the online version of this article ( doi:10.1007/s10858 - 013 - 9739 - 5 ) contains supplementary material , which is available to authorized users .
modern multidimensional nmr spectroscopy allows successful determination of three - dimensional structure for double- or triple - labeled proteins with molecular weights of up to 50  kda ( kay 2005 ) .
typically protein structure elucidation can be split into two main parts ( wthrich 1986 ) : sequence - specific assignment of chemical shifts , and extraction of distances between proton pairs from noesy spectra .
the precision of determined structures depends primarily on a number of observed noe contacts and their proper assignment .
the main difficulty arises due to the ambiguity of noe assignment since chemical shifts are derived from nmr measurements with a certain level of precision .
it was shown that in larger systems less than 10  % of noe cross peaks can be assigned unambiguously ( mumenthaler et al .
several dedicated protocols for automatic noe assignment were developed ( gronwald et al . 2002 ; herrmann et al . 2002b ; nilges and odonoghue 1998 ) .
here we report an nmr measurement that allows to dramatically decrease the ambiguity of assignment of noe between aromatic and aliphatic protons .
it was shown previously ( jee and guntert 2003 ) that chemical shifts of aromatic side chains are crucial for noe assignment .
these residues are buried in the hydrophobic core of a protein and give rise to many long - range noe contacts .
therefore , the ability to obtain unambiguous contacts among aromatic and aliphatic protons can be a valuable tool for determination of protein structure with improved precision .
the intrinsic uncertainty of noe assignment due to flips of aromatic rings and frequently degenerated chemical shifts is alleviated by introduction of pseudo - atoms or other solutions ( wthrich et al .
although three - dimensional noesy methods are most commonly applied ( zhang et al . 1994 ; muhandiram et al . 1993 ) , the full potential of n , c isotope labeling can be utilized with double - heteronuclear - edited 4d spectra ( luan et al .
it should be emphasized that the reasonable resolution of these spectra can be preserved by employing non - uniform sampling ( nus ) of indirect time domains . due to the strict requirements regarding high dynamic range and linearity of peak intensities
, nus noesy spectra are particularly demanding for processing methods ; this is reflected by a limited number of applications published to date ( luan et al .
diagonal - free noesy experiments have attracted a considerable attention since the spectral reconstruction from sparse data is less severe for spectra with a limited dynamic range of signal amplitudes .
recently , a non - uniformly sampled ( nus ) 4d n , n - edited trosy - noesy - trosy experiment based on the orthogonal spin state selection was reported ( werner - allen et al .
the utility of an alternative approach to the diagonal peak suppression based on the straightforward diagonal subtraction ( wu et al .
2004 ) was also demonstrated for methyl  methyl noesy spectroscopy ( wen et al . 2012 ) . in these methods , however , the sensitivity per unit of time is reduced by the non - negligible factor of 2 .
2012 ) is an example of the most straightforward approach to the acquisition of diagonal - free noesy spectra . of the particular relevance
we propose a novel four - dimensional aliphatic  aromatic noesy experiment in which diagonal peaks are efficiently suppressed by the selective manipulation of c spins of different kinds .
the major aim of this experiment is to retain high sensitivity of the method while achieving a reasonable level of selectivity and associated diagonal peak suppression .
the proposed method complements the set of recently reported diagonal - free 4d aliphatic  amide ( stanek et al . 2012 ) , amide  amide ( werner - allen et al . 2010 ) and aliphatic  aliphatic ( wen et al . 2012 ) nus noesy experiments .
two possible solutions are discussed here : aliphatic - to - aromatic ( fig . 
1b ) hmqc - noesy - hsqc . in both cases the optimized hmqc scheme ( stanek et al .
2012 ) was incorporated for t1 ( h ) and t2 ( c ) evolution as it utilizes the multiple - quantum line narrowing effect for c  h coherences ( grzesiek et al .
1995 ) . in the previous work on 3d h(aro)-noesy - ch3,hn and 3d c(aro)-noesy - ch3,hn ( xia et al .
2001 ) the refocused inept was utilized for the selection of protons coupled to aromatic c spins . in this case
selective transfer can be achieved employing shaped inversion pulses and pulsed field gradients ( pfgs ) that suppress undesired coherences in the subsequent z - filtration .
we have found that the same task is far more demanding using hmqc . in this case pfgs can not be used to distinguish aromatic and aliphatic mq h 
c coherences as both have equal coherence order after initial 1/2jch delay and  hard excitation pulse .
if the selective excitation pulse is employed pfgs can be useful , however , sensitivity loss of a factor of \documentclass[12pt]{minimal } 
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				 \begin{document}$$ \sqrt 2 $ $ \end{document } is incurred and additional time is required for gradient encoding when c magnetization is transverse .
we thus conclude that the optimal solution includes phase cycling of selective excitation pulses . despite these difficulties hmqc
is preferred over refocused inept owing to ( 1 ) the apparently slower relaxation of mq coherences and ( 2 ) the possibility to incorporate both magnetization transfer delays ( 1/jch in total ) for the shared - time proton evolution ( t1 ) that leads to increased sensitivity ( stanek et al .
1pulse sequence scheme for ( a ) c(aliph)hmqc - noesy - c(aro)hsqc and ( b ) c(aro)hmqc - noesy - c(aliph)hsqc .
90 and 180  hard pulses are represented by filled and open bars , respectively .
shaped pulses are represented as follows : ( a ) 40  ppm selective pulse of the iburp-2 profile ( geen and freeman 1991 ) ( 659  s duration , 7.6  khz peak r.f .
field ) is shown as wide open bell - shaped pulse ( denoted  e ) .
wide grey rectangular pulses (  a and  c ) are of duration of 61  s and peak r.f .
4.1  khz ( calibrated to give null excitation 90  ppm off -resonance ) .
( b ) wide grey bell - shaped pulse denotes 80  ppm - selective hyperbolic secant adiabatic pulse ( silver et al .
narrow grey bell - shaped pulses (  f and  h ) utilize gaussian profile ( bauer et al .
