Ivanov et al. 10.1073/pnas.0603468104. |
Fig. 5. To estimate the magnitude of hysteresis effects on the calculated free energy profile we carried out the thermodynamic integration in the reverse direction for part of the free energy curve from -1.2 to -0.4 Å. Comparison between the forward (green line) and reverse (blue line) directions (0.5-ps equilibration; 2-ps sampling) indeed shows non-negligible hysteresis. Displayed are systematically higher constraint forces and, respectively, potential of mean force points, with the difference growing to 0.9 kcal/mol at ξ -0.4 Ε (and presumably larger over the entire profile).
Fig. 6. Comparison of product structures after proton release. (a) Product structure after phosphate group proton release. The proton originally associated with the phosphate moiety was moved to the leaving group oxyanion, and the structure was relaxed by using unrestrained AIMD for 1 ps. (b) Experimentally determined product structure (Protein Data Bank ID code 1QUM). Characteristic Zn coordination distances are given in Å.
Table 1. Characteristic Zn coordination distances
Distance, Å | X-ray | Endo IV/OH- | Endo IV/H2O | Endo IV/TS |
Zn1 - Nδ(His69) | 2.06 | 2.11 ± 0.077 | 2.10 ± 0.066 | 2.12 ± 0.071 |
Zn1 - Nδ(His109) | 1.94 | 1.94 ± 0.043 | 1.92 ± 0.031 | 1.94 ± 0.036 |
Zn1 - O1(Glu145) | 2.00 | 2.36 ± 0.024 | 2.79 ± 0.524 | 2.24 ± 0.105 |
Zn2 - O2(Glu145) | 2.21 | 2.19 ± 0.105 | 2.11 ± 0.088 | 2.16 ± 0.084 |
Zn2 - O1(Asp179) | 2.15 | 2.12 ± 0.125 | 2.04 ± 0.076 | 2.19 ± 0.162 |
Zn2 - O1(Glu261) | 2.25 | 2.35 ± 0.139 | 2.41 ± 0.257 | 2.26 ± 0.083 |
Zn2 - Nδ(His216) | 2.30 | 2.20 ± 0.110 | 2.84 ± 0.436 | 2.26 ± 0.068 |
Zn2 - O2P(sub)* | - | 3.46 ± 0.375 | 2.07 ± 0.090 | 2.27 ± 0.146 |
Zn3 - O2P(sub)* | - | 2.07 ± 0.121 | 2.26 ± 0.197 | 2.29 ± 0.120 |
Zn3 - O1(Asp229) | 2.21 | 2.72 ± 0.422 | 2.12 ± 0.095 | 2.21 ± 0.094 |
Zn3 - O2(Asp229) | 2.67 | 2.39 ± 0.462 | 3.07 ± 0.217 | 3.01 ± 0.248 |
Zn3 - Nδ(His231) | 2.16 | 2.07 ± 0.066 | 2.06 ± 0.068 | 2.12 ± 0.075 |
Zn3 - Nδ(His182) | 2.07 | 2.07 ± 0.073 | 2.05 ± 0.074 | 2.11 ± 0.087 |
Zn3 - OP'(sub) | - | 2.94 ± 0.314 | 2.72 ± 0.330 | 2.11 ± 0.090 |
Zn1 - O1P(sub) | - | 2.99 ± 0.732 | 2.55 ± 0.540 | 2.29 ± 0.184 |
Zn1 - O* | 2.01 | 2.01 ± 0.096 | 2.27 ± 0.249 | 2.17 ± 0.122 |
Zn2 - O* | 2.48 | 1.99 ± 0.082 | 2.16 ± 0.165 | 2.24 ± 0.132 |
Zn1 - Zn2 | 3.78 | 3.56 ± 0.101 | 3.81 ± 0.280 | 3.75 ± 0.106 |
Zn2 - Zn3 | 4.11 | 4.65 ± 0.184 | 4.18 ± 0.368 | 4.31 ± 0.142 |
Zn1 - Zn3 | 5.75 | 5.86 ± 0.307 | 5.66 ± 0.150 | 5.73 ± 0.163 |
Presented are the distances (in Å) from the crystal structure; averaged distances for the two models (A and B) from the direct dynamics runs and for the transition state structure from constrained dynamics (= 0). The corresponding standard deviations are given in Å.
Table 2
. Zn coordination distances in the forward and reverse thermodynamic integration runsDistance, Å | Initial state = 1.2 Å | TS reverse | TS forward |
O* - OP' | 4.54 | 3.89 | 3.91 |
O* - OP' | 2.87 | 1.95 | 2.04 |
O* - OP' | 1.67 | 1.95 | 2.04 |
Zn2 - O2P | 2.03 | 2.22 | 2.27 |
Zn3 - O2P | 3.02 | 2.14 | 2.29 |
Zn3 - OP' | 1.95 | 2.18 | 2.11 |
Zn1 - O1P | 2.00 | 2.08 | 2.29 |
Zn1 - O* | 3.01 | 2.41 | 2.17 |
Zn2 - O* | 3.14 | 2.23 | 2.24 |
Zn1 - Zn2 | 4.45 | 3.86 | 3.75 |
Zn2 - Zn3 | 4.47 | 4.28 | 4.31 |
Zn1 - Zn3 | 5.89 | 5.67 | 5.73 |
Zn coordination distances (in Å) for the transition state (TS) structures obtained in the forward and reverse thermodynamic integration procedure. The studied distances show a hysteresis of up to 0.24 Å in magnitude.
Table 3. Zinc atom charges from natural bond orbital (NBO) analysis
NBO charges | Endo IV reactant | Endo IV transition state | Endo IV product |
Zn1 | 1.647 ± 0.00478 (0.047) | 1.657 ± 0.00417 (0.029) | 1.657 ± 0.00415 (0.032) |
Zn2 | 1.642 ± 0.00441 (0.038) | 1.648 ± 0.00516 (0.030) | 1.660 ± 0.00522 (0.036) |
Zn3 | 1.635 ± 0.00414 (0.038) | 1.631 ± 0.00350 (0.023) | 1.616 ± 0.00277 (0.019) |
Charges on the three zinc atoms from resulting from NBO analysis are shown. The calculations were performed at the B3LYP/6-31G level of theory by using seven regularly spaced snapshots from the constrained trajectories for = 1.6 (reactant), = 0 (transition state), and = -1.6 (product), respectively. The absolute values of the charges depend on the particular charge-partitioning scheme. Thus, the NBO charges are different from the atoms-in-molecules (AIM) charges. Nevertheless, they remain practically invariant along the reaction coordinate, independently confirming our observations from AIM. The corresponding SEM and range of variation (in parentheses) are also included.