The Mulliken and NPA charges calculated by B3LYP/6-31G* basis for different conformations are given in Table 3.1 and 3.2. The partial atomic charges obtained from the ESP methods such as CHELPG and MK with varying grid points (1-6) can be better represented in graphical form as shown in Figures 3.6 and 3.7 respectively. The partial atomic charges obtained from MK method by increasing the shells (2-9) are shown in Figure 3.8. The RESP charges obtained from using Mulliken and NPA charges as initial charges for the harmonic restraint and the electrostatic potential obtained from CHELPG and MK with varying grid points and shells are given in electronic supporting information. All the partial atomic charges obtained of five different conformations 1-120, 2-135, 3-150, 4-165 and 5-180 are given in electronic supporting information.
3.3.1 M
ULLIKEN CHARGESThe Mulliken charges calculated by B3LYP/6-31G* basis for different conformations are given in Table 3.1. Mulliken charges range from -0.73 to +0.60 (Table 3.1). There is a little variation in the partial atomic charge distribution as a function of the dihedral rotations. When the atomic charges of the heavy atoms are compared, Mulliken charges remain more negative in side chain of atom type 2Asn-ND2. All the oxygen atoms in the side chain show atomic charges in the range of -0.51 to -0.56. The atomic charge of nitrogen atoms in the backbone range from -0.58 to -0.61. Mulliken charges are used as initial target charge for the RESP method.
3.3.2 NPA
CHARGESThe NPA charges calculated by B3LYP/6-31G* basis for different conformations are given in Table 3.2. The NPA charges tend to be larger in magnitude compared to the Mulliken charges. NPA charges range from -0.83 to +0.71 (Table 3.2). The atom type 2Asn-ND2 has more negative charge similar to that of Mulliken charge. The variation of the atomic charge distribution as a function of the dihedral rotations is less compared to the Mulliken charges.
3.3.3 CHELPG
CHARGESThe CHELPG method is an improved version of CHELP method for computing potential derived charges. It is shown that the charges derived from CHELPG method are considerably less dependent on molecular orientation than CHELP method. All atomic charges calculated by CHELPG method are given in the electronic supporting information. The atomic charges of the heavy atoms in the backbone and the side chains are shown in Figure 3.6 and 3.7 (A.1 to A.6) respectively. The ESP charges exhibit a much stronger conformational dependence than the Mulliken and NPA charges. All the atomic charges shown in Figure 3.6 and 3.7 (A.1 to A.6) were obtained by varying the grid points from 1 to 6, to get suitable point sampling where the charges do not show any dependency to the conformation. The density of points are increased to include more sample point in the ESP fit to find out the reasonable points per square angstrom. From Figure 3.6 and 3.7, it is clear that increasing the sampling points do not have any influence on the charges of different conformations.
3.3.4 MK
CHARGESAll atomic charges calculated by MK method are given in the electronic supporting informa-tion. The atomic charges of the heavy atoms in the backbone and the side chains are given in Figure 3.6 and 3.7 (B.1 to B.6) respectively. Like CHELPG charges, the MK charges also exhibit a much stronger conformational dependency than the Mulliken and NPA charges.
Compared to the CHELPG charges, the MK charges show more conformational dependency.
In CHELPG method the charges were obtained from the electrostatic potentials using a grid based method, a point selection algorithm similar to the one employed by Cox and Williams [157] which dramatically reduces these orientation dependencies where as in MK method the charges were obtained from the electrostatic potentials using the Connolly surface. All the
