their versatility stems from the ability 
 to tune their redox properties over a very wide range , achieved by 
 interactions with the protein environment of the quinone binding site . however , in no case is the nature of these interactions fully characterized 
 or understood . the bacterial photosynthetic reaction center ( rc ) , 
 with two quinones , qa and qb , has proven to 
 be an exceptional model for studying the underlying structure sphaeroides , the quinones acting as qa and 
 qb are both 
 identical ubiquinone-10 molecules but exhibit very different functionalities . the primary acceptor qa is a tightly bound prosthetic 
 group , while the secondary quinone qb serves as a mobile 
 carrier of two reducing equivalents . the properties of the two quinones 
 are largely determined by the protein environments of the two quinone 
 sites . existing rc crystal structures show significant uncertainty 
 in the conformations of the two quinones , and especially a wide variability 
 of the qb binding . there are 
 several different proposed orientations of qb , including 
 binding in a location distal from a central fe(his)4 complex . however , the proximal binding 
 of qb seen in earlier structures is also that seen in illuminated 
 crystal structures , which likely traps the semiquinone state ( sqb ) in the active position . the potential 
 hydrogen bond donors to qb include the four residues his - l190 , 
 ser - l223 , ile - l224 , and gly - l225 , inferred from x - ray structures . an alternative way to characterize the sq state in proteins is 
 through epr , exploiting its paramagnetism . epr 
 measures the interaction between the electron spin of the sq and the 
 nearby magnetic nuclei ( h , c , n or n , o ) of the quinone and protein . 
 using high - resolution pulsed epr techniques ( endor , eseem ) , detailed 
 information on the ohn hydrogen 
 bonds can be obtained . this includes the h and n hfi tensors ( which depend on the geometry of the h - bonds and the 
 spin density distribution over the sq and h - bonds ) and the n nqi tensors ( which reflect the chemical type of the coupled nitrogen , 
 and the population and configuration of its electronic orbitals ) . x - band ( 9.7 ghz ) n and n 2d eseem 
 spectra clearly show the interaction of two nitrogens with sqb , each carrying transferred unpaired spin density . quadrupole coupling constants estimated from 
 the n spectra indicate them to be a protonated nitrogen 
 of an imidazole residue and an amide nitrogen of a peptide group . the imidazole nitrogen ( isotropic coupling a(n ) = 1.5 mhz ) can only be assigned to n of his - l190 , consistent with existing x - ray structures . the second 
 nitrogen ( a(n ) = 0.5 mhz ) could not 
 be specified between two candidates ( ile - l224 and gly - l225 ) , and selective n isotope labeling is needed for unambiguous assignment of 
 this nitrogen . however , computational work assigned the a(n ) = 0.5 mhz coupling to the peptide nitrogen ( np ) of gly - l225 . the hfi coupling 
 of other protein nitrogens with sqb was not resolved ( < 0.1 
 mhz ) , indicating that h - bonds with other nitrogens were much weaker 
 or absent . in our previous study , the principal 
 values of the hfi tensors and their directions relative to the g - tensor 
 axes for the two h - bonded nitrogens were undetermined because simulations 
 of n 2d eseem spectra were performed separately for each 
 nitrogen without a common coordinate system defining the principal 
 axes for all nuclear tensors . additionally , the principal values and 
 directions of the nqi tensors of the two n ( with hfi 
 couplings |a(n)|  1.5 mhz ) were 
 not determined experimentally from the x - band spectra due to substantial 
 deviations from the cancelation condition |n this prevented the observation of the 
 nuclear transitions with pure zero - field nqi frequencies that would 
 provide the principal values of the nqi tensor . performing the experiments 
 at lower microwave frequencies and consequently a lower zeeman frequency ( 14n ) should improve the fulfillment of the cancelation 
 condition and allow for the observation of the zero - field nqi frequencies . in this article , therefore , we present the results of an s - band 
 ( 3.6 ghz ) n eseem study of sqb and 
 its analysis in conjunction with previously reported x - band n 1d and 2d eseem spectra . simulations of x- and s - band spectra provide 
 the hfi and nqi tensors of both nitrogens to sqb and a 
 reliable estimation of the n quadrupole coupling 
 constants . this topic is important , as the experimental background 
