sequence - defined biopolymers , 
 such as proteins and nucleic acids , 
 incorporate backbone and side - chain constituents that endow these 
 macromolecules with the ability to fold into well - defined secondary 
 and tertiary structures .
the complexity and functionality of these 
 folded biopolymers has spurred intensive research toward a predictive 
 understanding of the relationships between their sequences , structures , 
 and functions .
computational strategies to engineer proteins and nucleic 
 acids have matured to the point where de novo design of elaborate 
 new protein and nucleic acid structures can be conducted with some 
 reliability .
the development of computational tools for the design 
 of proteins also provides a valuable blueprint for building analogous 
 tools to enable design of other abiotic folded oligomeric systems , 
 termed foldamers . a key component of many 
 protein design programs is the discretization of side - chain degrees 
 of freedom by representing side chains as conformational isomers , 
 termed 
we describe general methods to build rotamer libraries for peptidomimetic 
 foldamers , and apply these methods specifically to a family of peptoid 
 foldamers composed of n - substituted glycine monomers . in this way
, 
 we aim to remove a fundamental roadblock and enable design methods 
 for diverse foldamers incorporating abiotic monomer types .
foldamers 
 are a class of oligomeric molecules for which noncovalent 
 interactions dictate the self - organization of stable secondary and 
 tertiary structures .
there is now a veritable 
 bestiary of foldamer species and hybrids . a large community of researchers are actively developing functional 
 peptoids to address a diverse set of goals .
the intensity and diversity of 
 these efforts punctuates the need for general computational tools 
 to aid in the pursuit of many complex design tasks . in this study
, 
 we provide the computational tools and develop the theoretical background 
 necessary to design the next generation of folded and functional peptoid 
 oligomers . the solid phase submonomer peptoid synthesis protocol 
 introduced 
 by zuckermann et al .
facilitates the 
 introduction of a myriad of side - chain types by utilization of readily 
 available primary amines as synthons .
peptoids have been the subject of considerable research 
 aimed at developing sequence  structure as well as 
 structure  function relationships .
these efforts have established that peptoids can 
 populate a range of secondary structure types and that peptoids exhibit 
 strong interactions between side chain and backbone degrees of freedom . 
 despite the absence of stabilizing backbone hydrogen - bonds ,
peptoids 
 have been shown to fold , and their folds can be predictably controlled 
 by variation of the monomer sequence to achive a desired functionality .
additionally , new native chemical ligation strategies have been 
 developed to ligate peptoids to peptides .
this ligation protocol will enable the synthesis of hybrid biomacromolecules 
 aimed at achieving advanced functions .
rotamer libraries are 
 an essential part of the protein design toolbox . based upon the observation that protein side 
 chains populate distinct areas of side - chain dihedral angle conformation 
 space and that dihedral angle conformations are in some cases strongly 
 dependent on the adjacent  and  backbone dihedral angles ,
side - chain conformations have been grouped together into bins that 
 represent frequent rotational - isomers and given the moniker  rotamer  . 
 for canonical amino acids ( caas ) , methods to find these regular clusters 
 of conformations rely on statistical analysis of the protein data 
 bank ( pdb ) .
the large number of structures for each side chain across 
 the spectrum of allowed backbone dihedral angles allows for the determination 
 of relative rotamer energies by fitting a boltzmann distribution to 
 the population of side - chain conformations .
current rotamer libraries 
 are backbone dependent : given  and  backbone torsion 
 angles , the rotamer library specifies a set of allowable rotamers , 
 the estimated probability of each rotamer , and some measure of the 
 deviation within the cluster of similar conformations represented 
 by that rotamer .
enumerating the set of side - chain conformations and 
 their likelihoods allows for rapid searching of low energy side - chain 
 conformation in discrete steps .
these libraries are key constituents 
 in several structural bioinformatics approaches including methods 
 for placing side chains on homology models , protein structure prediction , 
 and protein design .
statistically derived rotamer libraries 
 are not feasible for systems 
 with few experimental structures . in the case of peptoids , there are 
 fewer than 20 experimentally determined high - resolution peptoid structures , 
 the largest of which includes only 16 residues .
this limitation necessitates 
 the use of mm based force - field energy calculations and qm calculations 
 to derive estimates for the relative conformer energies of peptoid 
 foldamers . from these computed estimates
, we can then establish a 
 rotamer - like treatment of side - chain probabilities .
previous attempts 
 at developing rotamer libraries for noncanonical -amino acid and -amino acid side chains have 
 also used mm - based force - fields .
there are many conceivable 
 algorithmic options to determine rotamer 
 minima placement . in this study
, we devised two distinct rotamer library 
 development methods and find they achieve similar levels of quality 
 in structure prediction and design task performance .
we evaluated 
 the quality of these rotamer libraries within the context of the molecular 
 modeling suite rosetta .
in addition to 
 creating rotamer libraries for peptoids , we introduce several substantial 
 modifications to the rosetta code to enable design with noncanonical 
 backbone chemistry .
rosetta was initially built to predict protein 
 function , but has been expanded to include protocols for docking , 
 protein design , rna structure prediction , and other macromolecular 
 structure and design tasks .
the code is widely distributed and used 
 by more than 1500 research groups worldwide . by incorporating our 
 work on peptidomimetic design into rosetta ,
we make available a large 
 number of computational protocols for scoring , kinematics ( moving 
 the backbone ) , docking , and optimization .
this enables utilization 
 of peptoids in existing rosetta design protocols , such as designing 
 peptoid sequences to interact with proteins .
below we describe the methods used for the creation of rotamer 
 libraries , methods used to evaluate the assumptions made in utilizing 
 rotamers , as well as methods used to characterize the performance 
 of the resultant rotamer libraries .
we have recently 
 compiled a database of all high - resolution peptoid structures ( the 
 peptoid data bank ) .
we 
 additionally included structures of peptoid / peptide hybrids bound 
 to sh3 and ww domains .
selection criteria and modifications 
 to structures are detailed in the supporting information . in the set of oligo - peptoid structures
, there are 9 different 
 peptoid side chains , at 87 positions and with 93 unique conformations . 

