International
Tables for
Crystallography
Volume F
Crystallography of biological macromolecules
Edited by M. G. Rossmann and E. Arnold

International Tables for Crystallography (2006). Vol. F, ch. 18.3, pp. 384-390   | 1 | 2 |

Section 18.3.2.3. Bonds and angles

R. A. Engha* and R. Huberb

aPharmaceutical Research, Roche Diagnostics GmbH, Max Planck Institut für Biochemie, 82152 Martinsried, Germany, and bMax-Planck-Institut für Biochemie, 82152 Martinsried, Germany
Correspondence e-mail:  engh@biochem.mpg.de

18.3.2.3. Bonds and angles

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18.3.2.3.1. Peptide parameters: proline, glycine, alanine and CB substitution

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Fragments representing five-atom lengths of the backbone currently provide adequate statistics for peptide compositions of varieties including glycine, proline and side chains branched at CB. Peptide cyclicity was generally allowed on the assumption that this does not introduce distortions greater than typical protein secondary-structure interactions. The results are presented in Table 18.3.2.3[link]. With one exception, none of the values deviates from those of 1991 by more than one sample standard deviation. However, the very large σ values for the proline C—N—CA and C—N—CD angles (Table 18.3.2.1[link]) are conspicuous. Using high-resolution protein structures, Lamzin et al. (1995)[link] identified geometries of proline that were inconsistent with high-resolution protein structures and also noted inconsistencies in C—CA—CB angle parameters (see also the sections on individual amino acids below). In the case of proline, a bimodal distribution of these parameters could be resolved with the discrimination between cis and trans forms (Fig. 18.3.2.1[link]). A scatter plot of the angles against ω torsion angle resolves the averages (and σ's) of 122.6 (50) and 125.4 (44)° for C—N—CA and C—N—CD, respectively, into cis- and trans-dependent values with much smaller sample deviations (see Table 18.3.2.2[link]). The large σ value for CB—CG remains, however, particularly for trans-proline. Its origin is unknown, but proline pucker may play a role.

Table 18.3.2.1| top | pdf |
Bond lengths of standard amino-acid side chains

EH denotes the values of Engh & Huber (1991)[link], which were clustered according to atom type. The EH99 values are taken from recent Cambridge Structural Database releases with clustering of parameters only in the choice of fragments, based on amino acids. Parameters marked with an asterisk involving CA—CB bonds were taken from peptide fragment geometries. Two asterisks mark long-chain aliphatic parameters taken from arginine statistics. The number of fragments and the number of structures containing these fragments are noted after the amino-acid name. The fragments used for generating the statistics are described after the amino-acid name: incomplete valences indicate unspecified substituents with, however, specified orbital hybridization.

Alanine, 163/268, CO—NH—CH(CH3)—CO—NH

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.521 0.033 1.520 0.021

Arginine, 71/98, CH—(CH2)3—NH—C(NH2)2

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.530 0.020 1.535[^{*}] 0.022[^{*}]
CB—CG 1.520 0.030 1.521 0.027
CG—CD 1.520 0.030 1.515 0.025
CD—NE 1.460 0.018 1.460 0.017
NE—CZ 1.329 0.014 1.326 0.013
CZ—NH(1,2) 1.326 0.018 1.326 0.013

Asparagine, 145/247, —C—CH2—CO—NH2

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.530 0.020 1.527 0.026
CB—CG 1.516 0.025 1.506 0.023
CG—OD1 1.231 0.020 1.235 0.022
CG—ND2 1.328 0.021 1.324 0.025

Aspartate, 265/404, C—CH2—CO2

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.530 0.020 1.535[^{*}] 0.022[^{*}]
CB—CG 1.516 0.025 1.513 0.021
CG—OD(1,2) 1.249 0.019 1.249 0.023

Cysteine, 10/17, N—CH(CO)—CH2—SH

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.530 0.020 1.526 0.013
CB—SG 1.808 0.033 1.812 0.016

Disulfides, 53/68, C—CH2—S—S—CH2—C

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.530 0.020 1.535[^{*}] 0.022[^{*}]
CB—SG 1.808 0.033 1.818 0.017
SG—SG 2.030 0.008 2.033 0.016

