清华大学：《生物核磁共振波谱学》课程教学资源（文献资料，英文版）The use of nmr methods for conformational

S.S. Wijmenga, B N.M. van Buuren/Progress in Nuclear Magnetic Resonance Spectroscopy 32(1998)287-387 5.1. JHC- and Jcc-couplings J-couplings such as given here should be of great value for the rational design and improvement of The JcH and Jce-couplings are given in Table 2 through-bond assignment strategies discussed in and Table 3, respectively [49]. To a large extent these Section 7 J-couplings are independent of conformation, but have often indicated a small conformation dependent 5.3. Ribose sugan variation. For example, the JcI'HI-couplings have been found to convey x torsion angle information Traditionally, the sugar pucker has been [49, 82].The J-couplings, JH3'c3 and JH?' c?, depend determined mainly from the JHH-couplings in the on the puckering [49]. Finally, the JHs'cs and JHs"cs" sugar ring. They can be derived from the generalized have distinctly different values, namely 151 Hz and Karplus equation [62, 83, 84] which is given by 141 Hz, respectively, when the torsion angle y is in the gauche domain, these differences are retained JHH= Pl cos o+ P2 cos o when the rotamer population is not purely gauche [49). Thus, the latter J-couplings can be used for stereospecific assignment of the H5" and H5"res +∑(P3+P4cos(;+P5△x)△x+△J nances. These conformational dependencies are extremely useful, especially since the JHCx couplings are very easy to measure. They will discussed in more detail below in the appropriate△x=△xa+P6∑△x (13) 5.2. Overview of J-couplings in the bases A complete overview of the homonuclear and heteronuclear J-couplings, found in the bases A, G, U and C, involving both newly measured as well as redetermined J-couplings, has recently been pub lished by lppel et al. [49]. They are summarized here in Fig. 3(and Tables 2 and 3). As can be appre Scheme 1 ciated from Fig. 3(and also Tables 2 and 3), the homonuclear and heteronuclear J-couplings in Here Axia and Ax y a are the difference in Huggins the bases form a complex network. Consequently, electronegativity between hydrogen and the a and B such a detailed, accurate, and complete set of these substituents in the Hasla(sllB, S12B, S13B) Fig 3. From left to right, J-, J- and J-coupling constants(in Hz) in the bases of 5-AMP, 5-GMP, 5-UMP and 5'-CMP. This figure is lapted from a similar one in Ref [49]. All the given J-coupling values were(re )determined in that study, except those indicated with rl, r2, r3, 4 and rs, which were taken from Refs. [231, 112, 259, 233, 232], respectively. J-couplings for which the assignment was, in Ref. [) found to ambiguous are indicated by the lower case letters a, b, c and d, with: (a)Two equal Jo-couplings were found on C6, with a sum value of (b)The C2 r gning 7.5 Hz to JceNI leaves -7.5 Hz for the other caw-coupling, which can arise either from JceN or JceN3 or cGNorJc ing of 15 lines(intensity, 1: 2: 2: 2: 2: 2: 3: 4: 3: 2: 2: 2: 2: 2: 1)in the ID(H)decouple spectrum. Since the Jcxcs has a value of 3.7 Hz, the observed multiplet can be simulated by incorporating four additional J-couplings with alues of approximately 3.9, 76, 15.2 and 23 Hz; the 23 Hz coupling can be assigned to Jc2N2 on the basis of a similarly large value for the orresponding coupling in CMP and AMP; the J-couplings of 7.6 and 15.2 Hz can tentatively be assigned to JciNi and Jc2N3, respectively,or the reverse, the smallest of these four J-couplings, i.e. 3.9 Hz, can then be assigned to Jo uming that the four-bond coupling, Jc2nz ndetectably small (c)Computer simulation of the G C4 resonance multiplet in the ID(Hl-decoupledC spectrum yields two JaN-couplil constants of approximately 20 and 8.5 Hz, respectively. The largest coupling constant can be assigned to Jc analogy to that in 5-AMP the J-coupling of 8.5 Hz can be d to either one of the couplings CanT, canz. JcANI or JCANz-(d)Computer simulation of the H5 resonance multiplet in the fully coupled ID H spectrum yielded two more not yet assigned values, namely 2.6 and 4. 4 Hz, which can be attributed to JHsNi and JHsNi, respectively, or the reverse