four of the most commonly observed peptoid side chains ( nspe , 21 ; nmeo , 17 ; nphe , 15 ; ns1ne , 11 ) , making up 69% of unique conformations in the 
 peptoid data bank , are described in the main body of the text and 
 are shown in scheme 1 .
side chains for which 
 fewer experimental examples exist ( nary , 16 ; nrch , 5 ; npe , 4 ; n1nap , 
 3 ; nrpe , 1 ) are detailed in the supporting information .
in addition to the 9 side chains mentioned above , we chose 
 45 side 
 chains to include within the rosetta framework , based on their prevalence 
 in the literature and the ease with which they could be incorporated 
 into oligomers via standard synthetic routes .
a full list of the 54 peptoid side chains that were incorporated 
 into rosetta and for which we created rotamer libraries are shown 
 in figures s1s7 .
previous 
 studies of oligo - peptoid structures have defined both atom names and 
 dihedral angles in different ways .
our choice of atom names was strongly 
 influenced by peptide atom naming for compatibility with protein modeling 
 programs and is similar to that used by huang and co - workers .
whereas previous studies 
 have defined the 1 dihedral angle relative to the 
 preceding carbonyl carbon , rosetta requires that the atoms that define 
 a  dihedral angle be contained within the residue unit .
we therefore deviated from past work by defining 1 with respect 
 to the c1 atom ( c in peptides ) .
our atom name and torsion 
 angle naming conventions are shown for 
 an nspe residue in scheme 2 .
atom names shown as red italics 
 in torsion angle definitions are atoms in the preceding (  ) 
 or following (  ) residues in a oligo - peptoid chain and not shown 
 in scheme . in our analysis of peptoid side 
 chain conformations below , we use 
 the rotamer notation originally set forth by lovell et al . for its 
 clarity and brevity , where p is used to represent  plus  

( trans , 180 ) . for side chains with dihedral 
 angles that are commonly found at angles other than 60 , 
 60 , or 180 ,
the angle is shown in the notation . when referring 
 to the 1 rotamer wells , unless otherwise noted , 
 we use m and p to refer to 90 
 and 90 , respectively ( e.g. , a side chain listed with a rotamer 
 of mm would have a 1 dihedral angle 
 near 90 and a 2 dihedral angle near 
 60 , while an m90 rotamer would have 
 a 1 dihedral near 90 and a 2 dihedral near 90 ) .
qm energy landscapes 
 of 1 , n , and c as a function of the preceding- dihedral in the context of 
 a tertiary amide bond ( tab ) model ( scheme 3 ) were computed .
the tab model contains the minimum set of atoms 
 needed to simultaneously describe the preceding- and 1 dihedral angle of an oligo - peptoid residue .
all qm geometry 
 optimizations and single point energy calculations of tab models were 
 evaluated at the b3lyp/6 - 311+g(d , p ) level of theory using gaussian09 .
atoms are named as in scheme 2 , and names shown as green italics represent atoms 
 from preceding residues in a oligo - peptoid chain .
two sets of tab models were constructed that combinatorially sample 
 the  dihedral angle and the 1 dihedral angle 
 when the  dihedral is in either a cis or trans conformation .
the set of cis- 
 input tab models sampled  from 40 to 40 in 10 
 intervals .
the set of trans- input tab models 
 sampled  from 140 to 140 in 10 intervals . 

both sets of tab model inputs sample the 1 dihedral 
 angle through a full rotation in 10 intervals .
two additional sets of tab model inputs were constructed 
 to quantify 
 the changes in the location of the energy minima .
these additional 
 sets sample the same cis and trans ranges but set 1 to 90 or 90. 
 both sets of inputs were subjected to qm geometry optimization where 
 only the  dihedral angle values were fixed followed by a single 
 point energy calculation .
the calculations of the  versus c and  versus n energy landscapes 
 are detailed in the supporting information .
the results are shown in figures 2 and s8 . to compare the qm based energy 
 landscape to the rosetta mm_std(34 )
( a mm - based force - field ) based energy landscape , we calculated the 
 energy landscapes for four of the most common side chains in the context 
 of both backbone - independent ( bbi ) and backbone - dependent ( bbd ) model 
 compounds ( scheme 4 ) .
the bbi model was used 
 to quantify the  dependence of side - chain energy landscapes . 

models were initialized at 10 intervals for each  angle , 
 keeping  and the other  dihedral angles fixed .
all other 
 parameters were allowed to optimize . to further quantify the concerted 
 effects that  ,  , and  might have on the energetic 
 landscape , we repeated the  dihedral scan on the bbd model 
 system while keeping the  ,  , and  angles fixed 
 at 0 , 90 , and 180 , respectively , as a majority 
 of peptoid structures have these approximate backbone dihedral configurations . 

all qm geometry optimizations and single point energies were evaluated 
 at the b3lyp/6 - 311+g(d , p ) level of theory using gaussian09 .
similar energy scans were repeated with the 
 same model compounds using the rosetta mm_std force - field 
 without geometrical optimization .
we have previously shown that 
 using the mm - based mm_std energy function in rosetta , 
 we can produce rotamer libraries for proteins and noncanonical -amino 
 acids that are comparable to statistically derived rotamer libraries . to explore and compare the relative merits of 
 context and scoring approximations we describe two methods : ( 1 )
quantum 
 mechanically seeded ( qms ) : which uses a highly accurate qm based scoring 
 function , but a minimal model of the peptoid backbone / environment , 
 and ( 2 ) k - means clustering ( kmc ) : which uses a more efficient molecular 
 mechanics scoring function , but more extensively explores a model 
 of the peptoid backbone .
both 
 protocols require a residuetype parameter file that instructs 
 rosetta how the side chain is allowed to move and how the energy of 
 the residue is to be calculated . drew et al .
the residuetype parameter file 
 describes the atom names and types , the chemical connectivity of the 
 side chain and an  ideal  internal - coordinate representation 
 used when rosetta needs to create new instances of the side chain . 