Glutamate, 74/88, C—CH2—CH2—CO2

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.530 0.020 1.535[^{*}] 0.022[^{*}]
CB—CG 1.520 0.030 1.517 0.019
CG—CD 1.516 0.025 1.515 0.015
CD—OE(1,2) 1.249 0.019 1.252 0.011

Glutamine, 145/247, —C—CH2—CO—NH2

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.530 0.020 1.535[^{*}] 0.022[^{*}]
CB—CG 1.520 0.030 1.521[^{**}] 0.027[^{**}]
CG—CD 1.516 0.025 1.506 0.023
CD—OE1 1.231 0.020 1.235 0.022
CD—NE2 1.328 0.021 1.324 0.025

Glycine: see peptide parameters, Table 18.3.2.3[link]

Histidine (HISE), 35/37, C—CH2—imidazole; NE protonated

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.530 0.020 1.535[^{*}] 0.022[^{*}]
CB—CG 1.497 0.014 1.496 0.018
CG—ND1 1.371 0.017 1.383 0.022
CG—CD2 1.356 0.011 1.353 0.014
ND1—CE1 1.319 0.013 1.323 0.015
CD2—NE2 1.374 0.021 1.375 0.022
CE1—NE2 1.345 0.020 1.333 0.019

Histidine (HISD), 10/12, C—CH2—imidazole; ND protonated

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.530 0.020 1.535[^{*}] 0.022[^{*}]
CB—CG 1.497 0.014 1.492 0.016
CG—ND1 1.378 0.011 1.369 0.015
CG—CD2 1.356 0.011 1.353 0.017
ND1—CE1 1.345 0.020 1.343 0.025
CD2—NE2 1.382 0.030 1.415 0.021
CE1—NE2 1.319 0.013 1.322 0.023

Histidine (HISH), 50/54, C—CH2—imidazole; NE, ND protonated

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.530 0.020 1.535[^{*}] 0.022[^{*}]
CB—CG 1.497 0.014 1.492 0.010
CG—ND1 1.378 0.011 1.380 0.010
CG—CD2 1.354 0.011 1.354 0.009
ND1—CE1 1.321 0.010 1.326 0.010
CD2—NE2 1.374 0.011 1.373 0.011
CE1—NE2 1.321 0.010 1.317 0.011

Isoleucine, 54/80, NH—CH(CO)—CH(CH3)—CH2—CH3

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.540 0.027 1.544 0.023
CB—CG1 1.530 0.020 1.536 0.028
CB—CG2 1.521 0.033 1.524 0.031
CG1—CD1 1.513 0.039 1.500 0.069[^{*}]

Leucine, 178/288, NH—CH(CO)—CH2—CH(CH3)2

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.530 0.020 1.533 0.023
CB—CG 1.530 0.020 1.521 0.029
CG—CD(1,2) 1.521 0.033 1.514 0.037

Lysine, 232/380, —(CH2)3—NH3

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.530 0.020 1.535[^{*}] 0.022[^{*}]
CB—CG 1.520 0.030 1.521[^{**}] 0.027[^{**}]
CG—CD 1.520 0.030 1.520 0.034
CD—CE 1.520 0.030 1.508 0.025
CE—NZ 1.489 0.030 1.486 0.025

Methionine, 37/49, C—(CH2)2—S—CH3

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.530 0.020 1.535[^{*}] 0.022[^{*}]
CB—CG 1.520 0.030 1.509 0.032
CG—SD 1.803 0.034 1.807 0.026
SD—CE 1.791 0.059 1.774 0.056[^{*}]

Phenylalanine, 1076/1616, C—CH2—phenyl

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.530 0.020 1.535[^{*}] 0.022[^{*}]
CB—CG 1.502 0.023 1.509 0.017
CG—CD(1,2) 1.384 0.021 1.383 0.015
CD(1,2)—CE(1,2) 1.382 0.030 1.388 0.020
CE(1,2)—CZ 1.382 0.030 1.369 0.019

Proline, 262/255, trans, C—CO—pyrrolidine—CO—N

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.530 0.020 1.531 0.020
CB—CG 1.492 0.050 1.495 0.050
CG—CD 1.503 0.034 1.502 0.033
CD—N 1.473 0.014 1.474 0.014

Proline, 262/158, cis, C—CO—pyrrolidine—CO—N

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.530 0.020 1.533 0.018
CB—CG 1.492 0.050 1.506 0.039
CG—CD 1.503 0.034 1.512 0.027
CD—N 1.473 0.014 1.474 0.014