 for theoretical investigations relies upon an understanding of the 
 relationship between tensor characteristics and the strength ( energy ) 
 and geometry of h - bonds . unexpectedly , we find that the nqi and hfi 
 values for the peptide np of gly - l225 lead to suppression 
 of its contribution to the spectrum , despite the near - cancelation 
 condition of np at s - band . an explanation for this observation , 
 with full support from dft calculations , is presented . cells were grown under the natural abundance 
 of n or in a n background using n - labeled ammonium sulfate ( cambridge isotopes ) . in order to isolate 
 sq epr signals , procedures for biochemical metal exchange , 
 along with the methods of bacterial cell growth and rc isolation , 
 were as previously described . the sqb radical was generated by exposing the rcs to a single 532 
 nm nd : yag laser pulse in the presence of ferrocytochrome c ( to quickly rereduce the bacteriochlorophyll dimer after charge 
 separation ) . upon radical formation the s - band epr experiments 
 were performed 
 on an s - band upgraded pulsed epr elexsys e-580 bruker spectrometer 
 equipped with an oxford cf 935 cryostat and er 4118s - ms5 resonator 
 at 80 k. the frequency of the microwave source was 3.6 ghz , which 
 corresponds to a resonance field of 129 mt for paramagnetic species 
 with a g - factor of 2 . spectral processing of eseem time - domain 
 patterns , including subtraction of the relaxation decay ( fitting by 
 polynomials of 36 degree ) , apodization ( hamming window ) , zero 
 filling , and fast fourier transformation ( ft ) , was performed using 
 bruker software win - epr v2.22 rev . processed data were then imported 
 into matlab r2013a to be simulated by easyspin . in this work , we have 
 also used x - band 
 spectra of sqb obtained from previously described experiments using n and n three - pulse 
 eseem and the 2d eseem technique , hyscore ( hyperfine sublevel correlation 
 spectroscopy ) . the n nucleus interacting with 
 an unpaired electron 
 spin s = 1/2 can produce up to six lines in an eseem 
 spectrum . these lines are from transitions between three nuclear energy 
 sublevels in each of the two electron spin manifolds with ms = + 1/2 or 1/2 . because of differences 
 in orientation dependence , not all transitions contribute equally 
 to the spectra in eseem measurements of powder - type samples ( such 
 as the frozen rc suspensions used in these experiments ) . the eseem 
 spectrum expected from n with a predominantly isotropic 
 hyperfine coupling is governed by the ratio between the effective 
 nuclear frequency in each manifold , ef , given 
 by ef = |14n  |a(n)|/2| ( where a(n ) is the effective hyperfine coupling ) , and the quadrupole coupling 
 constant ( qcc ) , k = eqq/4h . if ef/k  
 0 , i.e. , ef  0 ( the situation known 
 as the cancelation condition , because 14n  a(n)/2 ) , the three nuclear frequencies of the 
 corresponding manifold will be close to the three pure ( zero - field ) 
 nuclear quadrupole resonance frequencies with n transitions1with the energy levels defined 
 by the principal 
 values of the nqi tensor2both eqs 1 and 2 are 
 completely described by k and 
 the asymmetry parameter  , which ranges in value from 0 to 1 . 
 in this case , three narrow peaks at the frequencies given in eq 1 will be present in the powder eseem spectrum . these 
 frequencies possess the property + =  + 0 and can appear in the spectrum 
 up to a ratio of ef/k  0.751 . however , the intensities of these 
 peaks are also strongly dependent on the time  chosen between 
 the first two pulses of the eseem experiment , so it is important to 
 perform the experiment at multiple values of  so as to not 
 miss any transitions . if ef/k > 1 , only a single line is expected , 
 without pronounced orientation 
 dependence from each corresponding manifold . this line is produced 
 by a transition at the maximum frequency , which is actually a double - quantum 
 transition between the two nuclear outer states with m14n = 1 and + 1 . the frequency of this transition 
 is well described by3two other 
 single - quantum transitions , involving 
 the central states with m14n = 0 , usually 
 do not show any resolved peaks because of a significant orientation 
 dependence from the quadrupole interaction . a more thorough 
 analysis , taking into account the influence of 
 the anisotropic hyperfine interaction , has shown that these simple 
 rules can also be applied to interpret eseem spectra when fulfillment 
 of the cancelation condition is considered individually for each principal 
