Project I Chemistry 8021, Spring 2005/2/23 This document was turned in by a student as a homework paper. 1. Methods First, the cartesian coordinates of 5021 and 8021 molecules (Fig. 1) are generated, in which the total number of atoms are 16 and 23, respectively. In the topology file, each neutral group in these two molecules was grouped as shown in Fig. 1. Since the cartesian coordinates of these two compounds were already built up, therefore, no internal coordinates were necessarily included in the topology (see Supplement). Afterwards, give specifically unique names and atomic charges for the atoms of these two molecules by typing in ATOM cards, respectively. Following, make covalent bonds we needed between the unique atoms on the BOND card (see Supplement). The missing parameters in these two compounds were added in the parameter file (see Table 1). 5021 8021 Figure 1. Molecules geometries of 5021 and 8021. Each neutral group in CHARMM topology was grouped in dash circle. Table 1. Parameters Added in CHARMM Parameter File bond k b (kcal/mol/å 2 ) b 0 (Å) HA3 CT3 322.000 1.1110 angle k θ (kcal/mol/rad 2 ) θ (degrees) k ub (kcal/mol/å 2 ) s 0 (Å) HA3 CT3 HA3 35.500 109.00 5.40 1.802 NH1 CT2 CA 50.000 110.8000 Dihedrals k φ (kcal/mol) n δ(degrees) C NH1 CT2 CA 0.2000 1 170.60 H NH1 CT2 CA 0.0000 1 16.6 C O NH1 CT3 90.0000 0 0.0000 NH1 H CT2 C 20.0000 0 0.0000 Structure optimizations were calculated by adopted-basis Newton Raphson (ABNR) minimization, and then followed by Newton-Raphson (NRAP) minimization. The optimization steps were stopped while the root-mean-square gradient was less than 0.0001 kcal/mol/å during a cycle of the geometry minimization.
Once satisfactory geometries of 5021 and 8021 were obtained, these optimization geometries were used to calculate the vibration frequencies (Table 4 and Table 6, respectively) and project them onto the internal coordinates in CHARMM (Table 5 and Table 7), respectively. The vibration frequencies were also calculated at HF/6-31G(d) level by using the geometries optimized at the same theoretical level. Results Comparison of Geometries. The geometric data for the experimental (CSD entry: CRESOL01, R- factor = 8.5%) 3 and computational structures of 4-methylphenol (5021) calculated with CHARMM and by ab initio methods at HF/6-31G(d) level were summarized in Table 2. And the geometric data for 8021 were summarized in Table 3. For 5021 (see Table 2), the bond lengths and angles are in satisfactory agreement with the experimental data with rmsd of 0.0527 and 1.495 in bond length and angle. Although the NRAP optimization structure has smaller rmsd in bond length compared with the geometry computed at HF/6-31G(d) level, its rmsd of bond angle is larger than that computed at HF/6-31G(d) level. This is mainly due to the underestimated CZ OH HH bond angle and the overestimated CD1 CG CD2 bond angle in the NRAP optimization geometry. Further, the HH OH CZ CE1 dihedral angle obtained in NRAP and ab initio optimization geometries are both overestimated the experimental structure with 7.4º and 7.2º, respectively. Table 2. Geometric Data b on 4-methylphenol (5021) bond length c exp. e CHARMM b HF/6-31G(d) CG CB 1.512 1.50 1.51 CB HB a 1.057 1.11 1.09 CG CD a 1.394 1.40 1.39 CD CE a 1.397 1.40 1.38 CZ CE a 1.380 1.40 1.38 CZ OH 1.422 1.41 1.35 OH HH 1.086 0.96 0.95 rmsd 0.0527 f 0.0599 f angle d exp. e CHARMM b HF/6-31G(d) CB CG CD1 121.1 120.4 121.3 CD1 CG CD2 117.9 119.1 117.5 CE1 CZ CE2 120.6 120.1 119.5 CZ OH HH 110.0 107.4 110.8 rmsd 1.495 f 0.716 f dihedral angle d exp. e CHARMM b HF/6-31G(d) CB CG CD1 CE1 179.7 179.6 179.8 HH OH CZ CE1 172.6 180.0 179.8