Serine, 33/39, NH—CH(CO)—CH2—OH

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.530 0.020 1.525 0.015
CB—OG 1.417 0.020 1.418 0.013

Threonine, 20/25, NH—CH(CO)—CH(OH)—CH3

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.540 0.027 1.529 0.026
CB—OG1 1.433 0.016 1.428 0.020
CB—CG2 1.521 0.033 1.519 0.033

Tryptophan, 123/135, CH2—indole

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.530 0.020 1.535[^{*}] 0.022[^{*}]
CB—CG 1.498 0.031 1.498 0.018
CG—CD1 1.365 0.025 1.363 0.014
CG—CD2 1.433 0.018 1.432 0.017
CD1—NE1 1.374 0.021 1.375 0.017
NE1—CE2 1.370 0.011 1.371 0.013
CD2—CE2 1.409 0.017 1.409 0.012
CD2—CE3 1.398 0.016 1.399 0.015
CE2—CZ2 1.394 0.021 1.393 0.017
CE3—CZ3 1.382 0.030 1.380 0.017
CZ2—CH2 1.368 0.019 1.369 0.019
CZ3—CH2 1.400 0.025 1.396 0.016

Tyrosine, 124/161, para-(—C—CH2)—phenol

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.530 0.020 1.535[^{*}] 0.022[^{*}]
CB—CG 1.512 0.022 1.512 0.015
CG—CD(1,2) 1.389 0.021 1.387 0.013
CD(1,2)—CE(1,2) 1.382 0.030 1.389 0.015
CE(1,2)—CZ 1.378 0.024 1.381 0.013
CZ—OH 1.376 0.021 1.374 0.017

Valine, 198/313, N—CH(CO)—CH—(CH3)2

BondEH (Å)σ EH (Å)EH99 (Å)σ EH99 (Å)
CA—CB 1.540 0.027 1.543 0.021
CB—CG(1,2) 1.521 0.033 1.524 0.021

Table 18.3.2.2| top | pdf |
Bond angles of standard amino-acid side chains

For details see Table 18.3.2.1[link].

Alanine, 163/268, CO—NH—CH(CH3)—CO—NH

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 110.4 1.5 110.1 1.4
CB—CA—C 110.5 1.5 110.1 1.5

Arginine, 71/98, CH—(CH2)3—NH—C(NH2)2

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 110.5 1.7 110.6[^{*}] 1.8[^{*}]
CB—CA—C 110.1 1.9 110.4[^{*}] 2.0[^{*}]
CA—CB—CG 114.1 2.0 113.4 2.2
CB—CG—CD 111.3 2.3 111.6 2.6
CG—CD—NE 112.0 2.2 111.8 2.1
CD—NE—CZ 124.2 1.5 123.6 1.4
NE—CZ—NH(1,2) 120.0 1.9 120.3 0.5
NH1—CZ—NH2 119.7 1.8 119.4 1.1

Asparagine, 145/247, —C—CH2—CO—NH2

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 110.5 1.7 110.6[^{*}] 1.8[^{*}]
CB—CA—C 110.1 1.9 110.4[^{*}] 2.0[^{*}]
CA—CB—CG 112.6 1.0 113.4[^{**}] 2.2[^{**}]
CB—CG—ND2 116.4 1.5 116.7 2.4
CB—CG—OD1 120.8 2.0 121.6 2.0
ND2—CG—OD1 122.6 1.0 121.9 2.3

Aspartate, 265/404, C—CO2

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 110.5 1.7 110.6[^{*}] 1.8[^{*}]
CB—CA—C 110.1 1.9 110.4[^{*}] 2.0[^{*}]
CA—CB—CG 112.6 1.0 113.4[^{*}] 2.2[^{**}]
CB—CG—OD(1,2) 118.4 2.3 118.3 0.9
OD1—CG—OD2 122.9 2.4 123.3 1.9

Cysteine, 10/17, N—CH(CO)—CH2—SH

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 110.5 1.7 110.8 1.5
CB—CA—C 110.1 1.9 111.5 1.2
CA—CB—SG 114.4 2.3 114.2 1.1

Disulfides, 53/68, C—CH2—S—S—CH2—C

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 110.5 1.7 110.6[^{*}] 1.8[^{*}]
CB—CA—C 110.1 1.9 110.4[^{*}] 2.0[^{*}]
CA—CB—SG 114.4 2.3 114.0 1.8
CB—SG—SG 103.8 1.8 104.3 2.3

