coiled - coil structural specificity through mechanisms 
 such as electrostatic attraction / repulsion and beta - branch residue 
 packing / clashing . sequence space 1 differed from 
 sequence space 2 by the addition of glutamate as a choice at a positions . statistics from the coiled - coil databases we 
 analyzed show a 3-fold frequency enrichment of glutamate in a sites of antiparallel dimers relative to parallel dimers 
 ( table s5 ) ; this difference has also been 
 noted by straussman et al . ( a , 
 b ) diagram of target and off - target states included in two design 
 calculations . colors represent distinct sequences , and colored circles 
 indicate the n - terminus of each helix . an energetic constraint ,  , 
 was enforced between the energy of each target antiparallel homodimer 
 state ( e , e , e ) and every off - target state that 
 peptide could participate in ( examples shown with gray dashed lines ) . 
 the sequence space used for each design different numbers 
 of off - target states were included for sequence space 1 ( a ) vs sequence 
 space 2 ( b ) . ( c , d ) the total energy e = e + e + e vs  is plotted for sequence 
 space 1 ( c ) and sequence space 2 ( d ) . each value of  led to 
 a set of optimized sequences , and the gray squares mark the solutions 
 chosen for experimental testing . to design three noninteracting coiled coils , we optimized 
 the sum 
 of the ce energies of three antiparallel homodimers using classy . constraints were added to allow no more than two hydrophilic residues 
 at a positions and no more than one at d positions . this maintained the hydrophobicity of the design solutions 
 at these positions close to that of known antiparallel dimers of lengths 
 greater than four heptads . , all design calculations 
 treated all three possible antiparallel heterodimer states as undesired 
 states . without these constraints , the global energy minimum would 
 correspond to three copies of the lowest - energy antiparallel homodimer . constraints on the off - target states were imposed as an energy gap 
 by requiring the energy of each antiparallel homodimer to be lower 
 than the energy of each of the off - target states that sequence could 
 participate in , by a fixed amount ( figure 2 ) . classy design was done iteratively , by progressively increasing 
 the energy gap that was imposed between the target antiparallel homodimers 
 and off - target antiparallel heterodimer states . as the gap to off - target 
 states increased , the total predicted stability of the three antiparallel 
 homodimers decreased ( figure 2c , d ) . this type 
 of stability - specificity trade - off has been observed previously in 
 the case of parallel dimer design using classy . two sets of solutions , one from each of the sequence spaces , 
 were rationally chosen based on good stability - specificity trade - offs . the designs in sequence space 1 are referred to as aphi , aphii , and aphiii . the designs in sequence 
 space 2 are referred to as aphiv , aphv , aphvi. for each set of designed sequences , parallel 
 and antiparallel homo- and heterodimer states were scored with the 
 original dfire * structure - based model to predict relative energies 
 of target and off - target structures . for the antiparallel homodimers 
 designed in sequence space 1 , the predicted energies of all parallel 
 and antiparallel off - target dimers were much higher than the predicted 
 energies for the antiparallel homodimers . the smallest gap , of 0.77 
 au , was between the antiparallel homodimer state of aphiii and a parallel heterodimer consisting of aphiii and aphi ( figure s2a ) . the aphi antiparallel homodimer gap to this state was 1.13 au . at gaps of 
 this magnitude , dfire * predicts the orientation preference of native 
 sequences with an auc = 1.0 . thus , no additional states were added 
 to the optimization protocol for sequence space 1 . for sequence space 
 2 , we observed that one of the parallel homodimers was predicted to 
 be lower in energy than the corresponding antiparallel homodimer ( figure s2b ) . furthermore , other parallel homodimer 
 states were closer in energy to the antiparallel homodimers than when 
 design was done in sequence space 1 . to address this , we added parallel 