 value of the hfi tensor . the epr - ii basis set was used for all 
 atoms except zn where 6 - 31g(d ) was employed . the model for the calculations 
 was the qm portion of the qm / mm optimized geometry , as described previously . the interactions of sqb with 
 the protein environment 
 in rcs with a natural abundance of nitrogen ( n isotope 
 - 99.63% ) and with uniform n labeling have been previously 
 studied in detail by x - band pulsed epr.n hyscore spectra clearly resolved the contribution from two nitrogens 
 n1 and n2 carrying unpaired spin density detected through the isotropic 
 hfi coupling . these nitrogens possess different characteristics , i.e. , 
 qcc k = 0.350.40 mhz and isotropic hfi coupling 
 constant a(n )  1.5 mhz for n1 
 and k = 0.650.75 mhz and a(n )  0.5 mhz for n2 . the values of k characterize the chemical type 
 and electronic configuration of the n atoms interacting 
 with sqb . for instance , the value of k for n1 most closely corresponds to the protonated nitrogen from 
 an imidazole residue , and that of n2 is typical for a peptide amide 
 nitrogen . on the basis of the x - ray structure and dft calculations , 
 n1 was identified as n of his - l190 and n2 was assigned 
 as the peptide np of gly - l225 ( figure 1 ) . interaction of sqb with its 
 two resolved nitrogen donors 
 his - l190 n and gly - l225 np , which are 
 h - bonded to carbonyl oxygens o4 and o1 , respectively . the principal axes of the g - tensor are labeled as x , y , and z. the gx axis 
 lies along the line connecting the two oxygen atoms , which carry most 
 of the spin density ; the gz axis is perpendicular to the molecular plane , and gy is perpendicular to both 
 other principal axes . the principal values of the sqb g - tensor 
 are gx = 2.00626 , gy = 2.00527 , and gz = 2.00213 . for both nitrogens , the estimated 
 values of hfi couplings and qcc 
 give a ratio of ef/k in 
 the x - band that deviates by 0.751.0 from the cancelation condition 
 ( ef/k  0 ) . this 
 is in contrast to sqa where two h - bonded nitrogens , from 
 n of his - m219 and the backbone np of 
 ala - m260 , possess larger couplings of 2.5 and 1.9 mhz , respectively , 
 with smaller deviations of ef/k from the cancelation condition . in agreement with this conclusion , x - band eseem spectra of sqa contain well - resolved nqi lines 
 ( eq 1 ) from the his and ala nitrogens , both 
 identified by parameters k and  as a consequence 
 of the principal values of their nqi tensors . this analysis suggests that the cancelation condition for n1 and 
 n2 in the qb site , required for the full determination 
 of the nqi tensor , would be achieved at lower microwave frequencies , 
 yielding a smaller 14n . in this work , we used s - band 
 with a resonant magnetic field of 128.3 mt for sqb , corresponding 
 to 14n = 0.395 mhz . this decrease in magnetic field 
 strength lowers ef/k ( especially 
 for np of gly - l225 , to 0.2 ) , and should promote 
 the appearance of the nqi triplets from both nitrogens in the s - band 
 spectrum . figure 2 shows the s - band three - pulse 
 eseem 
 spectrum of sqb in a stacked representation . the peak at 
 5.5 mhz corresponds to the matrix h feature at the s - band 
 resonant magnetic field . peaks 
 appearing at 0.55 , 0.92 , and 1.47 mhz ( all 0.06 mhz ) can be 
 attributed to n. formal analysis of these peaks using 
 eq 1 for the nqi triplet gives k = 0.40 mhz and  = 0.69 , which are strongly characteristic 
 of the protonated nitrogen of an imidazole residue . according to previous 
 studies , the nqi values of n from histidine hydrogen 
 bonded with the sqs of several quinone sites vary within a narrow 
 interval of k  0.350.43 mhz and  
  0.60.8 . under this interpretation , there is seemingly no trace of gly - l225 np in the spectrum , 
 despite the fact that s - band should have brought it even closer to 
 exact cancelation than for his - l190 n. this result 
 is very much unexpected but is accounted for by our simulations of 
 the epr spectra and dft calculations as detailed below . stacked representation 
 of the two - dimensional set of the s - band 
 three - pulse eseem spectra for sqb in bacterial rcs . the 
 spectra show the modulus of the fourier transform along the time t axis at different times , . the initial time  
 is 192 ns in the blue trace and was increased in steps of 128 ns in 
 successive traces . the nuclear quadrupole resonance frequencies assigned 
 to his - l190 n are marked with stars . a full 3d view 
 is available in the supporting information ( figure s6 ) . experimental parameters : magnetic field 128.3 mt , microwave 
