the 
 majority of the protein structures deposited in the protein data bank are determined either by 
 x - ray crystallography or solution - state nuclear magnetic resonance spectroscopy ( nmr ) .
while 
 x - ray crystal structures are derived from electron density data and are often of higher 
 accuracy , protein nmr structure determination in solution may more accurately reflect molecular 
 dynamics and has the advantage of not requiring crystallization . solution nmr structure determination is generally based on three classes of experimental 
 restraints : distance restraints , dihedral angle restraints , and orientation restraints . in 
 combination with these restraints ,
different algorithms and force fields have been implemented 
 to determine nmr structure using a variety of programs .
two groups of simulated annealing based 
 programs are most commonly used by the nmr community : xplor / cns and dyana / cyana . aside from the accuracy and completeness of 
 experimental data ,
the quality of nmr structures also depends on the programs utilized in 
 structure calculation and structure refinement .
in particular , as demonstrated by many studies , 
 the quality of nmr structures can be improved by structure refinement in state - of - the - art force 
 field with explicit or implicit solvent .
using such advanced refinement protocols , a few large - scale 
 rerefinement studies have been done to improve the quality of nmr structures , especially for nmr 
 structures determined prior to 2000 .
one is 
 the assessment of how well the structures fit with the experimental nmr data , including 
 noe - based distance restraint violations , dihedral angle restraint violations , noe 
 completeness , and goodness - of - fit with nmr noesy peak 
 list and rdc data .
the second class includes knowledge - based normality scores 
 relative to high - resolution x - ray crystal structures , such as bond length , bond angle , backbone 
 or side chain dihedral angle , and packing statistics .
recent studies comparing various methods for automated analysis of nmr data 
 and structure generation , such as the critical assessment of structure determination by nmr 
 ( casd - nmr ) study , 
 demonstrate that the algorithms and force fields utilized in nmr structure refinement can 
 significantly improve these normality scores .
for example , protein nmr structures refined by 
 rosetta without restraints generally have excellent knowledge - based stereochemical and geometric 
 quality scores , but sometimes have poorer fit to the original experimental 
 data .
the rosetta molecular modeling program was first developed for de novo 
 protein structure prediction , homology modeling , and protein design .
however , it has also been used in protein crystallography as part of improved 
 protocols for determining crystallographic phases by molecular replacement and for nmr structure determination and unrestrained nmr structure 
 refinement . 

have shown that unrestrained rosetta refinement can improve 
 the phasing power of an nmr structure by moving it closer to its x - ray crystal structure 
 counterpart .
this observation has been corroborated for two additional nmr structures as part of 
 a systematic investigation of using nmr structures in molecular replacement .
these results are intriguing , as they suggest that the force field of rosetta may be even 
 more accurate than the nmr data themselves in defining the protein structure .
however , only 
 one or two examples are reported in these two papers . 
 in order to assess the generality of unrestrained rosetta refinement , it is necessary to perform 
 a systematic study using a much larger data set .
another intriguing observation is that the number of restraint violations significantly 
 increases after unrestrained rosetta refinement , which begs the question : do those violated restraints reflect 
 true structural differences between nmr structures and x - ray crystal structures ? if that is the 
 case , then would incorporating those nmr experimental restraints into rosetta refinement drive 
 the nmr structure away from its x - ray counterpart ?
more generally , what is the most efficient 
 protocol for using rosetta to improve the accuracy of protein nmr structures ?
the northeast structural genomics consortium ( nesg ; http://www.nesg.org ) is one of several large - scale structure production centers of the 
 protein structure initiative ( psi ) .
the nesg has contributed more than 500 nmr structures to the 
 pdb over the past 12 years ( summarized at http://www.nesg.org/statistics.html ) , representing some 5% of the 10  000 
 nmr structures available in the pdb .
although most nesg structures have been solved by either 
 nmr or x - ray crystallography , as of december , 2011 the nesg consortium had solved 41 pairs of 
 protein structures for identical construct sequences using both x - ray crystallography and nmr 
 methods . these 3d structures of proteins with identical sequences , together with the raw nmr and 
 crystallography data available in the biomagresbank ( bmrb ) and protein data 
 bank ( pdb ) , are an extremely valuable composite data set available for 
 studies directed at understanding structural variations between solution and crystal states and 
 for new methods development . in this study
, we carried out a comprehensive and systematic study of both unrestrained and 
 restrained rosetta refinement for the nmr structures of 40 nesg nmr / x - ray structure pairs .
nesg 
 target gr4 was excluded from this study , since it s deposited nmr structure is a single 
 model and our protocol requires the input nmr structure as an ensemble of multiple models . for a 
 subset of these pairs
, we also assessed the value of the restrained cs - rosetta 
 method carried out starting from extended conformations .
the accuracy of ( i ) 
 previously deposited pdb nmr structures , which were mostly refined using cns with explicit 
 solvent , ( ii ) unrestrained rosetta refined structures , ( iii ) restrained rosetta refined 
 structures , and ( iv ) restrained cs - rosetta structures generated with nmr restraints starting 
 from extended conformations , were assessed by various structural validation metrics , including 
 restraint violation analysis , comparison against unassigned noesy peak list data , convergence 
 based on ensemble rmsd calculation , and various knowledge - based stereochemical and packing 
 statistics .
the rosetta refined structures were further assessed based on their structural 
 similarity with corresponding x - ray crystal structures and by analysis of how useful they are as 
 molecular replacement ( mr ) templates for solving the corresponding x - ray crystal structure .
this 
 comprehensive study demonstrates the significant value of restrained rosetta refinement of 
 protein nmr structures , and provides efficient standard protocols for restrained rosetta 
 refinement that will be broadly useful to the protein nmr community .
experimental data for this study were obtained by the nesg consortium for 40 proteins or 
 protein domains solved by both solution nmr and x - ray crystallography and deposited in the pdb 
 as of december 31 , 2011 .
the structures range in size from 5 to 22 kda and include 7 
 homodimers .
most of these nmr structures were refined using a standard nesg refinement protocol 
 involving initial structure generation with cyana followed by structure refinement with cns in explicit water 
 solvent , as described in detail at http://www.nmr2.buffalo.edu / nesg.wiki/. 
 the coordinate files of both nmr structures and x - ray crystal structures were downloaded from 
 the pdb database , along with the nmr restraint and x - ray structure factor files .
structure 
 factor files , downloaded in mmcif format , were converted to mtz format using the ccp4 program 
 cif2mtz ( collaborative computational project , number 4 , 1994 ) .
these protein data sets , 
 together with citations to the corresponding pdb files , are summarized in supplementary table s1 .
another ccp4 program uniquefy was used to 
 standardize the mtz files and select reflections for free r calculation .
the 
 nmr restraints files are either in cyana format or in xplor / cns format .
the extensive 
 experimental data for the 40 nmr and x - ray structures have been organized in a single publicly 
 available database ( http://psvs-1_4-dev.nesg.org / results / rosetta_mr / dataset.html ) .
this compilation of nmr 
 and crystallographic data , which was done as part of this study , will be valuable for future 
 methods development projects .
the robetta 
 fragment server was 
 used to generate a fragment library , based on the target protein sequence ( excluding chemical 
 shift data ) .
