protein 
 dynamics plays critical roles in biological functions such 
 as enzyme catalysis , ligand binding , and signal transduction . it has drawn increasing research attention in recent studies , as 
 protein structures alone do not fully explain biological activities . x - ray diffraction ( xrd ) and nuclear magnetic resonance ( nmr ) are the 
 premier methods to determine protein conformation . xrd reports primarily 
 on structure , and the protein flexibility is only indirectly reflected 
 in b - factors . therefore , it is problematic to address protein dynamics 
 solely from b - factors , which also are affected by crystal packing 
 defects , whole - body motions and refinement artifacts . further , b - factors are insensitive to reorientation motions and 
 are unable to distinguish motions covering different time scales . protein dynamics can be elucidated by nmr along with several other techniques , including md simulations , fluorescence spectroscopy , and electron paramagnetic 
 resonance ( epr ) . nmr is the premier technique 
 for probing motions in proteins and widely implemented to investigate 
 protein mobility at the atomic level . well - developed methods in solution - state nmr include 
 spin relaxation ( r1 , r2 , and r1 ) , carr  purcell meiboom  gill ( cpmg ) relaxation 
 dispersion , residual dipolar couplings ( rdcs ) , hydrogen  deuterium exchange , and deuterium relaxation . these measurements 
 capture motions with time scales from picoseconds to seconds , which substantially expand our 
 understanding of protein structure and dynamics . for example , a recent 
 study successfully quantified side - chain 1 distributions by 
 rdcs for the third domain of protein g. slow molecular tumbling leads to poor spectral resolution and sensitivity , 
 which hinder the application of solution - state nmr to large proteins . in addition , chemical shift anisotropy ( csa ) , dipolar coupling , and 
 quadrupolar coupling line shapes convey rich information on site - specific 
 motional modes and rates . in contrast , in solid - state 
 nmr , the anisotropic line shapes are retrieved and can be detected 
 accurately to illustrate dynamics of chemical groups in a protein . similar to solution - state nmr , spin relaxation is routinely implemented 
 in solid - state nmr for investigating dynamics . for example , a recent study determined 
 13 sets of bulk nmr relaxation times for the 1 immunoglobulin 
 binding domain of protein g ( gb1 ) microcrystals at various temperatures . the results explored the hierarchical distribution 
 of backbone and side - chain motions as well as protein solvent 
 motion coupling for microcrystalline gb1 over the temperature window 
 of 105280 k. recent studies showed that the cpmg relaxation 
 dispersion approach was applicable in the solid state . these solid - state nmr developments paved the 
 way for the elucidation of dynamics in large proteins and especially 
 benefit the study of membrane proteins . further , high similarity was 
 shown for picosecond to submicrosecond dynamics elucidated by solid - state 
 and solution - state nmr for sh3 and ubiquitin , implying the validation 
 of extrapolating solid - state dynamics information to proteins in their 
 native states . extensive effort has been devoted to develop 
 solid - state nmr pulse 
 sequences for dynamics detection by utilizing dipole for example , studies managed to 
 determine order parameters from scaled h  c dipolar couplings measured using homonuclear coupling attenuation 
 pulse schemes such as t - mrev , phase - modulated 
 lee  goldberg irradiation , rotational - echo 
 double resonance ( redor ) , cross polarization combined with phase inversion 
 ( cppi ) , and symmetry - based pulse sequences . moreover , the use of these dipolar recoupling 
 techniques in solid - state nmr has enabled the elucidation of dynamics 
 for a number of proteins . the most commonly used quadrupolar nuclei in biological studies 
 is deuterium , which can be enriched by replacing protons without altering 
 critical chemical and physical properties of the systems . in comparison 
 with the dipolar interaction and csa , the h quadrupolar 
 coupling constant ( cq ) is significantly 
 larger ( 200 khz ) , which gives rise to opportunities to study 
 dynamics as well as several spectroscopic challenges . the large amplitude 
 of the h cq enables much more 
 accurate measurements than those of the dipolar coupling or csa . currently , however , the ability to quantitatively evaluate protein 
 dynamics is partially complicated by the absence of a complete understanding 
 of rigid - limit quadrupolar tensor values ( addressed in the following 
 section ) . h line shape and relaxation time together enable 
 the characterization of protein dynamics covering time scales from 
 picoseconds to seconds . on the other hand , limitations 
 of nmr hardware and pulse sequences impede the application of h cq measurements in large proteins or other macromolecules . solid - state nmr probes enabling high power irradiation of h , simultaneously with h and c and/or n , combined with high magic angle spinning ( mas ) rates , allow 
 the efficient excitation and detection of h signals in 
 a site - specific fashion with multidimensional nmr . cross - polarization 
 ( cp ) is one of the most common pulse elements 
 exploited to transfer magnetization in multidimensional solid - state 
 nmr . c tangent cp transfers in two-/three - dimensional ( 2d/3d ) 
 experiments to indirectly detect h quadrupolar line shapes 
 and spin  lattice ( t1 ) relaxation 
 times to probe dynamics of nav , amino 
 acids , sh3 protein , and silk proteins . as pointed out in previous 
 studies and observed in the current work , conventional h c cp schemes lead to nonuniform magnetization 
 transfer across the broad h powder pattern . the optimal cp condition providing accurate h line shape covers an extraordinarily narrow rf band ( < 1 
 khz ) and is sensitive to h cq . thus , it is challenging to measure 
 quadrupolar parameters accurately for sites with different cq values using one particular cp condition . c cp in multidimensional nmr to extract h quadrupolar 
 information for proteins as the range of motional averaged cq is up to 185 khz . a recently 
 invented polarization transfer pulse scheme , rotor - echo - short - pulse - irradiation 
 ( respiration ) cp , shows the potential to overcome the nonuniformity of magnetization 
 transfer observed in conventional cp . c cp and is more tolerant to the variation of experimental 
 conditions such as rf mismatching , probe detuning , and spinning instability . later studies demonstrated that adiabatic respiration 
 cp further improves the performance even using very low rf field strengths . these studies primarily focused on the cp efficiency enhancement 
 illustrated by numerical simulations and experimental data . c cp matching profile in adiabatic 
 respiration cp implies that an optimal cp condition concurrently satisfies 
 chemical groups with different cq s , 
 namely , allowing accurate measurement of quadrupolar coupling parameters 
 for all sites in complicated systems like perdeuterated proteins . in the present work , c  c 
 solid - state nmr experiment to elucidate site - specific protein backbone 
 and side - chain dynamics . spc-5 is employed in the 3d experiment to build c  c correlations in order to resolve h sites . in 
 comparison with first , 
 the resulting h powder patterns are on the order of 100 
 khz , which is significantly larger than h second , dipolar 
 measurements have higher demands on experimental conditions including 
 spinning rates and recoupling pulses in order to efficiently suppress 
 homonuclear dipolar couplings and reintroduce heteronuclear dipolar 
 couplings under mas . in contrast , the 3d h  c  c experiment is more robust because 
 the accuracy of the obtained h spectra solely depends 
 on the h c cp step and is ensured 
 by the use of the adiabatic respiration cp . c approach 
 is that it offers improved spectral resolution through using samples 
 which are typically fully deuterated , relative to dipolar measurements 
 requiring protonated samples . however , one drawback to h nmr is that the current understanding of rigid - limit cq values for proteins is incomplete , consequently impeding 
 the ability to access quantitative dynamics information . specifically , 
 due to a general lack of systematic studies , the variation of quadrupolar 
 rigid - limit cq values for deuterium bonded 
 to sp - hybridized carbon has not been fully evaluated for 
 proteins . to assist quantification of protein side - chain motions using h relaxation times , two recent solution - state nmr studies 
 indirectly determined the rigid - limit cq values for cd3 in the n - terminal drk sh3 domain as well as cd 
 in both ubiquitin and gb1 proteins . the 
 methyl deuterium rigid - limit cq values 
 were found to be approximately uniform , at 167  1.5 khz.h rigid - limit cq values were determined to be 174 khz on average with 
 68% uncertainty which the authors attribute to possible measurement 
 uncertainties rather than actual cq variation . together , these two studies suggest that the 
 rigid - limit cq values for deuterium at 
 methyl and c sites in a protein are likely uniform . it is worth 
 noting that the quantification of rigid - limit cq values in these studies may be associated with nontrivial 
 uncertainties resulting from a number of factors . to date , the rigid - limit cq values for 
 deuterium at sites other than methyl and c sites have not been 
 systematically evaluated for proteins . the inherent variation of deuterium 
 quadrupolar interactions in the rigid lattice requires further investigation 
 in order to guide the h solution - state and solid - state 
 nmr dynamics studies for proteins . for example , one straightforward 
 approach to obtain the rigid - limit cq values 
 is by the measurement of h line shapes for proteins with 
 multidimensional mas solid - state nmr at ultralow temperatures where 
 the motions are quenched , which can be performed with the state - of - the - art 
 nmr instrumentation and is an interesting topic for future studies . 