Residue Atom Type 1-120 2-135 3-150 4-165 5-180 x¯ σ Backbone:
1Ala CAY -0.5407 -0.5330 -0.5433 -0.5461 -0.5330 -0.5392 0.0054
CY 0.6087 0.6016 0.6079 0.6060 0.5945 0.6037 0.0052
N -0.5832 -0.5925 -0.5793 -0.5738 -0.6050 -0.5868 0.0110 CA -0.0264 -0.0526 -0.0322 -0.0374 -0.0299 -0.0357 0.0092
C 0.6583 0.6305 0.6563 0.6450 0.6134 0.6407 0.0169
2Asn N -0.6161 -0.6321 -0.6170 -0.6214 -0.6324 -0.6238 0.0071 CA -0.0317 -0.0297 -0.0374 -0.0248 -0.0158 -0.0279 0.0073
C 0.5890 0.5929 0.6069 0.5991 0.5954 0.5967 0.0061
3Ala N -0.6132 -0.6248 -0.6262 -0.6182 -0.6150 -0.6195 0.0052 CA -0.0565 -0.0563 -0.0584 -0.0553 -0.0571 -0.0567 0.0010
C 0.6048 0.6028 0.6055 0.6043 0.6028 0.6040 0.0011
NT -0.6336 -0.6333 -0.6299 -0.6264 -0.6304 -0.6307 0.0026 CAT -0.2954 -0.2935 -0.2934 -0.3111 -0.3080 -0.3003 0.0077 Side chain:
1Ala OY -0.5182 -0.5123 -0.5162 -0.5207 -0.5220 -0.5179 0.0034 CB -0.4854 -0.4610 -0.4816 -0.4764 -0.4463 -0.4701 0.0145 O -0.5695 -0.5610 -0.5733 -0.5559 -0.5468 -0.5613 0.0095 2Asn CB -0.3753 -0.3664 -0.3733 -0.3854 -0.3842 -0.3769 0.0071
CG 0.5562 0.5596 0.5717 0.6173 0.6187 0.5847 0.0277
ND2 -0.7396 -0.7371 -0.7252 -0.7377 -0.7382 -0.7356 0.0052 OD1 -0.5309 -0.5262 -0.5274 -0.5424 -0.5391 -0.5332 0.0064 3Ala O -0.5164 -0.5077 -0.5269 -0.5330 -0.5346 -0.5237 0.0102 CB -0.4437 -0.4458 -0.4506 -0.4454 -0.4430 -0.4457 0.0027 O -0.5295 -0.5324 -0.5331 -0.5328 -0.5299 -0.5315 0.0015
Table 3.1. Mulliken charges of the heavy atoms in the tripeptide backbone and side chains. Partial atomic charges of the heavy atoms obtained at B3LYP/6-31G* basis set, the average (¯x) and standard deviations (σ) of atomic charges are given.
atomic charged shown in the Figures 3.6 and 3.7 (B.1 to B.6) were obtained by increasing the grid points from 1 to 6 and the number of shells are increased from 2 to 9 the maximum limit.
Similar to CHELPG method, the MK method also show that increasing the sampling points per square angstrom do not have any influence on the charges of different conformations.
Figure 3.8 show the MK charges obtained with different shells for different conformations.
There is a slight deviation in the atomic charges when 2 shells are used. When the shells are
Residue Atom Type 1-120 2-135 3-150 4-165 5-180 ¯x σ Backbone:
1Ala CAY -0.7635 -0.7612 -0.7638 -0.7648 -0.7601 -0.7627 0.0017
CY 0.7010 0.6969 0.7018 0.7028 0.6910 0.6987 0.0043
N -0.6541 -0.6529 -0.6558 -0.6567 -0.6623 -0.6564 0.0032 CA -0.1311 -0.1406 -0.1331 -0.1356 -0.1411 -0.1363 0.0040
C 0.7071 0.6953 0.6950 0.6882 0.6969 0.6965 0.0061
2Asn N -0.6338 -0.6434 -0.6424 -0.6505 -0.6514 -0.6443 0.0064 CA -0.1352 -0.1360 -0.1312 -0.1304 -0.1295 -0.1325 0.0026
C 0.6973 0.6937 0.6942 0.6928 0.6894 0.6935 0.0025
3Ala N -0.6616 -0.6648 -0.6567 -0.6519 -0.6468 -0.6564 0.0065 CA -0.1448 -0.1461 -0.1473 -0.1482 -0.1484 -0.1470 0.0014
C 0.6780 0.6790 0.6793 0.6808 0.6801 0.6794 0.0010
NT -0.6614 -0.6617 -0.6604 -0.6568 -0.6584 -0.6597 0.0019 CAT -0.4740 -0.4737 -0.4736 -0.4769 -0.4765 -0.4749 0.0014 Side chain:
1Ala OY -0.6361 -0.6440 -0.6322 -0.6347 -0.6440 -0.6382 0.0049 CB -0.6851 -0.6875 -0.6844 -0.6835 -0.6801 -0.6841 0.0024 O -0.6810 -0.6828 -0.6746 -0.6509 -0.6560 -0.6691 0.0131 2Asn CB -0.5536 -0.5503 -0.5559 -0.5628 -0.5622 -0.5570 0.0049
CG 0.6911 0.6931 0.6956 0.7105 0.7075 0.6996 0.0079
ND2 -0.8399 -0.8411 -0.8354 -0.8355 -0.8373 -0.8378 0.0023 OD1 -0.6743 -0.6722 -0.6737 -0.6808 -0.6733 -0.6749 0.0030 3Ala O -0.6253 -0.6189 -0.6388 -0.6483 -0.6487 -0.6360 0.0121 CB -0.6775 -0.6772 -0.6779 -0.6770 -0.6777 -0.6775 0.0003 O -0.6397 -0.6423 -0.6426 -0.6463 -0.6421 -0.6426 0.0021
Table 3.2. NPA charges of the heavy atoms in the tripeptide backbone and side chains.