although this process could be done using chemical shift data in the fragment 
 selection , for the refinement protocols developed in this work , chemical shift data were not 
 used in the fragment generation for the rosetta refinement calculations .
tests using 
 chemical - shift - based fragment selection demonstrated no significant improvement in the 
 refinement protocol , although there is no a priori reason not to use chemical 
 shift data in the fragment selection for restrained rosetta refinement .
for each target protein , fragments from the target protein itself were eliminated from the 
 fragment library .
loop regions were then defined by the consensus of ( i ) secondary structure , 
 ( ii )   not - well - defined residues identified by the psvs server 
 based on dihedral angle order parameter values , and ( iii ) noncore residues determined by findcore . for these regions ,
loop rebuilding was done together with all - atom refinement of 
 the entire structure using the loopmodeling application of rosetta version 3.3 , based on cyclic 
 coordinate descent ( ccd ) and kinematic closure ( kic ) .
fastrelax mode was used to allow the 
 whole structure to relax in rosetta all - atom force field .
the process was used to sample side 
 chain conformations of the well - defined regions and both backbone and side chain conformations 
 of the loop and not - well - defined regions .
the fast relax modes work by running many side chain 
 repack and minimization cycles to locate a low - energy state for the input model .
the structural 
 divergence of the starting model to the relaxed model is determined by the resulting energy 
 gap .
the structure can change up to 23  from the starting conformation during the 
 minimization cycles . for restrained rosetta refinement ,
rosetta formatted distance restraints and dihedral angle 
 restraints were generated using the pdbstat restraint converter software 
 and were merged into a single restraint file . although dihedrals are restrained by 
 rosetta s energy terms , where chemical shift data provide reliable dihedral restraint 
 data using talos+ , these dihedral restraints were retained in the 
 refinement process .
these distance restraints were used in restrained rosetta refinement with 
 an upper - bound tolerance of 0.3  , to allow the structure to better relax energetically in 
 the rosetta force field . details of the restraint violation penalty functions are provided in 
 the supporting information . for each individual conformer of the nmr 
 structure ensemble ,
the restrained rosetta refinement was used to generate 10 decoys , and the 
 one with lowest rosetta energy was selected as the final rosetta refined model for this 
 specific conformer . for homodimeric nmr structures , a symmetry definition file , restraining the 
 structures of protomers to be identical ,
is generated by rosetta and used to guide rosetta 
 refinement , as outlined in supporting information .
the other steps 
 in the restrained rosetta refinement were exactly the same as those outlined above for 
 unrestrained rosetta refinement .
sophisticated methods could be used to define the relative weight , w , 
 between knowledge - based rosetta energy terms and experimental restraint terms . in this study , 

the rational was that at this value of 
 w , plots of total energy ( rosetta energy + restraint energy ) vs 
 w exhibit a minimum ( as shown in supplementary table s3 
 and figure s5 ) . a detailed protocol for restrained cs - rosetta ( rcs - rosetta ) calculations , starting from 
 extended conformations , is also included as supporting information . 

chemical shift information is used in rosetta fragment picking by mfr method using the updated fragment library .
then , a total of 10  000 decoys were generated using the 
 abinitiorelax application of rosetta 3.3 with the nmr restraints . for 9 targets in 1022 
 kda range ,
20  000 decoys were generated for each target instead of 10  000 decoys . 

chemical shift rescores were then calculated for the 1000 lowest rosetta energy decoys , and the 
 20 lowest rescore decoys are selected as the final rcs - rosetta model .
gdt.ts stands for global distance test total score , which measures the 3d similarity of two 
 structures with identical amino acid sequences .
the global distance test 
 performs many different sequence - independent superpositions of the model and the  gold 
 standard  structure and calculates the percentage of structurally equivalent pairs of 
 c atoms that are within specified distance cutoffs d. the gdt.ts score 
 is the arithmetic mean of four scores obtained with distance cutoffs of d = 1 , 
 2 , 4 , and 8  .
the protein structure validation software suite ( psvs ) ( http://psvs.nesg.org/ ) was used for structure quality 
 assessment analysis .
psvs provides z scores for a variety of widely adopted 
 structural quality measures , such as procheck g factor , 
 molprobity clash score 
 and other structure quality assessment metrics .
the procheck all dihedral angle 
 g factor is determined by the stereochemical quality of both backbone and 
 side - chain dihedral angles of proteins , and the molprobity clash score is calculated by the 
 program probe is a measure to reflect the number of high - energy contacts in a 
 structure .
structure quality assessments also include ensemble rmsd analysis , restraint 
 violations , ( 46 ) and rpf - dp statistics .
z scores are computed relative to a 
 set of 252 high - resolution x - ray structures and normalized so that more positive 
 z scores corresponding to better structure quality scores .
( 21 ) to evaluate structural similarity between nmr structure models and their x - ray counterparts , 
 we utilized the programs findcore and pdbstat v5.9 to 
 calculate the rmsd of backbone atom and/or all heavy atom positions , for both well - defined 
 residues and for all residues ( including those that are ill - defined in the pdb nmr structures ) . 

we also used the tm - score program to calculate the gdt.ts global superimposition scores .
to further determine rmsd for specific subset of 
 atoms , such as side chain atoms of -helix residues , we used pymol 
 to superimpose nmr structures with reference x - ray crystal structures , then calculated average 
 rmsd based on the structural superimposition .
the same procedures were performed to evaluate 
 structural similarity between rosetta refined structures and the corresponding x - ray crystal 
 structures .
well - ordered residues are defined by dihedral angle order parameters 
 with s( ) + s( )  1.8 units , and 
 
core atoms were calculated using the findcore program 
 based on interatomic distance variance matrices .
the dssp program was utilized for annotating secondary 
 structure elements , and solvent accessible areas of atoms were calculated by areaimol program 
 in ccp4 package .
the program phaser ( version 2.1 ) was used for estimating diffraction 
 phases by molecular replacement .
the 
 programs arp / warp 
 version 7.0 and/or phenix.autobuild were used for automatic model 
 building , based on the phaser mr solution .
the arp / warp expert system mode was employed for 
 automatic model building , and refmac5 was used in refinement , staring from 
 the positioned search model , and a maximum of 10 building cycles were allowed .
forty nesg nmr structures which have corresponding x - ray crystal structures were downloaded 
 from the pdb and refined using unrestrained and restrained rosetta protocols , as outlined in 
 supporting information .
more comprehensive structure quality statistics for these 
 structures are available on line at http://psvs-1_4-dev.nesg.org / results / rosetta_mr / rosettamr_psvs_summary.html .
we assessed distance restraint and dihedral angle restraint violations for the 40 protein nmr 
 structures downloaded from the pdb and for the corresponding unrestrained and restrained 
 rosetta refined structures .
restraint violations were assessed using the standardized methods 
 of the pdbstat program , against the original distance and dihedral 
 restraint lists ( i.e. , not accounting for the 0.3  upper - bound tolerance used in the 
 restrained rosetta calculations ) .
distance restraint violations were divided into three 
 categories based on the level of severity ; i.e. , distance restraint violations between 0.1 and 
 0.2  , between 0.2 and 0.5  , and higher than 0.5  .
dihedral angle restraint 
 violations were divided into two categories : between 1 and 10 and higher than 
 10. the mean and standard deviations of the number of restraint violations in each 
 category were calculated .
these restraint violation statistics for each nmr structure ensemble 
 are summarized in table s2 , and the average violations per conformer 
 of the 40 nmr structures assessed for each of the restraint violation categories and for each 
 of three methods are presented in table 1 .
these distributions of restraint 
 violations obtained for these three data sets are also illustrated graphically in figure 1 .
the number of restraint violations is significantly reduced by incorporating nmr restraints 
 into rosetta refinement .
restraint violations were assessed using pdbstat , 
 across the complete set of 40 nesg nmr structures used in this study .