Glutamate, 74/88, C—CH2—CH2—CO2

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 110.5 1.7 110.6[^{*}] 1.8[^{*}]
CB—CA—C 110.1 1.9 110.4[^{*}] 2.0[^{*}]
CA—CB—CG 114.1 2.0 113.4[^{**}] 2.2[^{**}]
CB—CG—CD 112.6 1.7 114.2 2.7
CG—CD—OE(1,2) 118.4 2.3 118.3 2.0
OE1—CD—OE2 122.9 2.4 123.3 1.2

Glutamine, 145/247, —C—CH2—CO—NH2

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 110.5 1.7 110.6[^{*}] 1.8[^{*}]
CB—CA—C 110.1 1.9 110.4[^{*}] 2.0[^{*}]
CA—CB—CG 114.1 2.0 113.4[^{**}] 2.2[^{**}]
CB—CG—CD 112.6 1.7 111.6[^{**}] 2.6[^{**}]
CG—CD—OE1 120.8 2.0 121.6 2.0
CG—CD—NE2 116.4 1.5 116.7 2.4
OE1—CD—NE2 122.6 1.0 121.9 2.3

Glycine: see Table 18.3.2.3[link]

Histidine (HISE), 35/37, C—CH2—imidazole; NE protonated

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 110.5 1.7 110.6[^{*}] 1.8[^{*}]
CB—CA—C 110.1 1.9 110.4[^{*}] 2.0[^{*}]
CA—CB—CG 113.8 1.0 113.6 1.7
CB—CG—ND1 121.6 1.5 121.4 1.3
CB—CG—CD2 129.1 1.3 129.7 1.6
CG—ND1—CE1 105.6 1.0 105.7 1.3
ND1—CE1—NE2 111.7 1.3 111.5 1.3
CE1—NE2—CD2 106.9 1.3 107.1 1.1
NE2—CD2—CG 106.5 1.0 106.7 1.2
CD2—CG—ND1 109.2 0.7 108.8 1.4

Histidine (HISD), 10/12, C—CH2— imidazole; ND protonated

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 110.5 1.7 110.6[^{*}] 1.8[^{*}]
CB—CA—C 110.1 1.9 110.4[^{*}] 2.0[^{*}]
CA—CB—CG 113.8 1.0 113.6 1.7
CB—CG—ND1 122.7 1.5 123.2 2.5
CB—CG—CD2 129.1 1.3 130.8 3.1
CG—ND1—CE1 109.0 1.7 108.2 1.4
ND1—CE1—NE2 111.7 1.3 109.9 2.2
CE1—NE2—CD2 107.0 3.0 106.6 2.5
NE2—CD2—CG 109.5 2.3 109.2 1.9
CD2—CG—ND1 105.2 1.0 106.0 1.4

Histidine (HISH), 50/54, C—CH2—imidazole; NE, ND protonated

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 110.5 1.7 110.6[^{*}] 1.8[^{*}]
CB—CA—C 110.1 1.9 110.4[^{*}] 2.0[^{*}]
CA—CB—CG 113.8 1.0 113.6 1.6
CB—CG—ND1 122.7 1.5 122.5 1.3
CB—CG—CD2 131.2 1.3 131.4 1.2
CG—ND1—CE1 109.3 1.7 109.0 1.0
ND1—CE1—NE2 108.4 1.0 108.5 1.1
CE1—NE2—CD2 109.0 1.0 109.0 0.7
NE2—CD2—CG 107.2 1.0 107.3 0.7
CD2—CG—ND1 106.1 1.0 106.1 0.8

Isoleucine, 54/80, NH—CH(CO)—CH(CH3)—CH2—CH3

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 111.5 1.7 110.8 2.3
CB—CA—C 109.1 2.2 111.6 2.0
CA—CB—CG1 110.4 1.7 111.0 1.9
CB—CG1—CD1 113.8 2.1 113.9 2.8
CA—CB—CG2 110.5 1.7 110.9 2.0
CG1—CB—CG2 110.7 3.0 111.4 2.2