a qm geometry optimization of a bbd  dipeptoid  , using 
 gaussian09 at the b3lyp/6 - 311+g(d , p ) level of theory , is used to generate 
 the idealized internal coordinates that serve as a starting point 
 for the kmc and qms protocols .
workflow for the k - means clustering ( kmc ) 
 and quantum mechanically 
 seeded ( qms ) rotamer library construction protocols .
boxes shaded 
 in green are qm geometry optimizations of backbone - dependent ( bbd ) 
 or backbone - independent ( bbi ) models ; red , inputs to rosetta ; blue , 
 geometry optimization using the rosetta mm_std energy 
 function ; yellow , identification of local energy minima .
our previously described 
 rotamer library construction protocol was adapted for peptoids as shown in figure 1 .
model system , a peptoid residue with an acetylated n - terminus and 
 a n - dimethylamide c - terminus , has been previously used to examine 
 backbone - side - chain interactions in peptoids as it mimics the environment of the side chain with its own backbone 
 and the backbones of the preceding and following residues .
the additional 
 dependence of peptoid side chain conformations on the preceding- 
 backbone dihedral angle necessitated modification to the protocol 
 to sample and produce rotamer libraries that are dependent on the 
 preceding- angle as well as  and  dihedrals . 

the  and  backbone dihedrals were sampled through a 
 complete rotation in 10 intervals to produce 36  and 
 36  bins . in the set of rosetta compatible peptoid data bank 
 structures , cis and trans
preceding- 
 backbone dihedrals were sampled between 30 to 30 
 and 150 to 150 in 10 intervals to produce 
 14  bins .
a combinatorial sampling of all ,, 
 bins yields 18  144 backbone bins . for each backbone bin , 

 dipeptoids  were constructed that combinatorially sample 
 the side - chain dihedral angles .
side - chain dihedral angles were sampled 
 at user - defined sets of angles relating to the number of  angles , 
 the chemical connectivity and the expected number of rotamers ; typically 
 10 intervals ( e.g. , nspe has 36 1 and 36 2 samples to produce 1296  dipeptoids  
 for each ,, bin ) .
the set of minimized  dipeptoids  was then k - means clustered 
 based on the similarity of the minimized side - chain dihedral angles . 

the final rotamers for a given backbone dihedral bin are the side - chain 
 dihedral angles of the lowest energy  dipeptoid  from 
 each cluster in that bin .
the side - chain conformation of each final 
 rotamer was sampled about the local minima until the energy increased 
 by 0.5 rosetta energy units ( reu ) to obtain an approximation of the 
 width of the local energy minima .
this local energy minima width is 
 used as a proxy for the standard deviation of the side - chain conformations 
 in a single rotamer bin .
we devised an alternative 
 methodology 
 to use qm energy scans of a bbi model of the peptoid side chains as 
 shown in figure 1 .
the minimum energy wells 
 identified from qm energy landscapes were used as starting points 
 for lower level mm optimization and energy evaluation on a bbd model 
 system .
the bbi model containing each side chain is initialized in 
 gaussian09 into discrete intervals spanning the entire 1n ( where n is the total number of  angles ) with a fixed  
 backbone dihedral angle at either 0 for cis or 180 for trans conformations and allowed 
 to geometrically minimize while keeping the  dihedral fixed . 

the qm derived minima from those single point energy scans converge 
 to small clusters . from each cluster ,
this set of  angles for 
 both cis and trans conformations 
 serves as the complete set of bbi energy wells . the bbi energy well 
  dihedral angle coordinates were then initialized onto the 
 bbd model in rosetta in the same range of backbone bins as the kmc 
 protocol .
the bbi energy well coordinates were then minimized using 
 the rosetta mm_std scoring functions and their relative 
 energies were used to determine rotamer probabilities assuming a boltzmann 
 distribution of the resulting energies .
all geometry optimizations 
 of the molecules in the bbi qm - derived minima scans were performed 
 at the b3lyp/6 - 311+g(d , p ) level of theory .
rotamer recovery benchmarks tested the 
 performance of the two rotamer libraries at reproducing the low energy 
 packed side - chain conformations observed in experimental structures 
 in both the presence ( when applicable ) and absence of the symmetry 
 related partner molecules in the oligo - peptoid structures . a rosetta 
 protocol was written to carry out fixed - backbone side - chain repacking 
 using the packrotamersmover followed by a comparison 
 between the original and repacked side - chain conformations .
the packrotamersmover simultaneously repacks all side - chain positions 
 using a metropolis monte carlo simulated annealing procedure that 
 attempts to find the lowest energy set of side - chain conformations 
 given the current backbone conformation .
calculations were performed with the ex1 , ex2 , and ex3 command line flags set to  true  ; 
 and the extrachi_cutoff flag set to 0 .
these flags force 
 rosetta to sample 1 , 2 , and 3 rotamers at their mean  one standard deviation at all 
 positions . in order to model only side - chain conformations described 
 by the rotamer library
, the use_input_sc flag is set 
 to  false  to exclude the experimentally determined 
 side - chain conformation of the input structures in sampling .
a residue s 
 side chain is considered predicted correctly if the  angle 
 of the repacked model was within 20 of the position in 
 the native structure .
although peptoid oligomers 
 can readily be synthesized to incorporate 
 a wide diversity of side chains , there are 
 only a handful of experimentally determined peptoid structures .
there 
 has yet to be a systematic analysis of side - chain conformations in 
 all peptoid structures that explores side - chain conformations given 
 all energetically feasible backbone conformations . additionally , to 
 determine if a rotameric treatment of peptoid side chains is appropriate , 
 it is necessary to establish that the dihedral angle values of the 
 experimental side - chain conformations cluster and that there is a 
 multidimensional interdependence between the locations and frequency 
 of those clusters .
here we briefly describe 
 our results for a small set of side chains for which there are sufficient 
 experimental data to allow for proper validation . following these 
 case studies ,
first , we explore our ability to fit existing 
 structures by quantifying the distance between experimental side - chain 
 conformations and the corresponding closest rotamers in our library . 