 homodimer states as off - target states in the optimization protocol 
 used for sequence space 2 , and chose a new set of solutions in that 
 space . the final six designed sequences are shown in table 1 , with aphi , aphii and aphiii resulting from design in sequence space 1 , and aphiv , aphv and aphvi from design in sequence 
 space 2 . the two sets of designed sequences were also scored for cross - reactivity 
 using dfire*. predicted energies for all parallel and antiparallel 
 heterodimers that could be formed between sets were significantly 
 larger than predicted energies for the antiparallel homodimer states , 
 with the smallest energy gap of 0.61 au between the antiparallel and 
 parallel homodimer states of aphiv . the molecular weights 
 of complexes formed by designed peptides aphi  aphvi were determined using sedimentation equilibrium analytical 
 ultracentrifugation ( see materials and methods ) . we anticipate that the aph coiled coils will be used as fusion 
 proteins in many applications , so we did two sets of experiments : 
 one in which the peptides were fused to maltose binding protein ( mbp ) 
 and one in which they were not . the data for two designed peptides , aphiii and aphvi , were consistent with these peptides forming 
 homodimers . aphi was determined to have a molecular weight 
 greater than that expected for a dimer , and no further data were collected 
 on this construct . single - species fits to aphii and aphiv gave molecular weights less than and greater than what was 
 expected for a dimer , respectively . aphii and aphiv were retested at higher concentrations to stabilize higher - order 
 states . at 20 m , aphii formed a homodimer , whereas 
 aphiv formed a homotrimer . further experiments were carried 
 out only on designs aphii , aphiii and aphvi , which we renamed aph2 , aph3 and aph4 , respectively ( see 
 table 2 ) . data collected using interference 
 optics , and a construct not fused to mbp . to determine 
 the helix orientation in complexes formed by aph2 , aph3 , and aph4 , 
 we performed disulfide - exchange experiments , and resolved the products 
 of the reactions using hplc ( see materials and methods ) . key peaks are labeled in figure 3 , which 
 shows changes in the chromatograms over time . for all three designs , 
 starting with a combination of oxidized parallel species and/or reduced 
 peptides , only one oxidized peak was detected at the end of 5 h , corresponding 
 to a disulfide - linked antiparallel homodimer . on the basis of the 
 smallest detectable peak area , we estimated a minimum 10-fold preference for forming antiparallel complexes over parallel 
 complexes for all designs . designed peptides aph2 , aph3 , and aph4 adopt 
 an antiparallel helix 
 orientation . the wavy line indicates two amino acids added 
 to the designed sequence to change peptide retention times ( aph2 = 
 yy , aph3 = qw , aph4 = yy ) . ( b , c , d ) hplc chromatograms show the results for the 
 disulfide - exchange reactions upon mixing equimolar amounts of n - terminal 
 and c - terminal cysteine variants of each design sequence ( 20 m 
 each ) . the reactions were quenched at 0 min ( red ) , 15 min ( black ) , 
 or 5 h ( blue ) . peaks are labeled according to the scheme shown in 
 panel a , with g indicating a glutathione adduct . the same constructs that were used to measure orientation 
 preferences 
 were used to determine whether the designs formed heterodimers . each design formed a disulfide cross - linked antiparallel 
 homodimer over time , but we did not detect any disulfide bond formation 
 between any pairs of designed peptides . each design was additionally 
 measured for cross reactivity with the antiparallel homodimer - forming 
 peptide aph , in a pairwise manner ( figure 5 ) . no design showed any detectable cross - reactivity with aph , in 
 either orientation , extending the number of orthogonal antiparallel 
 homodimers from three to four . a ) cartoon showing four cysteine - containing peptides , two for each 
 of two designs , which were included in the disulfide - exchange cross - reactivity 
 assay . ( b , c , d ) hplc traces for all pairwise mixtures of designed 
 peptides after equilibration for 15 min . the blue and red traces are 