Partial atomic charges of the heavy atoms obtained at B3LYP/6-31G* basis set, the average (¯x) and standard deviations (σ) of atomic charges are given.
increased from 3 to 9, there is much change in the atomic charges, but increasing the shells do not help to find conformationally independent charges.
3.3.5 RESP
CHARGESRESP charges were obtained for different conformations using different combination of ini-tial charges and the electrostatic potenini-tials. The models used to obtain RESP charges are
described below. For the Model 1 to 4, both strong and weak restraint weights are used to assess the impact of the scaling factors on the charges and the quality of the fit. The RESP charges were calculated by a standard two-stage fitting procedure using the RESP program which is freely available [155]. We are interested in ascertaining the optimal parameters to obtain conformationally independent charges of the tripeptide Ala-Asn-Ala. The RESP charges obtained by using ESP from CHELPG and MK methods in combination with Mulliken charges and NPA charges as initial charges are given in Figure 3.9. The following scaling factors are used for strong harmonic restraint: 0.05(0.1), 0.5(0.1), 0.01(0.1) and 0.1(0.1) and the weak harmonic restraints as follows, 0.00005(0.0001), 0.0005(0.001), 0.005(0.01), 0.0001(0.001), 0.001(0.01). The values in the parenthesis show the restraint used for the second stage fit to obtain equal charges for the methyl groups.
Model 1: Harmonic restraint to the Mulliken charges are used with the combination of elec-trostatic potential from CHELPG method with varying grid points from 1 to 3 (see Figure 3.9).
Model 2: Harmonic restraint to the NPA charges are used with the combination of electrostatic potential from CHELPG method with varying grid points from 1 to 3 (see Figure 3.9).
Model 3: Harmonic restraint to the Mulliken charges are used with the combination of elec-trostatic potential from MK method with varying grid points from 1 to 6 (see Figure 3.9).
Model 4: Harmonic restraint to the NPA charges are used with the combination of electrostatic potential from MK method with varying grid points from 1 to 6 (see Figure 3.9).
Model 5: Harmonic restraint to the NPA charges are used with the combination of electrostatic potential from MK method with varying shells from 2 to 9.
MODEL1
The ESP obtained from CHELPG method by varying grid points from 1-3 are used to calcu-late the RESP charges, whereas Mulliken charges are used as initial charges for harmonic restraint. The combination of the less grid points with strong harmonic restraint 0.5 or 0.1 in the first stage fit, the RESP charges approach the Mulliken charges. When weak restraints are used the RESP charges approach the ESP charges. The weak restraint beyond 0.00005 does not change the atomic charges much. Still the RESP charges depend on the confor-mation of the peptide because the ESP used to obtain RESP charges already depend on the conformations.
MODEL2
In Model 2, the NPA charges are used as initial charges instead of Mulliken charges for har-monic restraint. The RESP charges show the same trend as model 1 i.e., when less grid points and strong restraint 0.5 or 0.1 are used 0.5 in the first stage fit, the RESP charges approach the NPA charges. Similar to model 1, restraint beyond 0.00005 does not change the atomic charges much. The restraint factor 0.0005 or 0.001 appeared to be optimal for both model 1 and model 2 to have a balance between the initial charges (Mulliken and NPA) and ESP charges (CHELPG charges).
MODEL3
In model 3, the ESP obtained from MK method by varying grid points from 1-6 are used to calculate RESP charges and the Mulliken charges are used as initial charges for harmonic restraint. As in model 1, when less grid points and strong restraint 0.5 or 0.1 are used in the first stage fit, the RESP charges approach the Mulliken charges. When the grid points are increased from 3 to 4, there in no change in the charge and increasing the sampling points do not have any effect on the charges. The calculations show that at least 3 point per square angstrom should be used to get a stable charges and the restraint factor of 0.0005 should be used to get a reasonable charges.
MODEL4
In Model 4, the NPA charges are used as initial charges with the combination of ESP from MK method. The trends are almost same. Analysis of the RESP charges also show that more than 3 points per square angstrom should be used to get stable charge with combination of restraint factor 0.0005.
MODEL5
In Model 5, the RESP charges are calculated by using the ESP obtained from MK method by varying the shells from 2 to 9. There is an irregular trend in the RESP charges with respect to the conformations. The analysis shows that at least more than 4 shells should be used to get a stable charges for each conformations.
All the models show that the RESP charges approach the initial charges (Mulliken and NPA) when strong restraint is used and the RESP charges approach the ESP charges (CHELPG and MK) when weak restraint is used. The restraint beyond 0.00005 does not make any change in the charges.