experimental approaches 
 such as x - ray and electron crystallography 
 and microscopy have traditionally excelled at determining the structure 
 of single folded proteins and large protein complexes . however , intrinsically disordered proteins ( idps ) 
 are not amenable to these static structural determination methods .
idps represent a new frontier in structural biology 
 in that the idp structure must be characterized as a diverse ensemble 
 of interconverting conformational substates , as opposed to a single 
 dominant 3d structure .
this necessitates 
 an adjustment in the core methodology of protein structure determination 
 for this class of protein .
the experimental identification of proteins with 
 global intrinsic disorder can be performed using various spectroscopic 
 techniques including circular dichroism ( cd ) , nmr , infrared spectroscopy 
 ( ir ) , uv spectroscopy , and fluorescence spectroscopy . cd and ir report on the amount of secondary structure , while lack 
 of chemical shift dispersion in nmr spectra is a good indication of 
 high flexibility .
hydrodynamic techniques such as saxs , gel filtration , 
 and dynamic light scattering can also aid in idp identification as 
 they report on the radius of the protein , which is often larger for 
 an idp or denatured protein than a folded protein of the same mass . 

lack of a cooperative folding transition , solubility at high temperatures , 
 and proteolytic sensitivity are also attributes of idps that are useful 
 in forming a complete picture of a certain protein s level 
 of disorder .
a subset of these techniques is generally employed to 
 determine that a protein is an idp . recently increased importance 
 has been placed on characterizing 
 the conformational substates within idp ensembles since they each 
 may have distinct functional roles or could lead to hypotheses about disease origin . in order to achieve both better ensemble classification 
 and a detailed description of conformational substates ,
we must critically 
 assess how we build these complex structural ensembles from experimental 
 data and theoretical models .
nmr is the experimental tool of choice 
 for characterizing the solution structure and dynamics of biological 
 molecules since it reports on the native distribution of conformations 
 in an aqueous environment , and more importantly is a dynamical experiment 
 that probes the nanosecond to millisecond time scales of conformational 
 motion .
observables 
 from these experiments include chemical shifts , which are characteristic 
 of functional groups and their surrounding environment , and spin 
spin 
 couplings ( j - couplings ) , which independently report on backbone dihedral 
 angles .
dipole interactions 
 give rise to the nuclear overhauser effect ( noe ) that reports on tertiary 
 structure contacts , and more recently , residual dipolar couplings 
 ( rdcs ) have been used to describe the relative orientation of spatially 
 separated regions of a protein .
paramagnetic relaxation enhancements ( pres ) , which 
 can produce longer distance restraints than noes have also been used 
 in the context of idps ; however , this measurement requires chemical modification 
 of the protein with a nitroxide spin label or an amino - terminal copper 
 binding motif , which sometimes requires sequence modification to attach 
 the probe , and which may perturb the monomeric idp conformations .
nanoseconds  milliseconds time scale of the nmr experiment , 
 leading to an averaging of the nmr observables across structural subpopulations . 

this uniform average hinders the structural characterization of all 
 the conformational substates , and can even obscure the overall ensemble 
 classification , as we will see for the amyloid peptides in this study . 
 building the connection between the averaged nmr observables and the 
 complete idp structural ensemble therefore depends critically on computational 
 models .
the goal of the computational 
 model is to provide a properly weighted set of the diverse subpopulations 
 of the idp most consistent with the nmr observables and perhaps other 
 experimental measures such as circular dichrosim , small - angle x - ray scattering , or pres .
thus , multiple types of nmr or 
 other experimental observables are necessary for validation of the 
 computational model .
currently there are two 
 primary but very different computational 
 approaches to building an idp structural ensemble , which can be loosely 
 contrasted as first principle or de novo molecular 
 dynamics ( md ) methods versus knowledge - based approaches .
the de novo approach implements md simulations based on the 
 theoretical foundations of statistical mechanical sampling and model - derived 
 potential energy force fields .
de novo md generates 
 a structural ensemble that is representative of given thermodynamic 
 conditions according to the force field employed , i.e. , a boltzmann 
 weighted ensemble of conformational subpopulations and their time 
 scales , independent of experimental input .
the md trajectories also 
 allow calculation of the time correlation functions that underlie 
 the nmr experiment .