 for reactions with equimolar amounts of n- and c - terminal cysteine 
 variants of a single designed peptide ( 20 m each ) . the black 
 trace is for a reaction with equimolar amounts of all four peptides 
 in panel a ( 20 m each ) . ( b ) aph2 + aph3 , ( c ) aph2 + aph4 , ( d ) 
 aph3 + aph4 . designed peptides aph2 , 
 aph3 , and aph4 do not heterodimerize with 
 aph . ( a , b , c ) hplc traces for all pairwise combinations of aph with 
 the designed coiled coils , with experimental conditions as for figure 4 . the blue and red traces are for equimolar mixtures 
 of n- and c - terminal cysteine variants of aph ( blue ) or aph2 , aph3 
 or aph4 ( red ) ( 20 m each ) . the black trace is for a mixture 
 of four peptides , aph and the indicated design , each modified at the 
 n- or c - terminus with a cysteine residue ( 20 m each ) . ( a ) aph 
 + aph2 , ( b ) aph + aph3 , ( c ) aph + aph4 . to determine whether mixtures of more than two aph coiled 
 coils 
 formed complexes other than the expected dimers , mbp fusions of all 
 four aph peptides were mixed at 20 or 40 m of each aph design 
 and analyzed by sedimentation equilibrium ultracentrifugation ( as 
 done for individual mbp fusion proteins , see materials 
 and methods ) . the ratio of the fitted mass to the dimer mass 
 was 0.91 , with good fit quality ( representative data in figure s3 ) , indicating that dimers formed as 
 expected and no higher - order species were present in a mixture of 
 all four aph fusion proteins . we measured the circular 
 dichroism ( cd ) spectra of the three designed peptides aph2 , aph3 , 
 and aph4 , using the n - terminal cysteine constructs in a reduced state . each construct contained 65 residues , of which 43 corresponded to 
 the designed coiled - coil sequence ( table s3 ) . our aph construct contained 66 residues , of which 44 corresponded 
 to the aph sequence . the cd spectra of all three designs were characteristic 
 of coiled coils , with distinct minima at 208 and 222 nm ( figure 6a ) . the mean residue ellipticity ( mre ) of the designed 
 peptides was similar to that of aph , which is longer by one residue 
 in the coiled - coil region . thermal denaturation experiments established 
 that all designs unfolded cooperatively , which is a characteristic 
 property of coiled coils ( figure 6b ) . the thermal 
 stabilities ( tm ) of the designs at 20 
 m ranged from 47.4 c for aph2 , to 59.3 c for aph4 
 and 78.3 c for aph3 , with aph3 being slightly less stable then 
 aph , which had a tm of 79.3 c . , all peptides regained 95% 
 of the original mre , and fits of refolding curves gave melting temperatures 
 within 1.5 c of values obtained from the denaturing curves . estimating peptide helicity from the cd data using the method of 
 morrisett et al . indicated that linkers and tags appended to the designed 
 coiled coil contributed helical signal , as shown in figure s4 however , most of this 
  extra  signal was lost gradually with temperature in 
 the pretransition baseline , indicating these regions are not part 
 of the cooperative unfolding event . furthermore , these linker residues 
 were not present in the mbp - fusion constructs used in the sedimentation 
 equilibrium centrifugation experiments , consistent with them not being 
 necessary for the specific interactions observed in those experiments . finally , making aph in the construct that we used for cd experiments 
 did not change its melting temperature from the value reported in 
 the literature for only the coiled coil . ( a ) 
 cd spectra and ( b ) thermal denaturation curves measured at 25 c 
 in pbs with 1 mm dtt . aph ( red ) , aph2 ( blue ) , aph3 ( green ) and aph4 
 ( orange ) . an 
 expanded toolkit of coiled - coil interaction parts would be of 
 great utility in protein engineering . many papers have reported the 
 successful design of coiled - coil structures of diverse topologies , 
 but apart from parallel dimers , the number of biochemically characterized 
 complexes of any one type is limited . designing coiled coils de novo is complicated by 
 the fact that different coiled - coil topologies have similar sequence 
 requirements , and small sequence changes can alter coiled - coil structure . 