5.1. 1 JHC- and 1 JCC-couplings The 1 JCH and 1 JCC-couplings are given in Table 2 and Table 3, respectively [49]. To a large extent these J-couplings are independent of conformation, but have often indicated a small conformation dependent variation. For example, the 1 JC19H19-couplings have been found to convey x torsion angle information [49,82]. The J-couplings, 1 JH39C39 and 1 JH29C29, depend on the puckering [49]. Finally, the 1 JH59C59 and 1 JH50C59 have distinctly different values, namely 151 Hz and 141 Hz, respectively, when the torsion angle g is in the gauche þ domain; these differences are retained when the rotamer population is not purely gauche þ [49]. Thus, the latter J-couplings can be used for stereospecific assignment of the H59 and H50 reso￾nances. These conformational dependencies are extremely useful, especially since the 1 JHxCx￾couplings are very easy to measure. They will be discussed in more detail below in the appropriate sections. 5.2. Overview of J-couplings in the bases A complete overview of the homonuclear and heteronuclear J-couplings, found in the bases A, G, U and C, involving both newly measured as well as redetermined J-couplings, has recently been pub￾lished by Ippel et al. [49]. They are summarized here in Fig. 3 (and Tables 2 and 3). As can be appre￾ciated from Fig. 3 (and also Tables 2 and 3), the homonuclear and heteronuclear J-couplings in the bases form a complex network. Consequently, such a detailed, accurate, and complete set of these J-couplings such as given here should be of great value for the rational design and improvement of through-bond assignment strategies discussed in Section 7. 5.3. Ribose sugar Traditionally, the sugar pucker has been determined mainly from the 3 JHH-couplings in the sugar ring. They can be derived from the generalized Karplus equation [62,83,84] which is given by: 3 JHH ¼ P1 cos2 f þ P2 cos f þ X 4 i ¼ 1 (P3 þ P4 cos2 (zif þ P5lDxil))Dxi þ DJ ð12Þ Dxi ¼ Dxi, a þ P6 X 3 j ¼ 1 Dxij, b (13) Here Dxi,a and Dxij,b are the difference in Huggins electronegativity between hydrogen and the a and b substituents in the HaS1a(S11b,S12b,S13b) Fig. 3. From left to right, 1 J-, 2 J- and 3 J-coupling constants (in Hz) in the bases of 59-AMP, 59-GMP, 59-UMP and 59-CMP. This figure is adapted from a similar one in Ref. [49]. All the given J-coupling values were (re)determined in that study, except those indicated with r1, r2, r3, r4 and r5, which were taken from Refs. [231,112,259,233,232], respectively. J-couplings for which the assignment was, in Ref. [49], found to be ambiguous are indicated by the lower case letters a, b, c and d, with: (a) Two equal n JCN-couplings were found on C6, with a sum value of 14.9 Hz; assigning 7.5 Hz to 1 J C6N1 leaves ,7.5 Hz for the other J C6N-coupling, which can arise either from 3 JC6N2 or 3 JC6N3 or 2 JC6N7 or 3 JC6N9. (b) The C2 resonance exhibits a multiplet pattern consisting of 15 lines (intensity, 1:2:2:2:2:2:3:4:3:2:2:2:2:2:1) in the 1D ( 1 H)-decoupled 13C spectrum. Since the 3 JC2C5 has a value of 3.7 Hz, the observed multiplet can be simulated by incorporating four additional J-couplings with values of approximately 3.9, 7.6, 15.2 and 23 Hz; the 23 Hz coupling can be assigned to 1 JC2N2 on the basis of a similarly large value for the corresponding coupling in CMP and AMP; the J-couplings of 7.6 and 15.2 Hz can tentatively be assigned to 1 JC2N1 and 1 JC2N3, respectively, or the reverse; the smallest of these four J-couplings, i.e. 3.9 Hz, can then be assigned to 3 JC2N9, assuming that the four-bond coupling, 4 JC2N7, is undetectably small. (c) Computer simulation of the G C4 resonance multiplet in the 1D ( 1 H)-decoupled 13C spectrum yields two JCN-coupling constants of approximately 20 and 8.5 Hz, respectively. The largest coupling constant can be assigned to 1 JC4N9 in analogy to that in 59-AMP; the J-coupling of 8.5 Hz can be unassigned to either one of the couplings 1 JC4N3, 2 JC4N7, 3 JC4N1 or 3 JC4N2. (d) Computer simulation of the H5 resonance multiplet in the fully coupled 1D 1 H spectrum yielded two more not yet assigned values, namely 2.6 and 4.4 Hz, which can be attributed to 3 J H5N1 and 3 J H5N3, respectively, or the reverse. Scheme 1. S.S. Wijmenga, B.N.M. van Buuren/Progress in Nuclear Magnetic Resonance Spectroscopy 32 (1998) 287–387 307