the complementary use of md and nmr data to determine 
 structure and dynamics of folded and unfolded proteins has been a 
 highly active area over the last two decades , particularly for relaxation measurements that require a dynamical 
 interpretation of the nmr data at the picosecond and nanosecond time 
 scales . for the de novo md method ,
multiple nmr or other experimental data are necessary 
 to validate the md ensemble through direct back - calculation 
 of observables , many of which depend on the time scales of motion , 
 in order to directly compare to the experiment .
once validated , md 
 simulations provide a prediction of the complete idp structural ensemble , 
 allowing overall classification as well as the study of individual 
 conformational substates , which can be analyzed with some confidence .
in contrast , we define knowledge - based approaches as those that 
 use experimental nmr information directly to derive the structural 
 ensemble .
such methods are the foundation of nmr structure determination 
 of folded proteins using experimentally derived conformational constraints 
 based on chemical shifts , j - couplings , and noe data embodied in software 
 packages such as candid , cyana , and x - plor - nih .
while md is 
 often used to generate atomistic predictions independent of nmr experimental 
 input , as in our de novo method , a number of researchers 
 have advanced the combination of applying knowledge from nmr to restrain 
 the md ensemble .
for example , md simulations have been combined with 
 rdc restraint data for folded proteins that then allows for the analysis of other features of the ensemble , 
 such as conformational fluctuations .
nmr restrained md has also been 
 applied to idps such as -synuclein , a disease protein indicted 
 in parkinson s disease .
this study incorporated distance restraints 
 derived from pre experiments in order to guide the md so that the 
 protein s radius of gyration distribution is in good agreement 
 with the experimental value .
other 
 knowledge - based approaches for idps forego md simulations 
 altogether and instead use an extensive set of statistical coil conformations ; this starting pool , which can be generated using a variety of heuristics , 
 can be thought of as a basis set of structures .
subsequently , the 
 starting pool of structures is then culled for the subset of conformations 
 that are in best agreement with experimental data to create the idp 
 ensemble . in the energy - minima mapping and weighting ( emw ) method , 
 stultz and
co - workers used end - to - end distance restraints to develop 
 a pool of conformations with varying radii of gyration ; they then 
 selected , via monte carlo , a weighted ensemble of 15 structures to 
 optimize the agreement with experimental c and n chemical shifts and j - couplings .
blackledge 
 and co - workers have developed the program flexible - meccano to create a pool of structures based on random coil backbone dihedral 
 angles , on which they employ a genetic search algorithm in their asteroids 
 software program to select structures that together best match experimental 
 chemical shifts , pres , or rdcs . the ensemble method , developed by forman - kay and co - workers , 
 typically 
 defines the starting pool of idp conformational states as an ensemble 
 of extended or random coil states generated using trades , with an 
 option for biasing the secondary structure of the ensemble at certain 
 places in the sequence that are known to be partially structured .
structures are selected from this pool using a monte carlo selection 
 algorithm with an energy - weighting scheme for each type of experimental 
 input .
the ensemble program includes modules for several different 
 experimental data types including chemical shifts , rdcs , pres , j - couplings , 
 and contact distances derived from noes , and is a user - friendly and 
 publically available software package . although there are some specific differences , ensemble is largely 
 representative of the knowledge - based approaches and is qualitatively 
 equivalent to the combination of flexible - meccano and asteroids software .
it is important to note that such techniques largely ignore the 
 inherent dynamical information of certain types of the nmr data that 
 can be important for discriminating between different idp structural 
 ensembles .
the primary objective of this work is to compare 
 the de 
 novo and knowledge - based approaches for deriving idp structural 
 ensembles in context of the intrinsically disordered alzheimer s 
 disease peptides amyloid- 140 ( a40 ) and amyloid- 
 142 ( a42 ) .
we implement the ensemble knowledge - based 
 method by building an ensemble from a pool of statistical coil structures , 
 and compare this knowledge - based ensemble to md generated ensembles , 
 which are qualitatively different in that they are comprised of mostly 
 cooperative secondary structure and tertiary contacts .
this comparison 
 also exposes the relative utility of different types of nmr data for 
 refining or validating the idp computational ensemble .
we find that 
 chemical shifts and j - coupling constants are not particularly useful 
 for distinguishing between qualitatively different idp ensembles of 
 the amyloid- peptides .
finally we show that the combination 
 of de novo md methods that provide boltzmann weighted 
 samples with the ability to measure time correlation functions , and 
 knowledge - based methods for conformation selection , provides the best 
 agreement with the nmr data .