 for these reasons , it is often necessary to explicitly consider competing 
 states in the design process . treating off - target states in computational protein design 
 can 
 be costly , particularly when there are many such states that must 
 be modeled . one strategy is to incorporate a design element known 
 to strongly destabilize a set of off - target topologies , to reduce 
 the number of off - target states that must be modeled . for instance , 
 thomas et al . observed that the de novo design of parallel heterodimeric 
 coiled coils composed entirely of isoleucine and leucine cores did 
 not reliably destabilize higher - order states . but the same design strategy in the background of a single asparagine  asparagine 
 interaction , which was known from prior work to favor parallel dimer 
 states over higher - order states , consistently gave dimeric assemblies . unfortunately , incorporating simple design elements 
 that reliably destabilize all off - target topologies , in all sequence 
 contexts , is not feasible . exceptions have been reported for even 
 the most thoroughly studied coiled - coil structural specificity determinants , and for many coiled - coil topologies , the sequence - structure relationship 
 is not well understood . of relevance for this work , there are 
 few sequence features known 
 to favor antiparallel over parallel helical alignments . oakley et 
 al . showed that , in analogy to the role of asparagines favoring dimers 
 over higher - order states , paired asparagines can be introduced at 
 opposing a and d positions 
 to favor an antiparallel helix alignment . charge interactions 
 at e and g positions across the 
 interface can impart an antiparallel vs parallel preference . placed an isoleucine at a d heptad position and an alanine residue at an opposing a heptad position to favor an antiparallel homodimer 
 state over a parallel homodimer state in the designed sequence aph . further evidence supporting this interaction 
 as an orientation specificity determinant was obtained via thiol - thioester 
 exchange studies by hadley et al . although 
 simple rules do have some utility for design , hadley et al . showed 
 that residue residue interactions in antiparallel coiled coils 
 can also be highly context dependent , helping explain why rules extracted 
 from studies of model systems do not satisfactorily explain the orientations 
 of native coiled coils . modeling off - target 
 states explicitly and including them in the 
 design process provides a broadly applicable mechanism for engineering 
 specificity . in this work , we used explicit negative design to disfavor 
 antiparallel heterodimer states by imposing energy gaps between antiparallel 
 homo and heterodimers . most of the sequence elements in our aph designs 
 that disfavored antiparallel heterodimerization within a design set 
 involved charged residues predicted to participate in repulsive interactions 
 in heterodimer states . for example , all antiparallel heterodimer states 
 contained a - to - e and d - to - g charge  charge repulsions 
 between lysine or arginine residues . charge repulsions between glutamate residues . these 
 core - to - edge charge charge repulsions were the most destabilizing 
 weights available to the antiparallel ce dfire * model in the design 
 sequence spaces chosen , with lysine at d to arginine 
 at g being the most destabilizing . the design strategies that led to destabilization of parallel homodimers 
 differed in sequences spaces 1 and 2 . in sequence space 1 , we allowed 
 glutamate at a positions , and all designed sequences 
 included this element . in fact , we identified a motif consisting of 
 two glutamate residues at a and g , and a lysine at d with an arginine at e on the opposing helix that was present in all 
 of the sequence space 1 designs ( figure s5 ) . interactions between residues in this motif contain the first 
 and fourth most favorable weights available in the ce dfire * model 
 in sequence space 1 , such that the motif is predicted to contribute 
 strongly to antiparallel homodimer stability . interestingly , in a 
 parallel homodimer , the residues of this motif form unfavorable interactions 
 sufficient to provide a large energy gap between parallel and antiparallel 
 states . certain unfavorable weights are shown in figure s5 , and this can be further demonstrated by modeling 
 an artificial homodimer that includes the motif embedded in a poly - alanine 
 sequence . because of the symmetry of the homodimer , this results in 
 two copies of the motif in the structure . scoring parallel and antiparallel 
 homodimeric structures with this sequence using dfire * revealed a 
 significant preference of 1.64 energy units for the antiparallel state 
 ( poly alanine alone has a preference of 0.14 energy units for the 
 antiparallel state using this model ) . thus , in sequence space 1 , charge 
 networks predicted to stabilize the antiparallel state led to substantial 
 destabilization of parallel homodimers , without explicit negative 
 design . the situation was different in sequence space 2 , which did 
 not include glutamate residues at a positions . in 
 this sequence space , designing antiparallel homodimers while disfavoring 
 heterodimers did not automatically lead to large energy gaps to parallel 