second , we evaluate the performance of our rotamer library in the 
 context of a peptoid design task by evaluating repacking of peptoid 
 side chains within existing peptoid crystal structures .
lastly , we 
 evaluate our ability to model peptoid side chain conformation at an 
 experimentally validated protein - peptoid interface ( in comparison 
 to x - ray crystal structures of the interfaces ) .
in all three cases , 
 we achieved good performance for rotamers developed from both the 
 quantum mechanically seeded ( qms ) and k - means clustering ( kmc ) methods . 

this strongly indicates that peptoid side chain conformations can 
 be approximated by a rotameric treatment and that our rotamer libraries 
 are suitable for several design tasks .
peptoids , unlike 
 peptides , have greater flexibility around  , 
 with some monomer types readily populating both cis and trans ( e / z )  angle conformations with a substantial range of deviation 
 around the ideal angles of 0 and 180 for cis and trans , respectively .
the rotation of the preceding- torsion angle has been both 
 predicted and observed to alter the preferred 1 value , 
 as well as pyramidalization of the backbone nitrogen ( n ) and backbone carbonyl carbon ( c ) atoms . to quantify the effect  
 has on these side - chain conformations , and to justify development 
 of a backbone dependent rotamer library that includes this additional 
 dihedral angle variability
, we explored the -dependent energy 
 landscapes . in the development of rotamers based upon the tab 
 ( scheme 3 ) ,
system we sought to ensure that 
 rotamers developed using an inflexible amide bond model would be applicable 
 for design in systems with slight deviations from ideal bond lengths , 
 angles , and dihedral parameters .
the rotamer libraries used by rosetta 
 only include information about side - chain torsion angles with respect 
 to the backbone torsion angle values . in order to use a rotameric 
 treatment of peptoid side - chain conformations ,
the degrees of freedom 
 that are not described in the rotamer library need to be relatively 
 stable or invariant to perturbations of the backbone torsion angles . 
 to verify that this was the case for peptoids
, we quantified the relationships 
 between the  backbone dihedral angle and the 1 dihedral angle ( figure 2 ) as well as carbon ( c ) and nitrogen ( n ) dunitz amide bond puckering parameters ( figure s8 ) . from these 
 energy landscapes , there are several notable dihedral 
 angle dependencies .
we found that the 1 rotamer 
 energetic preferences for the tab model were most significant ( 0.5 
 kcal / mol ) at extreme  dihedral angle deviations from planarity . 

the 1 dihedral angle minima as denoted by the solid 
 and dashed lines ( figure 2 ) had notable ( 20 ) 
 deviations from 90 and 90 , dependent upon the 
  dihedral angle .
this result confirms the necessity to develop 
 rotamer libraries dependent on not only the  and  , but 
 also on  backbone dihedral angles , as the effects of  
 deviations on 1 have now been quantified and have 
 been found to be significant .
the n and c dunitz parameters varied as a linear function of . 
 these puckering trends are built into the 1 energy 
 landscapes , resulting in the observation that even with extreme  
 dihedral angles and deviation of the amide bond from planarity , the 
 1 energetic preferences vary by only 0.5 
 kcal / mol .
this stability buttresses our confidence that idealized 
 amide bonds are a reasonable starting approximation for -dependent 
 peptoid rotamer libraries . from this result , we are confident that 
 rotamer libraries that include an  dependence will be able 
 to accurately capture the energetic preferences of diverse peptoid 
 oligomer species .
energy landscapes were generated by fixing 
 the 
 dihedral angles of the tab model to simultaneously achieve the desired 
 1 or . cis- angles 
 can be found on the left , trans- can be found 
 at the right .
crystal structure data are shown as circles and crosses 
 for angles and parameters found in cyclic and linear peptoid structures , 
 respectively . in the trans- energy landscapes , 
 crystal structure values for the  nary  

monomer are not plotted , as this parameter does not match the chemistry 
 of the tab model system .
the minimum energy parameters are plotted 
 across the full range of  values as well as for positive ( solid 
 line ) and negative ( dashed line ) 1 values .
all molecules 
 were minimized and energies evaluated at the b3lyp/6 - 311+g(d , p ) level 
 of theory , and heatmaps generated using the lowest energy for each 
 plot as the zero kcal / mol baseline .
we used two protocols to generate 
 backbone dependent ( bbd ) rotamer libraries for peptoid side chains 
 in order to enable comparisons between approaches for identifying 
 rotamers , scoring conformations , and modeling backbone - side - chain 
 conformation interdependence .
the first protocol is a modification 
 of the method previously published to 
 calculate -amino acid side - chain rotamer libraries , referred 
 to as the kmc method .
it uses the molecular mechanics ( mm ) based rosetta mm_std energy function in the context of a bbd molecule to 
 evaluate rotamer energies .
previous studies using quantum 
 mechanics ( qm ) have shown a complex interaction between the peptoid 
 side chain and backbone .
while qm is accurate , it is also computationally 
 intensive and can not solely be used to create a full rotamer library 
 or for side - chain repacking and design calculations .
our second method 
 is a new rotamer library creation protocol that uses input from qm 
 calculations carried out on backbone - independent ( bbi ) molecules and 
 is referred to as the qms method .
the qms method then passes these 
 qm - bbi minima to rosetta to estimate interactions with the backbone . 