 in this paper , we focus on the comparison of motionally averaged quadrupolar 
 coupling constant ( ) values for side chains of microcrystalline 
 protein gb1 to gain dynamics information . because of the lack of the 
 quantitative rigid - limit cq values and 
 the complexity brought by the nonzero motional averaged asymmetry 
 parameters (  ) , we interpret the data by comparing   values instead of using generalized order 
 parameters . such comparisons are performed between the same chemical 
 groups of the same type of residues to minimize uncertainties originating 
 from the potential rigid - limit cq differences . this semiquantitative analysis provides critical insights into protein 
 dynamics , especially those of side chains , which have not been systematically 
 studied in detail . in this study c experiment on 
 microcrystalline gb1 , 
 in order to extract h quadrupolar information for each 
 chemical group . the obtained   and  elucidate the backbone 
 and side - chain motions for the majority of residues in a site - specific 
 manner . to our knowledge , this is the first example in which the backbone 
 and side - chain dynamic network is fully mapped based on h quadrupolar coupling parameters extracted from a single solid - state 
 nmr experiment . the results illustrate that side - chain dynamics of 
 gb1 highly correlate with its structure stability and biological functions . we envisage that this approach will be widely applicable to investigate 
 backbone and side - chain motions in various biological systems such 
 as protein microcrystals / nanocrystals , insoluble fibrils , and membrane 
 proteins . uniformly labeled h , c , n - gb1 was expressed in e. coli bl12(de3 ) using a 
 previously published protocol . the protein 
 solution was buffer exchanged against 90/10 
 d2o / h2o to replace 10% of the exchangeable deuterons 
 with protons and then was concentrated to 25 mg / ml and precipitated 
 with 3.0 equiv of 2-methyl-2,4-pentanediol ( mpd ) and isopropanol ( ipa ) 
 solution ( 2:1 mpd / ipa volume ratio ) . microcrystalline 
 gb1 was packed into a 1.6 mm standard wall fastmas rotor ( agilent 
 technologies inc . ) for use in solid - state nmr experiments . data were collected on 
 a customized 500 mhz varian vnmrs directdrive spectrometer equipped 
 with actively biased transmit  receive circuits and a 1.6 mm 
 fastmas quadruple resonance h a 22.222 khz mas was chosen 
 as a compromise between peak sensitivity and the number of sidebands 
 present from the h manifold . the variable temperature 
 was 0 c , and the actual sample temperature was 3 c because 
 of frictional heating induced by mas ( as determined by an ethylene 
 glycol calibration ) . c solid - state nmr pulse 
 sequence is displayed in figure 1a and will be discussed in detail in the following 
 section . the h , c , h , and n /2 pulse widths were 1.5 , 1.6 , 2.9 , and 4.5 s , 
 respectively . in experiments performed on gb1 , 86 khz h and 100 khz c spin - lock rf field strengths and a 900 
 s contact time were used for adiabatic respiration cp magnetization 
 transfer . the rotor - synchronized adiabatic respiration cp waveform 
 was defined by the following optimized parameters :  = 4000 
 rad / s and b = 5000/2 hz and respiration pulse 
 p = 1.8 s ( see jain et al . for parameter 
 definition ) . the spc-5 homonuclear recoupling 
 scheme was implemented to build c  c correlations with a 1.086 ms mixing time . additional experimental 
 parameters include a 100 ms recycle delay , 400 khz h sweep 
 width , 22.222 khz and 50 khz c sweep width for the second 
 and third dimension , 192 t1 increment 
 points , 160 t2 increment points , and a 
 20.48 ms acquisition time . low - power h xix and n waltz decoupling was employed during the pulse periods as indicated 
 in figure 1a . data 
 were processed in nmrpipe and analyzed 
 in sparky ( t. d. goddard and d. g. kneller , university of california , 
 san francisco ) . c  c nmr 
 pulse sequence that was used for detecting h quadrupolar 
 line shapes . the initial excited h magnetization was transferred 
 to the directly bonded c and detected through c  c correlation . one critical element is the 
 cp transfer that dictates the accuracy of the extracted h line shapes and the sensitivity of the experiment . conventional 
 tangent cp was previously employed in 2d h  c experiments to establish heteronuclear correlation in order 
 to extract h line shapes for peptides and proteins . one drawback of the approach is that polarization transfer efficiency 
 is not uniform across h mas manifolds . thus , an optimal cp condition providing accurate h line shape is valid only for sites with a particular cq . it is unfeasible to use conventional cp to accurately 
 determine h line shapes for all sites of a system , particularly 
 in a protein where deuterium cq values 
 span 185 khz range . a newly invented polarization transfer 
 scheme , the so - called adiabatic respiration cp , shows the capability 
 to overcome this issue . motivated by the better performance of this 
 cp scheme over conventional methods , in this section , we focus on 
 evaluating the cross - polarization uniformity that was not previously 
 discussed in detail . c adiabatic 
 respiration cp was first performed on ala crystalline powder using 
 a pulse sequence displayed in figure s1a . polarization efficiency 
 at the optimal condition is enhanced by a factor of 2.4 and 1.8 for 
 ala methine and methyl groups , respectively , in adiabatic respiration 
 cp compared with conventional tangent cp . the significantly broader 
 plateau of matching condition observed in the former case illustrates 
 that polarization transfer is less sensitive to cp rf field strength 
 variation ( figure s1b ) . as shown in a previous 
 study , in a 2d experiment with conventional tangent h c cp , no cp condition provides accurate h line 
 shapes for both of the ala aliphatic groups concurrently . in other words , the cp condition yielding an 
 optimal h line shape for one ala group fails to provide 
 similar cp efficiency for other sites . this arises from the fact that 
 magnetization transfer is nonuniform across the h powder 
 pattern in the conventional cp approach . c correlation experiments were performed with various cp conditions . 