a Average distance. b Newton-Raphson (NRAP) minimization. c Bond lengths in Å. d Angle in degree. e Ref. 3. f Compare with experimental crystal structure (CSD entry: CRESOL01, R-factor = 8.5%). For 8021 (see Table 3), comparing the NRAP optimization structure with that optimized at HF/6-31G(d) level, the bond lengths, angles, and dihedral angles are in difference of ±0.06 Å, ±3.13º, and ±18.4º. The main deviation of the dihedral angle is due to the C N CB CG dihedral angle, which is overestimated (18.4º) in the NRAP optimization structure. Table 3. Geometric Data on 8021 bond length c CHARMM b HF/6-31G(d) CG CB 1.50 1.51 CB HB a 1.11 1.09 CB N 1.44 1.45 N HN 0.99 0.99 N C 1.34 1.35 C=O 1.22 1.20 C CO 1.48 1.51 CO HC a 1.11 1.08 CG CD a 1.40 1.39 CD CE a 1.40 1.38 CZ CE a 1.40 1.39 CZ OH 1.41 1.35 OH HH 0.96 0.95 angle d CHARMM b HF/6-31G(d) CO C N 116.42 115.6 C N CB 123.35 122.3 N CB CG 110.29 111.1 CB CG CD a 120.44 121.0 CD1 CG CD2 119.00 118.0 CE1 CZ CE2 120.11 119.7 CZ OH HH 107.57 110.7 dihedral angle d CHARMM b HF/6-31G(d) O=C N CB 0.0 5.1 C N CB CG 178.0 159.6 CB CG CD1 CE1 179.9 179.4 HH OH CZ CE1 179.2 179.2 a Average distance. b Newton-Raphson (NRAP) minimization. c Bond lengths in Å. d Angle in degree.
Analysis of Vibration Modes. The total number of the vibration frequencies of 5021 is 42 (3N 6, N = 16, see Table 4). The lowest vibration frequency of 5021 was 21.52 cm 1 (mode 7). After projecting vectors onto the internal coordinates in CHARMM, we can find that the largest component for mode 7 vector is the torsion rotation of the HB CB CG CD dihedral angle (Table 5). This result is in agreement with that computed at HF/6-31G(d). Table 4. Vibrational Data a for 5021 b (298 K) 7 21.52 14 440.81 21 920.81 28 1120.09 35 1425.29 42 2915.81 8 148.37 15 486.96 22 952.58 29 1168.27 36 1455.49 43 2916.54 9 285.38 16 613.52 23 1014.24 30 1216.73 37 1457.93 44 3053.64 10 287.17 17 662.95 24 1016.22 31 1282.06 38 1493.19 45 3055.11 11 337.07 18 675.06 25 1052.15 32 1352.54 39 1509.79 46 3056.59 12 408.33 19 838.68 26 1059.31 33 1418.4 40 1544.68 47 3059.79 13 413.53 20 907.43 27 1094.79 34 1424.07 41 2844.93 48 3683.41 a Frequencies in cm 1. b Structure optimization at NRAP minimization. Table 5. Lowest Vibrational Modes for 8021 CHARMM HF/6-31G(d) mode frequencies a assignment frequencies a assignment 7 21.52 HB CB CG CD b 39.30 τch 3 CG a Frequencies in cm 1. τ indicates torsion rotation. b From the result of projection of the HB CB CG CD dihedral angle. The total number of the vibration frequencies of 8021 is 63 (3N 6, N = 23, see Table 6). The lowest vibration frequency of 8021 was 22.84 cm 1 (mode 7). After projection of the internal coordinates, we can find that the two largest component for mode 7 vector is the torsion of the HB CB CG CD dihedral angle and the CB CG CD angle (Table 5). On the other hand, In the ab initio calculation at HF/6-31+G(d) level, the vibration mode of the lowest vibration frequency is torsion rotation between the ( CH 2 NH CO CH 3 ) group and the phenol ring via the CB N bond. Table 6. Vibrational Data a for 8021 b 7 22.84 16 334.84 25 675.65 34 967.92 43 1250.47 52 1450.78 61 2916.78 8 33.20 17 406.40 26 687.27 35 1014.75 44 1260.82 53 1452.63 62 2975.43 9 63.64 18 413.06 27 811.92 36 1040.29 45 1282.97 54 1489.40 63 2975.49 10 65.25 19 442.57 28 824.61 37 1053.76 46 1369.04 55 1500.71 64 3053.59 11 167.10 20 474.58 29 849.43 38 1086.04 47 1379.84 56 1539.83 65 3055.07 12 181.80 21 526.83 30 918.94 39 1097.25 48 1411.85 57 1602.22 66 3056.53 13 198.46 22 567.62 31 922.24 40 1124.84 49 1419.32 58 1682.52 67 3059.72 14 289.69 23 655.46 32 925.52 41 1170.50 50 1424.74 59 2805.99 68 3326.23 15 291.04 24 674.51 33 952.95 42 1217.16 51 1434.64 60 2845.75 69 3683.25 a Frequencies in cm 1. b Structure optimization at Newton-Raphson (NRAP) minimization.
