computer modeling in molecular biology.pdf

8 Path Energy Minimization 233Table 8-2. Progress of PEM procedure for the simulation of a conformational rearrangementof D-xylose in D-xylose isomerase.No. moving positions Steps c. g. minimizationa Objective functioneoc + pC2Maximum energyb3 500sd + 345 11.36 11.21 (11.21)4 215 10.32 10.15 (10.21)5 100 10.12 9.97 (9.97)6 4 10.16 9.95 (9.95)7* 131 10.07 9.91 (9.91)8* 40 10.10 9.90 (9.90)12* 6 10.15 9.90 (9.90)eoc-pC1 (1)3 500sd + 433 16.48 16.30 (16.48)4 346 15.17 14.94 (14.99)5 106 14.91 14.73 (14.73)6 41 14.88 14.70 (14.70)7 40 14.89 14.68 (14.69)8* 71 14.88 14.69 (14.69)12* 70 14.89 14.69 (14.69)eoc+pCl (2)3 600sd + 563 14.83 14.66 (15.14)4 376 11.68 11.54 (11.90)5 348 10.45 10.33 (10.38)6 164 10.18 10.04 (10.06)7 51 10.08 9.91 (9.91)8* 89 10.08 9.90 (9.90)9* 1 10.13 9.90 (9.90)13* 38 10.18 9.89 (9.89)Ref. [32] 11.01a c. g. conjugate gradients, s. d. steepest descents.Energies in kcal/mol relative to the lower energy minimum (eoc). Three intermediate samplepoints were taken in each interval (Ninte, = 3). The figures given in brackets are a check onthe result with N,,, set to 7. Minimization was continued until the r.m.s. objectivederivative fell below 0.03 kcal/(molA) except for the runs marked * where a0.01 kcal/(molA) limit was used.(1) Path obtained starting from linearly interpolated route in Cartesian space.(2)Path obtained starting from 3*pC2 intermediate (see text of details).The procedure was then applied to find a path linking the eoc and pC1 conformations.Once again the initial path was set to a series of conformations taken fromthe line through Cartesian space. The final result of the procedure was a path witha peak energy of 14.69 kcal/mol relative to the eoc form. The result shows that thePEM method in common with all optimization procedures will find the optimumroute local to the starting position. To show this a further trial was undertaken to