 as presented in figures s2 and s3 , ala c adiabatic respiration cp experiments remain consistent 
 over a wide range of h cp rf carrier frequency offsets . further , these values agree very well with the quadrupolar parameters 
 obtained from the h one - pulse excitation experiment ( figures s2 and s4 ) . table s1 shows   values of ala h and h extracted 
 from 2d experiments utilizing c cp rf field strengths 
 varying between 22 and 77 khz with the matching h rf condition . the differences among the   values obtained at various cp conditions 
 are negligible , and the values agree with literature reports for the 
 two ala aliphatic groups . these results demonstrate that adiabatic 
 respiration cp fulfills cp transfer uniformity over the h powder pattern . further , it implies that the cp condition providing 
 accurate h line shapes is insensitive to rf strengths . this performance is much improved in comparison with tangent cp , where 
 1 khz rf strength variation can easily lead to 10% or more   difference , as observed in the current 
 work and the previous study . to summarize , 
 utilizing adiabatic respiration cp for the h  c correlation step in multidimensional experiments to indirectly 
 extract h line shapes provides the following advantages . second , cp transfer is uniform across the h 
 powder pattern , ensuring the accuracy of the indirectly extracted h line shapes . third , both cp efficiency and uniformity are 
 much less sensitive to cp condition variation that allows for stable 
 data collection of 3d/4d solid - state nmr spectra . these three features 
 are essential for detecting site - specific deuterium quadrupolar information 
 for proteins possessing deuterium cq values 
 typically covering the range of 0 to 185 khz . a 3d solid - state mas nmr experiment 
 utilizing adiabatic respiration cp and spc-5 homonuclear recoupling 
 to achieve h c and c  c correlation , respectively , was designed in order to extract 
 site - specific h line shapes for large systems like proteins 
 ( figure 1a ) . the pulse 
 sequence allows h resonances to be resolved with the assistance 
 of c  c correlation and the accurate 
 line shapes to be extracted from the first indirect dimension . figure 1b displays 2d planes 
 of the 3d spectrum collected for microcrystalline gb1 , where h line shapes are extracted for the aliphatic groups of e56 . the motional averaged h quadrupolar parameters are readily 
 obtained from line - shape fitting . h line shapes were extracted 
 from the 3d spectrum for the majority of aliphatic groups , except 
 those subject to resonance overlap or signal absence and aromatic 
 rings exhibiting inefficient cp . line - shape fitting was performed 
 to extract motional averaged quadrupolar parameters ,   and  , for 140 chemical groups 
 in gb1 , and the fitting results are presented in figure s5 . the obtained h quadrupolar parameters 
 convey rich information about protein dynamics that correlate with 
 structure , local chemical environment , salt bridges , hydrogen bonds , 
 and other interactions . to our knowledge , this is the first example 
 that h motional averaged quadrupolar parameters have been 
 determined for most sites in a protein . in the following section , 
 discussion will first focus on the side - chain motions and then on 
 the backbone flexibility for microcrystalline gb1 . ( b ) 2d h  c planes of the 3d h  c  c spectrum collected 
 for microcrystalline gb1 and the extracted h line shapes 
 for the e56 residue . experimental line shapes 
 ( black ) , fits ( red ) , and fitting residuals ( blue ) are displayed in 
 the right column . in the 2d planes , signals with positive and negative 
 intensities h line shapes 
 for aliphatic groups of lys were extracted from the 3d h table 1 shows   and  values for lys aliphatic 
 groups in microcrystalline gb1 . the values present a large difference 
 between h and side - chain h as well 
 as among lys residues , indicating various backbone and side - chain 
 motions .   and contain detailed information 
 about the motional process , requiring analysis on a case - by - case basis 
 depending on the physical property of a chemical group . for example , 
 the line shape of k28 h gives a   of 125.4  1.8 khz and a  
 of 0.60  0.05 . if a reorientation in the fast - motion regime 
 between two sites with equal population is assumed for the k28 ( ch2 )  group , the reorientation angle satisfies cos  
 = 0.5 , which is derived from the experimental . thus , 
 a   of 125.4 khz corresponds to a cq(rigid 
 limit ) equal to 200.6 khz . this large cq(rigid - limit ) value is physically impossible 
 for a deuteron bonded with an sp - hybrized carbon . it infers that the k28 ( ch2) 
 group exhibits more complex dynamics than a simple two - site reorientation , 
 resulting from the combined effect of cc and 
 cc librations ; yet , the motional details involved 
 in this effect are beyond the scope of the current study . here , the 
 focus is put on the evaluation of the   that is proportional to order parameter 
 derived from /cq(rigid - limit ) . it is rational to illustrate mobility by comparing   values of amino acid aliphatic groups in 
 a protein , even though they do not provide motional details . for 
 deuterium undergoing large - amplitude 
 motion ,  was set to zero for line - shape fitting . the cc and cc 
 cross peaks of k4 severely overlap with those of k10 . the same h and h quadrupolar values were 
 assigned to k4 and k10 , which were obtained from the overlapped h line shapes . ( a ) crystal 
 structure of gb1 ( pdb : 2lgi ) with lys aliphatic groups shown in van 
 der waals spheres and coded with color scaling to   values . ( b ) k50 , ( c ) k31 , ( d ) k13 , ( e ) k4 , 
 ( f ) k10 , and ( g ) k28 local chemical environment in gb1 . the k31 ( ch2) group is color coded with cyan as the   value is not determined . the residues having 
 atoms within 5  away for the corresponding lys residue are shown 
 in sticks . the salt bridges between k50 and d47 , e27 , and k31 and 
 the hydrogen bond between k13 side chain nh3 and g9 backbone 
 co are displayed by dash lines . the gb1 crystal structure is displayed in figure 2a with lys residues shown in 
 van der waals 
 spheres color coded by   values . the observed large   variation indicates that molecular dynamics 
 differ significantly among lys residues in protein gb1 . values listed in table 1 show that the k50 side chain exhibits much 
 more restricted movement than other lys residues . the flexibility 
 of the amino acid backbone and side chain depends upon the local packing 
 density , salt bridges , hydrogen bonds , and solvent accessibility and 
 can in turn validate these phenomena . this residue is in the turn connecting 3 and is 
 exposed to the bulk solvent with more potential for interacting with 
 water molecules ( 31 water molecules 10  away from its 
 side chain based upon pdb : 2qmt(90 ) ) . it suggests that a 
 very dynamic side chain is expected for k50 that is controversial 
 to the experimental observation . the motion of the k50 side chain 
 is likely restricted by a stable salt bridge formed between k50 ( nh3) and d47 o with a n  o distance 
 of 3.07  ( pdb : 2qmt(90 ) ) . five out of ten solid - state nmr energy 
 minimum structures ( pdb : 2lgi(91 ) ) show that the formation 
 of this salt bridge is allowed where the two groups are 2.733.09 
  apart . the existence of a stable salt bridge indicated by the 
 rigid k50 side chain can be used to evaluate the validity of a protein 
 structure model . similarly , k31 and k13 exhibit moderate side - chain 
 dynamics among the five lys in gb1 , as implied by the   values . a salt bridge built between k31 
 ( nh3) and e27 o appears to be 
 the reason for restricted k31 side - chain motion ( figure 2c ) . n distance 
 is 2.76  in the xrd structure ( pdb : 2qmt(90 ) ) and 4 