( a ) boxplot of the 
 number of distance restraint violations between 0.1  and 0.2  .
( b ) boxplot of the 
 number of distance restraint violations between 0.2  and 0.5  .
( c ) boxplot of the 
 number of distance restraint violations larger than 0.5  .
( d ) boxplot of the number of 
 dihedral angle restraint violations between 1 deg and 10 deg .
( e ) boxplot of the number of 
 dihedral angle restraint violations larger than 10 deg .
knowledge - based statistics 
 were calculated using the programs verify3d , prosaii , procheck , and molprobity , normalized to z = 0 
 for a set of 252 high - resolution x - ray crystal structures .
structure quality scores were calculated for the nmr structures available from the pdb 
 ( pdb ) and for the unrestrained rosetta ( r3 ) and restrained rosetta ( r3rst ) structures . for 
 each statistic ,
the mean and standard deviation were computed across the 40 nmr structures 
 and are formatted as mean  sd .
computed following superimposition of atoms with well - defined atomic positions , as 
 determined by the dihedral angle order parameter method as implemented 
 in psvs .
bb_ord , backbone atoms ( n , c , c ) in well - ordered residues ; hvy_ord , 
 all heavy ( n , c , o , s ) atoms in well - ordered residues ; bb_all , backbone atoms of all 
 residues ; hvy_all , all heavy atoms in all residues .
rpf - dp scores were computed for 35 nmr structures for which noesy peak list data is 
 available , and provide a statistical assessment of the consistency of the 3d nmr structure 
 ensemble with the noesy peak list as provided by the rpf software . as expected , unrestrained rosetta refinement results in a significant number of restraint 
 violations , especially for the most severe violation categories . however , in restrained rosetta 
 refined structures the number and distribution of restraint violations per conformer is similar 
 to , though slightly higher than , those assessed for the nmr structure ensembles deposited in 
 the pdb ( table 1 and figure 1 ) . from this analysis
we 
 conclude that protocols for incorporating nmr restraints into rosetta refinement are effective 
 in generating rosetta refined nmr structures that satisfy the experimental distance and 
 dihedral angle restraint data as well as the structures deposited in the pdb that have been 
 refined by conventional methods .
the resolution of electron density maps and atomic b - factors reflect the 
 precision of x - ray crystal structures .
however , there are no such experimental observables to 
 define the precision of solution nmr structures .
usually , the rmsd of the ensemble of 
 superimposed nmr conformers is considered to be a useful measure of its overall precision , 
 although as discussed elsewhere this measure can be problematic if there are extensive 
 intramolecular dynamics .
we calculated the ensemble rmsd of pdb nmr 
 structures ( pdb ) , unrestrained rosetta refined structures ( r3 ) , and restrained rosetta refined 
 structures ( r3rst ) for each of the 40 protein nmr structure ensembles in our data set .
four 
 categories of rmsd were calculated : ( i ) backbone rmsd of well - defined residues , defined by 
 dihedral angle order parameters , ( ii ) backbone rmsd of all residues , ( iii ) heavy atom rmsd of 
 well - defined residues , defined by dihedral angle order parameters , and ( iv ) heavy atom rmsd of 
 all residues .
the mean and standard deviations of rmsds for backbone and for all heavy atoms in 
 these well - defined residues are listed in table 1 , and the values for each of 
 the 40 ensembles generated by each of the three protocols are plotted in supplementary figure s1 .
the rmsd s of unrestrained rosetta - refined structures 
 are higher than pdb nmr structures in all four categories , for both backbone atom and all - heavy 
 atom classes ( figure s1a 
d ) . ignoring experimental restraints 
 in rosetta refinement ( r3 ) generally increases structural uncertainty for all the backbone and 
 side chain atoms of all residues .
for restrained rosetta refined structures ( r3rst ) , in 
 well - defined regions the average rmsd of backbone atoms is comparable with pdb nmr structures 
 ( figure s1a ) , and the average rmsd of all heavy atoms is about 10% 
 lower than pdb nmr structures ( supplementary figure s1c ) . for most 
 targets restrained rosetta refined structures
have lower ensemble rmsds in well - defined regions 
 for all heavy atoms ( including both backbone and side chain atoms ) than pdb nmr structures . 

these results demonstrate that restrained rosetta refinement has the potential to improve the 
 precision of side - chain atoms . on the other hand ,
the average ensemble rmsd statistics for all residues ( including atoms 
 that are not well - defined in the original pdb nmr ensembles ) , for both unrestrained and 
 restrained rosetta refined structures , are higher than for the corresponding pdb nmr structures 
 ( supplementary figure s1b , d ) .
this demonstrates that when 
 restraints are included , the loop rebuilding process implemented in our rosetta refinement 
 protocol does a better job of sampling the wide range of conformations which are consistent 
 with the experimental data .
rpf - dp is a metric 
 used to evaluate how well a protein nmr model fits the experimental unassigned noesy peak list 
 and resonance assignment data .
the program calculates recall , precision , and dp scores of the 
 match between short distances in the model and all possible noesy crosspeak assignments .
recall 
 is defined as the percentage of peaks in the noesy peak list that are consistent with the 
 interproton distances of the 3d structures .
precision is defined as the percentage of close 
 distances ( general set at < 5  ) between proton pairs in the query structures whose back 
 calculated noe cross peaks are also actually detected in nmr experiments .
the dp score is a 
 normalized f - score calculated from the recall and precision to measure the 
 overall fit between the query structure and the experimental data , with a freely rotating chain 
 model and the quality of the noesy data set defining the lower and upper bounds , respectively , 
 of the f - measure .
noesy peak list data are available for 35 of the 40 protein nmr / x - ray structure pairs used in 
 this study .
the mean and standard deviations of recall , precision , and dp score are listed 
 table 1 , and boxplots of recall , precision , and dp score are shown in figure 
 2 .
unrestrained rosetta refined structures generally have precision similar 
 to pdb nmr structures but lower recall and dp scores , i.e. , in general , the unrestrained 
 rosetta refined structure does not fit the noesy peak list data as well at the pdb nmr 
 structures . on the other hand ,
restrained rosetta refined structures have recall , precision , 
 and dp scores that are essential identical to those of the pdb nmr structures ( table 1 and figure 2a  c ) .
while the majority of the nmr structures generated by 
 unrestrained rosetta refinement ( r3 ) have dp scores lower than the pdb nmr structures , most 
 structures refined by the restrained rosetta protocol ( r3rst ) have dp scores similar to pdb nmr 
 structures ( figure 2c , d ) . in a few cases ,
the restrained rosetta refined nmr 
 structures have significantly better dp scores compared with the corresponding pdb nmr 
 structure ( figure 2d ) .
rosetta - refined structures have rpf - dp scores , comparing the structure against the 
 unassigned noesy peak list , similar to those of structures deposited in the pdb .