Leucine, 178/288, NH—CH(CO)—CH2—CH(CH3)2

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 110.5 1.7 110.4 2.0
CB—CA—C 110.1 1.9 110.2 1.9
CA—CB—CG 116.3 3.5 115.3 2.3
CB—CG—CD(1,2) 110.7 3.0 111.0 1.7
CD1—CG—CD2 110.8 2.2 110.5 3.0

Lysine, 232/380, —(CH2)3—NH3

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 110.5 1.7 110.6[^{*}] 1.8[^{*}]
CB—CA—C 110.1 1.9 110.4[^{*}] 2.0[^{*}]
CA—CB—CG 114.1 2.0 113.4[^{*}] 2.2[^{**}]
CB—CG—CD 111.3 2.3 111.6[^{**}] 2.6[^{**}]
CG—CD—CE 111.3 2.3 111.9 3.0
CD—CE—NZ 111.9 3.2 111.7 2.3

Methionine, 37/49, C—(CH2)2—S—CH3

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 110.5 1.7 110.6[^{*}] 1.8[^{*}]
CB—CA—C 110.1 1.9 110.4[^{*}] 2.0[^{*}]
CA—CB—CG 114.1 2.0 113.3 1.7
CB—CG—SD 112.7 3.0 112.4 3.0
CG—SD—CE 100.9 2.2 100.2 1.6

Phenylalanine, 1076/1616, C—CH2—phenyl

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 110.5 1.7 110.6[^{*}] 1.8[^{*}]
CB—CA—C 110.1 1.9 110.4[^{*}] 2.0[^{*}]
CA—CB—CG 113.8 1.0 113.9 2.4
CB—CG—CD(1,2) 120.7 1.7 120.8 0.7
CD(1,2)—CG—CD(2,1) 118.6 1.5 118.3 1.3
CG—CD(1,2)—CE(1,2) 120.7 1.7 120.8 1.1
CD(1,2)—CE(1,2)—CZ 120.0 1.8 120.1 1.2
CE(1,2)—CZ—CE(2,1) 120.0 1.8 120.0 1.8

Proline, 262/255, trans, C—CO—pyrrolidine—CO—N

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 103.0 1.1 103.3 1.2
CB—CA—C 110.1 1.9 111.7 2.1
CA—CB—CG 104.5 1.9 104.8 1.9
CB—CG—CD 106.1 3.2 106.5 3.9
CG—CD—N 103.2 1.5 103.2 1.5
CA—N—CD 112.0 1.4 111.7 1.4
C—N—CA 122.6 5.0 119.3 1.5
C—N—CD 125.0 4.1 128.4 2.1

Proline, 262/158, cis, C—CO—pyrrolidine—CO—N

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 103.0 1.1 102.6 1.1
CB—CA—C 110.1 1.9 112.0 2.5
CA—CB—CG 104.5 1.9 104.0 1.9
CB—CG—CD 106.1 3.2 105.4 2.3
CG—CD—N 103.2 1.5 103.8 1.2
CA—N—CD 112.0 1.4 111.5 1.4
C—N—CA 122.6 5.0 127.0 2.4
C—N—CD 125.0 4.1 120.6 2.2

Serine, 33/39, NH—CH(CO)—CH2—OH

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 110.5 1.7 110.5 1.5
CB—CA—C 110.1 1.9 110.1 1.9
CA—CB—OG 111.1 2.0 111.2 2.7

Threonine, 20/25, NH—CH(CO)—CH(OH)—CH3

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 111.5 1.7 110.3 1.9
CB—CA—C 109.1 2.2 111.6 2.7
CA—CB—OG1 109.6 1.5 109.0 2.1
CA—CB—CG2 110.5 1.7 112.4 1.4
OG1—CB—CG2 109.3 2.0 110.0 2.3

Tryptophan, 123/135, CH2—indole

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 110.5 1.7 110.6[^{*}] 1.8[^{*}]
CB—CA—C 110.1 1.9 110.4[^{*}] 2.0[^{*}]
CA—CB—CG 113.6 1.9 113.7 1.9
CB—CG—CD1 126.9 1.5 127.0 1.3
CB—CG—CD2 126.8 1.4 126.6 1.3
CD1—CG—CD2 106.3 1.6 106.3 0.8
CG—CD1—NE1 110.2 1.3 110.1 1.0
CD1—NE1—CE2 108.9 1.8 109.0 0.9
NE1—CE2—CD2 107.4 1.3 107.3 1.0
CE2—CD2—CG 107.2 1.2 107.3 0.8
CG—CD2—CE3 133.9 1.0 133.9 0.9
NE1—CE2—CZ2 130.1 1.5 130.4 1.1
CE3—CD2—CE2 118.8 1.0 118.7 1.2
CD2—CE2—CZ2 122.4 1.0 122.3 1.2
CE2—CZ2—CH2 117.5 1.3 117.4 1.0
CZ2—CH2—CZ3 121.5 1.3 121.6 1.2
CH2—CZ3—CE3 121.1 1.3 121.2 1.1
CZ3—CE3—CD2 118.6 1.3 118.8 1.3

