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. 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) are conspicuous. Using high-resolution protein structures, Lamzin et al. (1995) 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). 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). The large σ value for CB—CG remains, however, particularly for trans-proline. Its origin is unknown, but proline pucker may play a role.
Bond | EH (Å) | σ EH (Å) | EH99 (Å) | σ EH99 (Å) |
---|
CA—CB | 1.521 | 0.033 | 1.520 | 0.021 |
Bond | EH (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 |
Bond | EH (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 |
Bond | EH (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 |
Bond | EH (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 |
Bond | EH (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 |
Bond | EH (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 |
Bond | EH (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 |
Bond | EH (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 |
Bond | EH (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 |
Bond | EH (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 |
Bond | EH (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 |
Bond | EH (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 |
Bond | EH (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 |
Bond | EH (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 |
Bond | EH (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 |
Bond | EH (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 |
Bond | EH (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 |
Bond | EH (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 |
Bond | EH (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 |
Bond | EH (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 |
Bond | EH (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 |
Bond | EH (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 |
|
Angle | EH (°) | 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 |
Angle | EH (°) | 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 |
Angle | EH (°) | 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 |
Angle | EH (°) | 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 |
Angle | EH (°) | 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 |
Angle | EH (°) | 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 |
Angle | EH (°) | 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 |
Angle | EH (°) | 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 |
Angle | EH (°) | 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 |
Angle | EH (°) | 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 |
Angle | EH (°) | 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 |
Angle | EH (°) | 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 |
Angle | EH (°) | 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 |
Angle | EH (°) | 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 |
Angle | EH (°) | 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 |
Angle | EH (°) | 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 |
Angle | EH (°) | 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 |
Angle | EH (°) | 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 |
Angle | EH (°) | 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 |
Angle | EH (°) | 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 |
Angle | EH (°) | 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 |
Angle | EH (°) | 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‡ |
Angle | EH (°) | 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| 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) 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), were not analysed here. With 50–60 relevant fragments from the predominantly α-helical ROP protein, Vlassi et al. (1998) 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.
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). 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| top | pdf | Bimodal distributions for tyrosine. (a) The Cɛ—Cζ—Oη angle distributions involving the tyrosine alcohol have maxima at 120 (2)°. (b) A scatter plot of the Cɛ2—Cζ—Oη angle against the Cɛ1—Cζ—Oη angle confirms that the Cζ—Oη bond projects asymmetrically away from the aromatic ring. |
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, see the discussion of peptide fragments above). The statistics here show that the EH (1991) parameters were too small by about 2°.
| Peptide (1165) | Proline (297) | Glycine (83) | EH | EH proline | EH 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 |
| Peptide (1165) | Proline (297) | Glycine (83) | EH | EH proline | EH 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) |
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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.
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.
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.
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.