Table 7. Lowest Two Vibrational Modes for 8021 CHARMM HF/6-31G(d) mode frequencies a assignment frequencies a assignment 7 22.84 CD CG CB N b CB CG CD c 21.49 τ CB N a Frequencies in cm 1. τ indicates torsion rotation. b From the result of projecting the CD CG CB N dihedral angle. c From the result of projecting the CB CG CD angle.
2. Bovine Pancreatic Trypsin Inhibitor (BPTI): Methods The BPTI structure was selected from the Protein Data Bank 1 crystal structure 4PTI 2 with resolution of 1.5 Å. This crystal structure contains 58 amino acid residues and 60 crystal water molecules, with no other hetero atoms or groups, for example, metal ions (e.g. Mg 2+ ) or anions (e.g. Cl or SO 2 4 ). Hydrogen atoms of the BPTI protein and crystal waters were then added with HBUILD facility in CHARMM. Further, there are three disulfide bonds within this BPTI structure. Cys5 Cys55 connects a 3 10 helix (Asp3 to Glu7) with a α-helix (Ser47 to Gly56). Cys14 Cys38 join the α-helix to a double-stranded antiparallel β-sheet (Ala16 to Asn24 and Gly28 to Gly36), which is the main body of the protein. And Cys30 Cys51 connects the loop region at Gly12 to Lys15 with the other loop region at Gly37 to Ala40. Therefore, these disulfide bonds were afterward built by PATCH facility in CHARMM. Structure optimizations were calculated by adopted-basis Newton Raphson (ABNR) minimization with 123, 500, 1000, and 5000 steps in CHARMM, respectively. TOLERENCE was applied in the 5000-step ABNR minimization. Therefore, the minimization routine will stop if the energy change is less than or equal to 0.0001 kcal/mol during a cycle of the minimization. Room-mean-square (rms) differences between the calculated structures and 4PTI crystal structure were calculated for the whole protein structure and for the specified backbone atoms (C, N, C α, O) after the minimization with 123, 500, 1000, 2304 steps, respectively (Table 8). Results After optimizing the BPTI structure with a 2304-step ABNR minimization, the room-mean-square gradient (GRMS) of the final structure was 0.004 kcal/mol/å. Compare the optimization structure with the initial PDB structure, the rmsd for the whole protein and for the backbone were 1.81 Å and 1.21 Å, respectively. This indicates that the fluctuation of the side chain is larger than that of the backbone. The 4PTI crystal structure and ABNR minimization structure were superimposed to understand how well the peptide backbone of the optimization structure matching that of the initially experimental structure (Fig. 2). The superimposing result shows that the peptide backbone of the ABNR minimization structure was quite close to the experimental structure, although the initial x- ray structure was not in the energetic minimum state since the rmsd of the whole protein was 1.81 Å between the experimental and theoretical structures.