 homodimer states for all sequences ( see figure 
 s2b ) ; it was necessary to include parallel structures as off - target 
 states in the optimization problem . doing so led to sequences that 
 placed more isoleucines at d heptad positions to 
 favor antiparallel over parallel homodimers . for example , of the three 
 sequences originally chosen in sequence space 2 , two sequences had 
 one isoleucine residue at a d position , while one 
 sequence had no isoleucine residues at all . after placing constraints 
 on the energies of the parallel homodimer states , all design sequences 
 contained one or two isoleucine residues at d heptad 
 positions . each designed isoleucine at a d position 
 introduced a d  d 
 isoleucine pairing across the coiled - coil interface in the parallel 
 homodimer state . as previously mentioned , this interaction destabilizes 
 parallel dimers . . explicit consideration of off - target states requires enumerating 
 and modeling the relevant competing states . we successfully used this 
 strategy to destabilize antiparallel heterodimer states in sequence 
 spaces 1 and 2 , and to destabilize parallel homodimers when designing 
 in sequence space 2 . but we did not explicitly model formation of 
 higher - order assemblies , and as a result , oligomers larger than dimers 
 were formed by designs aphi and aphiv . modeling 
 higher - order coiled coils is challenging due to the many different 
 topologies that are possible . each helix pair can be antiparallel 
 or parallel , heteroassemblies can form with different stoichiometries , 
 and the geometry of helix associations can vary in subtle ways . it is therefore difficult to include a comprehensive set of competing 
 states and , even if such a set could be generated , the computational 
 modeling costs for considering all possibilities explicitly would 
 be high . one approach to disfavoring higher - order states could 
 be to include 
 just a small number of trimer and tetramer topologies in the calculations . adding representative off - target structures would minimally alter 
 the computational complexity of the design framework , yet might lead 
 to broader destabilization of additional higher - order states . indeed , 
 our study provided an example where specificity was obtained against 
 states that were not explicitly modeled , possibly due to constraints 
 on specificity against related states . the design solutions from sequence 
 space 1 were predicted not to form heterodimers with design solutions 
 from sequence space 2 , despite these interactions not being explicitly 
 constrained during optimization . we hypothesize that this occurred 
 because the consideration of many off - target dimer states gave rise 
 to interfaces with charge patterns low in symmetry , as well as hydrophobic 
 cores with unique geometries due to the placements of beta - branched 
 residues in the core . as a result , the probability of cross - reacting 
 with another sequence to form dimers was low . considering just 
 a few higher - order states may also have the effect 
 of reducing or removing design features known to favor higher - order 
 states generally . for example , isoleucines at d heptad 
 positions are known to favor parallel trimer and tetramer states in 
 preference to parallel dimer states . yet isoleucines 
 at d heptad positions also favor antiparallel dimers 
 over parallel dimers , and were included in many of our designs for 
 this reason , as discussed above ( also see table 1 ) . interestingly , in native coiled coils isoleucines are approximately 
 4-fold more common in antiparallel dimers than in parallel dimers 
 ( table s5 ) . isoleucines at d heptad positions that were included in the design to favor antiparallel 
 dimers might have promoted the formation of higher - order assemblies , 
 which were not treated in the model . a constraint to disfavor just 
 a few trimers or tetramers might be sufficient to limit the use of 
 this sequence element , or to drive inclusion of compensating elements 
 that are poorly accommodated in higher - order assemblies . a significant 
 obstacle to including even a few higher - order states 
 in design is the small amount of structural data available for coiled - coil 
 trimers and tetramers of a specific toplogy . benchmarking the predictive power of models using experimental data 
 is important for assessing performance , and is useful for setting 
 meaningful energy cutoffs in design calculations . however , very few 
 known structures of higher - order states of any specific topology passed 
 our orientation test set filters of 50% sequence identity 
 and > 27 residues ( 0 antiparallel trimers , 6 antiparallel tetramers , 
 and 9 parallel tetramers in the august 18 , 2010 cc+ database ) . for 
 these reasons , we did not benchmark dfire * on the problem of predicting 
 oligomerization state , and we did not attempt to use it for this purpose . we examined the structure - prediction power of other methods when 
 applied to our antiparallel coiled coils . logicoil is a computational 
 predictor trained on coiled - coil sequences in the cc+ database to 
 discriminate parallel dimers , antiparallel dimers , trimers and tetramers . for aph2 , aph3 , and aph4 , logicoil makes 