thus , each method uses a different strategy to reduce the complexity 
 of the problem and arrive at a protocol with computational efficiency 
 sufficient to allow calculation of rotamer libraries for multiple 
 side chains .
there are more than 200 peptoid side chains that are 
 synthetically feasible ; however , only 
 9 different side chains have been used in experimentally determined 
 peptoid structures .
it is therefore essential that both protocols 
 are general methods that do not incorporate or require structural 
 information from experimentally determined peptoid structures as training 
 data .
we tested these two methods to determine if our rotamers , in 
 conjunction with the mm based rosetta mm_std energy function , 
 could accurately capture the behavior of peptoid side chains to the 
 extent required by tools developed for protein modeling .
we show that 
 the two methods , despite taking different approaches , ultimately find 
 similar rotamers .
a discussion of the rotameric states of the side - chain 
 conformations observed in the current set of peptoid structures and 
 how they compare to the side - chain conformations of the rotamer libraries 
 produced here are included in the supporting information .
additionally , an excerpt of the side - chain dihedral angles from 
 the rotamer library are included in supporting 
 information tables s1s4 .
the energy landscape 
 generated in the initial steps of the qms protocol uses the bbi model 
 ( scheme 4 ) .
this minimal model was chosen due 
 to the fact that qms single point energy evaluation of the energy 
 landscape including the backbone  and  torsions for 
 all possible dihedral angles is computationally intractable .
the reduced 
 representation contains all of the side - chain atoms but only the  
 torsion angle of the preceding residue . to investigate if this model 
 is sufficient , we computed side - chain dihedral ( 1 and 2 ) energy landscapes of four common side chains 
 with bbd  dipeptoid
 models at common low energy backbone 
 conformations using qm and the rosetta mm_std energy 
 function and compared them to the landscape of bbi models ( figure 3 ) .
most notable is the 
 absence of the 1 minima near 90 that 
 are present in the bbi model energy landscape but absent in the bbd 
 energy landscape for the four common side chains .
the absence is the 
 result of steric interaction between the c1 of the side chain 
 and the c atom of the backbone which has a fixed  dihedral 
 of 90. if the  angles are fixed at 90 , 
 we observe an absence of 1 minima near 90. 
 these results can be rationalized by the similar repulsive effects 
 observed in the syn - pentane model system .
the loss of the 90 minima seen 
 in the backbone - dependent energy landscapes is analogous to the repulsive 
 effects observed in syn - pentane which has been extrapolated 
 to explain forbidden rotamers at certain  and  dihedral 
 angles of amino acids .
additionally , the appearance of the m0 and p0 rotamers of nspe 
 and nphe in the bbd molecule in peptoid structures 
 indicates that the bbi screen is not always successful in capturing 
 the complete ensemble of side - chain conformations observed in peptoid 
 structures .
the qms protocol is also limited to two  angles , 
 as a complete screen of side chains with many rotatable bonds is computationally 
 intensive and often intractable with qm .
differences between cis and trans bbi models show that while 
 the relative energy varies , the location of the minima remain similar 
 between the two ( figure s9 ) . the minima 
 from the bbi model landscape found as small clustered circles in figure s9 are represented as large diamonds in 
 the bbi portion of figure 3 .
these minima are 
 then initiated onto a bbd model and the model is allowed to minimize 
 using linear gradient minimization and the rosetta mm_std scoring function .
the diamonds on the bbd portion of figure 3 represent these minimized rotamer positions in 
 the presence of the backbone model .
it can also be observed that the 
 qm and mm bbd energy landscapes closely resemble one another , with 
 only minor differences .
rosetta and other computational protein modeling 
 packages use side - chain dihedral angles in rotamer libraries to discretize 
 the search for low energy side - chain conformations ( protein repacking ) 
 or sequences ( protein design ) for a given backbone conformation . an 
 accurate rotamer library will contain side - chain dihedral angle values 
 close to values observed in experimentally determined structures . 