 frequency 3.601 ghz , /2 pulse length = 36 ns , temperature 80 
 k. the n x - band hyscore spectrum 
 of sqb ( figure 3 ) consists of a 
 narrow diagonal peak at ( 15n , 15n ) from weakly coupled nitrogens , 
 and two pairs of cross - peaks 1 and 2 from 
 n1 and n2 , respectively . they are located symmetrically around the 
 diagonal peak along the antidiagonal , with maxima at ( 2.53 , 0.49 ) 
 mhz ( 1 ) and ( 1.83 , 1.16 ) mhz ( 2 ) with a1(n )  2.1 mhz and a2(n )  0.7 mhz , respectively . previous analysis based on axial hfi tensor 
 simulations of the individual powder n hyscore spectra 
 of n1 and n2 showed a significant disagreement in the relative intensity 
 of the cross - peaks 1 and 2 . we suggested that further improvement would necessitate 
 simulating n1 and n2 together , with both hfi tensors defined in the 
 same coordinate system . comparison of experimental and simulated x - band n 
 hyscore spectra of sqb in bacterial rcs in stacked ( left ) 
 and contour ( right ) presentation . peaks labeled as 1 and 2 are assigned to his - l190 n and gly - l225 
 np , respectively . experimental 
 parameters : magnetic field 345.4 mt , time between first and second 
 pulses  = 136 ns , microwave frequency 9.688 ghz , temperature 
 80 k. the experimental spectrum is taken from ref ( 10 ) . simulations of the eseem spectra were performed in the g - tensor 
 coordinate system of sqb . the principal axes of the g - tensor 
 ( x , y , z ) with respect to the molecular structure 
 of the quinone have been defined by single - crystal epr experiments 
 for sqa , and are shown in 
 figure 1 . the simulated peak maxima were in 
 strong agreement with the experimental peak positions ( table s1 , supporting information ) . the orientations of 
 the hfi and nqi tensor principal axes for n of his - l190 
 and np of gly - l225 were defined relative to the g - tensor 
 axes with euler angles (  ,  , and  ) in accordance 
 with the easyspin program ( http://www.easyspin.org ) and as described in the supporting information . comparison of the 
 experimental and simulated n hyscore 
 spectra for sqb is shown in figure 3 . simulations were found to be relatively 
 insensitive to euler angles , especially for  and . therefore , 
 euler angles were determined with better confidence from the n spectra . the weak dependence between the euler angles and 
 the resulting n spectrum is likely due to the low level 
 of hfi anisotropy . principal values of the rhombic 
 hfi tensor : a + 2 t , a  t(1 ranges from 0 
 to 1 corresponding to axial and rhombic tensors , respectively . hfi tensors with  = 0 ( axial ) 
 only require the  and  euler angles for their full description , 
 so  was set to zero in these cases . the choice of hfi tensor principal values , on the 
 other hand , had 
 a large impact on the resulting n hyscore simulation . initial parameters for the tensors were taken from the previous analysis 
 of contour line shapes and separate simulations for n1 and n2 . the correct intensity ratio of the two features 
 could be obtained when np of gly - l225 was assigned an axial 
 hfi tensor and n of his - l190 with a more rhombic 
 tensor . simulation parameters for the spectrum giving the optimum 
 relative intensity for cross - peaks n1 and n2 and a reasonable line 
 shape in comparison with the experimental spectrum are listed in table 1 . euler angles included in table 1 were determined from the n spectra as discussed 
 below . the x - band n hyscore spectrum of sqb ( figure 4 ) exhibits intense and extended cross - ridges 1 possessing a maximum at ( 3.96 , 1.51 ) mhz and a second pair 
 of cross - peaks 2 of circular shape with smaller intensity 
 and a maximum at ( 3.86 , 2.98 ) mhz . simulations 
 produced reasonable agreement with these experimental maxima ( table 
 s1 , supporting information ) . previous analysis 
 has shown that cross - peaks 1 and 2 correlate 
 double - quantum ( dq ) transitions from opposite manifolds , i.e. , dq+ and dq , for n1 and n2 , respectively . a significant 
 orientation dependence of the single - quantum transitions very likely 
 explains the lack of additional features . the corresponding x - band 
 three - pulse eseem spectrum ( figure 5 ) also 
 shows dq features as an intense line at 1.5 mhz , a weak peak at 2.9 
 mhz , and a broad feature around 3.8 mhz . at lower frequency , there 
 is a peak at 0.3 mhz and a feature around 0.7 mhz that appears 
 to contain overlapping lines . the shapes of these peaks are affected 