( a ) boxplots 
 of recall scores for structures deposited in the pdb or refined with rosetta protocols .
( b ) 
 boxplots of precision scores for structures deposited in the pdb or refined with rosetta 
 protocols .
( c ) boxplots of dp- scores for structures deposited in the pdb or refined with 
 rosetta protocols .
dp - scores of the pdb nmr structures are plotted 
 on the x - axis , while the dp - scores of both the unrestrained rosetta refined structures 
 represented by red solid triangle symbols ( r3 ) and restrained rosetta refined structures 
 represented by blue solid rectangle symbols ( r3rst ) are plotted on the y - axis .
the black 
 dashed line indicates y = x. data are presented for 35 nmr structures for which noesy peak 
 list data are available .
as no distance restraints are enforced during the unrestrained rosetta refinement process , 
 the refined structures do not satisfy distance restraints as well as the pdb nmr structures . 

they also do not fit as well to the unassigned noesy peak lists data because the distance 
 restraints are directly derived from noesy peak lists . on the other hand , when distance 
 restraints are incorporated into rosetta refinement
, the refined structures generally fit the 
 noesy peak list data as well or better than the pdb nmr structures that have been refined by 
 conventional methods .
we used psvs to calculate a variety of knowledge - based structural quality z 
 scores , including verify3d , prosa , procheck backbone g factor ( procheck_bb ) , 
 procheck all dihedral angle g factor ( procheck_all ) , and molprobity clash 
 scores .
these scores are normalized so that more positive z scores correspond 
 to better values of these knowledge - based metrics .
the mean and standard deviation of those 
 z scores for the 40 nmr structures generated by the three methods ( nmr pdb , 
 unrestrained rosetta , and restrained rosetta ) are summarized in table 1 .
both 
 unrestrained and restrained rosetta refined structures have better ( i.e. , more positive ) 
 z scores for all the five measures , especially for procheck all dihedral 
 angle g factor and molprobity clash score z scores
. boxplots 
 of procheck_bb , procheck_all , molprobity clash score z scores for these nmr 
 pdb and unrestrained and restrained rosetta refined structures are shown in figure 3a , c , e .
rosetta refined structures consistently have improved procheck_bb , 
 procheck_all , and molprobity clash score z scores .
( a ) 
 boxplot of procheck backbone dihedral angle g - factor z - scores for 
 structures refined with different protocols .
( b ) scatterplot of procheck 
 backbone dihedral angle g - factor z - scores .
( c ) boxplot of procheck all 
 dihedral angle g - factor z - scores for structures refined with different protocols .
( d ) 
 scatterplot of procheck all dihedral angle g - factor z - scores .
( e ) 
 boxplot of molprobity clashscore z - scores for structures refined with different protocols .
( f ) scatterplot 
 of molprobity clashscore z - scores . in the scatter plots ( b ) , ( d ) and ( f ) , the z - scores of 
 unrestrained rosetta refined structures ( r3 ) are plotted on the x - axis , while the z - scores of 
 restrained rosetta refined structures ( r3rst ) are plotted on the y - axis . in order to further investigate the effect of incorporating experimental restraints into 
 rosetta refinement on these knowledge - based z scores , we also made 2d scatter 
 plots of procheck_bb , procheck_all , and molprobity clash score z scores 
 comparing unrestrained and restrained rosetta refined structures . in figure 3b , d ,
f the z scores of unrestrained ( r3 ) and restrained rosetta refined 
 structures ( r3rst ) are plotted on x- and y - axes respectively . 

the procheck_bb z scores of restrained rosetta refined structures are 
 consistently better than unrestrained rosetta refined structures ( figure 3a , b ) .
this is attributable to the fact that the experimental dihedral angle restraints and 
 local noe data are very helpful in guiding rosetta to generate decoys with more accurate 
 backbone stereochemical quality .
procheck_all z scores , which include side 
 chain dihedrals , are also marginally improved for the restrained rosetta refined structures 
 ( figure 3c , d ) . on the contrary , the molprobity clash score z 
 scores of unrestrained rosetta refined structures are generally better than restrained rosetta 
 refined structures ( figure 3f ) .
however , while the unrestrained rosetta refined 
 structures have fewer molprobity clashes , they are less converged and sometimes underpacked 
 relative to restrained rosetta refined structures .
overall , these data demonstrate that stereochemical quality and geometry of pdb nmr 
 structures can be significantly improved by rosetta refinement carried out with or without 
 restraints .
however , the restrained rosetta refinement protocol provides structures that have 
 both improved z scores ( figure 3 ) and simultaneously fit well 
 to both the experimental distance restraints ( figure 1 ) and the unassigned 
 noesy peak list data ( figure 2 ) . theoretically , solution nmr structures need not necessarily be identical to x - ray crystal 
 structures , which are determined in a crystalline environment .
in addition , these crystal 
 structures were determined with cryoprotection at 77 k , while the nmr structures were 
 determined in solution at 300 k. in particular , crystal packing effects may stabilize 
 conformers that do not predominate in solution . however , since x - ray structures are highly 
 hydrated , with relatively few intermolecular contacts , one might expect that such effects are 
 the exception rather than the rule and that the dominant structure in solution characterized by 
 nmr should generally be very similar to the x - ray crystal structure that is obtained for the 
 same protein construct .
this conclusion is supported by comparisons of protein structures in 
 different crystal forms , which generally agree within an rmsd of < 0.5 
  .
based on 
 these considerations , and assuming the x - ray structure to be a accurate representation of the 
 predominant solution structure , we also assessed whether or not rosetta refinement , with or 
 without experimental restraints , moves the pdb nmr structures closer to their x - ray 
 counterparts . for this assessment , we calculated the gdt.ts between ( i ) pdb nmr structures , ( ii ) 
 unrestrained rosetta refined structures , and ( iii ) restrained rosetta refined structures , with 
 their corresponding x - ray structures .
nesg target drr147d was left out of this analysis because 
 its solution nmr structure is a monomer solved at ph 4.5 , while its x - ray structure is a dimer 
 solved at ph 6.0 , and nmr studies demonstrate a significant structural change over this ph 
 range ( data not shown ) . these results for the remaining 39 nesg
nmr / x - ray pairs are summarized 
 in a gdt.ts scatterplot ( figure 4 ) , with the gdt.ts of pdb nmr structures 
 relative to the corresponding x - ray crystal structure on the x - axis and gdt.ts 
 of the unrestrained or restrained rosetta refined structures on the y - axis . 
 based on observations of previous studies done with a much small number ( i.e. , 1 or 2 ) of protein targets , 
 we expected unrestrained rosetta refinement would generally move nmr structures closer to their 
 x - ray counterparts . however , as illustrated in figure 4 , using this larger 
 data set of 39 nmr / x - ray pairs
after unrestrained 
 rosetta refinement ( r3 ) , only 17 of 39 targets exhibit higher gdt.ts values , 6 targets remain 
 about the same , and 16 of the protein ensembles have lower gdt.ts values than the nmr 
 structures refined by conventional methods and deposited in the pdb . on average ,
unrestrained 
 rosetta refinement improved the gdt.ts by only 0.4% . on the other hand , as illustrated in 
 figure 4 , restrained rosetta refinement ( r3rst ) generally improved the gdt.ts 
 score to the x - ray crystal structure , compared with the nmr structure deposited in the pdb ; 32 
 of 39 targets have better gdt.ts values , 4 targets remain about the same , and only 3 targets 
 have slightly lower gdt.ts values . on average ,
restrained rosetta refinement improved the 
 gdt.ts scores of the pdb nmr structures by 2.5% , with some increasing by as much as 10% .