  ( 3.493.78  ) in seven of the ten solid - state nmr 
 minimum energy structures ( pdb : 2lgi(91 ) ) , allowing 
 the formation of a salt bridge . the   values of k13 side - chain deuterium are 
 very similar to those of k31 . the solvent - exposure feature of k13 
 dictates that its side chain likely displays a large degree of mobility 
 ( figure 2d ) ; however , 
 this expectation does not agree with the determined   values . thus , the mobility must be quenched 
 by a salt bridge and/or a hydrogen bond . the local chemical environment 
 suggests that no nearby negatively charged groups are available for 
 forming a salt bridge with k13 side - chain amide group ( figure 2d ) . upon the basis of the nmr 
 ( pdb : 2lgi(91 ) ) and xrd ( pdb : 2qmt(90 ) ) structures , 
 a hydrogen bond is likely formed between k13 ( nh3) and the g9 backbone co groups with the o < 2.5  ( 2.73  in xrd structure ) and the o  h  n 
 angle in the range of 122128. in addition , the n8 side - chain 
 co group serves as another potential acceptor for a hydrogen bond 
 formed with k13 ( nh3) as indicated in 
 the xrd structure and one of the ten nmr minimum energy structures . these hydrogen bonds overcome the desolvation energy barrier for k13 
 and are responsible for rigidifying its side chain . much more dynamic 
 side chains are observed for k4 , k10 , and k28 . the three residues 
 are completely extended into the solvent and have no neighboring electron 
 acceptors available to form a stable hydrogen bond or a salt bridge 
 ( figure 2e  g ) . it is noted that a salt bridge could be formed between k4 and e15 
 side chains based on the distance ( 3.17  ) shown in the xrd structure 
 ( 2qmt ) . in addition , two intermolecular salt bridges , 
 k4e42 ( 4.81  ) and k10d40 ( 4.95  ) , exist 
 in the x - ray crystal structure ( 2qmt ) . the presence 
 of these salt bridges seems inconsistent with the large - amplitude 
 side - chain motions observed for k4 and k10 . it is likely that the 
 salt bridges are dynamic and are undergoing continual breaking and 
 reformation . alternatively , it is possible that these salt bridges 
 are absent in the structure of the currently studied gb1 sample , which 
 was prepared with crystallization conditions subtly different from 
 the x - ray study . for deuterium undergoing large - amplitude 
 motion ,  was set to zero for line - shape fitting . motional averaged 
 deuterium quadrupolar coupling constants and asymmetry parameters 
 for asp and asn residues are listed in table 2 . considerable variation is observed for 
 the backbone h and side - chain h 
 ( figure 3a ) . in general , 
 the large   values indicate that asp / asn local backbones 
 exhibit restricted motions . the side chains are less flexible than 
 those of lys residues due to the shorter side chains possessing more 
 limited spatial extension . it is shown that the side - chain dynamics 
 are likely further quenched by hydrogen bonds , salt bridges , and desolvation 
 for d22 , d36 , n37 , d46 , and d47 . as discussed above , d47 ( coo ) forms a stable salt bridge with k50 ( nh3) , resulting in the stiffness of side chains for 
 both residues ( figure 3b ) . upon the basis of the chemical environment of d22 ( figure 3c ) , a strong hydrogen bond 
 likely established between the d22 side chain coo group with t25 backbone nh , where the o n 
 angles are in the range of 1.772.02  and 138142 , 
 respectively . thus , the hydrogen bond contributes to the restricted 
 side - chain motion of d22 . further , it presumes that this strong hydrogen 
 bond formed between the loop and the  helix contributes to 
 the structural stability of gb1 . it 
 infers that the rigid side - chain motion of d46 is due to the hydrogen 
 bonds between coo and the a48 backbone nh with 
 an o  n distance of 2.662.71  and an o  h n 
 angle of 138143 according to the solid - state nmr structure 
 ( pdb : 2lgi(91 ) ) . the t49 nh is another possible electron donor 
 involved in forming a hydrogen bond , which is weaker as the o h  n angle 
 is 144148. the validity of the hydrogen bonding is further 
 supported by the absence of a competing electron acceptor for d46 . n distance for the two hydrogen bonds 
 is larger based upon the xrd structure ( pdb : 2qmt(90 ) ) , 3.11 and 4.13  , most likely due to minor structural 
 variation between the solid - state nmr and xrd structures originating 
 from subtle sample preparation differences . the inflexible d36 ( ch2) group is contradictory to its solvent exposure and 
 the lack of hydrogen bonds and a salt bridge ( figure 3e ) . the possible explanation is that d36 
 packs close to itself in the crystal lattice , deactivating the side - chain 
 motions . this tight packing is also found to be responsible for its 
 coo pka value being 
 higher than expected . the   values of n37 imply the immobility of the 
 side chain that resides at the edge of the open pocket formed between 
  strands and the  helix and is partially exposed to 
 solvent ( figure 3f ) . it is noted that the y33 aromatic ring is right above n37 ( nh2)2 , allowing the formation of a n h 
 hydrogen bond between the two . impacted by this hydrogen bond , n37 
 side - chain motion is significantly restricted . h 
 hydrogen bond is often observed in proteins and greatly contributes 
 to structure stability . ( a ) crystal structure 
 of gb1 ( pdb : 2lgi ) with asp and asn aliphatic groups shown 
 in van der waals spheres and coded with color scaling to   values . ( b ) d47 , ( c ) d22 , ( d ) d46 , ( e ) d36 , 
 ( f ) n37 , ( g ) n35 , ( h ) d40 , and ( i ) n8 local chemical environment in 
 gb1 . the residues having atoms within 5  away for the corresponding 
 asn or asp residue are shown in sticks . the salt bridge between d47 
 and k50 and the hydrogen bonds between d22 and t25 , d46 and a48/t49 , 
 and n8 and t55 are presented by dashed lines . n8 , n35 , and d40 possess more flexible side chains compared 
 with 
 other asn and asp residues discussed above . among the three , n35 is 
 the most dynamic one as it points outward from the protein surface 
 and interacts with surrounding solvent molecules ( figure 3 g ) . because of the similar 
 situation , large - amplitude side - chain motion is expected for d40 ( figure 3h ) . however , it is 
 impacted by an intermolecular interaction , where d40 forms a salt 
 bridge with k10 ( 4.95  ) . as discussed above 
 for k10 , the salt bridge , if it exists , is highly dynamic and only 
 slightly rigidifies the d40 and k10 side chains . the n8 side chain 
 presents moderate flexibility due to the coexistence of opposite effects being 
 mobilized by the surrounding solvent and potentially restricted by 
 hydrogen bonds ( figure 3i ) . three out of the ten minimum energy solid - state nmr structures 
 show that a hydrogen bond tends to form between n8 ( nh2) and t55 ( oh)1 . n angle are 2.562.59  and 141148 , 
 respectively , according to the nmr structure ( pdb : 2lgi(91 ) ) . further , k13 ( nh3) serves 
 as another possible electron donor for hydrogen bonding with the n8 
 side - chain carbonyl group based upon one of the ten minimum energy 
 solid - state nmr structures ( pdb : 2lgi(91 ) ) and the 
 xrd structure ( pdb : 2qmt(90 ) ) . the validity of these hydrogen bonds 
 is not supported concurrently by the solid - state nmr and xrd structures , 
 which is likely due to minor structural differences originated from 
 the distinct protein crystallization conditions . despite this , it 
 is rational to conclude at this point that the hydrogen bonds discussed 
 here likely obstruct n8 side chain motions and compensate for the 
 solvent mobilization effect . table 3 lists motionally 
 averaged deuterium 
 quadrupolar coupling constants and asymmetry parameters for gln and 
 glu residues in microcrystalline gb1 . the data imply that dynamics 
 vary significantly among these residues , particularly for side chains . 