S.S. Wijmenga, B.N.M. van Buuren/Progress in Nuclear Magnetic Resonance Spectroscopy 32(1998)287-387 S3a(S31BS32BS33B)-C1-C2- S2o(S21BS22BS23B) related to the pseudorotation angle P and pucker s4c(S4l426S43 Hb fragment;△xa△xgB=13 amplitudeφmvia62 (O,0.4(C),0.85(N)and-0.05(P)( Scheme 1) The parameter S: is +1 or -I depending on the 12=121.4+1.03m cos(P-144) orientation of the substituent as indicated. The d12"=0.9+1.034mCos(P-144) arameters Pl to P6 depend on the number of non- hydrogen a substituents d2y=24+1.039mcos(P d2"y=121.9+1.03mcos(P) a substituents P1 P3 13.89-0.961.02-3.4014.90.24 y4=124.0+1.034mcOs(P+144) 13.22-0990.87-2461990.00 13.24-0.910.53-2.4115.50.19 The values of Jr? to J3 4 are given as a function overall 13.70-0.730.56-2.4716.90.14 of pseudorotation angle P and pucker amplitude m in Fig. 4(A)-(E). Ribose sugar rings are not rigid but interconvert rapidly between N-and S-type conforma From this generalized Karplus equation it follows tions. These sugar puckering states are descr that the JHH-couplings in the ribose ring are given by PN and N for the N-state, and Ps and m, for the 3Jm=13.22co32-0.99cosd S-state. The relative population can be found via the fraction S-conformer, pS. The parameters pm and s +∑087-246c03(+19.1△x)△x nd to be fairly constant and 40, while p ranges from-10°to20° and ps lies between120°and180°.The3 JHH-coupl in the +A (14) ring are then the weighted average of the JHu-cou- plings in the two conformations Ax;=△xi (21) (forJ12,Jy2",J2..3) (15)3m=(1-pS)3J+psJB 4=1324co32-0.91csd Thus, JaB and as depend on P and Pm in thei respective states. Although PN, PS, sm and s can be determined in principle from the complete set of +2(0.53-2.41 cos2(s, o +15.5lAx)Ax; ribose JHH-couplings, in practice, these values are assumed to be known for the least populated state and to correspond to the middle values of P and m 35, P.=160 and m= 35. For the most highly △x=△ 0.19△ (17) populated state it is thus possible to derive P and Pm. We finally note that a straightforward check In addition, a correction for the so-called Barfield whether the assumption of an equilibrium between transmission effect is required for J12 and J23 N-type and S-type conformers applies, is to plot ese two J-couplings have a 412=-2.0 cos2(P-234)144<P<324(18) reverse dependence on the fraction of N-type sugar, which is incompatible with a P value intermediate △l2y=-0.5c03(P-288)180°<P<360; between N-type and S-type sugars [62, 80]. The most commonly used program to derive P, pm and pS from 0°<P<18 (19) HH-couplings is PSEUROT, developed by van den Hoogen et al. [85]. Alternatively, one can add NOE The torsion angle q in the above equations can be information to determine the puckering state [62, 64

S3a(S31bS32bS33b) -C1-C2- S2a(S21bS22bS23b) S4a(S41bS42bS43b)Hb fragment; Dxi,a, Dxij,b ¼ 1.3 (O), 0.4 (C), 0.85 (N) and ¹0.05 (P) (Scheme 1). The parameter zi is þ1 or ¹1 depending on the orientation of the substituent as indicated. The parameters P1 to P6 depend on the number of non￾hydrogen a substituents: # a substituents P1 P2 P3 P4 P5 P6 2 13.89 ¹0.96 1.02 ¹3.40 14.9 0.24 3 13.22 ¹0.99 0.87 ¹2.46 19.9 0.00 4 13.24 ¹0.91 0.53 ¹2.41 15.5 0.19 overall 13.70 ¹0.73 0.56 ¹2.47 16.9 0.14 From this generalized Karplus equation it follows that the 3 JHH-couplings in the ribose ring are given by: 3 JHH ¼ 13:22 cos2 f ¹ 0:99 cos f þ X 4 i ¼ 1 (0:87 ¹ 2:46 cos2 (zif þ 19:1lDxil))Dxi þ DJ ð14Þ Dxi ¼ Dxi, a (15) (for J1929, J1920, J2939 and J2039) 3 J3949 ¼ 13:24 cos2 f ¹ 0:91 cos f þ X 4 i ¼ 1 (0:53 ¹ 2:41 cos2 (zif þ 15:5lDxil))Dxi þ DJ ð16Þ Dxi ¼ Dxi, a ¹ 0:19 X 3 j ¼ 1 Dxij, b (17) In addition, a correction for the so-called Barfield