1984 ) ( truncated at 1  % , duration of 178  s , peak r.f .
note that for some hardware the shaped 90 pulses (  a ,  c ,  f and
 h ) may require small angle phase adjustment to compensate 0th order phase shift with respect to refocusing pulses (  b and  g ) which are applied at full power .
n refocusing pulse enclosed in dashed - line box ( sequence b ) is optional and may be used if delay complementing to half - dwell time ,   =  [ ( sw3 )    pw180(n)]/2 , is positive .
refocusing of caliph - c couplings in t2 ( a ) or t3 ( b ) may be considered if max .
the composite 34.2x123x197.6x288.8x pulse (  d and  i ) was used in hmqc for broadband inversion of c spins ( shaka 1985 ) .
watergate ( piotto et al . 1992 ) with 3 - 9 - 19 pulses separated by ( 3.2  khz ) was employed for experiment ( a ) .
c composite pulse decoupling was performed employing wurst scheme ( kupe and freeman 1995 ) .
/2 pulses were 7.1 , 14.3 and 31  s for h , c and n , respectively .
1 , 2 and 3 are incremented for quadrature detection in t1 , t2 and t3 using states ( 1 ) or states - tppi ( 2 , 3 ) method .
four - step phase cycle is as follows : 1  =  45 ; 2  =  x , x ; 3  =  2(x ) , 2(x ) ; 4  =  2(x ) , 2(x ) ; 5  =  135 ; rec  =  x ,
delays are set as follows : a  =  1.79  ms    ( 4  jchaliph ) , b  =  1.56  ms    ( 4  jcharom ) .
noesy mixing time m  =  150  ms was used . for the semi - constant time evolution in t1 ( h ) the delays 1 , 2 and 3 are t1/2 , t1(1    2/t1,max)/2 and (1    t1/t1,max ) , where   =  2a , or   =  2b for sequences ( a ) and
gradient levels and durations are : g1 ( 2  ms , 6.5  gs / cm ) , g2 ( 2  ms , 14.2  gs / cm ) , g3 ( 0.5  ms , 1.77  gs / cm ) , g4 ( 2  ms ,  11.3  gs / cm ) , g5 ( 2  ms , 12.9  gs / cm ) , g6  ( 0.5  ms , 5.4  gs / cm ) .
proton carrier frequency was set on resonance with water ( 4.68  ppm ) , carbon carrier was set to 35  ppm and switched to 125  ppm as indicated by the vertical arrow ; n carrier was set to 117  ppm and shifted to 162  ppm at the beginning of noesy mixing period . for the aliphatic - to - aromatic noesy ( a ) 4,400 sampling points ( t1,t2,t3 ) were randomly chosen from 120    84    30 cartesian grid according to gaussian probability distribution , p(t )  =  exp[(t / tmax)/2 ] ,   =  0.5 , with poisson disk restrictions ( kazimierczuk et al . 2008 ) .
maximum evolution times of 15 ( t1 ) , 6  ( t2 ) and 5  ms ( t3 ) were achieved in the indirectly detected dimensions .
spectral widths of 8 , 14 , 6 and 12  khz were set in 1 , 2 , 3 and 4 dimensions , respectively . in the full 4d spectrum
any residual diagonal peaks can be folded in c ( 2 and 3 ) dimensions without the risk of overlap and misinterpretation with genuine peaks .
the only requirement is to ensure proper h ( 1 ) spectral width to avoid aliasing in this indirect dimension .
the restriction of c spectral widths is very practical as it saves vast amounts of disk space .
the total experimental time was 57  h pulse sequence scheme for ( a ) c(aliph)hmqc - noesy - c(aro)hsqc and ( b ) c(aro)hmqc - noesy - c(aliph)hsqc . 90 and 180
shaped pulses are represented as follows : ( a ) 40  ppm selective pulse of the iburp-2 profile ( geen and freeman 1991 ) ( 659  s duration , 7.6  khz peak r.f .
field ) is shown as wide open bell - shaped pulse ( denoted  e ) .
wide grey rectangular pulses (  a and  c ) are of duration of 61  s and peak r.f .
4.1  khz ( calibrated to give null excitation 90  ppm off -resonance ) .
( b ) wide grey bell - shaped pulse denotes 80  ppm - selective hyperbolic secant adiabatic pulse ( silver et al .
narrow grey bell - shaped pulses (  f and  h ) utilize gaussian profile ( bauer et al .
1984 ) ( truncated at 1  % , duration of 178  s , peak r.f .
note that for some hardware the shaped 90 pulses (  a ,  c ,  f and
 h ) may require small angle phase adjustment to compensate 0th order phase shift with respect to refocusing pulses (  b and  g ) which are applied at full power .
n refocusing pulse enclosed in dashed - line box ( sequence b ) is optional and may be used if delay complementing to half - dwell time ,   =  [ ( sw3 )    pw180(n)]/2 , is positive .
refocusing of caliph - c couplings in t2 ( a ) or t3 ( b ) may be considered if max .
evolution time of aliphatic c spins exceeds 9  ms . the composite 34.2x123x197.6x288.8x pulse (  d and  i ) was used in hmqc for broadband inversion of c spins ( shaka 1985 ) .
watergate ( piotto et al . 1992 ) with 3 - 9 - 19 pulses separated by ( 3.2  khz ) was employed for experiment ( a ) .
c composite pulse decoupling was performed employing wurst scheme ( kupe and freeman 1995 ) .
/2 pulses were 7.1 , 14.3 and 31  s for h , c and n , respectively .
1 , 2 and 3 are incremented for quadrature detection in t1 , t2 and t3 using states ( 1 ) or states - tppi ( 2 , 3 ) method . four - step phase cycle is as follows : 1  =  45 ; 2  =  x , x ;
3  =  2(x ) , 2(x ) ; 4  =  2(x ) , 2(x ) ; 5  =  135 ; rec  =  x , x , x , x .
delays are set as follows : a  =  1.79  ms    ( 4  jchaliph ) , b  =  1.56  ms    ( 4  jcharom ) .
for the semi - constant time evolution in t1 ( h ) the delays 1 , 2 and 3 are t1/2 , t1(1    2/t1,max)/2 and (1    t1/t1,max ) , where   =  2a , or   =  2b for sequences ( a ) and ( b ) , respectively ( stanek et al . 2012 ) .
gradient levels and durations are : g1 ( 2  ms , 6.5  gs / cm ) , g2 ( 2  ms , 14.2  gs / cm ) , g3 ( 0.5  ms , 1.77  gs / cm ) , g4 ( 2  ms ,  11.3  gs / cm ) , g5 ( 2  ms , 12.9  gs / cm ) , g6  ( 0.5  ms , 5.4  gs / cm ) .