Tyrosine 124/161, para—C—CH2—phenyl—OH

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 110.5 1.7 110.6[^{*}] 1.8[^{*}]
CB—CA—C 110.1 1.9 110.4[^{*}] 2.0[^{*}]
CA—CB—CG 113.9 1.8 113.4 1.9
CB—CG—CD(1,2) 120.8 1.5 121.0 0.6
CD(1,2)—CG—CD(2,1) 118.1 1.5 117.9 1.1
CG—CD(1,2)—CE(1,2) 121.2 1.5 121.3 0.8
CD(1,2)—CE(1,2)—CZ 119.6 1.8 119.8 0.9
CE(1,2)—CZ—CE(2,1) 120.3 2.0 119.8 1.6
CE(1,2)—CZ—OH 119.9 3.0 120.1 2.7

Valine, 198/313, N—CH(CO)—CH—(CH3)2

AngleEH (°)σ EH (°)EH99 (°)σ EH99 (°)
N—CA—CB 111.5 1.7 111.5 2.2
CB—CA—C 109.1 2.2 111.4 1.9
CA—CB—CG(1,2) 110.5 1.7 110.9 1.5
CG1—CB—CG2 110.8 2.2 110.9 1.6
Alternate fragment definition including CA.
Bimodal distribution (see text).
[Figure 18.3.2.1]

Figure 18.3.2.1 | top | pdf |

Torsion dependence of proline angle geometry. A one-dimensional frequency plot of either C—N—Cα or C—N—Cδ angles shows a broad and bimodal distribution. (a) A scatter plot of the two angles shows a very strong anticorrelation and suggests two minima. (b) Plotting either angle against the ω torsion angle resolves the broad distribution into two separate peaks.

Glycine, with its unique CH2 as CA, required new atom-type definitions for Engh & Huber (EH) (1991)[link] parameterization to account for parameter-average differences of about one-half of a sample standard deviation. These also included C—N—CA, for which the average angles were 120.6° for glycine and 121.7° for the rest. The new statistics with 83 C—CO—NH—CH2—C fragments estimate a larger value of 122.3° for the glycine C—N—CA angle.

`Extended atom'-type parameterizations, which cluster carbon atoms according to the number of bound hydrogen atoms, naturally separate parameters involving CB into values representing alanine and branched and unbranched side chains. Separate analyses of the bonds and angles for fragments depending on the number of hydrogen atoms at CB (1, 2 or 3) revealed significant variation for the C—CA—CB and N—CA—CB angles. The fragments chosen for peptide parameterization did not cover all possibilities for the peptide chain. In particular, effects of charges at the termini were not analysed. Also, specific residue sequences likely to have statistical effects, such as Pro-Pro (Bansal & Ananthanarayanan, 1988[link]), were not analysed here. With 50–60 relevant fragments from the predominantly α-helical ROP protein, Vlassi et al. (1998)[link] were able to compile statistics for main-chain bonds and angles and compare them with protein refinement parameters. Differences from EH were particularly significant for CO and CA—C bonds (1.237 and 1.508 Å, respectively) and for the O—C—N angle (121.35°). Excepting the proline O—C—N angle, for which the new CSD statistics predict an average value lowered to 121.1°, these values remained relatively unchanged. A likely source of the difference might be the predominantly helical structure of the ROP protein; the helical hydrogen bonding directly involves the C—O group in a systematic way.