transmission effect is required for J1920 and J 2939: DJ1920 ¼ ¹ 2:0 cos2 (P ¹ 234) 1448 , P , 3248 (18) DJ2939 ¼ ¹ 0:5 cos2 (P ¹ 288) 1808 , P , 3608; 08 , P , 188 ð19Þ The torsion angle f in the above equations can be related to the pseudorotation angle P and pucker amplitude Jm via [62]: f1929 ¼ 121:4 þ 1:03Jm cos(P ¹ 144) (20) f1920 ¼ 0:9 þ 1:03Jm cos(P ¹ 144) f2939 ¼ 2:4 þ 1:03Jm cos(P) f2039 ¼ 121:9 þ 1:03Jm cos(P) f3949 ¼ 124:0 þ 1:03Jm cos(P þ 144) The values of 3 J1929 to 3 J3949 are given as a function of pseudorotation angle P and pucker amplitude Jm in Fig. 4(A)–(E). Ribose sugar rings are not rigid but interconvert rapidly between N- and S-type conforma￾tions. These sugar puckering states are described by their pseudorotation angles and amplitudes, namely, PN and Jm N, for the N-state, and PS and Jm S , for the S-state. The relative population can be found via the fraction S-conformer, pS. The parameters Jm N and Jm S tend to be fairly constant and range from 32 to 40, while PN ranges from ¹ 108 to 208 and PS lies between 1208 and 1808. The 3 JHH-couplings in the ring are then the weighted average of the 3 JHH-cou￾plings in the two conformations: 3 Jav ab ¼ (1 ¹ pS)· 3 JN ab þ pS· 3 JS ab (21) Thus, 3 JN ab and 3 JS ab depend on P and Jm in their respective states. Although PN, PS , Jm N and Jm S can be determined in principle from the complete set of ribose 3 JHH-couplings, in practice, these values are assumed to be known for the least populated state, and to correspond to the middle values of P and Jm in the N- or S-puckered state, i.e. PN ¼ 10 and Jm N ¼ 35, PS ¼ 160 and Jm S ¼ 35. For the most highly populated state it is thus possible to derive P and Jm. We finally note that a straightforward check whether the assumption of an equilibrium between N-type and S-type conformers applies, is to plot 3 J3949 against 3 J1929. These two J-couplings have a reverse dependence on the fraction of N-type sugar, which is incompatible with a P value intermediate between N-type and S-type sugars [62,80]. The most commonly used program to derive P, Jm and pS from 3 JHH-couplings is PSEUROT, developed by van den Hoogen et al. [85]. Alternatively, one can add NOE information to determine the puckering state [62,64]. 308 S.S. Wijmenga, B.N.M. van Buuren/Progress in Nuclear Magnetic Resonance Spectroscopy 32 (1998) 287–387

S.S. Wijmenga, B N.M. van Buuren/Progress in Nuclear Magnetic Resonance Spectroscopy 32(1998)287-387 Fig. 4.(A)-(E)Contour lines of H-coupling constants(Hz)in the sugar ring as a function of Pm and m: The coupling constants were calculated with the aid of the EOS-Karplus equation and corrected for the Barfield transmission effect(see text). (A)J12, (B)J1,(C)J2 (D)Jry and(E)J34

Fig. 4. (A)–(E) Contour lines of 3 J HH-coupling constants (Hz) in the sugar ring as a function of Pm and fm. The coupling constants were calculated with the aid of the EOS–Karplus equation and corrected for the Barfield transmission effect (see text). (A) 3 J 1929, (B) 3 J 1920, (C) 3 J 2939, (D) 3 J 2039 and (E) 3 J 3949. S.S. Wijmenga, B.N.M. van Buuren/Progress in Nuclear Magnetic Resonance Spectroscopy 32 (1998) 287–387 309

S.S. Wijmenga, B.N.M. van Buuren/Progress in Nuclear Magnetic Resonance Spectroscopy 32(1998)287-387 Conte et al. [ 64] use a program that incorporates both JHH-couplings and NOE information. Finally, as will systems can simply be predicted from the Newman be discussed in more detail in Section 5.3, the JHH. projection and the orientation of the electronegative couplings can also be derived from TOCSY data In substituents XI and X2 relative to the position of the the program developed by van Duynhoven et al. [86 proton coupled to C, XI and X2 can either be the puckering state, i.e. P, Pm and ps, are directly oxygen or nitrogen. A trans orientation of this derived from the (H, H) TOCSY cross pe relative to X leads to a positive value for JcH, whereas a gauche orientation gives rise to a negative Thanks to the availability of labeled compounds value for JcH. If two X