in order to evaluate 
 the alternative ensembles produced by knowledge - based and de novo approaches , we need a method of calculating the 
 chemical shifts , j - coupling constants , rdcs , and h  h noes as averages over the entire computationally generated 
 structural ensemble for comparison with experimental values .
general purpose chemical shift calculators such 
 as shiftx and shifts describe the isotropic shielding of the applied magnetic 
 field for the given atom , a quantity that depends sensitively on the 
 local electronic structure environment . even for folded proteins 
 with a dominant native conformer
, each atom type can exist in many 
 different local environments , and for disordered peptides and proteins 
 the ensemble average reflects an even more diverse set of chemical 
 environments .
whether one uses shiftx ( used in ensemble ) 
 or shifts to calculate chemical shifts , the results generated by the 
 two programs are consistent when applied to amyloid- and averaged 
 over the structural ensembles .
we report results using shiftx in this work . to calculate 
 the scalar coupling constants , jhnh
, we used the karplus equation1where  indicates the protein backbone 
 dihedral angle , with coefficients a = 6.51 , b = 1.76 , 
 and c = 1.60 corresponding to the parameter set by 
 vuister and bax .
however , sgourakis and 
 co - workers and our own previous work on 
 a42 found that the md results exhibited 
 a systematic shift of calculated j - couplings with the experimental 
 scalar couplings of wang and co - workers .
we delved into this issue 
 more deeply and derived an analytical correction , described in recent 
 work , that must be applied to the original 
 experimental j - coupling data from wang and co - workers .
in particular , it has been corrected for a missing 
 relaxation that makes scalar couplings determined from the hnh 3d experiment consistently lower than those from 
 cosy splittings by a small amount ( from 
 15% ) .
the j - coupling values are also averaged over 
 all structures in the ensemble as in , and then the calculations can be compared to the 
 corrected experimental jhnh values for both amyloid peptides .
the standard method in the field for calculation of rdcs is the 
 pales program , which we have used previously 
 for the a40 and a42 md ensembles .
the program computes the rdc by using steric 
 properties of the molecule to generate a global alignment orientation . 

then , the angle between the backbone amide bond vectors and the external 
 magnetic field is used to calculate the rdc for each conformation , 
 and the rdcs are averaged over all conformations of a given ensemble . 

the ensemble program by contrast , evaluates rdcs using a local alignment 
 program developed in the forman - kay lab , where 15 residue segments 
 along the protein are aligned separately over the ensemble of structures .
the local rdcs ( l - rdcs ) are also averaged over 
 all conformations of a given ensemble .
this local alignment has lower 
 computational cost and has been shown to give similar results to pales , 
 hence l - rdcs , rather than rdcs generated from a global alignment algorithm , 
 are optimized in the standard implementation of the ensemble approach . 
 similarly , the asteroids program by default employs a local alignment 
 tensor to optimize ensemble agreement with experimental rdc data .
we also note that the pales alignment and rdc 
 calculation were developed for folded proteins , and their application 
 to idps assumes individual idp conformations behave similarly to folded 
 proteins during the rdc experiment , which may not be the case for 
 idps such as amyloid-. we also evaluate the h  h noesy ( or 
 roesy ) spectra as we have described in previous studies by calculating the intensity 
 of the noe cross - peaks2where x and  are the eigenvectors 
 and 
 eigenvalues of the full relaxation matrix , composed of diagonal elements3aand off - diagonal elements3bthat are comprised of appropriate 
 combinations 
 of the spectral density functions4evaluated at the relevant larmor frequencies , 
  , and where k is given by5h is the gyromagnetic ratio 
 of h , 0 is the permeability of free 
 space , and  is planck s constant .
reff is the distance between the hydrogen atoms raised 
 to 6 power , averaged over all structures in the ensemble and 
 then raised to the 1/6 power to convert back to units of distance . 

these calculations account for all hydrogen atoms explicitly ( including 
 all methyl or methylene groups ) and hence reff and correlation functions for every pair of hydrogen atoms are evaluated .
the spectral density function 
 for each atom pair is calculated as the fourier transform of the correlation 
 function for the pair vector and water proton coordinates are ignored , 
 as is the standard assumption in the nmr experiment .
n noes as 
 we did in refs ( 14 and 48 ) by evaluating 
 the steady state noe enhancement factor of the n spin 
 by the h noe according to6where h and n are the gyromagnetic ratios of h and n , respectively .
n cross - relaxation 
 rate constant is given by7and the n self - relaxation by8 in this case , jhn( ) 
 is the spectral density function for the h  n covalently bonded pair .