 by the procedures preceding the ft analysis , particularly by the degree 
 of polynomial used for extraction of the relaxation decay . accordingly , 
 our original three - pulse eseem spectrum has been reanalyzed in this work to minimize suppression of the 
 low frequency peaks . comparison of experimental and simulated x - band n 
 hyscore spectra of sqb in bacterial rcs in stacked ( left ) 
 and contour ( right ) presentation . peaks labeled as 1 and 2 are assigned to his - l190 n and gly - l225 
 np , respectively . experimental 
 parameters : magnetic field 346.1 mt , time between first and second 
 pulses  = 136 ns , microwave frequency 9.705 ghz , temperature 
 80 k. the experimental spectrum is taken from ref ( 10 ) . comparison of experimental ( blue ) and simulated ( red ) x- ( top ) 
 and s- ( bottom ) band n three - pulse eseem spectra of sqb in bacterial rcs . experimental parameters : x - band , magnetic 
 field 346.1 mt , microwave frequency 9.705 ghz , time  = 100 
 ns ; s - band , magnetic field 128.3 mt , microwave frequency 3.601 ghz , 
 time  = 320 ns . n 1d and 2d eseem were simulated with full hfi 
 and 
 nqi tensors for both nuclei . it is well established that the principal 
 directions of the nqi tensor for the n imine nitrogen 
 are associated with the molecular axes of the imidazole residue ( figures 1 and s1 , supporting information ) . these axes are retained if this nitrogen is coordinated to a metal 
 or h - bonded , and thus can be used for the characterization of the 
 imidazole orientation . this approach has been verified by several 
 experiments showing that the principal directions of the nqi tensor 
 determined by magnetic resonance techniques provide the correct description 
 of the ligand geometry by comparison with x - ray crystal structures . the principal values of 
 the nqi tensor are |qmax| = 2k , |qmid| = k(1 +  ) , 
 and |qmin| = k(1  
  ) . the orientation 
 of the principal axes of the nqi tensor with respect to the molecular 
 frame has been theoretically analyzed for protonated nitrogens of 
 imidazole and peptide bonds in several different systems . for a hydrogen 
 bond between sqb and n of his - l190 , an 
 appropriate calculation of the nqi tensor is that of n - methylimidazole h - bonded to a semiquinone . h bond ( x axis ) , the qmax direction is perpendicular to the imidazole 
 plane ( z axis ) , and qmid is in the imidazole plane , perpendicular to the n  h bond 
 ( y axis ) ( figure s1 , supporting 
 information ) . however , especially short h - bonds ( as indicated 
 by a high  value ) resulted in an interchange of the qmax and qmid principal 
 directions . under this condition this orientation of qmax has been observed experimentally for the nh ( k = 0.35 mhz ,  = 0.66 ) in cu(ii)-doped 
 single crystals of l - histidine hydrochloride and in l - histidine monochloride monohydrate ( k = 0.32 mhz ,  = 0.946 ) . in contrast , qmax for nh ( k = 0.366 mhz ,  = 0.268 ) in l - histidine monochloride monohydrate was found to be normal to the 
 imidazole plane . the nqi diversity observed 
 in l - histidine monochloride was explained by differences 
 in intermolecular hydrogen bonding at each nitrogen . the h - bond length 
 ho 1.58  for the n is significantly 
 shorter than 1.94  for the n. this behavior is in agreement with the calculations of 
 fritscher . in reaction centers , the length 
 of the o4hn his - l190 h - bond in the optimized 
 structure of sqb is 1.58  , suggesting a strong hydrogen 
 bond , as supported by the hfi tensor of the h - bonding proton . additionally , the characteristics of the nqi 
 tensor of nh in cu(ii)-doped single crystals of l - histidine hydrochloride are very 
 close to the values observed for the histidine nitrogen h - bonded with 
 sqb . if one accepts that this system mimics well the his - l190 
 coordinated with zn(ii ) and h - bonded with o4 of sqb , then qmax for n is expected to have 
 a stable value of the order 0.700.86 mhz and a preferred 
 direction along the y molecular axis in the imidazole 
 plane . our dft calculations of sqb were in excellent agreement 
 with this assignment of the nqi tensor orientation , with the calculated 
 principal components having qmin approximately 
 along the x molecular axis , qmid perpendicular to the imidazole ring ( z axis ) , and qmax in - plane with the imidazole 
 ( y axis ) ( table 2 and figures 
 s2 and s3 , supporting information ) . however , 
 we note that when simulations were performed with qmax perpendicular to the imidazole plane ( euler angles 
 [ 170 30 10 ] ) accompanied by a small adjustment 