rotamer libraries should be succinct for computational efficiency , 
 but also sufficiently comprehensive to enable sampling of a large 
 fraction of energetically accessible conformations . to test 
 the completeness of the rotamer libraries produced by the kmc and 
 qms rotamer library creation protocols , we carried out rotamer library 
  coverage  tests .
these tests calculate the rmsd ( in 
 degrees ) between the experimentally observed side - chain rotamer conformation 
 and the closest rotamer in the given rotamer library .
results of the 
 rotamer library coverage tests for the four frequently observed side 
 chains are shown in figure 4 and table 1 .
results of the other experimental side chains 
 are shown in figures s10s14 and table 
 s5 .
for comparison , these tests were additionally carried out 
 for phenylalanine and methionine side chains in protein structures 
 in the top 8000 data set using the dunbrack 
 2002 bbd rotamer library , tables 1 and s7 . fixed
backbone rotamer energy landscapes for nphe , nspe , ns1ne , and n-(propyl)-glycine side chains in a backbone - independent 
 ( bbi ) and 
 backbone - dependent ( bbd ) context .
crystal structure dihedral angle 
 values are shown as circles and crosses for those observed in cyclic 
 and linear peptoid structures , respectively .
x - ray crystal dihedral 
 angles for the different side chains are plotted only for the monomers 
 in which the backbone dihedral angles were observed to be within 20 
 of the fixed backbone dihedral angles used in the energy landscape 
 calculations .
the minima from the bbi model landscapes ( figure s9 ) are represented as large diamonds 
 in the bbi portion of the figure on the left .
the diamonds on the 
 right portion of the figure represent these rotamer positions in the 
 context of the bbd model after rosetta mm_std energy 
 function minimization .
all landscapes underneath a qm header had energies 
 evaluated at the b3lyp/6 - 311+g(d , p ) level of theory .
heatmaps were generated using the lowest energy 
 as each plot s zero kcal / mol and zero reu ( rosetta energy units ) 
 baseline for qm and rosetta , respectively .
for each of the four most frequent peptoid side chains , either 
 the kmc or qms rotamer libraries contained rotamers with angles that 
 are , on average , within less than 20 of experimental side chain 
 values .
for the nspe side chain , only the p90 and p0 rotamers are experimentally observed 
 and accurately modeled by rotamers created with both the kmc and qms 
 method .
the experimental points occupy a wide energy valley that spans 
 from a 2 of 90 to 30. the kmc 
 method performs better than the qms as it is able to find a low probability 
 rotamer in this valley while the qms method predicts p0 rotamers closer to a 2 of 30. 
 for the nmeo side chain , the experimental conformations 
 adopt the traditional m , p , and t positions .
the 3 dihedral angle values did not 
 form tight clusters in the kmc protocol ( data not shown ) .
this results 
 in a relatively large rmsd value ( table 1 ) 
 despite 1 and 2 values being accurately 
 predicted ( figure 4c ) . for the nphe side chains ,
the rmsd value for the kmc rotamers is just over 
 the 20 threshold while the qms is significantly higher at 38. 
 the bbi screen of the qms method misses the high energy m0 and p0 rotamers ( figure 3a ) , and the qms rotamer library does not include these conformations . 
 the qm energy landscape with the backbone present shows an elongated 
 energy valley for 2 ( figure 3a ) .
the five experimental examples with 2 near 
 0 are missed by the qms method and contribute to the high rmsd 
 in table 1 .
the three experimental points near 
 the m0 rotamer are also significantly different 
 from the values in the kmc library .
deviations in 1 can arise from pyramidalization which can greatly affect the positioning 
 of the atoms making up the 1 dihedral angle , potentially 
 influencing the 1 calculated value .
when the experimental 
 points with a 2 near 0 are omitted , the qms 
 rotamers have almost the same rmsd to the experimental values as the 
 kmc rotamers for m90 and p90 
 rotamers ( 18.25 and 18.71 , respectively ) . for the ns1ne side chain ,
both the kmc and qms protocols perform 
 as well as the dunbrack 2002 library for protein data .
the large steric 
 bulk of the naphthyl group interacting with the c2 atom of 
 the ns1ne side chain and peptoid backbone restricts 
 the allowed conformations of the side chain .
only the pp rotamer is observed in the experimental data set , and both methods 
 predict this rotamer accurately . with few exceptions ,
rotamers 
 observed in peptoid structures are 
 found in the rotamer libraries produced by both methods .
both the 
 kmc and qms protocols produce similar rotamers with similar dihedral 
 angles .
the kmc protocol suitably evaluates longer side chains and 
 is able to find side - chain conformations that involve backbone interactions 
 such as the nphe rotamers with 2 near 0. the dunbrack 2002 rotamer library for the 20 
 canonical peptide 
 amino acids performs better than our rotamer libraries perform on 
 peptoid side chains .
however , compared to the top 8000 data set , there are far fewer examples of peptoid structures 
 than protein .
additionally , the data set employed for the protein 
 comparison is heavily pruned to only include the highest quality structures 
 available ; an option we do not have for peptoids .
we investigated if the combination of the peptoid rotamer libraries 
 and the mm_std scoring function have sufficient discriminatory 
 power to recapitulate the side - chain conformations in the experimentally 
 determined structures .
we therefore undertook side - chain conformation 
 recovery benchmarks similar to those employed in the early development 
 of protein design methodologies .
all non - hydrogen 
 atoms in the monomer 
 were used to calculate the rmsd .
positions from the top 8000 data 
 set with less than eight neighbors ; two 
 residues are considered neighbors if their neighbor atoms ( c 
 for glycine , c for all others ) are within 10  of each 
 other .
rotamer library coverage 
 plot for nphe , ns1ne , nmeo , and nspe 
 peptoid side chains .
interpolated  torsions and standard deviations 
 of the closest rotamer in the rotamer library based on the backbone 
 dihedral angles of each experimental point are shown as crosses , where 
 the center of the cross is at the mean and the length represents 1 
 standard deviation .
rotamers for the k - means clustering ( kmc ) method 
 are shown as red crosses and quantum mechanically seeded ( qms ) method 
 are shown in blue .
each example in the set of rosetta compatible peptoid structures 
 was repacked with rosetta using rotamer libraries from the kmc and 
 qms protocols and in the presence ( where applicable ) or absence of 
 crystal contacts from symmetry related partners .
the predicted side - chain 
 dihedral angles of the repacked structures were compared to those 
 in the experimental structure .
a  angle is judged to be correctly 
 predicted (  recovered  ) if it is within 20 of 
 the experimental value .
results of the rotamer recovery benchmark 
 in structures containing only peptoid residues are shown in table 2 and figure 5 .
rotamer 
 recovery rates in proteins improve with additional context 
 about the environment the side chain is in . for surface positions , 
 that additional context can be provided by the atoms from neighboring 
 chains in the symmetery related cyrstalographic neighbors .
the surrounding atoms in a protein s 
 core also provide additional context and can help determine correct 
 rotamer position .
previous studies on proteins found that rosetta achieved an over all rotamer recovery 
 of 75% for 1 and 53% for 1 + 2 using the mm_std energy function and the dunbrack 
 2002 rotamer library .
a recovery of 59% for 1 and 
 37% for 1 + 2 was achieved for 
 surface positions , and a recovery of 91% for 1 and 
 71% for 1 + 2 was achieved for 
 core positions using the same energy function and rotamer library . 