restrained rosetta refined structures are more similar to their corresponding x - ray crystal 
 structures than pdb nmr structures .
gdt.ts values of pdb nmr structures to corresponding 
 x - ray structures are plotted on the x - axis , and gdt.ts values of both unrestrained rosetta 
 refined structures ( r3 , represented by red solid triangle ) and restrained rosetta refined 
 structures ( r3rst , represented by blue solid rectangles ) to their corresponding x - ray 
 structures are plotted on the y - axis .
the 
 two green dash lines indicate gdt.ts of pdb nmr structures equal to 0.7 and 0.85 
 respectively .
the black dash line indicates y = x , and the two gray dash lines indicate y = x 
 + 0.05 and y = x  0.05 respectively .
further analysis of the data of figure 4 indicates that when the similarity 
 between the conventionally - refined nmr structure and the corresponding x - ray crystal structure 
 is moderate ( 0.7  gdt.ts  0.85 ) , more often than not , rosetta refinement can 
 move nmr structures closer to their x - ray counterparts when the experimental restraints are 
 incorporated . however , in cases where the similarity between nmr and x - ray structures is 
 initially high ( gdt.ts > 0.85 ) , more often than not , unrestrained rosetta refinement moves 
 nmr structures further from their x - ray counterparts , while the improvement provided by 
 restrained rosetta refinement is less dramatic ( figure 4 ) .
we further investigated in these data how restrained rosetta refinement improves the 
 similarity between nmr and x - ray structures by rmsd calculations .
as illustrated in figure 
 5 ( top panel ) , restrained rosetta refinement consistently improved the 
 agreement between nmr and x - ray structures for both backbone and side chain atoms .
the lower 
 panel provides some comparisons between the mediod nmr conformer ( i.e. , the single conformer in 
 the nmr ensemble most like all the other members of the ensemble ) before and after restrained rosetta 
 refinement , and the corresponding x - ray crystal structure coordinates .
typically , improvements 
 in accuracy are the result of better packing between secondary structure elements .
often , this 
 improves the accuracy of interhelical orientations , as shown for example in figure 5 for nesg targets hr3646e and hr4435b . for dhr29b , in order to emphasize the 
 structural changes , only the last two c - terminal  strands are plotted . in this case , the 
 two - residue strand ( 7677 ) of the nmr structure deposited in the pdb is extended to six 
 residues long ( 7681 ) after restrained rosetta , which is more consistent with 
 corresponding x - ray crystal structure .
the agreement between nmr structures and their x - ray counterparts are generally improved 
 following restrained rosetta refinement .
top : plot of differences of rmsd to x - ray crystal 
 structures before and after restrained rosetta refinement .
the nesg nmr / x - ray pair target 
 index is plotted on the x - axis , and the differences between the rmsd of pdb nmr structures to 
 their corresponding x - ray structures and the rmsd of restrained rosetta refined structures to 
 their corresponding x - ray structures are plotted on the y - axis in units of ngstroms . 
 the four subpanels summarize data for well - defined ( lower half ) and not - well defined ( upper 
 half ) residues , and for backbone ( left ) and sidechain ( right ) atoms .
well - defined vs not 
 well - defined residues are defined by s(phi)+s(psi )  1.8 .
bottom : superimposition of x - ray , nmr and restrained rosetta refined 
 structures . left  hr3646e ; middle  hr4435b ; right  dhr29b .
the 
 structures are color coded as : magenta- x - ray crystal structure ; cyan  nmr structure 
 deposited in pdb ; blue  restrained rosetta refined structure . for dhr29b ,
only the 
 last two c - terminal beta strands are plotted . on average , the improvement of structural similarity to corresponding x - ray structure 
 resulting from restrained rosetta refinement is modest .
however , restrained rosetta refinement 
 drives some nmr structures significantly closer to their x - ray counterparts , as much as 0.45 
 and 0.55  rmsd , respectively , for backbone and side chain atoms in well - defined regions 
 ( figure 5 top ) .
specific atom positions change by as much as 13  
 ( as illustrated in some of the examples of superimposed structures shown in figure 5 bottom ) .
these changes may be biologically significant and can have significant 
 effects on the phasing power of the structure , as illustrated below . the fact that restrained rosetta refinement consistently improves the accuracy of nmr 
 structures relative to the corresponding x - ray crystal structure is a significant observation . 
 in order to explore this in more detail
, we compared the rmsd between either refined nmr or 
 deposited nmr structures relative to x - ray crystal structures for several different classes of 
 atoms . these included ( i ) atoms in well - defined residues ( defined by dihedral angle order 
 parameters ) , ( ii ) well - defined core atom sets calculated by findcore program , ( iii ) atoms in 
 buried residues , and ( iv ) atoms in regular secondary structure elements .
comparisons were made 
 for both unrestrained rosetta refinements ( summarized in supplementary 
 figure s2 ) and for restrained rosetta refinements ( summarized in supplementary figure s3 ) .
more often than not , restrained rosetta refinement also 
 improved the agreement between nmr structures and x - ray structures for ( i ) not - well - defined 
 regions , ( ii ) noncore residues , ( iii ) surface residues , and ( iv ) loop regions as well as for 
 well - defined backbone and side - chain atoms . for classes of atoms in regions of the structure 

that are not - well - defined ( i.e. , less well converged ) in the nmr ensemble , the improvement is 
 often quite substantial , as illustrated in the top half of figure 5 for some 
 structures the accuracy relative to the corresponding crystal structure improves by 
 1.02.5  rmsd in loop regions .
this reflects the ability of rosetta to accurately 
 model regions of the protein structure , such as surface loops , that are under - restrained by the 
 experimental nmr data .
molecular replacement ( mr ) is widely used for addressing the phase problem in x - ray 
 crystallography . historically , the common notion in the structural biology community is that 
 the quality of nmr structure is often not good enough for mr , even when the sequence of the 
 search model is identical to the target x - ray structure . however , as demonstrated by a recent 
 study with 25 nesg nmr / x - ray pairs , protein nmr structures prepared by 
 excluding not - well - defined atom positions using an interatomic variance matrix - based protocol 
 can generally be used successfully as mr templates .
additionally , the phasing power of nmr 
 structures that failed to provide good mr solutions was observed to be improved by unrestrained 
 rosetta refinement in two cases . using the extensive set of nmr / x - ray pairs ,
we critically 
 assessed this hypothesis by comparing the phasing powers of the conventionally - refined pdb nmr 
 structures with those of unrestrained and restrained rosetta refined structures .
we prepared the mr starting models for pdb nmr structures , unrestrained rosetta refined 
 structures , and restrained rosetta refined structures by first eliminating not - well - defined 
 atoms using the  findcore protocol .