 due to the absence of signal , quadrupolar coupling values were not 
 determined for several groups as indicated in table 3 . the absence of signals can happen in one 
 of the three scenarios : inefficient h c cp transfer , significant h line broadening correlating 
 with 1010 s time scale 
 motion , or zero net c  c magnetization 
 transfer during spc-5 recoupling . the slow motion in the 1010 s regime unlikely exists as both the 
 backbone and side chains present < 10 s motion 
 as implied by   values measured in this study . further , 
 efficient c  c polarization transfer 
 is expected for c  c as high transfer efficiency 
 is observed in the direction of c  c for q2 
 and e19 . this rules out the third possibility that signal absence 
 is caused by zero net c  c magnetization 
 transfer during the spc-5 mixing period . c cross - polarization 
 is significantly quenched by large - amplitude motion for the groups 
 with undetermined gln / glu   and  values . for deuterium undergoing large - amplitude 
 motion ,  was set to zero for line - shape fitting . e27 has the largest   values among the seven residues , indicating 
 its rigidity in gb1 microcrystals ( table 3 and figure 4a ) . as discussed in the previous section , e27 coo forms a salt bridge with k31 ( nh3) that significantly hinders side - chain motions for the two residues 
 ( figure 4b ) . the moderate   values ( 130 khz ) imply that e56 
 exhibits restricted side - chain motion that is uncommon for a terminal 
 residue . figure 4c 
 displays the local chemical environment for e56 in gb1 crystal structure . the side chain points inward to the protein core and places coo in a unique position that has a strong tendency to 
 form hydrogen bonds with d40 and the k10 backbone nh . the strong  moderate 
 hydrogen bond between e56 and k10 is expected as the o  h n 
 distance is 2.603.08  according to the solid - state nmr 
 structures ( pdb : 2lgi(91 ) ) . in addition , a weak hydrogen bond 
 is presumably established between e56 coo and k10 
 considering the values of the o thus , e56 side - chain motion is significantly impeded by the two hydrogen 
 bonds . it also explains why strong nmr signals are observed for e56 
 despite it being the c - terminal residue . further , the two intrastrand 
 hydrogen bonds likely have great contribution to stabilize the protein 
 structure . the side chain of q32 is much more dynamic than e27 and 
 e56 illustrated by the   values . this is consistent with the local 
 structure , where no hydrogen bond or tight packing is indicated ( figure 4d ) . although a relatively 
 large   ( 141.1 khz ) is determined for e42 ( ch2) possibly 
 due to the backbone restriction , its ( ch2) exhibits 
 larger - amplitude motion in comparison with 
 glu / gln ( discussed above ) as indicated by the undetectable h  c cross - polarization . thus , e42 ( ch2) presents large - amplitude mobility because it is solvent 
 exposed and actively interacts with the surrounding water molecules . the significantly motional attenuated   ( 91.5 khz ) is observed for e15 h , indicating the side chain is more dynamic than those of 
 e15 , e27 , q32 , and e56 . this is further illustrated by that the mobility 
 of e15 ( ch2) is significantly enhanced leading to 
 inefficient h  c cross - polarization 
 transfer . the dynamic e15 side chain is consistent with that it points 
 outward from the protein surface and is unlikely to participate in 
 the formation of a hydrogen bond ( figure 4f ) . however , an intramolecular salt bridge 
 is likely formed between e15 coo and k4 ( nh3) as supported by the xrd structure ( pdb : 2qmt(90 ) ) and e15 ph titration behavior . this seems controversial to the large - amplitude side - chain motions 
 of both e15 and k4 . the most likely explanation is that the salt bridge 
 is continually broken and reformed and , therefore , shows negligible 
 impact on the residue side - chain motions . q2 and e19 possess the most 
 flexible side chains because they are exposed to solvent and have 
 no involvement in any hydrogen bonding or salt bridging ( figure 4 g and 4h ) . ( a ) crystal structure of gb1 ( pdb : 2lgi ) with glu and gln aliphatic groups shown 
 in van der waals spheres and coded with color scaling to   values . ( b ) e27 , ( c ) e56 , ( d ) q32 , ( e ) e42 , 
 ( f ) e15 , ( g ) e19 , and ( h ) q2 local chemical environment in gb1 . the residues having atoms within 5  away for the corresponding 
 glu or gln residue are shown in sticks . the salt bridge between e27 
 and k31 and the hydrogen bond between e56 and d40/k10 are presented 
 by dashed lines . the side - chain oh group 
 of thr shows a strong tendency to form a hydrogen bond , particularly 
 with the protein backbone , as it can act as either an electron donor 
 or acceptor . the hydrogen bond is expected 
 to impede the dynamics of the thr side chain to some extent . however , 
 this effect seems to be substantially attenuated based on   values determined for thr residues in microcrystalline 
 gb1 . table 4 lists 
 the motional averaged deuterium quadrupolar coupling parameters for 
 thr aliphatic groups . it implies that the ( ch2) 
 presents restricted motions as the   values are close to those of backbone h for t18 , t25 , t44 , t49 , t51 , and t55 . the difference 
 of   is < 8 khz among ( ch2) 
 groups for these residues , illustrating motions with similar amplitudes . based on the local chemical environment , no hydrogen bond is found 
 for side chain oh groups without ambiguity due to the divergence between 
 reported xrd and nmr structures as well as between different nmr conformers . 