18.3.2.3.2. Aromatic residues: tryptophan, phenylalanine, tyrosine, histidine

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With the exception of generally lower σ values, tryptophan parameters remain essentially unchanged. Phenylalanine, also with generally lower σ values, is also essentially unchanged with the assumption of Gaussian distributions. However, a scatter plot of the CB—CG—CD1 versus CB—CG—CD2 angles shows an inverse correlation between these two angles, corresponding to ring rotations about an axis perpendicular to the ring face. Non-Gaussian distributions were most evident for tyrosine. In addition to the phenomenon described for phenylalanine, a clearly multimodal distribution was observed for the CE(1,2)—CZ—OH angles, with maxima at 118 and 122° (Fig. 18.3.2.2[link]). The scatter plot of CE1—CZ—OH versus CE2—CZ—OH demonstrates that this distribution typifies individual fragments and does not arise from differing classes of fragments. This justifies an asymmetric parameterization for these angles; symmetric parameterization would require correspondingly soft force constants. The major difference between the histidine parameters listed here compared to those of EH arise from the appearance of HISD (uncharged; unprotonated at NE2) fragments in the CSD. The EH parameterization assumed values from other fragments. The total of 12 fragments is not large, but does predict some alterations in parameters involving the ring nitrogens. The fragment selection reported here did not investigate effects of noncovalent binding. For the aromatic residues, these include hydrogen-bonding effects (especially for histidine) and π-cloud interactions. Appropriate fragments exist in the database, so such dependencies are, in principle, accessible to investigation.

[Figure 18.3.2.2]

Figure 18.3.2.2 | top | pdf |

Bimodal distributions for tyrosine. (a) The C[epsilon]—Cζ—Oη angle distributions involving the tyrosine alcohol have maxima at 120 (2)°. (b) A scatter plot of the C[epsilon]2—Cζ—Oη angle against the C[epsilon]1—Cζ—Oη angle confirms that the Cζ—Oη bond projects asymmetrically away from the aromatic ring.

18.3.2.3.3. Aliphatic residues: leucine, isoleucine, valine

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Compared to EH parameterization, the only notable features of the aliphatic residues were the leucine bonds and the C—CA—CB angles of isoleucine and valine. The leucine CD—CG(1,2) bonds retained relatively large σ values, which rather increased compared to the previous values. The C—CA—CB angle values, clustered as bare carbon/tetrahedral CH extended atom/tetrahedral CH2 extended atom in EH, are sensitive to the degree of substitution at the CB carbon (Table 18.3.2.3,[link] see the discussion of peptide fragments above). The statistics here show that the EH (1991) parameters were too small by about 2°.

Table 18.3.2.3| top | pdf |
Bond lengths (Å) and angles (°) of peptide backbone fragments

EH denotes parameters from Engh & Huber (1991)[link]. Bold values mark important updates for angles involving proline (with cis and trans distinction) and branched CB atoms (isoleucine, valine, threonine). The number of fragments used for the statistics is given. The standard deviation of each value is given in parentheses following the value and is on the scale of the least significant digit of the value.

(a) Bonds

 Peptide (1165)Proline (297)Glycine (83)EHEH prolineEH glycine
N—CA 1.459 (20) 1.468 (17) 1.456 (15) 1.458 (19) 1.466 (15) 1.451 (16)
CA—C 1.525 (26) 1.524 (20) 1.514 (16) 1.525 (21) EH 1.516 (18)
C—O 1.229 (19) 1.228 (20) 1.232 (16) 1.231 (20) EH EH
CA—CB (all) 1.532 (31) 1.531 (20) 1.530 (20) EH
CA—CB (CH3) 1.521 (33) 1.521 (33)
CA—CB (CH2) 1.535 (22) 1.531 (20) 1.530 (20) EH
CA—CB (CH) 1.542 (23) 1.540 (27)
C—N 1.336 (23) 1.338 (19) 1.326 (18) 1.329 (14) 1.341 (16) EH