proton carrier frequency was set on resonance with water ( 4.68  ppm ) , carbon carrier was set to 35  ppm and switched to 125  ppm as indicated by the vertical arrow ; n carrier was set to 117  ppm and shifted to 162  ppm at the beginning of noesy mixing period . for the aliphatic - to - aromatic noesy ( a ) 4,400 sampling points ( t1,t2,t3 ) were randomly chosen from 120    84    30 cartesian grid according to gaussian probability distribution , p(t )  =  exp[(t / tmax)/2 ] ,   =  0.5 , with poisson disk restrictions ( kazimierczuk et al .
maximum evolution times of 15 ( t1 ) , 6  ( t2 ) and 5  ms ( t3 ) were achieved in the indirectly detected dimensions .
spectral widths of 8 , 14 , 6 and 12  khz were set in 1 , 2 , 3 and 4 dimensions , respectively . in the full 4d spectrum
any residual diagonal peaks can be folded in c ( 2 and 3 ) dimensions without the risk of overlap and misinterpretation with genuine peaks .
the only requirement is to ensure proper h ( 1 ) spectral width to avoid aliasing in this indirect dimension .
the restriction of c spectral widths is very practical as it saves vast amounts of disk space .
the total experimental time was 57  h here , the selection of either aliphatic ( fig . 
1b ) proton - carbon mq coherences is accomplished solely by band - selective excitation of c spins in conjunction with the four - step phase cycle of two /2 pulses (  a , 
f ,  h , respectively ) . therefore , the choice of selective /2 pulses is of the particular relevance .
apparently , it is quite straightforward not to excite aromatic c spins ( the sequence shown in fig . 
more advanced pulses such as gaussian cascade q5 ( emsley and bodenhausen 1992 ) or e - burp ( geen and freeman 1991 ) could be utilized as well , however , these pulses are ( 1 ) of significantly larger duration , ( 2 ) more sensitive to miscalibration and ( 3 ) require high peak r.f . field .
it was experimentally verified that these shortcomings offset theoretical benefits of high quality pulses and significant loss of sensitivity is incurred . for the aromatic - hmqc ( fig . 
due to the use of shaped /2 c pulses in hmqc the refocusing  pulse is obligatory for correct phase properties of signals in 2 dimension .
however , no additional selectivity improvement can be achieved by replacement of this pulse by a band - selective one .
similarly , the subsequent carbon inversion pulse in hmqc ( denoted  d and  i , respectively ) should be sufficiently broadband .
a shaped pulse here would only result in the t1-dependent jch evolution of unaffected coherences during total time of 1  +  2   
the resulting signals would be impossible to suppress using neither phase cycling nor pulsed field gradients .
all nmr experiments were performed for the e32q mutant of human s100a1 protein , for which resonance assignments are available in bmrb under accession code 17857 . the high resolution 3d structure based on the standard 3d c- and n - edited noesy - hsqc spectra ( zhang et al .
2011 ) , this protein mutant also exists in solution as a homodimer built up of noncovalently attached subunits ( molecular weight of the monomer is 10  kda ) .
nmr sample contained 1.0  mm n , c labeled protein ( the monomer concentration ) in 90  % /10  % h2o / d2o , 50  mm tris - d11 , 1.0  mm edta , 0.1  mm nan3 and 50  mm nacl with ph adjusted to 7.2 .
the experiments were performed at 37  c on a 700  mhz agilent / varian spectrometer equipped with the performa xyz pfg unit and the 5  mm h , c , n triple - resonance probehead . 3d noesy - hsqc and 4d hmqc - noesy - hsqc spectra were analyzed with sparky ( goddard and kneller ) . in both cases , peak picking and inspection of resulting peak lists
conventionally sampled 3d noesy - c - hsqc spectrum was acquired in 36  h and processed using nmrpipe program ( delaglio et al .
1995 ) . to derive noesy interproton distance constrains from the 4d c(ali),c(aro)-edited noesy , automatic noesy assignment procedure ( herrmann et al .
the final validation of obtained constraints was performed with xplor - nih program ( schwieters et al .
the processing of four - dimensional nus data was accomplished by the home - written ssa ( signal separation algorithm ) software package , which can be downloaded free of charge for non - commercial purposes from the website http://nmr.cent3.uw.edu.pl ( 64-bit versions for linux ) .
artefact suppression in ssa software ( cleaner4d program ) was intentionally disabled by setting maximum number of iterations to zero .
this is equivalent to the use of raw zero - augmented fourier transformation and limits cleaner4d to data conversion .
the actual computation of spectral data was performed using reconstructor4d program ( also from ssa package ) that implements ( a ) automatic choice between fft and dft whenever beneficial , ( b ) multi - threaded computations and ( c ) memory - mapped and asynchronous input  output disk operations to improve overall performance .
the total processing time on a pc equipped with intel i5 3.3  ghz cpu running under ubuntu 11 was 2  min and 6  min 30  s using 4 and 1 threads , respectively .
final spectrum stored in sparky format ( single - precision ) was of size of 10.1  gb . ssa software supports native agilent / varian as well as nmrpipe format as input data .
two possible solutions are discussed here : aliphatic - to - aromatic ( fig . 
1b ) hmqc - noesy - hsqc . in both cases the optimized hmqc scheme ( stanek et al .
2012 ) was incorporated for t1 ( h ) and t2 ( c ) evolution as it utilizes the multiple - quantum line narrowing effect for c  h coherences ( grzesiek et al .
1995 ) . in the previous work on 3d h(aro)-noesy - ch3,hn and 3d c(aro)-noesy - ch3,hn ( xia et al .