note that the homonuclear 
 and heteronuclear noe calculations require 
 correlation time information about the vector between each pair of 
 atoms given by  in eq 4 .
this dynamic 
 information is naturally supplied by the de novo md 
 method , which allows direct measurement of the autocorrelation of 
 the interatomic vector over the time of the simulation . however ,
dynamics 
 are not considered in the generation of ensembles that are used in 
 the knowledge - based approach .
this is an inherent limitation of ensembles 
 generated from a static perspective only , which we discuss further 
 below .
to determine an idp s 
 level of disorder , we first generate 
 several alternative ensembles , compare these ensembles to the available 
 nmr data , and select the best validated ensemble .
we consider the 
 creation of three qualitatively different conformational ensembles 
 that are typically used in the knowledge - based approaches for the a40 and a42 peptides .
the common null 
 hypothesis is that the disordered peptides can 
 be well represented by a random coil ( rc ) ensemble . the second type 
 of statistical coil ( pred - ss ) ensemble is also random , but incorporates 
 bioinformatics - based knowledge about what secondary structure category 
 is more likely for a given residue in the amino acid sequence . in 
 this case
, the random ensemble is biased to contain a statistical 
 probability of predicted secondary structure on a per residue basis , 
 but no cooperative secondary structure such as -helices , -hairpins , 
 or -sheets are generated from the random secondary structure 
 assignments .
computational methods such as trades and flexible - meccano are used to generate these type of random or statistical coil ensembles .
finally , a fully knowledge - based approach is considered , which culls 
 the rc or , in this case , pred - ss ensembles to derive a subset of conformations 
 that best agrees with the nmr data ( pred - ss - ens ) .
the ensemble software 
 package provides a working example of the knowledge - based approach 
 that performs this biased selection and which has been successfully 
 applied to a range of idps .
each of the above three ensembles can 
 then be compared against the ensembles generated by de novo md for both of the idps a40 and a42 .
details of the de novo md approach applied to amyloid- can be found 
 in other publications .
we also consider an additional fifth ensemble ( md - ens ) that combines 
 the knowledge - based and de novo md approaches , by 
 using ensemble to select structures from the de novo md starting pool , and which is described in our recent study .
table 1 shows the 
 average radius of gyration 
 ( rg ) values for each type of ensemble .
we see that the order from 
 most extended to most compact proceeds as pred - ss >
rc > pred - ss - ens 
 > md  md - ens , and thus the alternative ensembles span a 
 range 
 of idp classifications by the rg measure .
figure 1 provides the 
 propensities for the pred - ss , pred - ss - ens , de novo md , and md - ens ensembles to form turns , antiparallel -strands , 
 or helical structure by residue for a42 .
we do not show the 
 secondary structure profiles for the rc ensemble since it is similar 
 to the pred - ss ensemble ( see the supporting information ) .
percentage of a42 simulated ensemble in different types 
 of secondary structure by residue for ( a ) the pred - ss , ( b ) pred - ss - ens , 
 ( c ) de novo md , and ( d ) md - ens ensembles .
the red 
 line represents helix , the blue line for antiparallel sheet , and the 
 black line for -turns .
we note that the blue line represents 
 only antiparallel sheet structure ( the most common ) and not all sheets . for the radius of gyration ( rg ) 
 values
, we report both the ensemble average and rmsd . for chemical 
 shifts , we report  that measures agreement between 
 the computational ensembles and the experimentally measured chemical 
 shifts :  < 1 indicates no disagreement with 
 experiment within shiftx calculator error .
we also report the jhnh rmsd (  ) . some data reproduced from ref ( 14 ) .
this plot emphasizes that the md - based ensembles are 
 qualitatively 
 different from the rc or pred - ss ensembles , in that the a40 
 and a42 peptides samples some type of structured conformations 
 in 99% of the md ensemble , including complex strand 
 formation . from this
, we conclude that the 
 radius of gyration trends stem from the much larger propensity for 
 the md ensembles to form cooperative secondary structure 
 and collapsed tertiary contacts , as opposed to the random or knowledge - based 
 ensembles that do not generate contiguous blocks of secondary structure , 
 and hence are more extended on average .
although the secondary structure 
 content of the md - ens ensemble resembles that of the md ensemble , 
 figure 1 shows that there is some variation 
 in the percentages with which certain residues adopt different types 
 of secondary structure . for analysis 
 of a40 and a42 idps considered here , 

we have utilized a wide range of previously published nmr data including 
 chemical shifts from the zagorski group as well as j - coupling constants , rdcs , and heteronuclear h 
our group has collected h chemical shifts and noesy h  h homonuclear spectra for the full length a40 and a42 
 peptides as reported elsewhere .