 however , the existence of several hydrogen bonds is expected as supported 
 by nmr conformers and xrd structure . a hydrogen bond likely forms 
 between t55 ( oh)1 and n8 ( nh2)2 , where the distance of o  n and the angle of o  h n 
 is 2.562.59  and 141148 , respectively , 
 in three of the nmr conformers ( figure 5b ) . the positions of t25 in five of the lowest energy 
 nmr structures are such that its ( oh)1 tends to 
 form a hydrogen bond with a d22 backbone co group ( figure 5c ) . the o o distance 
 and o  h  o angle falls in the range of 3.093.10 
  and 159162 , respectively . as displayed in figure 5d , t51 has the ( oh)1 potentially involved in hydrogen bonding to the t49 backbone 
 nh as shown in the xrd structure ( o  o distance is 2.93  ) 
 and three nmr energy minimum structures ( o  n distance and o  h  n 
 angle is 3.153.19  and 124141 , respectively ) . despite the potential existence of these hydrogen bonds , the ( ch2) groups of the corresponding residues do not show 
 further restricted motions compared to those of t18 , t44 , and t49 . the motionally reduced cq of a thr 
 ( ch3)2 originates from two processes  methyl 
 rotation ( also considered as three - site reorientation ) along its c3v symmetry axis and c3v axis libration . the   of a methyl deuterium is equal to 55.67 
 khz if assuming a cq of 167  1.5 
 khz and an ideal tetrahedral geometry 
 for the methyl group and is further reduced by the c3v axis libration . the ( ch3)2 values of t18 , t25 , t44 , t49 , t51 , and 
 t55 are all close to this value but exhibit small discrepancies . these 
 deviations could be explained by a slight departure of the methyl 
 group geometry from the ideal tetrahedron . such methyl geometry distortions 
 have indeed been observed for proteins and small molecules in previous 
 studies . c angle deviation for methyl groups of human ubiquitin to 
 be 1 from 110.9. in 
 addition , mittermaier and kay reported that the angle between the 
 unique axis of the deuterium electric field gradient tensor and the c3v rotating axis ( referred 
 to as  ) was 109.5. it should 
 be noted that the h c 
 angle is not necessary to be identical to the  angle . if a 
 1 deviation from 109.5 is assumed for the  
 angle , a cq of 167  1.5 khz will 
 yield a   equaling 53.358.8 khz for a methyl 
 group undergoing fast rotation . the ( ch3)2 values for t18 , t25 , t44 , t49 , and t55 
 determined here all fall within experimental error of this range , 
 as shown in table 4 . one outlying group is t51 ( ch3)2 , 
 in which the   corresponds to its c3v axis departing at least 2.4 from 
 that of the ideal tetrahedral geometry , under the assumption that cq is 167  1.5 khz . nonetheless , discrepancies of this magnitude are indeed 
 likely to occur in nature , as deviations of 1.9 for the  
 angle from an ideal tetrahedron have been observed for proteins by 
 previous studies . the other possibilities contributing 
 to this large discrepancy include a slight deviation of the actual cq from 167  1.5 khz as well as any unidentified   measurement errors . overall , the six thr 
 residues exhibit very similar dynamics despite the large variation 
 of local chemical environment ; the t18 side - chain points inward to 
 the protein core , while t49 and t44 residues are completely exposed 
 to solvent ( figure 5e  g ) . it implies that thr ( ch2) motions 
 are dominantly restricted by the backbone and ( ch3)2 rotations are in the fast regime and are insensitive to the 
 local geometry as they do not require much free space . the side 
 chains of t11 , t16 , and t17 are much more dynamic . ( ch3)2 values are determined to be less than 46 
 khz , which are far smaller than that of a methyl group undergoing 
 three - site reorientation as discussed above . this observation implies 
 the presence of methyl c3v axis librations for these thr ( ch3)2 groups . this is typically observed for systems actively interacting 
 with solvent ( water ) molecules . the local environment indicates that 
 t11 , t16 , and t17 are fully extended into the solvent ( figure 5h  j ) . thus , surrounding 
 solvent significantly mobilizes the side chains of t11 , t16 , and t17 , 
 including the ( ch2) and ( ch3)2 groups . it is noted that the   is not determined for t17 ( ch2) due to weak signal as the h c cross - polarization transfer is reduced by the large - amplitude motion . 
 similarly , the absence of nmr signal for t53 ( ch2) 
 and ( ch3)2 indicates its significant 
 mobile side chain and is consistent with solvent exposure ( figure 5k ) . for 
 deuterium undergoing large - amplitude 
 motion ,  was set to zero for line - shape fitting . ( a ) crystal structure of gb1 ( pdb : 2lgi ) with thr aliphatic 
 groups shown in van 
 der waals spheres and coded with color scaling to   values . ( b ) t55 , ( c ) t25 , ( d ) t49 , ( e ) t18 , 
 ( f ) t44 , ( g ) t49 , ( h ) t11 , ( i ) t16 , ( j ) t17 , and ( k ) t53 local chemical 
 environment in gb1 . the residues having atoms within 5  away for the corresponding 
 thr residues are shown in sticks . the hydrogen bonds between t55 and 
 n8 , t25 and d22 , and t51 and t49 are presented by dashed lines . in 
 a protein , nonpolar residues are often directed toward the molecule 
 interior , and the side chains have no involvement in strong noncovalent 
 interactions such as hydrogen bonding and salt bridging . the side - chain 
 dynamics are typically dictated by local packing density and solvent 
 accessibility . here , we discuss the dynamics of the nonpolar residues 
 in gb1 using the determined site - specific deuterium quadrupolar coupling 
 parameters . motionally averaged   and  values are shown in table 5 for leu and ile residues . it implies that the ( ch2) and ( ch2) 
 groups in the three residues exhibit motions with similar amplitudes 
 and are dominantly restricted by the rigid backbone . as expected , 
 ( ch2) groups are slightly more flexible as they 
 extend further away from the backbone . the two ( ch3) 
 groups reside at the end of the side chain and are observed undergoing 
 rotations in the fast motion regime . again , in the current article , 
 we do not focus the subtle differences of   and  that contain detailed 
 dynamics information regarding motional modes . overall , the deuterium   values indicate that the side chain of 
 l5 is the most rigid one among the three . this is attributed to the 
 surrounding high packing density as the side chain is buried deeply 
 in the protein core ( figure 6 ) . the side chain of l12 is more dynamic compared with those 
 of l5 and l7 . the   values of its two ( ch3) 
 groups are significantly reduced to 40.5 and 44.5 khz , indicating 
 that the c3v axes of 
 the methyl groups undergo librations , while each deuterium is involved 
 in fast three - site reorientation . the high mobility of the l12 side 
 chain is a consequence of the much lower packing density and partial 
 solvent exposure as displayed in figure 6c . the moderately crowded local chemical 
 environment of l7 is responsible for the side - chain dynamics with 
 intermediate amplitude between that of l5 and l12 ( figure 6d ) . as discussed for thr residues 
 in the previous section , the   of a methyl group is reduced to 53.358.8 
 khz by three - site reorientation if we assume the cq equals 167  1.5 khz and the  angle possesses a 1.0 deviation from 109.5. thus , the   of the l7 ( ch3)2 group ( 59.3  
 1.5 khz ) infers the presence of fast methyl group 
 rotation and the immobility of the c3v axis which is equivalent to the rigidity of the 
 cc2 bond . in contrast , l5 ( ch3) groups possess   values larger than those for methyl groups 
 undergoing free three - site reorientations in the rigid lattice . the 
 ( ch3)2 , 61.0  1.6 khz , exhibits a small 
 discrepancy ( within error ) , possibly due to the methyl geometry departing 
 slightly further from the tetrahedron . the largest discrepancy is 
 observed for the   of l5 ( ch3)2 , which presents a  
 angle difference of at least 4.6 
 relative to an ideal tetrahedral geometry . it is noteworthy that 
 this deviation could simply result from an analytical uncertainty 
 due to the poor signal - to - noise ratio of the l5 ( ch3)2h spectrum ( figure s5 ) , which will require replicated data for error determination . in 
 addition , in the three cases , different   values are determined for the two ( ch2) groups . it results from the restricted cc 
 bond rotation and the distinguishable local pack densities that cause 
 appreciable different effects on the geometries and motions of the 