2001 ) the refocused inept was utilized for the selection of protons coupled to aromatic c spins . in this case
selective transfer can be achieved employing shaped inversion pulses and pulsed field gradients ( pfgs ) that suppress undesired coherences in the subsequent z - filtration .
we have found that the same task is far more demanding using hmqc . in this case pfgs can not be used to distinguish aromatic and aliphatic mq h 
c coherences as both have equal coherence order after initial 1/2jch delay and  hard excitation pulse .
if the selective excitation pulse is employed pfgs can be useful , however , sensitivity loss of a factor of \documentclass[12pt]{minimal } 
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				 \begin{document}$$ \sqrt 2 $ $ \end{document } is incurred and additional time is required for gradient encoding when c magnetization is transverse .
we thus conclude that the optimal solution includes phase cycling of selective excitation pulses . despite these difficulties hmqc
is preferred over refocused inept owing to ( 1 ) the apparently slower relaxation of mq coherences and ( 2 ) the possibility to incorporate both magnetization transfer delays ( 1/jch in total ) for the shared - time proton evolution ( t1 ) that leads to increased sensitivity ( stanek et al .
1pulse sequence scheme for ( a ) c(aliph)hmqc - noesy - c(aro)hsqc and ( b ) c(aro)hmqc - noesy - c(aliph)hsqc .
90 and 180  hard pulses are represented by filled and open bars , respectively .
shaped pulses are represented as follows : ( a ) 40  ppm selective pulse of the iburp-2 profile ( geen and freeman 1991 ) ( 659  s duration , 7.6  khz peak r.f .
field ) is shown as wide open bell - shaped pulse ( denoted  e ) .
wide grey rectangular pulses (  a and  c ) are of duration of 61  s and peak r.f .
4.1  khz ( calibrated to give null excitation 90  ppm off -resonance ) .
( b ) wide grey bell - shaped pulse denotes 80  ppm - selective hyperbolic secant adiabatic pulse ( silver et al .
narrow grey bell - shaped pulses (  f and  h ) utilize gaussian profile ( bauer et al .
1984 ) ( truncated at 1  % , duration of 178  s , peak r.f .
note that for some hardware the shaped 90 pulses (  a ,  c ,  f and
 h ) may require small angle phase adjustment to compensate 0th order phase shift with respect to refocusing pulses (  b and  g ) which are applied at full power .
n refocusing pulse enclosed in dashed - line box ( sequence b ) is optional and may be used if delay complementing to half - dwell time ,   =  [ ( sw3 )    pw180(n)]/2 , is positive .
refocusing of caliph - c couplings in t2 ( a ) or t3 ( b ) may be considered if max .
the composite 34.2x123x197.6x288.8x pulse (  d and  i ) was used in hmqc for broadband inversion of c spins ( shaka 1985 ) .
watergate ( piotto et al . 1992 ) with 3 - 9 - 19 pulses separated by ( 3.2  khz ) was employed for experiment ( a ) .
c composite pulse decoupling was performed employing wurst scheme ( kupe and freeman 1995 ) .
/2 pulses were 7.1 , 14.3 and 31  s for h , c and n , respectively .
1 , 2 and 3 are incremented for quadrature detection in t1 , t2 and t3 using states ( 1 ) or states - tppi ( 2 , 3 ) method .
four - step phase cycle is as follows : 1  =  45 ; 2  =  x , x ; 3  =  2(x ) , 2(x ) ; 4  =  2(x ) , 2(x ) ; 5  =  135 ; rec  =  x ,
delays are set as follows : a  =  1.79  ms    ( 4  jchaliph ) , b  =  1.56  ms    ( 4  jcharom ) .
noesy mixing time m  =  150  ms was used . for the semi - constant time evolution in t1 ( h ) the delays 1 , 2 and 3 are t1/2 , t1(1    2/t1,max)/2 and (1    t1/t1,max ) , where   =  2a , or   =  2b for sequences ( a ) and
gradient levels and durations are : g1 ( 2  ms , 6.5  gs / cm ) , g2 ( 2  ms , 14.2  gs / cm ) , g3 ( 0.5  ms , 1.77  gs / cm ) , g4 ( 2  ms ,  11.3  gs / cm ) , g5 ( 2  ms , 12.9  gs / cm ) , g6  ( 0.5  ms , 5.4  gs / cm ) .
proton carrier frequency was set on resonance with water ( 4.68  ppm ) , carbon carrier was set to 35  ppm and switched to 125  ppm as indicated by the vertical arrow ; n carrier was set to 117  ppm and shifted to 162  ppm at the beginning of noesy mixing period . for the aliphatic - to - aromatic noesy ( a ) 4,400 sampling points ( t1,t2,t3 ) were randomly chosen from 120    84    30 cartesian grid according to gaussian probability distribution , p(t )  =  exp[(t / tmax)/2 ] ,   =  0.5 , with poisson disk restrictions ( kazimierczuk et al . 2008 ) .
maximum evolution times of 15 ( t1 ) , 6  ( t2 ) and 5  ms ( t3 ) were achieved in the indirectly detected dimensions .
spectral widths of 8 , 14 , 6 and 12  khz were set in 1 , 2 , 3 and 4 dimensions , respectively . in the full 4d spectrum
any residual diagonal peaks can be folded in c ( 2 and 3 ) dimensions without the risk of overlap and misinterpretation with genuine peaks .
the only requirement is to ensure proper h ( 1 ) spectral width to avoid aliasing in this indirect dimension .
the restriction of c spectral widths is very practical as it saves vast amounts of disk space .
the total experimental time was 57  h pulse sequence scheme for ( a ) c(aliph)hmqc - noesy - c(aro)hsqc and ( b ) c(aro)hmqc - noesy - c(aliph)hsqc . 90 and 180
shaped pulses are represented as follows : ( a ) 40  ppm selective pulse of the iburp-2 profile ( geen and freeman 1991 ) ( 659  s duration , 7.6  khz peak r.f .
field ) is shown as wide open bell - shaped pulse ( denoted  e ) .
wide grey rectangular pulses (  a and  c ) are of duration of 61  s and peak r.f .
4.1  khz ( calibrated to give null excitation 90  ppm off -resonance ) .
( b ) wide grey bell - shaped pulse denotes 80  ppm - selective hyperbolic secant adiabatic pulse ( silver et al .
narrow grey bell - shaped pulses (  f and  h ) utilize gaussian profile ( bauer et al .