substituents are present onC JHc-couplings can be used as additional parameters the effects are additive. Thus, if both H to Xl and h to determine the sugar pucker. Ippel et al. [49] have X2 are oriented gauche to each other a negative value ecently determined parameters for the Karplus rela- is obtained for JHC. On the other hand, a trans orien- tions between JH3'CI', JHI'C3, JH2'CA' and JH4'c2 tation of H relative to XI and a gauche orientation of nd the sugar puckering. Since the ribose ring is in H relative to X2 will give rise to compensating effects rapid equilibrium between N-and S-conformers, and a JHc value which is approximately zero. For the JHc-couplings are the weighted average of example, JH2'c3, is predicted by this rule to be nega the JHc-couplings in the two conformations tive for an N-conformer, since O3 is oriented gauche ith respect to H2, and positive for an S-conformer Is orien WI and Jab are the JHc-coupling values in the exactly what is observed experimentally(see above) S-and N-puckered state, respectively, i.e. asCr= The other JHc-couplings in the sugar ring also follow 63Hz,3c=14H,3 this projection rule 4.2 Hz, 3JSrc3=0.3 Hz, JH.=2.7 Hz, s4C2,= Finally, the one-bond couplings JcH also convey I Hz and 1.0 Hz. Thus, this relation pre ugar pucker information JH3c3' has values of vides another opportunity to determine the sugar 149.6 Hz and 156.8 Hz for N- and s-type sugars, puckering. Note that JJH3'CI and JJH2'cA differ respectively, while JHr'c2 shows the reverse trend strongly between the N-and S-state and can thus be namely values of 158.4 Hz and 149.2 Hz for N-and used quite well to determine ps. The three-bond S-type sugars, respectively. When the sugar ring JHIc3 and JH H4'cr, remain small for occurs as a mixture of N-and S-conformers with inter- both the S- and N-puckered states and are thus less mediate values for pS, intermediate JH2'3' c21 values useful indicators of the sugar puckering. We finally are also found. We note that the torsion angle note that the JH3'cs-coupling, in principle, also moni- dependencies of the JHc-couplings are not very tors the puckering, namely via the torsion angle 8. well understood, in contrast to the case of the Unfortunately, its value does not differ significantly JHc- and the 2JHc-couplings. Nevertheless these between the N-and S-state [49] experimental observations remain useful as indicators a third source of information on the puckering state of the sugar pucker of the sugar ring is the JHc-couplings. The two-bond couplings H2'CI and JH3'c2 are found to be negative 5.4. Determination of the p torsion angle rings, while the reverse holds for H2c and V for S-puckered rings and positive for N-puck The B torsion angle has traditionally been deter- cators of the sugar ring on lings are thus good indi- mined by the JHP-coupling constants. The Karplus nformation. However, the equation describing the H5," -couplings is other sugar ring two-bond couplings, JHIC2 and JH4c3, do not change sign and remain negative for 3J15ysy=15.3cos2-62cos+1.5 23) both the N-puckered and the S-puckered state [49]. with =B-120 for H5" and =B+ 120 for H5 These signs of the JHc-couplings are in complete The most recent parametrization has been used here ccordance with the projection rule proposed by [62, 88]. The JHs'Ps'-and JHsps'-couplings describe Bock and Pederson [87]. According to this rule the the B torsion angle as shown in Fig. 5. As can be