 of the his - l190 hfi tensor orientation ( euler angles [ 60 110 
 10 ] ) but all other simulation parameters unchanged , 
 an equally good fit to the experimental data was achieved . therefore , 
 the possibility that qmax takes on a perpendicular 
 orientation relative to the imidazole plane can not be completely eliminated . the amide nitrogen 
 in free peptides , such as in metal complexes 
 of diglycine , which h - bonds to the inorganic sulfur atoms of iron  sulfur 
 clusters , has a narrow range of qcc ( k = 0.750.85 
 mhz ) determined by the electronic structure and the geometry of the 
 planar peptide group . this coupling constant is only slightly perturbed 
 by hydrogen bonding , as has been confirmed by calculations of the 
 nqi tensor . from these calculations , it was found that the qmax principal direction is normal to the local peptide 
 plane , the qmid direction almost coincides 
 with the c(o)n(h ) bond , and qmin points about 30 off of the n our dft calculations 
 were again in good agreement with this assigned orientation for the 
 peptide np gly - l225 nqi tensor axes ( table 2 and figures s2 and s3 , supporting information ) . reported qcc s of peptide nitrogens hydrogen bonded with 
 semiquinones of different quinone sites are also within the interval 
 indicated above . in the crystal structure 1dv3 , the main population 
 of qb is in the proximal 
 position . therefore , coordinates from this crystal structure were 
 combined with the theoretically predicted orientations of the principal 
 directions of the nqi tensor , and the corresponding euler angles relative 
 to the g - tensor axes for his - l190 n and gly - l225 
 np were calculated and fixed in the epr simulations . the 
 initial nqi parameters for his - l190 n were obtained 
 from the s - band spectrum for n as k = 0.40 mhz and  = 0.69 . for gly - l225 np , our n eseem data for np of ala - m260 h - bonded with 
 sqa were used as initial parameters , i.e. , k = 0.77 mhz and  = 0.63 mhz , following from the nqi triplet : 
 1.0 , 1.8 , 2.8 mhz . no assumptions were 
 made about the euler angles defining the orientations of the axes 
 for hfi tensors . to provide justification for the assignment 
 of the lines in the 
 s - band spectra , simulations were done simultaneously along with n x - band three - pulse and n hyscore spectra . 
 therefore , optimization involved judging the parameters ability 
 to reproduce all four spectra , as opposed to just one . once an optimal 
 set was found , a tolerance window of 0.1 mhz was given to the his - l190 
 n hfi and nqi coupling constant parameters ( tables 1 and 2 ) . this small degree 
 of flexibility reflects the error underlying the various assumptions 
 built into the simulations ( e.g. , ideal pulse shape and full excitation 
 of the sq line width ) . nevertheless , only minor adjustments to the 
 initial hfi and nqi tensors within the allotted tolerance window were 
 needed to obtain very satisfactory simulations , and the optimized 
 hfi euler angles were in excellent agreement with the dft calculated 
 values ( tables 1 and 2 , figures s4 and s5 , supporting information ) . all of the n simulations are shown in red in figures 3 , 4 , and 5 , overlaying the experimental spectra . in addition , we have 
 compared the three - pulse s - band simulations performed separately on 
 n from his - l190 and on np of gly - l225 
 to show np makes only a very small contribution to the 
 total s - band spectrum ( figure 6 ) . comparison 
 between separate n s - band eseem simulations 
 done for his - l190 n ( red ) and gly - l225 np ( black ) . with the given parameters ( tables 1 and 2 ) , gly - l225 np makes a minimal 
 contribution to the overall spectral intensity . the peculiarities of the s - band spectrum 
 can not be explained qualitatively using the simple approach based 
 on the approximation of a purely isotropic hfi . analysis of the simulation 
 results from tables 1 and 2 allows us to conclude that this approximation is not fully 
 satisfied , especially in the case of gly - l225 np . quantitatively , 
 variation of the hfi coupling in changing from a + 
 2 t to a  t ( under an axial approximation ) can be characterized by its range 
 3 t , which in our case is comparable with the n zeeman frequency in x - band or even exceeding 14n in s - band for both nitrogens ( table 3 ) . in this case , the peculiarities of the spectral features can be 
 understood by considering the fulfillment of the condition ef/k < 0.71.0 
 for different principal values of hfi tensors ( shown in bold in table 3 ) . principal values 