Table 8. Rms Differences of the Bovine Pancreatic Trypsin Inhibitor (BPTI) Crystal number of steps a GRMS b overall RMS c backbone RMS d (kcal/mol/å) (Å) (Å) 123 1.44 0.48 0.31 500 0.47 1.17 0.73 1000 0.11 1.17 0.73 2304 0.004 1.81 1.21 a Number of minimization steps in ABNR calculation. b Rms gradient. c Rms difference in Å for all the atoms to the 4PTI crystal structure. d Rms difference in Å for the specified backbone atoms (C, N, C α, O) to the 4PTI crystal structure. Figure 2. Diagram of superimposing the 4PTI crystal structure (purple) and the ABNR optimization structure with 2304 minimization steps (green). Reference (1) Bernstein, F. C., Koetzle, T. F., Williams, G. J. B., Meyer, E. F. Jr., Brice, M. D., Rodgers, J. R., Kennard, O. Shimanouchi, T., Tasumi, M., J. Mol. Biol., 1977, 112, 535-542. (2) Marquart, M., Walter, J., Deisenhofer, J., Bode, W., Huber, R., Acta Crystallogr. B, 1983, 39, 480-490. (3) Bois, C., Acta. Crystallogr., Sec. B, 1 9 7 0, 2 6, 2086.
Supplement 1. The original topology file of 5021: RESI PHEN! 0.00 HD1 HE1! ATOM CG CA! 0.00 HB1 CD1--CE1! // \\ ATOM CD1 CA! -0.115HB3--CB--CG CZ--OH ATOM HD1 HP 0.115! \ / \! HB2 CD2--CE2 HH ATOM CE1 CA! -0.115 ATOM HE1 HP! 0.115 HD2 HE2 ATOM CZ CA 0.11 ATOM OH OH1-0.54 ATOM HH H 0.43 ATOM CD2 CA -0.115 ATOM HD2 HP 0.115 ATOM CE2 CA -0.115 ATOM HE2 HP 0.115 ATOM CB CT3-0.27 ATOM HB1 HA3 0.09 ATOM HB2 HA3 0.09 ATOM HB3 HA3 0.09 BOND CB CG CG CD2 CG CD1 CD1 CE1 BOND CD2 CE2 CE1 CZ CE2 CZ CZ OH BOND OH HH CB HB1 CB HB2 CB HB3 BOND CD1 HD1 CE1 HE1 CD2 HD2 CE2 HE2 D O N O R H H O H A C C E P T O R O H PATCHING FIRST NONE LAST NONE
2. The original topology file of 8021: RESI TYR1! 0.00 HD1 HE1! ATOM C C! HN 0.51 HB1 CD1--CE1 ATOM O O! -0.51\ // \\! N--CB--CG CZ--OH ATOM N NH1-0.47! / \ / \ ATOM HN H 0.31! O=C HB2 CD2--CE2 HH ATOM CB CT2! -0.02 \ ATOM HB1 HA! 0.09HC1-CO-HC2 HD2 HE2 ATOM HB2 HA 0.09!! HC3 ATOM CO CT3-0.27 ATOM HC1 HA 0.09 ATOM HC2 HA 0.09 ATOM HC3 HA 0.09 ATOM CG CA 0.00 ATOM CD1 CA -0.115 ATOM HD1 HP 0.115 ATOM CE1 CA -0.115 ATOM HE1 HP 0.115 ATOM CZ CA 0.11 ATOM OH OH1-0.54 ATOM HH H 0.43 ATOM CD2 CA -0.115 ATOM HD2 HP 0.115 ATOM CE2 CA -0.115 ATOM HE2 HP 0.115 BOND N HN N C C O N CB BOND C CO CO HC1 CO HC2 CO HC3 BOND CB CG CG CD2 CG CD1 CD1 CE1 BOND CD2 CE2 CE1 CZ CE2 CZ CZ OH BOND OH HH CB HB1 CB HB2 BOND CD1 HD1 CE1 HE1 CD2 HD2 CE2 HE2 IMPR N HN CB C C O N CO D O N O R H N N D O N O R H H O H A C C E P T O R O H A C C E P T O R O PATCHING FIRST NONE LAST NONE