Section 20.2.8. Effect of crystallographic atomic resolution on structural stability during molecular dynamics

The variation in r.m.s. deviation between the initial crystallographic structure and the simulation coordinates for different protein trajectories (Fig. 20.2.7.1) raises the question of whether the atomic resolution of the starting X-ray structure influences the magnitude of this deviation. In order to investigate this issue, we calculated trajectories for bovine pancreatic trypsin inhibitor (BPTI), starting with crystallographic structures determined from data at three different atomic resolutions: 1bpi at 1.1 Å resolution (Parkin et al., 1999), 6pti at 1.7 Å resolution (Wlodawer et al., 1987) and 1bhc at 2.7 Å resolution (Hamiaux et al., 1999). The errors in the atomic coordinates estimated from the Luzzati plots are 0.06 Å for the 1.1 Å resolution structure and 0.41 Å for the 2.7 Å resolution structure. The protocol described in the previous section was followed for simulations starting with each of the three crystallographic structures over a 500 ps simulation time. The net charge of +6 e on BPTI was neutralized by adding six chloride anions to the solvated protein system, thus accomplishing the ideal conditions for a PME calculation for the electrostatic interaction. The truncated octahedra contain approximately 3700 water molecules, and the total number of atoms in the simulations is over 12 000. The simulations were carried out on an eight-node IBM/SP2 and required 4.5 h of CPU time per 10 ps of dynamics run.

Root-mean-square differences (r.m.s.d.'s) in atomic coordinates were calculated between all pairs of coordinates from the X-ray structures, the energy-minimized X-ray structures and the 10 ps average MD structure obtained near 300 ps of the simulation period. In Table 20.2.8.1, the upper diagonal r.m.s.d. values are the main-chain-atom differences, while the lower diagonal ones are the side-chain-atom differences. The r.m.s.d.'s between the three X-ray structures range from 0.4–0.5 Å for the main-chain atoms and 1.4–1.6 Å for the side-chain atoms. The larger r.m.s. values for averages over side-chain atoms imply alternative side-chain orientations. This degree of structural deviation is visualized with an overlay of the three X-ray structures of BPTI shown on the left-hand side of Fig. 20.2.8.1. Energy minimization with respect to the CHARMM force field alters the main-chain atoms of the X-ray structures by approximately 0.4 Å and increases the differences between two X-ray structures to 0.6–0.7 Å. The differences in the main-chain atoms between an MD average structure and an energy-minimized X-ray structure are only somewhat larger: 1.0–1.1 Å. Interestingly, these values are comparable to the values obtained when comparing the three MD average structures: 0.9–1.1 Å. The main-chain structural differences among the three 10 ps average MD structures are shown on the right-hand side of Fig. 20.2.8.1. The general trends observed for main-chain atoms are also found for side-chain atoms. Thus, the differences between the X-ray structures increase somewhat as a result of energy minimization, and the differences between MD average structures and X-ray structures (1.9–2.9 Å) are similar to those between two X-ray structures (1.5–2.8 Å) or two MD average structures (approximately 2.2 Å).

Figure 20.2.8.1| top | pdf | Cα tracings of BPTI. Left: crystallographic structures determined from data at three different resolutions: 1.1 (red), 1.7 (blue) and 2.7 Å (orange). Right: 10 ps average MD structures from simulations initiated with the energy-minimized crystallographic structure determined at 1.1 (pink), 1.7 (cyan) or 2.7 Å (yellow) resolution. The 10 ps average is over coordinates from 290 to 300 ps.

Similar r.m.s. values are found if the starting velocites for a simulation are varied while maintaining the same starting coordinates (Caves et al., 1998); the r.m.s.d.'s obtained from 120 ps MD simulations were 0.7–1.1 Å for the main-chain atoms with respect to the reference X-ray structure and 0.8–1.5 Å between MD individual trajectory averages. The results given in Table 20.2.8.1, together with those of Caves et al. (1998), suggest that sampling on the nanosecond timescale largely reflects the conformational variations due to thermal fluctuations that result from a potential-energy surface with multiple minima separated by low barriers (Cooper, 1976). In this context, MD simulations starting with different X-ray structures offer a more extensive sampling of the conformational space of the specific protein than simulations carried out from a single X-ray structure, although this conclusion remains to be demonstrated by a more thorough analysis. Our results do not support the conclusion that overall r.m.s.d.'s between MD average structures and the starting X-ray structures correlate with atomic resolution.

The r.m.s.d.'s between main-chain atoms in the starting X-ray structures and simulation snapshots as a function of time are presented in Fig. 20.2.8.2. The 1.1 Å resolution structure has the most stable trajectory during the 500 ps trajectory, with an average r.m.s. value of 1.01 (9) Å. The 1.7 Å resolution structure has an r.m.s. value of 0.98 (22) Å. In this simulation, the r.m.s.d.'s fluctuate more widely from the average value, with small differences in the first 200 ps, larger ones between 200 and 400 ps, and again smaller ones in the last 100 ps. For the 2.7 Å resolution structure, the average over the simulation is 1.28 (21) Å. From the results presented here, it is concluded that the higher-resolution structures are more stable during MD simulations and have a shorter equilibration period (50 ps for 1.1 Å resolution and over 300 ps for 2.7 Å resolution). This conclusion is consistent with larger errors in the atomic coordinates of X-ray structures determined from lower-resolution data.

Figure 20.2.8.2| top | pdf | BPTI r.m.s. coordinate differences between the energy-minimized crystallographic structure and MD snapshots from three simulations. A simulation was initiated from the energy-minimized crystallographic structure determined at 1.1 (black), 1.7 (red) or 2.7 Å (green) resolution. The r.m.s.d. is averaged over the main-chain atoms N, Cα and C.