1984 ) ( truncated at 1  % , duration of 178  s , peak r.f .
note that for some hardware the shaped 90 pulses (  a ,  c ,  f and
 h ) may require small angle phase adjustment to compensate 0th order phase shift with respect to refocusing pulses (  b and  g ) which are applied at full power .
n refocusing pulse enclosed in dashed - line box ( sequence b ) is optional and may be used if delay complementing to half - dwell time ,   =  [ ( sw3 )    pw180(n)]/2 , is positive .
refocusing of caliph - c couplings in t2 ( a ) or t3 ( b ) may be considered if max .
evolution time of aliphatic c spins exceeds 9  ms . the composite 34.2x123x197.6x288.8x pulse (  d and  i ) was used in hmqc for broadband inversion of c spins ( shaka 1985 ) .
watergate ( piotto et al . 1992 ) with 3 - 9 - 19 pulses separated by ( 3.2  khz ) was employed for experiment ( a ) .
c composite pulse decoupling was performed employing wurst scheme ( kupe and freeman 1995 ) .
/2 pulses were 7.1 , 14.3 and 31  s for h , c and n , respectively .
1 , 2 and 3 are incremented for quadrature detection in t1 , t2 and t3 using states ( 1 ) or states - tppi ( 2 , 3 ) method . four - step phase cycle is as follows : 1  =  45 ; 2  =  x , x ;
3  =  2(x ) , 2(x ) ; 4  =  2(x ) , 2(x ) ; 5  =  135 ; rec  =  x , x , x , x .
delays are set as follows : a  =  1.79  ms    ( 4  jchaliph ) , b  =  1.56  ms    ( 4  jcharom ) .
for the semi - constant time evolution in t1 ( h ) the delays 1 , 2 and 3 are t1/2 , t1(1    2/t1,max)/2 and (1    t1/t1,max ) , where   =  2a , or   =  2b for sequences ( a ) and ( b ) , respectively ( stanek et al . 2012 ) .
gradient levels and durations are : g1 ( 2  ms , 6.5  gs / cm ) , g2 ( 2  ms , 14.2  gs / cm ) , g3 ( 0.5  ms , 1.77  gs / cm ) , g4 ( 2  ms ,  11.3  gs / cm ) , g5 ( 2  ms , 12.9  gs / cm ) , g6  ( 0.5  ms , 5.4  gs / cm ) .
proton carrier frequency was set on resonance with water ( 4.68  ppm ) , carbon carrier was set to 35  ppm and switched to 125  ppm as indicated by the vertical arrow ; n carrier was set to 117  ppm and shifted to 162  ppm at the beginning of noesy mixing period . for the aliphatic - to - aromatic noesy ( a ) 4,400 sampling points ( t1,t2,t3 ) were randomly chosen from 120    84    30 cartesian grid according to gaussian probability distribution , p(t )  =  exp[(t / tmax)/2 ] ,   =  0.5 , with poisson disk restrictions ( kazimierczuk et al .
maximum evolution times of 15 ( t1 ) , 6  ( t2 ) and 5  ms ( t3 ) were achieved in the indirectly detected dimensions .
spectral widths of 8 , 14 , 6 and 12  khz were set in 1 , 2 , 3 and 4 dimensions , respectively . in the full 4d spectrum
any residual diagonal peaks can be folded in c ( 2 and 3 ) dimensions without the risk of overlap and misinterpretation with genuine peaks .
the only requirement is to ensure proper h ( 1 ) spectral width to avoid aliasing in this indirect dimension .
the restriction of c spectral widths is very practical as it saves vast amounts of disk space .
the total experimental time was 57  h here , the selection of either aliphatic ( fig . 
1b ) proton - carbon mq coherences is accomplished solely by band - selective excitation of c spins in conjunction with the four - step phase cycle of two /2 pulses (  a , 
f ,  h , respectively ) . therefore , the choice of selective /2 pulses is of the particular relevance .
apparently , it is quite straightforward not to excite aromatic c spins ( the sequence shown in fig . 
more advanced pulses such as gaussian cascade q5 ( emsley and bodenhausen 1992 ) or e - burp ( geen and freeman 1991 ) could be utilized as well , however , these pulses are ( 1 ) of significantly larger duration , ( 2 ) more sensitive to miscalibration and ( 3 ) require high peak r.f . field .
it was experimentally verified that these shortcomings offset theoretical benefits of high quality pulses and significant loss of sensitivity is incurred . for the aromatic - hmqc ( fig . 
due to the use of shaped /2 c pulses in hmqc the refocusing  pulse is obligatory for correct phase properties of signals in 2 dimension .
however , no additional selectivity improvement can be achieved by replacement of this pulse by a band - selective one .
similarly , the subsequent carbon inversion pulse in hmqc ( denoted  d and  i , respectively ) should be sufficiently broadband .
a shaped pulse here would only result in the t1-dependent jch evolution of unaffected coherences during total time of 1  +  2   
the resulting signals would be impossible to suppress using neither phase cycling nor pulsed field gradients .
all nmr experiments were performed for the e32q mutant of human s100a1 protein , for which resonance assignments are available in bmrb under accession code 17857 . the high resolution 3d structure based on the standard 3d c- and n - edited noesy - hsqc spectra ( zhang et al .
2011 ) , this protein mutant also exists in solution as a homodimer built up of noncovalently attached subunits ( molecular weight of the monomer is 10  kda ) .
nmr sample contained 1.0  mm n , c labeled protein ( the monomer concentration ) in 90  % /10  % h2o / d2o , 50  mm tris - d11 , 1.0  mm edta , 0.1  mm nan3 and 50  mm nacl with ph adjusted to 7.2 .
the experiments were performed at 37  c on a 700  mhz agilent / varian spectrometer equipped with the performa xyz pfg unit and the 5  mm h , c , n triple - resonance probehead . 3d noesy - hsqc and 4d hmqc - noesy - hsqc spectra were analyzed with sparky ( goddard and kneller ) . in both cases , peak picking and inspection of resulting peak lists was performed in approximately 30  min .
conventionally sampled 3d noesy - c - hsqc spectrum was acquired in 36  h and processed using nmrpipe program ( delaglio et al .