 predictions based on a single - chain sequence , without information 
 about interchain interactions that are crucial design elements in 
 the aph designs . additionally , the aph sequences are de novo designed 
 sequences , with intrachain pairwise frequencies that may not resemble 
 those in native sequences . ccbuilder is a new web - based application 
 that generates coiled - coil structures and can be used for predicting 
 coiled - coil topology . ccbuilder can model parallel dimers , antiparallel 
 dimers , parallel trimers , and parallel tetramers , and the program 
 computes the stability of coiled - coil complexes using two energy functions : 
 rosetta and bude . both energy functions , 
 used with default settings provided by the web site , correctly predict 
 that aph2 , aph3 , and aph4 favor the antiparallel dimer state over 
 the parallel dimer state . when higher - order states are considered , 
 both energy functions predict that aph2 and aph4 favor the trimer 
 state , and rosetta also predicts that aph3 will form a trimer . better methods for oligomerization state prediction are needed 
 and , if developed , could be incorporated into our design framework . the rankings of the thermal stabilities ( figure 6 ) are not predicted well by dfire*. dfire * instead predicts 
 that aph3 is the most stable complex , followed by aph2 , aph4 , and 
 aph . these predicted ranking are consistent with the favorable weights 
 that the ce of dfire * assigns between core and edge positions . but 
 the relative thermal stabilities of the aph coiled coils appear to 
 be related to the number of charged residues in the central two heptads 
 of the designed coiled coils ( figure 7 ) . aph2 , 
 which has the greatest number of charged residues in the central two 
 heptads , is the least stable . in contrast , both aph and aph3 contain 
 no charged residues in the central two heptads and are the most thermally 
 stable . this is consistent with many studies showing coiled - coil destabilization 
 by polar residues in the core . it should be noted that ccbuilder accurately predicts the thermal 
 stability rankings using rosetta or bude scores , if all structures 
 are scored as antiparallel dimers . helical - wheel diagrams of aph , aph2 , aph3 , 
 and aph4 as antiparallel 
 homodimers . positively and negatively charged amino acids are shown 
 in blue and red , respectively , with noncharged polar residues in orange 
 and hydrophobic residues in gray . the new aph designs have many 
 desirable properties for synthetic 
 biology and materials science . first , the surface residues of all 
 aph designs were engineered to be passive and may provide useful positions 
 for adding novel functions or modulating stability . the designed structures also provide users 
 with a range of thermal stabilities , and it may be possible to tune 
 the dimer stabilities using mutations of the surface residues , as 
 needed . finally , the designs are orthogonal to each other when used 
 in pairwise or higher - order combinations . proteins with this property 
 have been sought for many applications in synthetic biology and are 
 thought to be one of the limiting reagents slowing progress in this 
 field . it should also be noted that heterodimers 
 involving the aph proteins could be included as off - target states 
 in future design studies using the classy framework , allowing for 
 the extension of this set . in conclusion , the antiparallel homodimer 
 sequences represent a significant expansion to the coiled - coil toolkit , 
 which is currently dominated by parallel dimers , and thus may find 
 application in many molecular engineering projects .
molecular engineering of protein 
 assemblies , including the fabrication 
 of nanostructures and synthetic signaling pathways , relies on the 
 availability of modular parts that can be combined to give different 
 structures and functions . 
 currently , a limited number of well - characterized 
 protein interaction components are available . 
 coiled - coil interaction 
 modules have been demonstrated to be useful for biomolecular design , 
 and many parallel homodimers and heterodimers are available in the 
 coiled - coil toolkit . in this work , we sought to design a set of orthogonal 
 antiparallel homodimeric coiled coils using a computational approach . 
 there are very few antiparallel homodimers described in the literature , 
 and none have been measured for cross - reactivity . 
 we tested the ability 
 of the distance - dependent statistical potential dfire to predict orientation 
 preferences for coiled - coil dimers of known structure . 
 the dfire model 
 was then combined with the classy multistate protein design framework 
 to engineer sets of three orthogonal antiparallel homodimeric coiled 
 coils . 
 experimental measurements confirmed the successful design of 
 three peptides that preferentially formed antiparallel homodimers 
 that , furthermore , did not interact with one additional previously 
 reported antiparallel homodimer . 
 two designed peptides that formed 
 higher - order structures suggest how future design protocols could 
 be improved . 
 the successful designs represent a significant expansion 
 of the existing protein - interaction toolbox for molecular engineers .