two targets ( drr147d , er382a ) were excluded in this study due to the 
 following facts : the nmr structure of target er382a ( pdb i d : 2jn0 ) was solved as a monomer without a ligand , whereas its crystal 
 structure counterpart ( pdb i d : 3fif ) has 
 eight subunits in the asymmetric unit and was solved in complex with a heptapeptide ligand and 
 appears to have a distinct structure , i.e. , the c rmsd between the nmr structure and 
 chain a of the crystal structure is 2.44  .
as mentioned above , the nmr structure of 
 target drr147d ( pdb i d : 2kcz ) is a 
 monomer solved at ph 4.5 , while its crystal structure counterpart ( pdb i d : 3ggn ) is a dimer solved at ph 6.0 , with 
 significant structural changes in backbone structure due to ph - induced dissociation of the 
 dimer . the remaining 38 nmr / x - ray pairs were used to assess the impact of restrained rosetta 
 refinement on the mr phasing power of the nmr ensemble . for the initial rosetta refinement protocol , the decoys are picked solely based on rosetta 
 energy , that is , we picked the top 20 decoys with the lowest rosetta energy from the entire 
 pool of decoys generated from all the conformers in nmr structure ensemble .
it was observed , 
 however , that frequently those 20 decoys originated from the same one or two similar conformers 
 in the unrefined nmr ensemble ; thus the structural variance information within the nmr ensemble 
 is lost using this simple decoy picking process . in order to preserve the conformational 
 variability information within the nmr ensemble
, we adopted a protocol in which the one 
 lowest - energy rosetta decoy was selected from the ensemble of decoys generated from each nmr 
 conformer .
as shown in figure 6a , b , the resulting rosetta ensembles are much 
 better mr templates and also fit the noesy peak list data better than the rosetta ensembles 
 generated by our initial protocol , as manifested by the significantly improved tfz and dp 
 scores for the majority of the targets . these ensembles of rosetta refined ( with or without 
 restraints ) conformers were then trimmed to exclude not - well - defined atoms using findcore and 
 used as templates for phaser as described previously . for rosetta refinement of nmr structure , preserving ensemble information is beneficial for 
 mr success .
scatterplot of phaser tfz scores ( a ) and 
 dp - scores ( b ) for 
 two different protocols for selecting models for mr .
decoy(energy ) rosetta - refined structure 
 ensembles are composed of the 20 lowest rosetta energy decoys from the entire pool of decoys 
 generated from all the nmr conformers .
decoy(conformer+energy ) rosetta - refined structure 
 ensembles are composed of each lowest rosetta energy decoy generated from each nmr conformer . 

the scores of structures picked by decoy(energy ) protocol are plotted on the x - axis , and the 
 scores of structures picked by decoy(conformer+energy ) protocol are plotted on the y - axis . 

unrestrained rosetta refined structures are represented by red solid triangles and restrained 
 rosetta refined structures are represented by blue solid rectangles .
data are summarized for 
 38 nesg nmr / xray pairs used in the crystallographic mr study . starting from phaser mr solutions obtained by three methods [ nmr pdb , unrestrained rosetta 
 refinement ( r3 ) , and restrained rosetta refinement ( r3rst ) ] for 38 nmr structures , we utilized 
 phenix and arp / warp for automatic model rebuilding and refinement .
models generated by either 
 software with the lowest rfree values were chosen as the final 
 structures solved by mr . hence 114 crystal structures were determined from the nmr structures 
 and compared with the corresponding x - ray crystal structure available in the pdb . for each 
 target ,
the rfree values of the final mr structures are plotted 
 against the sources of their templates in figure 7 .
structures generated using 
 the ensembles of pdb nmr structures , unrestrained rosetta refined structures , and restrained 
 rosetta refined structures are represented by black , red , and green dots , respectively .
the 
 green dashed line indicates rfree = 0.3 , and the red dashed line 
 indicates rfree = 0.45 .
data points above the red dashed line 
 ( rfree > 0.45 ) are considered as failed mr solutions .
starting 
 from nmr structures deposited in the pdb as mr templates , seven targets ( zr18 , sgr145 , rpr324 , 
 str65 , spr104 , sr478 , hr4435b ) failed to provide valid mr solutions .
four of these ( rpr324 , 
 str65 , sr478 , hr4435b ) provided good mr solutions after rosetta refinement with or without 
 experimental restraints .
one target ( zr18 ) provided a good mr solution and another target 
 ( spr104 ) a borderline acceptable mr solution ( gdt.ts between mr structure and x - ray structure 
 is 0.875 ) only after restrained rosetta refinement .
two targets ( hr41 , srr115c ) , which 
 originally provided valid mr solutions when using their pdb nmr structures as mr templates , 
 failed to provide valid mr solutions after unrestrained rosetta refinement but could be solved 
 after restrained rosetta refinement .
only one target ( sgr145 ) failed to provide good mr 
 solutions with any of the protocols , even after restrained rosetta refinement .
sgr145 is a 
 sparse - restraint nmr structure , and its c rmsd to the corresponding 
 x - ray structure is relatively large ( 3.1  ) .  
restrained rosetta refined nmr structures provide better templates for mr , and generally 
 yield crystal structures with better rfree scores .
dotplot of rfree 
 values of mr structures using mr templates for 38 nesg nmr / x - ray pairs deposited in the pdb 
 or refined by rosetta .
pdb nmr structures ( pdb ) , unrestrained 
 rosetta refined structures ( r3 ) and restrained rosetta refined structures ( r3rst ) are colored 
 black , red and green respectively .
each subpanel represents one nesg target , and the 
 subpanels are organized in ascending order of the resolution of its x - ray crystal structure 
 from bottom left corner to top right corner .
the same conclusion can be drawn from figure s4 , comparing the 
 gdt.ts of the x - ray crystal structure models phased using the pdb nmr structures or rosetta 
 refined structures as mr templates , and autotraced , compared to the corresponding x - ray crystal 
 structures deposited in the pdb .
most of these crystal structures deposited in the pdb were 
 solved by anomalous dispersion ( sad or mad ) methods .
these data further demonstrate that when 
 the nmr structures available from the pdb are poor mr templates to start with , with gdt.ts 
 < 0.8 , their phasing power and the quality of the resulting crystal structure solution were 
 generally significantly improved by restrained rosetta refinement . as is also illustrated in figure 7 for targets srr115c , psr293 , and hr41 , if 
 the initial nmr structures are good mr templates , their phasing power can potentially 
 deteriorate by unrestrained rosetta refinement . therefore , despite the fact that unrestrained 
 rosetta refinement has been reported to sometimes improve the phasing power of nmr 
 structures , ignoring 
 the experimental restraints is not recommended when preparing nmr structures for use in phasing 
 crystallographic data by molecular replacement . for thirteen nmr structures with gdt.ts
< 0.85 relative to their x - ray counterparts , we 
 also carried out restrained cs - rosetta ( rcs - rosetta ) calculations , starting from 
 extended conformations , using the same restraints used in the corresponding restrained rosetta 
 refinement calculations .
rcs - rosetta calculations are much more cpu intensive than the 
 restrained rosetta refinement protocol outlined above , requiring 45 times more cpu time 
 for proteins in the size range of 510 kda and exponentially longer times for larger 
 proteins . these results are summarized in table 2 . for proteins
< 10 kda , 
 the restrained cs - rosetta structures ( cs - rrst ) were slightly closer to the x - ray structure than 
 the corresponding restrained rosetta refined structures ( r3rst ) , especially for targets er382a 
 and zr18 .