Conte et al. [64] use a program that incorporates both 3 JHH-couplings and NOE information. Finally, as will be discussed in more detail in Section 5.3, the 3 JHH￾couplings can also be derived from TOCSY data. In the program developed by van Duynhoven et al. [86] the puckering state, i.e. P, Jm and pS, are directly derived from the (H,H) TOCSY cross peak intensities. Thanks to the availability of labeled compounds, 3 JHC-couplings can be used as additional parameters to determine the sugar pucker. Ippel et al. [49] have recently determined parameters for the Karplus rela￾tions between 3 JH39C19, 3 JH19C39, 3 JH29C49 and 3 JH49C29 and the sugar puckering. Since the ribose ring is in rapid equilibrium between N- and S-conformers, the 3 JHC-couplings are the weighted average of the 3 JHC-couplings in the two conformations: 3 Jab ¼ pS· 3 JS ab þ (1 ¹ pS)· 3 JN ab (22) Here 3 JS ab and 3 JN ab are the 3 JHC-coupling values in the S- and N-puckered state, respectively, i.e. 3 JS H39C19 ¼ 6.3 Hz, 3 JN H39C19 ¼ 1.4 Hz, 3 JS H29C49 ¼ 0.3 Hz, 3 JN H29C49 ¼ 4.2 Hz, 3 JS H19C39 ¼ 0.3 Hz, 3 JN H19C39 ¼ 2.7 Hz, 3 JS H49C29 ¼ 1.1 Hz and 3 JN H49C29 ¼ 1.0 Hz. Thus, this relation pro￾vides another opportunity to determine the sugar puckering. Note that 3 JH39C19 and 3 JH29C49 differ strongly between the N- and S-state and can thus be used quite well to determine pS. The three-bond couplings, 3 JH19C39 and 3 JH49C29, remain small for both the S- and N-puckered states and are thus less useful indicators of the sugar puckering. We finally note that the 3 JH39C59-coupling, in principle, also moni￾tors the puckering, namely via the torsion angle d. Unfortunately, its value does not differ significantly between the N- and S-state [49]. A third source of information on the puckering state of the sugar ring is the 2 JHC-couplings. The two-bond couplings 2 JH29C19 and 2 JH39C29 are found to be negative for S-puckered rings and positive for N-puckered rings, while the reverse holds for 2 JH29C39 and 2 JH39C49 [49]. These two-bond J-couplings are thus good indi￾cators of the sugar ring conformation. However, the other sugar ring two-bond couplings, 2 JH19C29 and 3 JH49C39, do not change sign and remain negative for both the N-puckered and the S-puckered state [49]. These signs of the 2 JHC-couplings are in complete accordance with the projection rule proposed by Bock and Pederson [87]. According to this rule the sign of the 2 JHC-couplings in H–C– 13C–X1(X2) systems can simply be predicted from the Newman projection and the orientation of the electronegative substituents X1 and X2 relative to the position of the proton coupled to 13C; X1 and X2 can either be oxygen or nitrogen. A trans orientation of this H relative to X leads to a positive value for 2 JCH, whereas a gauche orientation gives rise to a negative value for 2 JCH. If two X substituents are present on 13C the effects are additive. Thus, if both H to X1 and H to X2 are oriented gauche to each other a negative value is obtained for 2 JHC. On the other hand, a trans orien￾tation of H relative to X1 and a gauche orientation of H relative to X2 will give rise to compensating effects and a 2 JHC value which is approximately zero. For example, 2 JH29C39 is predicted by this rule to be nega￾tive for an N-conformer, since O39 is oriented gauche with respect to H29, and positive for an S-conformer, since O39 is oriented trans with respect to H29. This is exactly what is observed experimentally (see above). The other 2 JHC-couplings in the sugar ring also follow this projection rule. Finally, the one-bond couplings 1 JCH also convey sugar pucker information; 1 JH39C39 has values of 149.6 Hz and 156.8 Hz for N- and S-type sugars, respectively, while 1 JH29C29 shows the reverse trend, namely values of 158.4 Hz and 149.2 Hz for N- and S-type sugars, respectively. When the sugar ring occurs as a mixture of N- and S-conformers with inter￾mediate values for pS, intermediate 1 JH29/39C29/39 values are also found. We note that the torsion angle dependencies of the 1 JHC-couplings are not very well understood, in contrast to the case of the 3 JHC- and the 2 JHC-couplings. Nevertheless these experimental observations remain useful as indicators of the sugar pucker. 5.4. Determination of the b torsion angle The b torsion angle has traditionally been deter￾mined by the 3,2JHP-coupling constants. The Karplus equation describing the 3 JH59/50P59-couplings is 3 JH59=50P59 ¼ 15:3 cos2 f ¹ 6:2 cos f þ 1:5 (23) with f ¼ b ¹ 1208 for H59 and f ¼ b þ 1208 for H50. The most recent parametrization has been used here [62,88]. The 3 JH59P59-and 3 JH50P59-couplings describe the b torsion angle as shown in Fig. 5. As can be 310 S.S. Wijmenga, B.N.M. van Buuren/Progress in Nuclear Magnetic Resonance Spectroscopy 32 (1998) 287–387