the data for the longer 
 peptides were processed as described in ref ( 48 ) in a similar approach 
 to that used for the a2130 fragment .
first we consider the chemical shift data , for which 
 we note that 
 the calculated chemical shifts have an uncertainty that is independent 
 of the quality or type of structural ensemble , and results from approximations 
 of the shiftx or shifts calculators themselves .
other research groups have reported 
 the uncertainty ,  ( ppm ) , for these calculators , 
 with the value depending on the atom type and its bonding chemistry . therefore the best way
validate the various idp ensembles with chemical 
 shift data is to calculate the difference between the experimental 
 chemical shift and the shift calculated from each of the structural 
 ensembles , normalizing it by the calculator uncertainty , to generate 
  values9reported uncertainties ( root mean 
 squared 
 difference , rmsd , from experiment ) for the shiftx calculator are  = 0.23 ppm for h ,  = 0.49 ppm for hn ,  = 0.98 ppm for c , and  = 1.10 ppm for c. any dominant 
 error due to the underlying structural ensemble would then correspond 
 to values of  > 1 .
table 1 displays the  agreement between experimentally measured proton and carbon chemical 
 shifts with those generated from each candidate ensemble for both 
 a40 and a42 .
experimental chemical shift data reported for the monomeric a40 
 and a42 peptides do not differ greatly from random coil values , 
 and therefore the rc ensemble falls within  uncertainty . since the pred - ss ensemble 
 shows almost no dssp defined secondary structure ( figure 1a ) , it remains largely equivalent to the rc ensemble 
 as deduced by chemical shifts .
the de novo md structural 
 ensemble is also in good agreement with the chemical shift data ; however , 99% of the md generated a conformations 
 contain one or more elements of cooperative secondary structure somewhere 
 along the peptide sequence ( figure 1b ) .
the 
 reason that the md ensemble is also in good agreement with the experimental 
 chemical shifts is that averaging over a large ensemble of cooperatively 
 formed secondary structure and tertiary contacts yields average chemical 
 shifts that are consistent with random coil values .
for example , averaging the chemical shifts of all folded proteins 
 in the pdb results in averages very similar to random coil values .
we have found that the ensemble optimization of the pred - ss and 
 md starting pools improves the  values , but all are within the calculator uncertainty .
not surprisingly , 
 if the knowledge - based ensemble approach were biased by chemical shift 
 data alone , they would show little deviation from their starting  soup 
, 
 and the structural interpretation would be highly dependent on the 
 starting ensemble .
for this reason we conclude that nmr chemical shifts 
 alone do not provide any qualitative discrimination between the alternative 
 ensembles , at least not for the a40 and a42 disease 
 idps .
it may still be useful to apply chemical 
 shift constraints in combination with other experimental observables 
 to optimize an idp ensemble , as we have done when generating the md - ens 
 ensemble .
sanity check against ensembles that fit other observables , 
 such as noes , but lead to unphysical chemical shift values .
similarly , j - couplings alone also do not discriminate between random 
 coil idps and those that are more structured with cooperative secondary 
 structure and tertiary structure contacts .
figure 2 illustrates this by plotting the agreement between experimentally 
 measured j(hn , h ) , and those calculated from the rc , pred - ss , 
 pred - ss - ens , de novo md , and md - ens ensembles for 
 a40 and a4 .
table 1 shows that 
 all ensembles yield an rmsd across all residues of 0.601.09 
 hz , and also reports 10with j = 0.73 hz . 

j - couplings report on the backbone  dihedral 
 angle , and therefore could in principle distinguish between an unstructured 
 peptide and a peptide with a defined secondary structure ; however , 
 in the case of the disease idp a , the presence of diverse secondary 
 structure in the md ensemble is not apparent from the calculated j - couplings . 

we believe that this stems from the fact that good agreement with 
 scalar coupling data for idps can largely be predicted by sampling 
 over the allowed regions of residue - specific ramachandran plots without 
 needing to assume any structure adopted by the full length sequence . 

thus j - couplings also do not provide an experimental measure for discriminating 
 among qualitatively different structural ensembles for the amyloid 
 peptides .
j - coupling constants for backbone amides for a40 and a42 . 