on the other hand , for proteins in the 10  22 kda range , the faster r3rst 
 restrained rosetta refinement protocol provides structures with accuracy , relative to their 
 x - ray counterparts , similar to the computationally - intensive cs - rrst protocol .
indeed , for the 
 19 kda target hr41 , the faster r3rst protocol provided a more accurate structure than the 
 restrained cs - rosetta protocol .
these results demonstrate that the two restrained rosetta 
 protocols described in this work , r3rst which refines a structure initially modeled with other 
 methods and cs - rst which generates a structure starting from an extended conformation , are well 
 suited for small to medium sized proteins , of up to about 25 kda .
while restrained cs - rosetta 
 ( cs - rst ) can provide slightly more accurate structures , the improvements relative to the 
 restrained cs - rosetta ( r3rst ) results are often marginal relative to the much longer cpu times 
 required .
number of residues , excluding short disordered purification tags . molecular weight ( kda ) .
the quality of solution nmr structures is mainly determined by two factors : the accuracy and 
 completeness of experimental data and the algorithm and energy force field used in structure 
 calculation and refinement . in the past few years
, several papers have demonstrated that 
 unrestrained rosetta refinement can improve the stereochemical quality of nmr structures and 
 move nmr structures closer to x - ray crystal structures .
these observations may be explained by an interesting 
 hypothesis : once the protein conformation has been placed in a near - native structure using 
 experimental restraints , energy minimization by all - atom relaxation in the rosetta energy field 
 without restraints can produce a more accurate structure than is obtained using the restraints . 
 in this interpretation ,
the small errors in the nmr experimental restraints , which are in 
 conflict with the x - ray structure , can be circumvented or corrected using the unrestrained 
 energy force field . in this study
, we tested this hypothesis in a large - scale investigation of 
 the impact of rosetta refinement on nmr structure accuracy , and the significance of experimental 
 restraints in rosetta refinement .
this analysis has allowed us to design a protocol for using 
 rosetta to improve the quality of protein nmr structures with tractable computational cpu 
 requirements . as would be expected , restrained rosetta refinement of nmr structures
produces models with 
 much fewer restraint violations than models generated by unrestrained rosetta refinement .
this 
 result is significant in that it demonstrates that our restrained rosetta refinement protocol 
 is self - consistent with respect to a large number of experimental restraints , validating the 
 accurate implementation of restraint conversions by pdbstat software and interpretations of 
 these restraints by the rosetta program .
we observed that if the relative weights on restraints are too high , 
 the final rosetta refined models are over restrained and often end up with poor rosetta 
 energies . on the other hand ,
if the weights of restraints are too low , the final rosetta 
 refined models exhibit a large number of restraint violations , and the restraint information is 
 not fully utilized . an important concern in assessing nmr method development regards which structure to used as 
 the  gold standard  of accuracy .
although the natural choice is the corresponding 
 x - ray crystal structure , this issue has been controversial insofar as the crystal structure may 
 be influenced by the structural and energetic requirements of intermolecular packing .
for 
 example , the crystal lattice may select for one of multiple conformational states of the 
 protein structure .
moreover , protein x - ray crystal structures are often determined using 
 cryoprotected crystals at 77 k , while nmr structures are generally determined at 
 2040 c .
none the less , as we have demonstrated elsewhere , 
 except under special circumstances , the solution nmr structure is generally quite similar to 
 the crystal structure and can be used for phasing by molecular replacement methods .
hence , we 
 contend that the crystal structure is an excellent proxy for nmr structure accuracy .
the 
 availability of these 40 nmr / x - ray pairs together with extensive raw experimental nmr and 
 diffraction data ( summarized in supplemental tables s1 and s2 ) will 
 greatly facilitate the testing and development of new methods for protein nmr structure 
 refinement and analyses of subtle structural differences between crystal and solution nmr 
 structures . judged by ensemble rmsd analysis , unrestrained rosetta refinement generally decreases the 
 precision of nmr structures , while restrained rosetta refinement can increase the precision of 
 the side chain heavy atoms of otherwise well - defined residues . additionally , restrained rosetta 
 refined structures fit the unassigned noesy peak list data significantly better than 
 unrestrained rosetta refined structures .
rosetta refinement can generally improve the 
 stereochemical quality and geometry of nmr structures . more specifically ,
the experimental 
 backbone dihedral angle restraints can guide rosetta to generate models with even better 
 backbone structures than is achieved without restraints . in most cases ,
restrained rosetta 
 refinement will move protein nmr structures closer to their x - ray counterparts , while 
 unrestrained rosetta refinement often fails to do so , especially when the structural similarity 
 between the nmr and x - ray structures is high ( gdt.ts > 0.85 ) . for nmr structures with poor 
 phasing power , rosetta refinement
can often be used to generate mr templates which are better 
 able to guide phasing software , such as phaser , to identify correct mr solutions .
the phasing 
 power of the template and the accuracy of the resulting crystal structures are better when 
 experimental restraints are utilized in rosetta refinement . indeed
, unrestrained rosetta 
 refinement can sometimes make nmr structures less useful mr templates , even when they are good 
 mr templates to start with .
with respect to our hypothesis regarding final - stage unrestrained rosetta refinement 
 providing more accurate structures than can be achieved using all of the experimental 
 restraints , this comprehensive study with 40 nmr / x - ray pairs demonstrates that the majority of 
 nmr experimental restraints are completely consistent with the corresponding x - ray structures . 
 while in some cases , a few inaccurate restraints may be identified using an unrestrained 
 rosetta refinement protocol as proposed by ramelot et al .
, the most 
 accurate structures , with the highest phasing power , were obtained by combining the 
 experimental restraints with the sophisticated algorithms and the more advanced force field of 
 rosetta .
we also computed rosetta energies of  relaxed x - ray  and  relaxed 
 nmr  structures .
the structures are first idealized using rosetta idealization 
 application and then are relaxed in rosetta all - atom energy field .
the relaxed x - ray structures 
 generally have lower rosetta energy per residue , while the relaxed nmr structures , the 
 r3-refined nmr structures , and the r3rst - refined nmr structures generally have slightly higher , 
 similar rosetta energies .
this suggests that even our r3rst - refined nmr structures have some 
 room for improvement in terms of their energies . while they are more accurate relative to the corresponding x - ray crystal structure and 
 generally satisfy the experimental restraint data , restrained rosetta refined structures have 
 modestly more small distance restraint violations than the nmr structures from which they are 
 derived . as discussed in detail elsewhere
, these small restraint 
 violations associated with rosetta refined nmr structures may reflect inaccuracies in the 
 interpretation of upper - bound distance restraints from noesy data due various effects , 
 including relaxation - modulation of noe intensities in heteronuclear filtered noesy data and the 
 effects of dynamic averaging .
it is generally not possible to satisfy all of the experimental restraints in a r3rst 
 refinement .
this is evidenced first from the fact that the lowest - energy rosetta structures 
 generated in this study [ i.e. , the unrestrained rosetta refined ( r3 ) structures ] have poorer 
 agreement with the noesy peak list data ( i.e. , lower dp scores summarized in figure 2 ) than restrained rosetta refined ( r3rst ) structures .
