Presentative coarse coordinates [27]. We note that our restraining potential, as a function of the Cartesian coordinates, is not Indolactam V cost guaranteed to be invariant upon a rigid-body translation or rotation of the entire protein. To eliminate such effects, we applied additional restraints in all umbrella-sampling simulations. Specifically, a harmonic restraint, ?with spring constant of 1,000 kcal/mol/A2, was applied on the ! center of the protein. In addition, using the crystal structure X OP as the reference, we applied another harmonic restraint, withAdenylate Kinase ConformationFigure 2. Time evolution of the unrestrained simulations along a conformational pathway. The pathway is represented by a ! ! parameterized curveX ?(see Methods). Each protein conformation X j in the simulation trajectories was projected onto this curve through the ! !??operator aj Pa X j (see Methods), which returns the curve parameter aj corresponding to the point X aj on the curve with the shortest distance ! to X j . This operator was implemented through a nonlinear minimization algorithm. The projected curve parameter is plotted as a function of time for each simulation trajectory. The green and red dashed lines indicate the projected curve parameters for the open (a = 0.42) and closed (a = 0.99) crystal structures, respectively. doi:10.1371/journal.pone.0068023.gconformation, as all observed transitions were in the closed-toopen direction. Similar behaviors were also observed in previous unrestrained 1315463 simulations [13,22]. The spontaneous transitions in simulations C1 4 allowed us to observe the AdK conformational changes in details. Rigorous quantitative methods, such as principal component analysis [41], are available to visualize or compare the trajectories in lower dimensions. Alternatively, some simpler intuitive measures, such as the distances from the CORE domain to the AMPbd and LIDdomains, have been used in many studies as a reduced UKI-1 web representation of the AdK conformation [22,42?4]. Here we thus calculated the distances (Fig. 3) between the centers of the Ca atoms in these domains throughout the trajectories of C1 4. ?Figure 2 shows a larger change (,10 A) in the LID-CORE ?distance than that (, 5 A) in the AMPbd-CORE distance, indicating a larger movement of the LID domain during the transition. As mentioned earlier (Fig. 2B), the transitions took place at the very beginning of simulations C1 4, as indicated by theTable 1. RMSDs between the average protein conformations from the unrestrained simulations and the AdK crystal structures.C1 ?Open (A) ?Closed (A) 2.19 6.C2 1.38 7.C3 1.99 7.C4 1.79 6.C5 1.21 7.C6 2.01 6.C7 3.06 5.C8 6.35 3.O1 1.64 7.O2 1.03 6.O3 1.51 6.O4 1.15 7.O5 1.57 6.O6 1.61 6.O7 1.55 8.The protein conformation (represented by its Ca coordinates) from each frame in the simulation trajectories was aligned against the crystal structure, and the mean conformation for each simulation was obtained by averaging the aligned Ca coordinates over the frames in the last 40 ns of the simulation. These mean conformations were compared to the open (4AKE) [7] and the closed (1AKE) [6] AdK crystal structures, with the RMSDs provided in the table. doi:10.1371/journal.pone.0068023.tAdenylate Kinase Conformationcolor code in Fig. 3. However, the exact pathway and evolution of the transitions are not identical among C1 4. In C2, e.g., the protein stayed in some intermediate states for a substantial amount of time before reaching the final open conformation. Ne.Presentative coarse coordinates [27]. We note that our restraining potential, as a function of the Cartesian coordinates, is not guaranteed to be invariant upon a rigid-body translation or rotation of the entire protein. To eliminate such effects, we applied additional restraints in all umbrella-sampling simulations. Specifically, a harmonic restraint, ?with spring constant of 1,000 kcal/mol/A2, was applied on the ! center of the protein. In addition, using the crystal structure X OP as the reference, we applied another harmonic restraint, withAdenylate Kinase ConformationFigure 2. Time evolution of the unrestrained simulations along a conformational pathway. The pathway is represented by a ! ! parameterized curveX ?(see Methods). Each protein conformation X j in the simulation trajectories was projected onto this curve through the ! !??operator aj Pa X j (see Methods), which returns the curve parameter aj corresponding to the point X aj on the curve with the shortest distance ! to X j . This operator was implemented through a nonlinear minimization algorithm. The projected curve parameter is plotted as a function of time for each simulation trajectory. The green and red dashed lines indicate the projected curve parameters for the open (a = 0.42) and closed (a = 0.99) crystal structures, respectively. doi:10.1371/journal.pone.0068023.gconformation, as all observed transitions were in the closed-toopen direction. Similar behaviors were also observed in previous unrestrained 1315463 simulations [13,22]. The spontaneous transitions in simulations C1 4 allowed us to observe the AdK conformational changes in details. Rigorous quantitative methods, such as principal component analysis [41], are available to visualize or compare the trajectories in lower dimensions. Alternatively, some simpler intuitive measures, such as the distances from the CORE domain to the AMPbd and LIDdomains, have been used in many studies as a reduced representation of the AdK conformation [22,42?4]. Here we thus calculated the distances (Fig. 3) between the centers of the Ca atoms in these domains throughout the trajectories of C1 4. ?Figure 2 shows a larger change (,10 A) in the LID-CORE ?distance than that (, 5 A) in the AMPbd-CORE distance, indicating a larger movement of the LID domain during the transition. As mentioned earlier (Fig. 2B), the transitions took place at the very beginning of simulations C1 4, as indicated by theTable 1. RMSDs between the average protein conformations from the unrestrained simulations and the AdK crystal structures.C1 ?Open (A) ?Closed (A) 2.19 6.C2 1.38 7.C3 1.99 7.C4 1.79 6.C5 1.21 7.C6 2.01 6.C7 3.06 5.C8 6.35 3.O1 1.64 7.O2 1.03 6.O3 1.51 6.O4 1.15 7.O5 1.57 6.O6 1.61 6.O7 1.55 8.The protein conformation (represented by its Ca coordinates) from each frame in the simulation trajectories was aligned against the crystal structure, and the mean conformation for each simulation was obtained by averaging the aligned Ca coordinates over the frames in the last 40 ns of the simulation. These mean conformations were compared to the open (4AKE) [7] and the closed (1AKE) [6] AdK crystal structures, with the RMSDs provided in the table. doi:10.1371/journal.pone.0068023.tAdenylate Kinase Conformationcolor code in Fig. 3. However, the exact pathway and evolution of the transitions are not identical among C1 4. In C2, e.g., the protein stayed in some intermediate states for a substantial amount of time before reaching the final open conformation. Ne.