 ( a )
a40 experimental j - coupling constants ( red squares ) compared 
 to rc ( green triangles ) and de novo md ( solid blue 
 circles ) .
( b ) a40 experimental j - coupling constants ( red squares ) 
 compared to pred - ss - ens ( black diamonds ) and md - ens ( blue circles ) . 

( c ) a42 experimental , rc , and de novo md j - coupling 
 constants .
( d ) a42 experimental , pred - ss - ens , and md - ens j - coupling 
 constants .
has been corrected to account for t1sel relaxation and bring j - couplings determined from a hnh 3d experiment to be consistent with those 
 from cosy splittings .
table 2 provides the assessment 
 of the five 
 alternative ensembles for a40 and a42 using rdc values 
 evaluated residue by residue using the pales program and l - rdcs based on local alignments . while the rc and pred - ss ensembles yield lower rmsd values , 
 1.31.5 hz , they are marginally better than the de 
 novo md rmsd of 2.2 hz .
this is in 
 part due to the fact that experimental rdc uncertainties for idps 
 are larger ( 0.9 hz for a40 and 0.5 hz for a42 ) 
 than the uncertainty observed for folded proteins of 0.1 hz .
in addition , there are large uncertainties in 
 the accuracy of rdc calculators using programs such as pales .
in fact , the reported rmsd of the pales calculator 
 for folded proteins is 2.0 hz , on the same order as the rmsd 
 for the de novo md ensemble . while the ensemble method 
 does significantly lower the rmsd for l - rdcs for the pred - ss - ens and 
 md - ens ensembles , the corresponding rmsd based on the global alignment 
 using pales is marginally better than the pred - ss and de novo md starting pools .
hence for this particular application 
 on disordered amyloid peptides , we have found that rdcs are not a 
 particularly good experimental metric for differentiating among the 
 different ensembles , and substantial disagreement between rdcs based 
 on local and global alignments are observed .
we report rmsds for the rdc calculator 
 pales and l - rdcs evaluated with ensemble using local alignments .
the 
 noes are back - calculated from the structural ensembles as described 
 in section 4 .
we evaluate the rmsd normalized 
 by the largest noe intensity , rmsdn and ( correlation coefficient , r ) with the h2o and d2o experiments . 
 some data reproduced from ref ( 14 ) .
finally , we 
 consider the performance of the different ensemble 
 methods for reproducing h 
we have presented the noe data collection for the 
 a42 peptide in which 700 cross - peaks are observed in 
 the noe spectra , but only 200 can be uniquely assigned from 
 experimental information alone .
the remaining cross - peaks 
 do not have a clear independent assignment ( and in fact require a 
 computational model to interpret them ) .
therefore 
 we have only compared the different methods against the noe cross - peaks 
 that can be assigned by experiment alone .
we note that quantitatively 
 reproducing noe intensities is a very high bar since peak volumes 
 are extremely sensitive to r distance 
 averaging , that also involve an appropriate time scale that is heterogeneous 
 across proton pairs .
geometric imperfections in the conformational 
 ensemble where contact differences differ by a factor of 2 ( difference between 1  and 1.12  ) will double the corresponding 
 intensity value , thereby driving up the rmsd error for all ensembles .
large absolute noe intensities 
 especially tend to dominate the rmsd error , and therefore we have 
 mitigated this effect by normalizing the rmsd ( rmsdn ) by the experimental 
 intensity for each noe as in ref ( 14 ) .
table 2 shows 
 that the predicted set of h  h noes 
 from de novo md 
 is better than any other ensemble , with rmsdns that are lower than 
 the rc and pred - ss ensembles values by 23 fold and with much 
 higher correlation coefficients .
the 
 pred - ss - ens ensemble performs better for a40 and a42 
 than the randomly generated ensembles because the noe restraints are 
 used in the knowledge - based ensemble selection .
however , the pred - ss - ens 
 ensemble still does not reproduce the data as well as the de novo md ensemble .
the noe validation clearly indicates 
 that the de novo md ensemble with its cooperative 
 secondary structure is a better representation of a40 and a42 
 than are the rc , pred - ss , or pred - ss - ens ensembles , which have no 
 cooperative secondary structure .
since time information is not available 
 for the static ensembles , we can only evaluate the noes for the statistical 
 ensembles under the assumption of one uniform correlation time applied 
 to all pairs of protons , for which we use a 1 ns correlation time , 
 which is on the same order as those observed in the md simulations . 