 of the rhombic 
 hfi tensor : a + 2 t , a  t(1 one can see that for n his - l190 at s - band the two 
 smallest principal values a1 and a2 of the hfi tensor give ef/k values of 0.16 and 0.55 , respectively . these 
 values of ef/k , which comprise 
 the perpendicular component of the hfi tensor under the axial approximation , 
 justify the appearance of the nqi triplet in the s - band spectra despite 
 the fact that a ratio of ef/k = 0.8 for an isotropic coupling a(n ) = 1.4 mhz of this nitrogen might suggest a distortion of this 
 triplet . the set of conformations in the ( a1 , a2 ) plane produces the triplet nqi 
 spectrum . the spread of ef/k leads to the observed line broadening surrounding the peak maxima . simulation of the x- and s - band spectra led to 
 only a very minor correction of the k value estimated 
 from the experimental spectrum ( table 2 ) . similarly to his - l190 n , the transition from 
 the x- to s - band shifts ef/k for all principal values of gly - l225 np toward a range 
 appropriate for the observation of the nqi triplet . however , the s - band 
 spectra do not exhibit lines typical for nqi frequencies of np . an explanation for this comes from previous computational 
 and theoretical analyses showing that the amplitudes of the nqi peaks 
 also vary with 14n / k . at a low 
 14n / k ratio , the energy levels 
 in both manifolds approach each other and eseem vanishes at about 
 14n / k < 0.3 . finally , the condition of exact cancelation is not sufficient 
 to produce intense eseem peaks , with an additional requirement being 
 that a(n )  k. if a(n ) < k , then the eseem intensity is expected 
 to be weak even at exact cancelation . transition from x- to 
 s - band decreases the 14n / k ratio 
 by almost 3-fold ( 2.68 ) , giving 14n / k  0.5 for np . the 
 simulated spectra ( figure 6 ) show substantial 
 suppression of spectral intensity from np in agreement 
 with the theoretical considerations provided above . this suggests 
 that the intensity of the spectrum would increase with an increase 
 of the isotropic coupling . figure 7 shows that 
 increasing the isotropic coupling 23-fold , without changing 
 any other parameters , significantly increases the spectral intensity 
 as expected . simulated three - pulse s - band eseem spectra of gly - l225 
 np as a function of increasing a(n ) in 
 steps of 0.2 mhz . all other parameters are fixed to the values listed 
 in tables 1 and 2 . previous analyses of eseem and nuclear 
 quadrupole resonance measurements 
 determined the values of eqq / h and  for imidazole n in different compounds to be sensitive to hydrogen - bond 
 formation through a change in electron occupancy of the nitrogen orbitals . it was concluded that a stronger h - bond would 
 lower the p orbital spin population 
 and increase the n  h orbital population , subsequently reducing 
 the eqq / h value and increasing . empirically , this 
 influence can be described with good accuracy by the linear dependence 
 between h / eqq and . figure 8 shows h / eqq and 
  values for histidine n interacting 
 with sqa in bacterial reaction centers and in photosystem 
 ii . the points in figure 8 are clustered in 
 the region with   0.7 . also shown is the point ( blue ) 
 corresponding to the previously reported sqbn nqi tensor values ( eqq / h = 1.65 mhz and  
 = 0.61 ) ; it is substantially 
 shifted to a lower  , away from the  qa area  , 
 suggesting the formation of a significantly weaker hydrogen bond . however , this estimation of the n nqi 
 tensor was based on the analysis of an x - band three - pulse eseem spectrum 
 not satisfying the cancelation condition , and therefore prone to distortion 
 of the peak maxima ( see discussion in ref ( 10 ) ) . the characteristics of the nqi tensor reported 
 in this work move the qb point ( red ) to within the range 
 of the qa points ; this is more consistent with the similar 
 value of the anisotropic hyperfine tensor component t  5.2 mhz for the proton involved in the h - bond between n and sqb , which is similar to the complementary t  5.4 mhz for the qa site in rcs from rb . values of h / eqq and  for histidine n interacting with sqa in bacterial 
 and psii rcs ( black ) 
 and sqb in bacterial rcs reported by lendzian et al . ( ref ( 40 ) ) ( blue ) and this work 
 ( red ) . the linear fit ( dashed line ) was performed for only the points 
 corresponding to sqa . ( 1 ) qb in rhodobacter sphaeroides ( ref ( 40 ) ) , ( 2 ) qb in rhodobacter sphaeroides ( this work ) , ( 3 ) qa in high - ph - treated 
 psii ph 9.2 ( ref ( 35 ) ) , ( 4 ) qa in cn - treated psii ph 5.5 