S.S. Wijmenga, B N.M. van Buuren/Progress in Nuclear Magnetic Resonance Spectroscopy 32(1998)287-387 311 A JHS"P5 270 Fig. 5. The JHS"PS", JH5Ps-and Jcaps-coupling constants calculated as a function of the torsion angle B on the basis of their Karplus relations seen, these two J-coupling constants define the p rotamer fraction is populated, to establish the range torsion angle quite well for the whole range of B of allowed torsion angles for that rotamer, i.e. the value width of the libration motion. But usually one tries The Jc4p5-couplings are described by to derive from the J-couplings the relative rotamer 3J4py=80c0s28-34cosB+0.5 (24) populations. An estimation of the fraction of the most common conformer, B, can be obtained from Here again the latest parametrization, as given by the equation Mooren et al. [88], is used. Fig. 5 also shows JCA'PS as a function of B. As can be seen, a fairly narrow f[25.5-UJHS'P5+JHs"Ps) range of B torsion angles can be derived from the 20.5 additional knowledge of this J-coupling constant Whether the flexibility plays a role or not can be This equation has been derived under the assumption that B torsion angle values of the B* and B co established by the concerted use of the difterent formers are 600 and 300% J-coupling constants. If the three J-coupling values do not indicate one value for the torsion angle, it can be values JHs'ps and JHsps, of these rotamers are then concluded that angular averaging is taking place. Th known. The value of Jc4'Ps can also be used to angular averaging can be either the result of libration calculate this fraction in a similar way motions within one rotamer domain or rapid inter conversion between different rotamers. It may even=.3 be possible under certain circumstances and making certain assumptions, for example that only one Finally, the JH4P5'-coupling can reach values as large

seen, these two J-coupling constants define the b torsion angle quite well for the whole range of b values. The 3 JC49P59-couplings are described by 3 JC49P59 ¼ 8:0 cos2 b ¹ 3:4 cos b þ 0:5 (24) Here again the latest parametrization, as given by Mooren et al. [88], is used. Fig. 5 also shows 3 JC49P59 as a function of b. As can be seen, a fairly narrow range of b torsion angles can be derived from the additional knowledge of this J-coupling constant. Whether the flexibility plays a role or not can be established by the concerted use of the different J-coupling constants. If the three J-coupling values do not indicate one value for the torsion angle, it can be concluded that angular averaging is taking place. The angular averaging can be either the result of libration motions within one rotamer domain or rapid inter￾conversion between different rotamers. It may even be possible under certain circumstances and making certain assumptions, for example that only one rotamer fraction is populated, to establish the range of allowed torsion angles for that rotamer, i.e. the width of the libration motion. But usually one tries to derive from the J-couplings the relative rotamer populations. An estimation of the fraction of the most common conformer, bt , can be obtained from the equation ft ¼ [25:5 ¹ (JH59P59 þ JH50P59)] 20:5 (25) This equation has been derived under the assumption that b torsion angle values of the bþ and b¹ con￾formers are 608 and 3008, respectively. The coupling values JH59P59 and JH50P59 of these rotamers are then known. The value of JC49P59 can also be used to calculate this fraction in a similar way: ft ¼ JC49P59 ¹ 1:3 9:8 (26) Finally, the 4 JH49P59-coupling can reach values as large Fig. 5. The 3 J H59P59-, 3 J H50P59- and 3 JC49P59-coupling constants calculated as a function of the torsion angle b on the basis of their Karplus relations (see text). S.S. Wijmenga, B.N.M. van Buuren/Progress in Nuclear Magnetic Resonance Spectroscopy 32 (1998) 287–387 311