of course the de novo md method can account for the 
 time scales explicitly and more importantly for the fact that different 
 pairs of hydrogen atoms do decay on different time scales .
thus the 
 statistically generated and knowledge - based ensembles agree relatively 
 poorly with the noe observables since the heterogeneity in correlation 
 times are unknown , and hence even the md - ens ensemble is in somewhat 
 worse agreement with the experimental noes than the de novo md ensemble ( table 2 ) .
the noe validation 
 emphasizes that an idp s diverse set of conformations gives 
 rise to a heterogeneous set of correlation times that must be described 
 in order to validate against experimental noes .
we further emphasize 
 that the calculation of heteronuclear noes , 
 being a purely dynamical measurement , is only possible with the de novo md method .
n noe intensities , measured by yan and wang , and those derived from our md simulation for a42 and a40 , 
 showing overall excellent agreement . unlike the h  h noes , these assignments are unambiguous 
 from experiment .
we find that , as in the experiment , there is an increase 
 in h 
n noe intensities calculated 
 from simulation for residues 3540 for a42 compared 
 to a40 , indicating that the longer peptide experiences slower 
 dynamics at the c - terminus .
n noes for a42 
 and a40 has previously been interpreted as evidence that a42 
 has greater structural rigidity in the c - terminus compared to a40 and we provide more analysis on this point in recently published 
 work .
agreement with experiment of simulated 
 ( a ) a40 and ( b ) a42 h 
we have shown that the 
 md and md - ens structural ensembles for the 
 idps a40 and a42 previously characterized yield substantially better agreement with a range of nmr data than 
 the random coil or statistical ensembles that are typically used with 
 knowledge based approaches .
the md ensembles are qualitatively different 
 from random coil or statistical ensembles in that the subpopulations 
 are richly structured , contain a diverse set of secondary structures 
 including -helix , -turns , and -strands , and span 
 the full range of compact to fully extended conformations .
furthermore , 
 while md generated ensembles are boltzmann weighted , the knowledge - based 
 approaches give equal statistical weight to all conformations and 
 thus are likely inconsistent with statistical mechanical weightings 
 that are inherent to the nmr experiment .
we have also shown 
 that some types of nmr data may not be helpful 
 for discriminating among qualitatively different structural ensemble 
 of idps .
in particular , averages over a diverse set of cooperative 
 secondary structure conformations yield experimental values of chemical 
 shifts that are superficially consistent with values expected from 
 a random coil ensemble . furthermore ,
if the chemical shifts are not 
 highly dispersed along the sequence of a particular idp , such as is 
 found for the amyloid- peptides , then the chemical shifts have 
 limited value as experimental refinement input or as a validation 
 measure .
j - couplings also do not provide discrimination between randomly 
 generated conformations and a diverse population of cooperative secondary 
 structure .
in fact , we found that scalar couplings calculated as averages 
 over the allowed regions of each residue - specific ramachandran plot 
 gave as good agreement with the experimental j - couplings for a40 
 and a42 as did averages over the structural populations . unlike others who have used rdc data to help interpret idp or unfolded 
 protein structural ensembles
this may be due to limitations 
 of rdc calculators such as pales , which 
 were originally developed and successfully applied to folded proteins , 
 but which are reported to have large uncertainties in their predicted 
 rdc values .
furthermore , calculated rdcs based on global alignment 
 algorithms such as pales diverge significantly 
 from rdcs evaluated from localized alignments for a40 and a42 , indicating that in cases like this 
 the ensemble package should be employed using the pales calculator 
 to fit rdcs , which is possible though not standard .
more research may be necessary to apply programs like pales 
 to disordered proteins , which likely do not align in an anisotropic 
 medium in the same way as folded proteins , in part due to the time 
 scale of interconversion of the conformational substates .
for example , 
 conventional methods for calculating rdcs can not be applied to the 
 motion of multidomain biomolecules , and 
 the local conformational sampling and long - range structure need to 
 be simultaneously accounted for because they both affect the experimental 
 rdc data .
however , progress is being 
 made in using rdcs to provide meaningful structural information for 
 other idps .
we speculate that success is greatest when all subpopulations 
 of the idp ensemble are homogeneously classifiable ( as extended disordered 
 conformations for example ) , so that the idp global alignment properties 
 are uniform and resulting averages provide meaningful and consistent 
 structural information .
h noe intensities and heteronuclear n  h noes are by themselves discriminating 
 with regard to the 
 tertiary contacts and backbone dynamics , respectively , that define 
 the important validation of the md - based ensembles over the statistical 
 coil ensembles .