1995 ) . to derive noesy interproton distance constrains from the 4d c(ali),c(aro)-edited noesy , automatic noesy assignment procedure ( herrmann et al . 2002a ) implemented in program cyana 3.0 ( guntert et al .
the final validation of obtained constraints was performed with xplor - nih program ( schwieters et al .
the processing of four - dimensional nus data was accomplished by the home - written ssa ( signal separation algorithm ) software package , which can be downloaded free of charge for non - commercial purposes from the website http://nmr.cent3.uw.edu.pl ( 64-bit versions for linux ) .
artefact suppression in ssa software ( cleaner4d program ) was intentionally disabled by setting maximum number of iterations to zero .
this is equivalent to the use of raw zero - augmented fourier transformation and limits cleaner4d to data conversion .
the actual computation of spectral data was performed using reconstructor4d program ( also from ssa package ) that implements ( a ) automatic choice between fft and dft whenever beneficial , ( b ) multi - threaded computations and ( c ) memory - mapped and asynchronous input  output disk operations to improve overall performance .
the total processing time on a pc equipped with intel i5 3.3  ghz cpu running under ubuntu 11 was 2  min and 6  min 30  s using 4 and 1 threads , respectively .
final spectrum stored in sparky format ( single - precision ) was of size of 10.1  gb .
ssa software supports native agilent / varian as well as nmrpipe format as input data .
the performance of proposed selective noesy experiments was first verified on conventionally sampled homonuclear 2d spectra ( fig .  2 ) .
for both possibilities considered here , namely aliphatic - to - aromatic ( fig . 
2d ) excellent suppression of undesired autocorrelation ( i. e. aliphatic  aliphatic and aromatic  aromatic ) signals was obtained .
noteworthy is that in the non - selective versions of these experiments ( i.e. without use of shaped pulses ) substantial amount of spectral artefacts appear that may distort relevant region of aromatic 
aliphatic cross - peaks ( see , e.g. , pseudo - diagonals in fig . 
pulses and decoupling schemes at high static magnetic fields the simultaneous acquisition of aromatic  aliphatic and aliphatic 
aromatic noesy cross - peaks is hardly achievable ( fig .  2b , e ) .
thus , selection of one possibility is not lossy in terms of structural information gained.fig . 
2the comparison of homonuclear ( 1 ( h)2 ( h ) ) versions of ( a ) selective aliphatic - to - aromatic , ( b ) non - selective aliphatic - to - aromatic ( see fig . 
1b ) , ( d ) selective aromatic - to - aliphatic and ( e ) non - selective aromatic - to - aliphatic noesy experiments .
spectra ( a ) and ( d ) were acquired using pulse sequences shown in fig . 
non - selective versions ( b ) and ( e ) utilize the same pulse sequences as ( a ) and ( d ) , respectively , with all the shaped pulses replaced by  hard ones .
spectra ( b ) and ( e ) show that non - selective experiments suffer from many spectral artefacts due to poor broadband performance of 
apart from sign inversions across the spectrum , intense axial peaks as well as phase - distorted pseudo - diagonals are present ( e ) .
selective experiments ( a , d ) achieve to filter - out virtually all diagonal signals with only slight decrease of intensity of cross - peaks .
( c ) superimposed 1d cross - sections across 1 ( h ) from spectra ( a , blue curves ) and ( b , green curves ) for 2 coordinates indicated by the vertical arrows ( 13 ) .
( f ) 2 ( h , direct dimension ) cross - sections of spectra ( d , blue ) and ( e , green curves ) at 1 coordinates indicated by the horizontal arrows ( 13 ) .
the cross - sections are plotted using the same intensity scale , thus they enable direct comparison of experimental sensitivity between selective and non - selective versions of experiments ( a vs. b , and d vs. e ) . for each experiment 120
spectral width of 8  khz in the indirect 1 ( h ) dimension was set the comparison of homonuclear ( 1 ( h)2 ( h ) ) versions of ( a ) selective aliphatic - to - aromatic , ( b ) non - selective aliphatic - to - aromatic ( see fig . 
1b ) , ( d ) selective aromatic - to - aliphatic and ( e ) non - selective aromatic - to - aliphatic noesy experiments . spectra ( a ) and ( d ) were acquired using pulse sequences shown in fig . 
1a , b , respectively . non - selective versions ( b ) and ( e ) utilize the same pulse sequences as ( a ) and ( d ) , respectively , with all the shaped pulses replaced by  hard ones .
spectra ( b ) and ( e ) show that non - selective experiments suffer from many spectral artefacts due to poor broadband performance of 
apart from sign inversions across the spectrum , intense axial peaks as well as phase - distorted pseudo - diagonals are present ( e ) .
selective experiments ( a , d ) achieve to filter - out virtually all diagonal signals with only slight decrease of intensity of cross - peaks . ( c )
superimposed 1d cross - sections across 1 ( h ) from spectra ( a , blue curves ) and ( b , green curves ) for 2 coordinates indicated by the vertical arrows ( 13 ) .
( f ) 2 ( h , direct dimension ) cross - sections of spectra ( d , blue ) and ( e , green curves ) at 1 coordinates indicated by the horizontal arrows ( 13 ) .
the cross - sections are plotted using the same intensity scale , thus they enable direct comparison of experimental sensitivity between selective and non - selective versions of experiments ( a vs. b , and d vs. e ) . for each experiment 120
spectral width of 8  khz in the indirect 1 ( h ) dimension was set the sensitivity of noesy experiments is a critical issue .
.  2 do not indicate any substantial signal degradation resulting from use of selective pulses .
indeed , the closer inspection of 1d traces showing noesy cross - peaks ( fig . 
2c , f ) reveals only minor decrease of sensitivity accompanied by virtually complete suppression of diagonal peaks .
aromatic cross - peaks . although quite imprecise and susceptible to presence of unrelated spectral artefacts ( as in fig . 
2a , d ) are approximately up to 10  % less intense than their non - selective counterparts ( fig . 
2b , e ) . in the context of non - uniform sampling employed for four - dimensional experiment a rather moderate price for elimination of strong diagonal peaks  and associated spectral artifacts 
1a , b ) seem to provide equivalent structural information , there is a number of practical considerations involved . since aliphatic protons are typically far more populated than aromatic ones high resolution in aliphatic h dimension is especially desired .
this suggests to prefer the aromatic - to - aliphatic variant which provides the optimal resolution of directly detected h dimension . in the alternative aliphatic - to - aromatic spectrum
the indirectly detected h dimension features lower resolution , however , the assignment is supported by additional c chemical shift .
noteworthy , aliphatic h and c nuclei exhibit a broader distribution of chemical shifts than aromatic ones , thus simplifying the assignment task . to sum up
frequently , samples in h2o / d2o solution are used also for acquisition of noesy spectra in order to avoid data inconsistency due to different sample preparation and isotopic effects . in this case
the evident advantage of c , c - separated noesy is that watergate ( piotto et al .