the increased recovery of protein cores strongly suggests that , for 
 a given position , the influence of surrounding side chains can enhance 
 the discretization of low energy side - chain conformations . in the 
 currently available set of peptoid structures ,
the number of neighbors 
 a given side chain has is more comparable to the surfaces rather than 
 cores of proteins . both the kmc and qms rotamer libraries are able 
 to correctly predict the 1 conformations of more 
 than 60% of peptoid positions
both in the absence and presence of 
 crystal structure contacts ( table 2 ) .
the kmc 
 and qms rotamer libraries achieve rates of peptoid side - chain recovery 
 comparable to the recovery rate of the dunbrack 2002 library for protein 
 side chains at surface positions .
percent rotamer 
 recovery  absent  
 crystal contacts totals have been adjusted to account for structures 
 determined by nmr .
our ability 
 to recover correct rotamers is dependent on the quality 
 of the rotamer library coverage .
the 12ac1 - 9-c structure , an nspe 9-mer , has the highest rate of side chains recovered 
 ( figure 5 ) because the rotamers produced by 
 the kmc and qms protocols have a low averaged rmsd compared to the 
 experimental side chain conformations for nspe ( table 1 ) .
in contrast , the 12ab4 - 16-m structure contains 
 only nmeo and nary side chains and 
 has the lowest fraction of rotamers recovered in the set .
the rotamer 
 library coverage for the nmeo and nary side chains is more complete relative to nspe 
 ( tables 1 and s5 ) , and the effect is that we poorly predict the side - chain conformations 
 within the 12ab4 - 16-m structure . to get a better understanding 
 of how rosetta will behave in repacking 
 a peptoid side chain in the core of a globular protein or buried at 
 protein  protein interfaces
, we carried out rotamer recovery 
 benchmarks in the context of the neighboring peptoid molecules in 
 the solid state defined by the crystallographic symmetry transformations 
 ( table 2 ) .
the addition of crystallographic 
 partners has been shown to increase the rate of rotamer recovery at 
 protein surface positions .
although not 
 a perfect analogue of a protein s hydrophobic core , increasing 
 the number of neighboring residues through the addition of crystal 
 contacts reduces the number of conformations assessable to the given 
 peptoid position . additionally , crystal contacts can direct the side 
 chain into conformations that are lower in energy as a result of the 
 additional contacts .
this allows rosetta to choose a rotamer closer 
 to those observed in the crystal structures .
for example , nspe-4 and nspe-8 monomers in the peptoid 
 data bank structure 12ac1 - 9-c are both correctly predicted by both 
 the kmc and qms rotamer libraries .
however , the angles of the selected 
 conformations are closer to the values in the experimental structure 
 when crystal contacts are included in rotamer repacking .
this effect 
 is highlighted in figure 5 with the side - chain 
 conformation predicted with crystal partners ( red ) closer to the experimental 
 conformation ( gray ) than without the crystal information ( blue ) .
there 
 are currently too few structures to determine if crystal contacts 
 direct side chains into off - rotamer conformations .
however , for the 
 two available nmr solution structures , rosetta has a 1/2 recovery of 67%/75% for kmc and 80%/75% for 
 qms . our ability to accurately model peptoid 
 side chain conformations with a rotameric treatment in rotamer recovery 
 benchmarks supports the notion that peptoids are indeed rotameric . 
 like peptides ,
each peptoid side chain is rotameric at varying levels 
 as a result of complex side chain to backbone intraresidue and steric 
 interactions .
overall , we find that the currently available set of 
 experimental side - chain conformations are sufficiently modeled with 
 our predicted rotamer conformations .
to more thoroughly evaluate the 
 degree to which peptoids are rotameric will likely require additional 
 peptoid structures with greater numbers of side - chain - side - chain contacts , 
 tighter packing , and a more diverse palate of side chains .
however , 
 with the currently available set of rosetta - compatible peptoid data 
 bank structures , we find that experimental side - chain conformations 
 cluster well and that those clusters correspond to minima found in 
 qm and rosetta mm_std energy landscapes .
it is clear 
 that some rotamers will simply not be observed due to steric clashes 
 with the backbone ; other predicted rotamers have not been observed 
 due to the small size of the current database of peptoid structures . 

this initial study indicates that similar to peptides , peptoids also 
 exhibit rotamer preferences .
furthermore , this finding suggests that 
 protein modeling tools can be readily adapted to accommodate them .
nguyen and co - workers have deposited three structures of sh3 domains 
 bound to inhibitory peptides in which each peptide has a single proline 
 position mutated to a different peptoid side chain .
these three structures provide us an opportunity to test our ability 
 to recover native rotamers in hybrid design contexts .
structure 1b07 contains two chains 
 ( labeled a and c in the deposited structure ) , while 2sem and 3sem contain four chains 
 each , two pairs of protein / peptide interactions ( a / c and b / d , respectively ) . 

as with the rotamer recovery of the oligo - peptoid structures , each 
 structure here was repacked and the side - chain dihedral angles were 
 compared to those in the experimental structure .
results of the rotamer 
 recovery benchmark in structures of peptoid / peptide hybrids are shown 
 in table s9 and figure s15 .
rosetta 
 is able to recover the rotamers of the 1b07 and 2sem structures using both the kmc and qms 
 rotamer libraries .
we are not able to recover the rotamer of the peptoid 
 side chain from the 3sem structure .
rosetta places the side chain in an alternative conformation 
 ( data not shown ) .
the peptoid side chain in the 3sem structure branches 
 at the second side chain atom and makes few contacts in the crystal 
 structure .
additionally , the average b - factors of the atoms in the 3sem side chains are 
 greater than 40 , indicating uncertainty in the exact position of the 
 peptoid side chain in this experimental structure ( table s9 ) . for these reasons
we exhibit good performance for both 
 structures with well - resolved peptoid side chains , but recognize that 
 the small sample size prevents us from generalizing further .
we present a general method for creating rotamer libraries needed 
 for rational design of peptidomimetic oligomer structures .
we apply 
 this method to the peptoid backbone and show performance is comparable 
 to protein side - chain rotamer libraries derived from statistical analysis 
 of the protein data bank ( pdb ) for protein surface positions .
this 
 pipeline relies on mm and qm simulations in lieu of statistical analysis 
 because far fewer crystal structures of peptoids exist than for proteins . 