the r3 structures also often 
 diverge from the x - ray structures ( figure 4 ) , our best proxy for a 
  gold standard. the inconsistency between the noe - derived distance restraints 
 and rosetta energy terms is also illustrated in analyses presented in supplementary figure s5 and table s3 ; increasing the relative weight on restraint 
 terms allows excellent satisfaction of restraints but results in structures with higher rosetta 
 conformational energies .
accordingly , there is some fundamental inconsistency between our 
 minimum rosetta energy structures , the noesy peak list data , the nmr restraints , and the 
  gold standard 
x - ray crystal structures . in order to further investigate potential inaccuracies on the noe - derived restraints 
 themselves
, we also assessed how well the corresponding x - ray crystal structures fit these nmr 
 restraint data .
hydrogen atoms were added to the x - ray structure coordinates using rosetta 
 idealization application , which rebuilds molecules using ideal bond lengths , bond angles , and 
 torsion angles .
all those resulting idealized x - ray structures have quite a few restraint 
 violations , and the number of restraint violations varies from target to target .
no attempt was 
 made to further adjust the x - ray crystal structures to better match the nmr restraint data . 

inconsistencies between the nmr restraints , the x - ray crystal structures , and the rosetta 
 energy function arise from several sources , including ( i ) the crystal lattice , which may 
 stabilize a subset of the conformations that are present in the solution nmr experiments and 
 that contribute to the noesy data , ( ii ) the noesy data arise from ensemble averages of dynamic 
 distributions which are not captured by the methods used in these studies to model restraints 
 and nmr structures , and ( iii ) there may be inaccuracies in the rosetta potential energy 
 function .
however , aside from these fundamental challenges in modeling protein structures from 
 nmr data , it is not surprising that the lowest - energy models do not perfectly satisfy the 
 noe - derived distance restraints .
these distance restraints are interpreted from noesy spectra 
 assuming a simple two - spin approximation , single isotropic rotational correlation time , uniform 
 linewidths , identical relaxation in filtering through bound c and n atoms , and many other 
 assumptions that are simply not correct .
the details of how upper bound distance restraint 
 violations were defined are different as various laboratories across the nesg use somewhat 
 different methods for calibrating these distances .
although noesy peak lists ( usually providing 
 resonance intensities ) are available for many of the data sets , the issues of linewidths and 
 differential relaxation in different x - filtered noesy spectra can not be addressed with the 
 available data .
it could be interesting to compare simulated spectra generated for r3 and r3rst 
 models using full - relaxation matrix analysis with relaxation - corrected , integrated , noesy 
 spectra data , but such an analysis is beyond the scope of the current work .
an alternative method for incorporating the rosetta force field into the nmr structure 
 determination process is restrained cs - rosetta ( rcs - rosetta ) in which structures are generated 
 starting from extended conformations with nmr restraints and the cs - rosetta protocol . 
 generally , for a 100-residue protein rcs - rosetta calculations require about 510 times 
 more cpu time to generate each decoy than restrained rosetta refinement .
the difference in cpu 
 time becomes even larger as the size of protein increases .
rcs - rosetta calculations generally 
 require tens of thousands decoys in order to ensure convergence , compared to only hundreds of 
 decoys required for restrained rosetta refinements which begin with native - like conformations 
 as the starting point .
hence , the restrained rosetta refinement protocols used here are some 
 200500 ( or more ) times faster than restrained cs - rosetta methods .
for example , for a 
 100 residue protein , rcs - rosetta calculations required about 4000 min to generate 10  000 
 decoys using 20 2.5 ghz processors ( 0.4 min per decoy ) .
for the same size protein , cyana 
 structure generation followed by restrained rosetta refinement requires about 1020 min 
 per for an ensemble of 20 conformers .
the rasac iterative cs - rosetta 
 protocol may sometimes provide more accurate structures using restrained cs - rosetta , 
 but it is even more cpu intensive .
therefore , for proteins of more than 10 kda , a good practice 
 is to use traditional methods for nmr structure generation , followed by restrained rosetta 
 refinement .
although rosetta refinement can modify the input conformation to some extent , rosetta refined 
 structures will not deviate significantly from the input structure because the rosetta 
 refinement protocol samples only conformations that are close to the initial nmr structure .
if 
 the nmr structures are highly inaccurate to begin with , these severe structural differences 
 can not be corrected by the restrained rosetta refinement protocol alone . moreover , for 
 sparse - restraint nmr structures , such as the sgr145 target , additional information , such as 
 evolutionary restraints , or more advanced sampling techniques , such as 
 rasrec rosetta , may also be required to obtain the most accurate nmr structures .
in comparison with nmr structures refined by traditional methods , restrained rosetta refined 
 structures fit the experimental nmr data equally well and are of significantly better 
 stereochemical and geometric quality .
rosetta refinement drives nmr structures to be more 
 similar to their x - ray counterparts , thus increasing their phasing power . despite the fact that 
 they are more accurate relative to the corresponding x - ray crystal structure , restrained rosetta 
 refined structures tend to have slightly higher distance restraint violations
. this may reflect 
 inaccuracies in the interpretation of nmr data in terms of upper bound restraints , providing 
 guidance to the experimentalist to confirm and possibly refine these interpretations of the raw 
 experimental data .
the restrained rosetta refinement protocols described here utilize nmr 
 structures initially determined by more conventional methods as input .
they are much less cpu 
 intensive than restrained cs - rosetta methods , which generate nmr structures from extended 
 starting structures , and provide comparable or better results .
all of the nmr and crystallographic experimental data used in this project are available on 
 line at : http://psvs-1_4-dev.nesg.org / results / rosetta_mr / data set.html .
coordinates of the 
 unrestrained and restrained rosetta refined structures , together with structure quality 
 assessment reports , are available on line at : http://psvs-1_4-dev.nesg.org / results / rosetta_mr / rosettamr_psvs_summary.html
 we have found that refinement of protein nmr structures using rosetta with experimental nmr 
 restraints yields more accurate protein nmr structures than those that have been deposited in 
 the pdb using standard refinement protocols . using 40 pairs of nmr and x - ray crystal 
 structures determined by the northeast structural genomics consortium , for proteins ranging in 
 size from 522 kda , 
 restrained rosetta refined structures fit better to the raw 
 experimental data , are in better agreement with their x - ray counterparts , and have better 
 phasing power compared to conventionally determined nmr structures . for 37 proteins for which 
 nmr ensembles were available and which had similar structures in solution and in the crystal , 
 all of the restrained rosetta refined nmr structures were sufficiently accurate to be used for 
 solving the corresponding x - ray crystal structures by molecular replacement . 
 the protocol for 
 restrained refinement of protein nmr structures was also compared with restrained cs - rosetta 
 calculations . for proteins smaller than 10 kda , restrained cs - rosetta , starting from extended 
 conformations , 
 provides slightly more accurate structures , while for proteins in the size 
 range of 1025 kda the less cpu intensive restrained rosetta refinement protocols 
 provided equally or more accurate structures . 
 the restrained rosetta protocols described here 
 can improve the accuracy of protein nmr structures and should find broad and general for 
 studies of protein structure and function . 