1992 ) can be employed without suppression of relevant resonances . on the other hand , for the c , c - separated noesy presaturation of hdo signal
it is also worth mentioning that in the case of the c , c - noesy the detection of aromatic protons decreases requirements on c decoupling during acquisition . as broadband decoupling at high b0 field can be quite detrimental for the probehead circuits , the c
, c - edited noesy might be easier to implement on some hardware ( e.g. , cryoprobes ) .
the most decisive argument in favor of the c , c - separated noesy is its higher sensitivity . although it is not manifested in 2d h  h versions of compared experiments ( fig . 
2a , d show similar intensity of cross - peaks ) , the direct comparison of four - dimensional c , c - edited spectra indicated that c , c - edited experiment is considerably more sensitive . as the effect of shaped pulses is similar for both sequences ,
the most likely reason for different sensitivity of these experiments is the different attenuation of transverse relaxation rate observed for multiple quantum aromatic and aliphatic c  h coherences stored during c t2 evolution period . the distinguishing feature of selective aliphatic 
aromatic noesy is the absence of strong diagonal signals which provide no additional structural information .
this has a crucial implication that resulting spectra acquired using non - uniform sampling are not distorted by sampling artefacts , or their impact can be neglected in comparison to thermal noise ( see the flat baselines of noise in fig . 
3c , d ) . therefore , more advanced processing schemes such as ssa or clean do not have a particular advantage over zero - augmented fourier transformation ( kazimierczuk et al . 2012 ) .
the practical consequence is that a full 4d spectral matrix can be rapidly reconstructed , usually in a few minutes , depending mostly on hard disk performance ( see  experimental  section ) .
additionally , the s / n of most intense cross - peaks found in the indirect 3d cubes 13 shown in fig . 
3a , b confirms the above mentioned difference in overall sensitivity of two variants of selective noesy.fig . 
3a , b maximum signal - to - noise ratio measured for peaks in the individual 3d cubes ( indirect domains 1    2    3 ) in each point of directly detected dimension ( 4 ) .
the plots show the ratio of the most intense spectral point ( absolute value ) to the noise level in the corresponding 3d cube ( c , d ) . assuming that cross - peaks do not overlap in the 4d spectrum these plots reflect the overall sensitivity of experiment .
considerable sensitivity advantage of the aliphatic - to - aromatic ( a , c ) over aromatic - to - aliphatic ( b , d ) noesy is apparent .
noise levels ( c , d ) in the 3d cubes for each point of directly detected dimension were measured as the median of absolute values of all spectral intensities . from the uniformity of noise level across
directly detected dimension one can conclude that advanced procedures for nus artifact suppression are not beneficial in this case , and that the both experiments are sensitivity - limited .
the scale was cut for intense water resonance ( at 4.68  ppm ) a , b maximum signal - to - noise ratio measured for peaks in the individual 3d cubes ( indirect domains 1    2    3 ) in each point of directly detected dimension ( 4 ) .
the plots show the ratio of the most intense spectral point ( absolute value ) to the noise level in the corresponding 3d cube ( c , d ) . assuming that cross - peaks do not overlap in the 4d spectrum these plots reflect the overall sensitivity of experiment .
considerable sensitivity advantage of the aliphatic - to - aromatic ( a , c ) over aromatic - to - aliphatic ( b , d ) noesy is apparent .
noise levels ( c , d ) in the 3d cubes for each point of directly detected dimension were measured as the median of absolute values of all spectral intensities . from the uniformity of noise level across
directly detected dimension one can conclude that advanced procedures for nus artifact suppression are not beneficial in this case , and that the both experiments are sensitivity - limited . the scale was cut for intense water resonance ( at 4.68  ppm ) e32q mutant of human s100a1 protein was used to demonstrate the advantage of 4d c(ali),c(aro)-edited noesy in identification of noes between aromatic and aliphatic protons .
after synchronization of the 3 and 4 axes with the aromatic region of c  hsqc , the peak picking can be performed manually .
majority of these correlations can be unambiguously assigned by visual comparison of particular aliphatic planes of 4d noesy and the aliphatic region of c - hsqc spectrum.fig . 
4schematic illustration of reliable cross - peak assignment strategy using 4d c(ali),c(aro)-edited noesy spectrum . in the top left panel a plane of 4d c(ali),c(aro)-edited noesy at tyr 74 h/c chemical shifts is presented with expanded methyl region of the spectrum on the right side . in the bottom left panel 2d h 
corresponding cross peaks in the cross - section of 4d spectrum and the methyl region of hsqc are connected by arrows .
relevant methyl - aromatic cross - peaks can be readily assigned ( even manually ) as the ambiguity is removed by additional aliphatic - c chemical shift ( 2 ) schematic illustration of reliable cross - peak assignment strategy using 4d c(ali),c(aro)-edited noesy spectrum . in the top left panel a plane of 4d c(ali),c(aro)-edited noesy at tyr 74 h/c chemical shifts is presented with expanded methyl region of the spectrum on the right side . in the bottom left panel 2d h 
corresponding cross peaks in the cross - section of 4d spectrum and the methyl region of hsqc are connected by arrows .
relevant methyl - aromatic cross - peaks can be readily assigned ( even manually ) as the ambiguity is removed by additional aliphatic - c chemical shift ( 2 ) it should be emphasized that most of proton chemical shift degeneracies observed in 3d c(aro)-edited noesy has been removed in 4d c(ali),c(aro)-edited noesy providing 21 new reliable structural constraints .
the cross peak present in the 3d noesy spectrum splits into two noe correlations in the 4d spectrum .