given the reliance on physics - based methods , we expect this method 
 can be applied to several other diverse peptidomimetic scaffolds ( such 
 as -peptides , d - amino acid , and hybrid oligomeric 
 systems ) .
a notable advantage of this method is that it can be used 
 to build rotamer libraries for any specified side chain .
this is demonstrated 
 by the development of rotamers for over 50 peptoid side chains ( shown 
 in figures s1s7 ) that are capable 
 of being incorporated via standard peptoid synthesis protocols .
peptoid data 
 bank structure 12ac1 - 9-c and side - chain conformations 
 after being repacked with ( a ) kmc rotamer libraries or ( b ) the qms 
 rotamer libraries .
experimental side - chain conformations are shown 
 in gray , repacked side chains in blue , and repacked in the context 
 of the symmetry related crystal partners in red .
positions for which 
 the same rotamer was chosen in both contexts are shown in purple .
comparisons between qm evaluations 
 of peptoid side - chain conformations 
 and our rotamers show good agreement between the qms and kmc rotamer 
 library construction pipelines .
our comparisons with qm suggest we 
 capture key features of the side - chain conformational landscape .
we 
 also find agreement with the side - chain conformations observed in 
 x - ray crystal and nmr structures of peptoid oligomers ( figure 4 ) .
there are currently too few experimentally determined 
 peptoid structures to derive peptoid rotamer libraries by statistical 
 analysis .
the currently available peptoid structures are of small 
 oligomers ( < 20 residues ) and are dominated by crystal contacts 
 and local structure interactions ( comparable to protein surface positions ) . 

we show that our rotamers agree with experimental side - chain conformations 
 with rmsd values comparable to best - in - class protein rotamer libraries 
 for -amino acids at surface positions ( figure 4 and table 1 ) .
a large number 
 of modifications to the rosetta design framework 
 were required to enable peptoid design with these rotamer libraries 
 ( described in the supporting information ) ; most notably , allowing for the use of bbd rotamer libraries that 
 include preceding- in addition to  and . these 
 modifications to the rosetta design procedure allowed us to evaluate 
 our performance on repacking tasks , and again we find that these rotamer 
 libraries will be sufficient for peptoids and hybrid peptoid - protein 
 design tasks ( such as designing peptoids to interrupt protein  protein 
 interfaces ) . despite the rosetta energy function being optimized for 
 biological molecules in aqueous media , it performs surprisingly well 
 at reproducing the side - chain conformations of relatively short oligo - peptoid 
 structures in nonaqueous media .
this indicates that the side - chain 
 conformations of peptoids are primarily determined through local interactions . 
 adding peptoid design capabilities to rosetta allows access to kinematics , 
 optimization , and scoring methods that enable a vast array of design 
 and modeling tasks for peptoid , peptoid 
these rotamer library development methods are also extendable 
 to other noncanonical backbones and peptidomimetic scaffolds .
future 
 work will include adding capabilities to model and design several 
 other peptidomimetic oligomer scaffolds .
a key remaining challenge 
 not addressed here , is to model mixed 
 oligomeric systems such as oligomers containing -amino acids 
 and peptoids .
additional study is required to determine if rotamer 
 libraries derived individually for peptoid and -amino acids 
 will perform well in these hybrid settings . in cases where a peptide side chain precedes a peptoid side chain , 
 both side chains would be separated by only two bonds along the backbone 
 and we speculate that this mixed system would require rotamer libraries 
 specific to the joint between the two oligomeric systems . for cases 
 in which peptoid side chains are n - terminal to peptide , the proximal 
 side chains will be separated by four bonds and it is likely that 
 the rotamers derived in this study would perform well in this mixed 
 setting .
other key areas for future work include the need for developing 
 better methods to estimate the unfolded state energies ( sometimes 
 referred to as the  reference energy  ) as well as new 
 methods for dealing with larger side chains .
as we design , build , 
 and refine peptoids , we will increase the 
 diversity and number of structures and thus increase our ability to 
 score and judge peptoid designs .
we thus intend to bootstrap our way 
 toward design capabilities for both peptoid and mixed protein 
peptidomimetic 
 systems that approach pure protein design in accuracy and breadth 
 of application .
 peptoids are a family of synthetic 
 oligomers composed of n - substituted 
 glycine units . along with other 
  foldamer  
 systems , 
 peptoid oligomer sequences can be predictably designed to form a variety 
 of stable secondary structures . 
 it is not yet evident if foldamer 
 design can be extended to reliably create tertiary structure features 
 that mimic more complex biomolecular folds and functions . 
 computational 
 modeling and prediction of peptoid conformations will likely play 
 a critical role in enabling complex biomimetic designs . 
 we introduce 
 a computational approach to provide accurate conformational and energetic 
 parameters for peptoid side chains needed for successful modeling 
 and design . 
 we find that peptoids can be described by a  rotamer  
 treatment , similar to that established for proteins , in which the 
 peptoid side chains display rotational isomerism to populate discrete 
 regions of the conformational landscape . because of the insufficient 
 number of solved peptoid structures 
 , we have calculated the relative 
 energies of side - chain conformational states to provide a backbone - dependent 
 ( bbd ) rotamer library for a set of 54 different peptoid side chains . 
 
 we evaluated two rotamer library development methods that employ quantum 
 mechanics ( qm ) and/or molecular mechanics ( mm ) energy calculations 
 to identify side - chain rotamers . 
 we show by comparison to experimental 
 peptoid structures that both methods provide an accurate prediction 
 of peptoid side chain placements in folded peptoid oligomers and at 
 protein interfaces . we have incorporated our peptoid rotamer libraries 
 into rosetta , a molecular design package previously validated in the 
 context of protein design and structure prediction . 
Introduction
Methods
Results
Discussion