 two methyl groups . i6 resides in the middle of 1 , and the side 
 chain points outward from the protein surface ( figure 6e ) . i6 ( ch2)1 possesses a much smaller motional averaged   compared with leu ( ch2) 
 due to that it is exposed to solvent and less branched . it is interesting 
 to note that the i6 methyl group is not as dynamic as l12 despite 
 the fact that they are both exposed to solvent . this is likely due 
 to the packing density and side - chain geometry differences correlated 
 with the side - chain dihedral angles . for deuterium undergoing large - amplitude 
 motion ,  was set to zero for line - shape fitting . quadrupolar 
 coupling parameters were not determined for l7 ( ch2)1 due to signal overlap . ( a ) crystal 
 structure of gb1 ( pdb : 2lgi ) with leu and ile aliphatic groups shown 
 in van der waals spheres and coded with color scaling to   values . ( b ) l5 , ( c ) l12 , ( d ) l7 , and ( e ) 
 i6 local chemical environment in gb1 . the residues having atoms within 5  away for the corresponding 
 leu / ile residue are shown in sticks . motional averaged deuterium quadrupolar coupling parameters 
 of 
 val residues in gb1 are displayed in table 6 . the parameters are not determined for the 
 v21 side chain due to the absence of signal . it indicates that this 
 side chain is significantly mobilized , leading to inefficient h  c cross - polarization transfer . this 
 is consistent with the local chemical environment in the protein structure , 
 where v21 is in a turn between 2 and the helix and fully extended 
 to the solvent ( figure 7a and b ) . in contrast , v54 is observed to be the most rigid val residue 
 in gb1 as indicated by the   values . the restricted motion is caused 
 by the high packing density , as this residue points inward and is 
 completely buried in the interior of the protein ( figure 7c ) . the chemical environment shows that v29 
 resides in the middle of the well - ordered amphipathic helix ( figure 7d ) . further , the 
 geometry of the local structure and the short side - chain length likely 
 reduce the possibility of v29 substantially interacting with solvent . v39 is in the loop between 3 and the helix and at the edge 
 of the protein core ( figure 7e ) . the absence of observable h  c transfer for v39 ( ch3)2 implies 
 that the dynamics of this group is significantly enhanced . one possible 
 explanation is that v39 is partially exposed to solvent as shown in figure 7e , and only ( ch3)2 actively interacts with solvent due to 
 the restricted cc rotation . the val dynamics 
 discovered here further explain the polarization transfer efficiency 
 observed for these residues in gb1 in a previous study . for 
 deuterium undergoing large - amplitude 
 motion ,  was set to zero for line - shape fitting . ( a ) crystal structure of gb1 ( pdb : 2lgi ) with val aliphatic 
 groups shown in van 
 der waals spheres and coded with color scaling to   values . ( b ) v21 , ( c ) v54 , ( d ) v29 , and 
 ( e ) v39 local chemical environment in gb1 . the residues having atoms within 5  away for the corresponding 
 val residue are shown in sticks . deuterium quadrupolar coupling parameters were determined 
 for ala 
 residues in gb1 as listed in table s2 . 
 despite the large variation in chemical environment , a20 , a23 , a34 , 
 and these values agree well with those 
 of methyl groups undergoing fast three - site reorientations in rigid 
 lattices . the small side chain methyl group makes its dynamics much 
 less sensitive to packing density . slightly larger   values are observed for a26 and a24 ( table s3 ) , likely due to similar small deviations 
 from ideal tetrahedral geometry , the discrepancies of the cq values , or a combination of the two ( as observed 
 for several thr , leu , and ile methyl groups discussed above ) . it is 
 noted that solvent exposure leads to negligible effect on the dynamics 
 of the ala side chain . similarly , weak correlation between dynamics 
 and chemical environment was previously reported for ala methyl groups 
 in several proteins in solution . figure 8h 
 shows the   values for all residues in microcrystalline 
 gb1 except for f52 of which the   is not determined due to signal overlap . it is noted that the h   values are close to those observed for 
 the rigid lattice in peptides and proteins , implying 
 that the backbone in gb1 exhibits high rigidity . further , the detected 
 nonzero  values infer that the rigid backbone undergoes 
 small - amplitude fluctuations and reorientations . the overall larger h   values infer that the backbone of gb1 microcrystals 
 exhibits motions with significantly smaller amplitudes in comparison 
 to the side chains . further , the small variation of the h   indicates the high similarity of local 
 backbone rigidity for all residues in microcrystalline gb1 , despite 
 the significant deviations of side - chain motions . this agrees with 
 previous nmr and md simulation studies showing that the backbone order 
 parameter covers a narrow window . the value for residue f52 was not determined 
 due to signal overlap . if a rigid - limit h cq value 
 of 174 
 khz is assumed , the backbone order parameters 
 derived from   /cq(rigid - limit ) 
 cover the range of 0.821.0 ( figure s7 ) , which shows a good overall agreement with n r1/r1 , ch , and nh dipolar coupling 
 solution - state and solid - state nmr measurements . particularly , the backbone order 
 parameters obtained in the present h measurements agree 
 very well with previously reported ch dipolar coupling 
 data within error on the per residue basis ( figure s7 ) . somewhat larger discrepancies are observed between the 
 current results and the previous relaxation and nh dipolar coupling 
 data , which likely originates from inherent protein properties and 
 various experimental conditions . first , the ch / cd and nh vectors are 
 motionally distinct from each other , resulting in the discrepancies 
 on the order parameters derived from h cq ( or ch dipolar couplings ) and nh dipolar couplings as well as h and n solution - state nmr relaxation rates . second , discrepancies also exist between ch vector order 
 parameters derived from the   values determined in this work ( figure 4s ) and those determined by the previous h solution - state 
 nmr relaxation studies . the disagreement 
 could be a consequence of a number of 
 factors , including the non - negligible differences between proteins 
 in solution and microcrystalline forms , experimental temperature differences 
 as well as unidentified systematic uncertainties of the methodologies . certainly , a quantitative discussion of these disagreements between 
 studies requires complete understanding of these factors ; however , 
 this is beyond the scope of the present paper . overall , the order 
 parameters obtained in the current work fall within the range of 0.821.0 
 and agree well with previous studies . pattern is observed primarily for the order parameters of the helix 
 regions , which can not be fully explained by the solvent exposure or 
 packing density . it is noteworthy that the above discussion excludes 
 the motional averaged tensor asymmetry parameters , of which the interpretation 
 is important to characterize details of protein dynamics when using 
 both quadrupolar and dipolar coupling measurements . slow motions at nanosecond time scales were explored for 
 the gb1 backbone by the solid - state n rotating - frame 
 relaxation rate . it is known that the h nmr line shapes report the motional modes but not the quantitative 
 motional rates at this dynamic regime , and h relaxation 
 measurements are typically employed to assist in elucidating correlation 
 time information . backbone fluctuation / reorientation 
 angles and rates can be extracted from h line shapes and 
 relaxation times . this type of analysis requires interpretation of   and  with nmr line shape 
 simulations on particular motional models , which is an interesting 
 topic for future studies . in order to understand the side - chain 
 dynamics of gb1 in the context of protein structure and biological 
 function , we map out the side - chain motions across the whole protein 
 as displayed in figure 9 . chain lengths , degrees of branching , and polarities have distinct 
 effects on the mobilities of different chemical groups of the side 
 chains . thus , the side - chain dynamics are identified as large , moderate , 
 and small amplitude motions based on comparisons within the same type 