 ( ref ( 35 ) ) , ( 5 ) qa in liclo4-treated psii ph 6.0 
 ( ref ( 39 ) ) , ( 6 ) qa in high - ph - treated psii ph 5.0 ( ref ( 35 ) ) , ( 7 ) qa in rhodobacter sphaeroides ( ref ( 34 ) ) , ( 8) qa in rhodopseudomonas viridis ( ref ( 38 ) , the nqi 
 tensor was reported incorrectly in the table of this reference : we 
 have reanalyzed their spectra on the basis of their assigned peak 
 positions ) . s - band 
 eseem was performed on sqb in bacterial rcs with 
 the aim of determining the principal values of the nqi tensor for 
 the hydrogen bond donors n of his - l190 and np of gly - l225 . the resulting three - pulse spectrum showed a 
 visible contribution only from n of his - l190 , despite 
 the shift of the n zeeman frequency toward a region expected 
 to nearly satisfy the cancelation condition for both nitrogens , as 
 predicted from the data obtained in previous x - band experiments . simultaneous 
 simulation of 1d and 2d x - band and s - band eseem spectra confirmed 
 this experimental result . analysis of the simulation parameters allowed 
 us to conclude that the np contribution to the s - band spectrum 
 is suppressed as a result of the typically large qcc of np in combination with its relatively small isotropic hyperfine coupling 
 and comparable hfi tensor anisotropy . eseem intensity vanishes under 
 these conditions , despite even better fulfillment of the cancelation 
 condition for np than for n of his - l190 . nevertheless , simulations successfully reproduced the experimental 
 x - band data for np , and were well supported by dft calculations . the observed triplet of lines for his - l190 corresponding to the 
 zero - field nqi frequencies ( eq 1 ) was simulated 
 as qcc eqq / h = 1.54  0.02 mhz with an asymmetry parameter  
 = 0.69 and defines the principal values ( eq 2 ) of the nqi tensor for n of his - l190 . these 
 data significantly improve upon a previous analysis not performed 
 under the cancelation condition . our 
 results show the strength and applicability of s - band for obtaining 
 accurate nqi parameters for weakly coupled nuclei . while estimation 
 of the hfi tensor alignment to the molecular frame 
 is best done by epr on single crystals , it is often very difficult 
 to obtain single crystal radical samples for a protein of interest . 
 in this study , we show that simultaneous simulation of the n s- and x - band three - pulse spectra and n hyscore 
 spectra ( with a tolerance window of 0.1 mhz ) produces remarkable agreement 
 with the dft calculated tensor orientations . the success of dft to 
 reproduce the experimentally determined hfi and nqi tensors highlights 
 the reliability of modern dft for predicting epr parameters . additionally , 
 our findings , taken as a whole , show promise for future eseem determinations 
 of euler angles for nuclei not suitable for high - frequency endor measurements ( such as weakly coupled nitrogens ) or in a spin system not readily 
 crystallizable in the radical state .
the 
 secondary quinone anion radical qb ( sqb ) in reaction centers of rhodobacter 
 sphaeroides interacts with n of 
 his - l190 and np ( peptide nitrogen ) of gly - l225 involved 
 in hydrogen bonds to the qb carbonyls . in this work , 
 s - band 
 ( 3.6 ghz ) eseem was used with the aim of obtaining a complete 
 characterization of the nuclear quadrupole interaction ( nqi ) tensors 
 for both nitrogens by approaching the cancelation condition between 
 the isotropic hyperfine coupling and 14n zeeman frequency 
 at lower microwave frequencies than traditional x - band ( 9.5 ghz ) . 
 by performing measurements at s - band , we found a dominating contribution 
 of n in the form of a zero - field nqi triplet at 
 0.55 , 0.92 , and 1.47 mhz , defining the quadrupole coupling constant k = e2qq/4h = 0.4 mhz and associated asymmetry parameter  = 
 0.69 . 
 estimates of the hyperfine interaction ( hfi ) tensors for n and np were obtained from simulations of 
 1d and 2d 14,15n x - band and three - pulse 14n 
 s - band spectra with all nuclear tensors defined in the sqb g - tensor coordinate system . from simulations , we conclude that the 
 contribution of np to the s - band spectrum is suppressed 
 by its strong nqi and weak isotropic hfi comparable to the level of 
 hyperfine anisotropy , despite the near - cancelation condition for np at s - band . the excellent agreement between our epr simulations 
 and dft calculations of the nitrogen hfi and nqi tensors to sqb is promising for the future application of powder eseem to 
 full tensor characterizations .