(b) Angles

 Peptide (1165)Proline (297)Glycine (83)EHEH prolineEH glycine
N—CA—C 111.0 (27) 112.1 (26) 113.1 (25) 111.2 (28) 111.8 (25) 112.5 (29)
N—CA—CB (all) 110.6 (21) 103.1 (12) 110.5 (17) 103.0 (11)
N—CA—CB (CH3) 110.4 (15) 110.4 (15) EH
N—CA—CB (CH2) 110.6 (18) 103.1 (12) 110.5 (17) 103.0 (11)
N—CA—CB (CH) 111.1 (23) 111.5 (17) EH
CA—C—N 117.2 (22) 117.1 (28) 116.2 (20) 116.2 (20) 116.9 (15) 116.4 (21)
CA—C—O 120.1 (21) 120.2 (24) 120.6 (18) 120.8 (17) EH 120.8 (21)
O—C—N 122.7 (16) 121.1 (19) 123.2 (17) 123.0 (16) 122.0 (14) EH
C—CA—CB 110.6 (23) 111.8 (20) 110.1 (19) EH
C—CA—CB (CH3) 110.5 (15) 110.5 (15)
C—CA—CB (CH2) 110.4 (20) 111.8 (20) 110.1 (19) EH
C—CA—CB (CH) 111.3 (20) 109.1 (22)
C—N—CA 121.7 (25) 122.0 (42) all
119.3 (15) trans
127.0 (24) cis
122.3 (21) 121.7 (18) 122.6 (50) 120.6 (17)

18.3.2.3.4. Neutral polar residues: serine, threonine, glutamine, asparagine

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These residues share neutral polarity, but are all geometrically distinct. Like leucine, valine and isoleucine described above, threonine is branched at CB, and the parameterization for C—CA—CB should be chosen accordingly. Additionally for threonine, the CA—CB—CG2 angle, clustered with valine as CH1E—CH1E—CH3E in EH (1991), should be altered from 110.5 to 112.4° according to the statistics reported here. The tabulated glutamine and asparagine parameters are taken from identical amide-group statistics, and parameters for the aliphatic atoms of glutamine are taken from arginine. This choice of fragments arose from a desire to maximize the number of fragments for the amide group; however, the individual residues might be expected to exhibit residue-specific amide structures.

18.3.2.3.5. Acidic residues: glutamate, aspartate

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The fragment definitions were chosen to select both symmetrically and asymmetrically encoded carboxylate structures; that is, the statistics include carboxylate groups with delocalized charges as well as carboxylate groups encoded with a single charged oxygen atom. This distribution presumably reflects the variations in proteins as well. For both glutamic and aspartic acids, statistical variation in the asymmetry of delocalization was evident. One measure of parameter variation as a function of varying charge delocalization is the anticorrelation of C—O bond lengths and CH2—C—O bond angles. For example, while the standard deviation of the corresponding aspartate bond lengths individually is 0.024 Å, the standard deviation of their pairwise average is 0.012 Å. Similarly, the standard deviation of the glutamate CH2—C—O bond angles individually is 2.1° but the standard deviation of the pairwise average is 0.6°. This coupling of parameters is an example of additional information potentially available for structure refinement, but which would require new formulations of restraints.

18.3.2.3.6. Basic residues: arginine, lysine

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The 98 arginine fragments in the database did not show alterations from the EH values, except generally tighter restraints at the guanidinium group. Lysine CD—CE bond lengths are somewhat shorter in the new statistics, while the two angles derived from the fragments remained similar.

18.3.2.3.7. Sulfur-containing residues: methionine, cysteine, disulfides

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One of the most conspicuous features of the EH parameters is the soft force constant for the methionine SD—CE bond length. The 49 fragments now in the CSD also show a sample deviation for the 1.774 Å average bond length of 0.056 Å, and after one 4σ outlier rejection, the tabulated value of 1.779 Å still has a large sample deviation of 0.041 Å. In practice, the use of soft restraints during refinement often leads to warnings of relatively large deviations from the target value. Inspection of the CSD structures did not reveal an artificial source of this greater variability. Cysteines and disulfides here show reduced sample σ values for generally similar average target values.

References

Bansal, M. & Ananthanarayanan, V. S. (1988). The role of hydroxyproline in collagen folding: conformational energy calculations on oligopeptides containing proline and hydroxyproline. Biopolymers, 27, 299–312.Google Scholar
Engh, R. A. & Huber, R. (1991). Accurate bond and angle parameters for X-ray protein structure refinement. Acta Cryst. A47, 392–400.Google Scholar
Lamzin, V. S., Dauter, Z. & Wilson, K. S. (1995). Dictionary of protein stereochemistry. J. Appl. Cryst. 28, 338–340.Google Scholar
Vlassi, M., Dauter, Z., Wilson, K. S. & Kokkinidis, M. (1998). Structural parameters for proteins derived from the atomic resolution (1.09 Å) structure of a designed variant of the ColE1 ROP protein. Acta Cryst. D54, 1245–1260.Google Scholar








































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