 of amino acids . the analyses are conducted for amino acids presenting 
 multiple times in gb1 , including lys , asn / asp , gln / glu , thr , leu , 
 and val , except for ala residues that exhibit similar dynamics . on 
 the basis of the   values , k4 , k10 , n35 , q2 , e15 , e19 , e42 , 
 t11 , t16 , t17 , t53 , l12 , and v21 exhibit large - amplitude side - chain 
 motions ; k13 , k28 , k31 , n8 , d40 , q32 , and v39 display moderate side - chain 
 flexibilities ; k50 , d22 , d36 , n37 , d46 , d47 , t18 , t25 , t44 , t49 , t51 , 
 t55 , l5 , l7 , v29 , and v54 present small - amplitude dynamics . the most 
 dynamic side chains in gb1 are primarily observed for the 2 
 strand and the loop between the 1 and 2 strands ( figure 9 ) . previous studies 
 revealed that these domains showed large chemical shift perturbations 
 when binding to immunoglobulin g ( igg ) and were involved in interacting 
 with igg . in addition , as shown in figure 9 , side - chain motions with large to moderate amplitudes 
 are present at the helix regions facing the 3 strand and the 
 loop between the helix and the 3 strand , which also serve as 
 binding domains during the interaction with igg . the overlap between 
 dynamic domains and binding regions suggests that the high degrees 
 of side - chain mobilities play important roles in the contacts and 
 interactions between gb1 and igg . it is interesting to note that the 
 helix regions facing the opposite direction of the mobile regions 
 ( facing way from the 3 strand ) possess highly rigid side chains 
 ( figure 9 ) . the corresponding 
 side chains are involved in hydrogen bonding or salt bridging and 
 likely contribute to the stability of the protein structures , while 
 the dynamic regions interact with igg . the 3 strand serves 
 as another protein binding interface , and the first residue on this 
  strand , e42 , exhibits significant perturbed chemical shifts 
 upon binding igg . our results indicate 
 that e42 is highly mobile , which likely contributes to the interaction 
 of gb1 with igg . it is noteworthy that the remaining residues of the 
 3 strand demonstrate small - amplitude side - chain motions . among 
 these , w43 and y45 have the aromatic rings buried in the core of the 
 protein , leading to the rigidity of side chains that are absent from 
 protein interactions . the other two residues ( t44 and d46 ) also present 
 somewhat restricted side - chain motions . further , the regions possessing 
 immobile side chains include the 4 strand , the middle portion 
 of the 1 strand , and the loop between the 3 and 4 
 strands , which are not involved in the interactions with igg . it is 
 also interesting to note that high flexibility is determined for the 
 side chain of t53 on the 4 strand . previous studies demonstrated 
 that large chemical shift perturbations occurred to t53 and suggested 
 that this residue might participate in the modulation of hydrogen 
 bonds during protein binding . thus , 
 the large - amplitude side - chain motions of t53 potentially assist the 
 hydrogen bonding modulation process . in addition , the first several 
 residues on the 1 strand possess flexible side chains as shown 
 in figure 9 , which 
 are expected for terminal regions . overall , the dynamics of gb1 side 
 chains highly correlate with its biological interactions with igg . the residues at the binding regions exhibit large - amplitude side - chain 
 motions , which likely facilitate protein contacts and interactions . in contrast , low side - chain mobility is primarily observed for regions 
 that are not involved in protein binding and interactions , and the 
 rigidity of the side chains likely assists in stabilizing the protein 
 structure . these high correlations highlight the importance of side - chain 
 motions in protein activities , which directly correlate to conformational 
 entropy and have critical contributions in energetics of biological 
 events as shown by a number of recent studies . protein 
 side - chain dynamics map for microcrystalline gb1 , shown 
 in three different viewpoints . lys , asn , asp , gln , glu , thr , leu , 
 and val residues exhibiting large , moderate , and small amplitude side - chain 
 motions are highlighted in red , orange , and blue , respectively . the 
 rest of the residues ( gray ) are not considered in this illustration . the 
 study of atomic - level protein dynamics has lagged far behind 
 structure determination due to the lack of high - resolution techniques . the significant role of molecular motions in protein biological function 
 has led to increased demand for developing new approaches to probe 
 molecular dynamics . in the current work c adiabatic 
 respriration cp implemented in the 3d pulse sequence allows for the 
 accurate detection of h line shapes for deuterium - residing 
 chemical groups in a protein in a site - specific fashion . the extracted 
 motional averaged deuterium quadrupolar parameters provide protein 
 backbone and side - chain dynamics for every isotopically labeled site . 
 here , h line shapes are extracted for 140 chemical groups 
 in the protein from the 3d h the site - specific side - chain dynamics are 
 interpreted by correlating with factors including local structure , 
 packing density , solvent exposure , salt bridging , and hydrogen bonding . it in turn allows for validating the presence of these factors and 
 their impact on protein dynamics and stability . further , high correlations 
 are demonstrated between gb1 side - chain dynamics and the biological 
 activities . large - amplitude side - chain motions are observed for regions 
 that are involved in interactions with igg . in contrast , rigid side 
 chains are primarily found for residues that are in the core of the 
 protein and are absent from protein binding and interactions . it infers 
 that the high mobility of gb1 side chains likely contributes to protein 
 contacts and binding , while the low flexibility of the side chains 
 facilitates maintaining its structures during biological activities . these results provide critical insights into the roles of side - chain 
 dynamics in protein biological functions . in perspective , we expect 
 this technique to have wide applications to studies of dynamics for 
 proteins including protein fibrils and microcrystals , as well as large 
 membrane proteins . further , to date , cq has been only systematically reported for h at methyl 
 and c sites in proteins by solution - state nmr studies . the current work is the first study that determines   values for the majority of the resolved 
 aliphatic deuterium sites in a protein . these data will enhance and 
 extend the interpretation of h relaxation analysis widely 
 used in solution - state and solid - state nmr .
2h quadrupolar line shapes deliver rich information 
 about protein dynamics . a newly designed 3d 2h13c13c solid - state nmr magic angle spinning 
 ( mas ) experiment is presented and demonstrated on the microcrystalline 
 1 immunoglobulin binding domain of protein g ( gb1 ) . 
 the implementation 
 of 2h13c adiabatic rotor - echo - short - pulse - irradiation 
 cross - polarization ( respiration cp ) ensures the accuracy of the extracted 
 line shapes and provides enhanced sensitivity relative to conventional 
 cp methods . 
 the 3d 2h13c13c spectrum reveals 2h line shapes for 140 resolved 
 aliphatic deuterium sites . 
 motional - averaged 2h quadrupolar 
 parameters obtained from the line - shape fitting identify side - chain 
 motions . restricted side - chain dynamics are observed for a number 
 of polar residues including k13 , d22 , e27 , k31 , d36 , n37 , d46 , d47 , 
 k50 , and e56 , which we attribute to the effects of salt bridges and 
 hydrogen bonds . 
 in contrast , we observe significantly enhanced side - chain 
 flexibility for q2 , k4 , k10 , e15 , e19 , n35 , n40 , and e42 , due to solvent 
 exposure and low packing density . 
 t11 , t16 , and t17 side chains exhibit 
 motions with larger amplitudes than other thr residues due to solvent 
 interactions . 
 the side chains of l5 , v54 , and v29 are highly rigid 
 because they are packed in the core of the protein . 
 high correlations 
 were demonstrated between gb1 side - chain dynamics and its biological 
 function . 
 large - amplitude side - chain motions are observed for regions 
 contacting and interacting with immunoglobulin g ( igg ) . 
 in contrast , 
 rigid side chains are primarily found for residues in the structural 
 core of the protein that are absent from protein binding and interactions .