furthermore , a correct picture 
 of the idp ensemble based on the experimental noe data would not be 
 possible without a computational model providing both details of individual 
 structures and the time scales for their interconversion . in turn , 
 although the homonuclear noes are averaged over all subpopulations , 
 they are still vital for deducing whether a given ensemble contains 
 subpopulations of structure with the right tertiary contacts to give 
 rise to the observed cross - peaks in the spectra .
because these cross - peak 
 intensities rely directly on the decay time scales of correlated proton 
 distances , the noes for idps are reporting on a heterogeneous population 
 of time scales .
one of the primary limitations of the statically generated 
 ensembles is that they are not associated with any information about 
 motional time scales that can be used to calculate noe observables . 

relaxation times can be used with the ensemble method , although they 
 are incorporated as structural rather than dynamic constraints .
this dynamic information is a 
 genuine strength of the de novo md methods , especially 
 for n  h noes , which can not be calculated 
 from the static ensembles .
we believe that the primary limitation 
 of knowledge - based methods 
 applied to the difficult amyloid case is 3-fold .
we note that 
 while there will be quantitative differences between ensemble and 
 other knowledge - based approaches such as asteroids , qualitatively 
 the problems will be similar .
basis set  of 
 conformations to select the final ensemble from ; i.e. , these methods 
 can not use the nmr data effectively to select for compact structures 
 with elements of cooperative secondary structure if the initial pool 
 of structures is largely composed of extended random coil structures . 

both ensemble and asteroids have relied on statistical coil ensembles 
 as the starting pool of structures , and while some  on - the - fly  
 addition of new structures is possible with these methods , they do 
 not yet support formation of complicated -sheet motifs . metrics of ensemble heterogeneity , such as those developed by the 
 onuchic and stultz research groups , will continue to be useful as 
 we explore the range of idps that can not be easily classified based 
 on their level of disorder .
second , for certain classes of 
 idps such as amyloid optimization of structures to reproduce 
 chemical shifts and scalar couplings does not discriminate among qualitatively 
 different structural ensembles .
third , the optimization phase of the 
 knowledge - based approaches relies on approximations to nmr observables , 
 which may diverge from a global property , as for l - rdcs , or from the 
 dynamical origins of noe intensities . at the same time
, the de novo md method is not 
 quantitatively perfect , and therefore the md ensemble provides an 
 excellent start state for subsequent refinement by knowledge - based 
 approaches .
an unambiguous future direction for the structural biology 
 of idps is the combined use of knowledge - based approaches and md that 
 supplies boltzmann weighted conformational substates as well as heterogeneous 
 time scales of motion . all together , the productive interplay 
 between nmr experiments , de novo md simulations , 
 and knowledge - based approaches , 
 along with supporting models , algorithms , and computer hardware , gives 
 us an ability to accurately identify structures present in idp ensembles 
 and use that knowledge to gain previously inaccessible functional 
 insights .
to further improve techniques for studying disordered proteins , 
 we as a community could establish a high throughput computational 
 infrastructure to predict idp structural ensembles using a combination 
 of md and nmr .
this would be similar to the establishment of x - ray 
 crystallography beamlines for the rapid solution of folded protein 
 structures that was launched during the structural genomics era .
the 
 ultimate goal in both cases is to use structural information to drive 
 the formation of hypotheses about protein function .
based on the success 
 of using structural information for functional characterization of 
 folded proteins and complexes , we hope and expect that structural 
 knowledge of idp ensembles can provide similar insight into idp function 
 and enable development of molecular hypotheses for disease idps .
 intrinsically 
 disordered proteins ( idps ) represent a new frontier 
 in structural biology since the primary characteristic of idps is 
 that structures need to be characterized as diverse ensembles of conformational 
 substates . 
 we compare two general but very different ways of combining 
 nmr spectroscopy with theoretical methods to derive structural ensembles 
 for the disease idps amyloid- 140 and amyloid- 
 142 , which are associated with alzheimer s disease . 
 
 we analyze the performance of de novo molecular dynamics 
 and knowledge - based approaches for generating structural ensembles 
 by assessing their ability to reproduce a range of nmr experimental 
 observables . 
 in addition to the comparison of computational methods , 
 we also evaluate the relative value of different types of nmr data 
 for refining or validating the idp structural ensembles for these 
 important disease peptides . 
Introduction
Methods
Results
Discussion