5an example showing removal of proton chemical shift degeneracy by addition of aliphatic carbon-13 dimension . in the standard 3d c - edited noesy - hsqc spectrum ( top left panel ) only two cross peaks are observed for h proton of phe 15 . in the bottom
aromatic noesy is presented , and one of the cross peaks splits into two . on the right panel the corresponding fragment of previously determined 3d structure of s100a1 e32q ( pdb code 2lhl ) is shown .
only the e70 hf15 h and k27 hf15 h interactions were marked an example showing removal of proton chemical shift degeneracy by addition of aliphatic carbon-13 dimension . in the standard 3d c - edited noesy - hsqc spectrum
( top left panel ) only two cross peaks are observed for h proton of phe 15 . in the bottom left panel a cross section from 4d aliphatic 
aromatic noesy is presented , and one of the cross peaks splits into two . on the right panel the corresponding fragment of previously determined 3d structure of s100a1 e32q ( pdb code 2lhl ) is shown .
only the e70 hf15 h and k27 hf15 h interactions were marked all constraints obtained from the 4d noesy spectrum were carefully validated against the previously determined structure of the e32q s100a1 protein ( pdb accession code 2lhl ) . as demonstrated for h/c of phe 15 , all nuclei contributing to observed noes are in spatial proximity ( cf .
the right panel of fig .  6 ) . additionally , it was verified that most cross - peaks identified in the 4d spectrum were assigned consistently with peaks present in its 3d counterpart .
the only few differences concern stereospecific assignment of noe contacts and peaks that have not be assigned in 3d spectrum due to ambiguity.fig . 
6 in the top left panel the slice of 3d c - edited noesy - hsqc for h/c of phe 15 is presented .
in the bottom left panel corresponding plane of 4d c(ali),c(aro)-edited noesy is presented . in the right panel a fragment of 3d structure derived previously is presented .
residues are color - coded as are the lines connecting corresponding peaks in the spectra , while phe 15 is presented in black in the top left panel the slice of 3d c - edited noesy - hsqc for h/c of phe 15 is presented . in the bottom left panel corresponding plane of 4d c(ali),c(aro)-edited noesy
is presented . in the right panel a fragment of 3d structure derived previously is presented .
residues are color - coded as are the lines connecting corresponding peaks in the spectra , while phe 15 is presented in black at present manual noesy cross peak assignment is rarely performed .
therefore , the standard automatic protocol for assignment of noe correlations , implemented in cyana software , was applied for the analysis of the 3d c(aro)-edited noesy - hsqc and 4d c(ali),c(aro)-edited noesy spectra .
it seems surprising that 3d spectrum resulted in a slightly larger number of constraints than the 4d one .
it should be borne in mind , however , that most of 3d - derived noe correlations in larger proteins are heavily degenerated .
current assignment algorithms deduce such a distance constraint on the basis of chemical shifts and the supposed proton spatial proximity in the tentative structure model .
consequently , a number of correlations are , to some extent , speculative and estimation of their intensities ( necessary for distance calibration ) is putative . on the other hand , most of 4d - derived noe correlations
it might be of crucial importance for de novo structure determination of an unknown system .
as shown in table  1 some weak correlations visible in 3d noesy were missing in the 4d spectrum due to its intrinsically lower sensitivity , however , these include mostly weak intraresidual h 
most importantly , the number of essential long range and intersubunit constraints was not affected.table  1the summary of noe constraints derived from standard 3d c - edited noesy hsqc ( tuned to aromatic carbons ) and 4d c(ali),c(aro)-edited noesy3d c(aro)-edited noesy hsqc4d c(ali),c(aro)-edited noesynumber of common constraints from 3d and 4d spectraconstraints between aromatic and aliphatic protons156131111intraresidual ( i    j    1)635044medium range ( 1  <  i    j  <  5)221410long range ( i    j    5)454437intersubunit2623204d spectrum provided 20 additional constraints that could not be assigned in the 3d spectrum . a number of weak noe contacts present in 3d spectrum were not detected in 4d noesy , including mostly intraresidual hh , hh and hh noe contacts .
nevertheless , the number of most relevant long range and intersubunit constraints remained virtually equal the summary of noe constraints derived from standard 3d c - edited noesy hsqc ( tuned to aromatic carbons ) and 4d c(ali),c(aro)-edited noesy 4d spectrum provided 20 additional constraints that could not be assigned in the 3d spectrum .
a number of weak noe contacts present in 3d spectrum were not detected in 4d noesy , including mostly intraresidual hh , hh and hh noe contacts .
nevertheless , the number of most relevant long range and intersubunit constraints remained virtually equal the final structural calculations were performed with xplor - nih program to confirm if the noe distance constraints from automatic procedure were calibrated correctly .
the substitution of constraints derived from 3d noesy with constraints from 4d c(ali),c(aro)-edited noesy did not lead to any constraint violations during calculations , or noticeable differences between obtained structures .
aromatic c , c - edited 4d noesy experiments . as these experiments inherently lack the diagonal signals , significant spectral artifacts originating from either non - uniform sampling , hardware instability or r.f .
thus , the applications of proposed experiment is not limited to small - sized proteins . owing to high spectral resolution and selection of a subset of noe contacts
it may become a valuable tool for three - dimensional structure elucidation of large proteins .
full benefits of the novel method presented here can be achieved when applied in conjunction with previously reported 4d amide  amide , amide 
 a band - selective aromatic  aliphatic c , c - edited four - dimensional noesy experiment is proposed here . 
 its key advantage is the absence of auto - correlation signals which makes it very attractive for joint use with non - uniform sampling . 
 it is demonstrated here that the sensitivity of the experiment is not significantly affected by utilization of selective pulses ( for either aromatic-13c or aliphatic-13c spins ) . 
 the method was applied to the sample of e32q mutant of human s100a1 protein , a homodimer of total molecular mass ~20  kda . 
 high - resolution 4d spectra were obtained from ~1.5  % of sampling points required conventionally . 
 it is shown that superior resolution facilitates unambiguous assignment of observed aliphatic  
 aromatic cross - peaks . 
 additionally , the addition of aliphatic-13c dimension enables to resolve peaks with degenerated aliphatic 1h chemical shifts . 
 all observed cross - peaks were validated against previously determined 3d structure of e32q mutant of s100a1 protein ( pdb 2lhl ) . 
 the increased reliability of structural constraints obtained from the proposed high - resolution 4d 13c(ali),13c(aro)-edited noesy can be exploited in the automated protocols of structure determination of proteins.electronic supplementary materialthe online version of this article ( doi:10.1007/s10858 - 013 - 9739 - 5 ) contains supplementary material , which is available to authorized users . 
Electronic supplementary material
Introduction
Materials and methods
Selective 4D HMQC-NOESY-HSQC experiments
Experimental
Results and discussion
Conclusions
Electronic supplementary material