PubChem3D: Conformer generation

1. Molecular size and flexibility of the PDB ligands

where N _ER is the number of effective rotors, N _R is the number of rotatable bonds, and N _NARA is the number of "non-aromatic" sp³-hybridized ring atoms. Note that the value of N _ER is not necessarily an integer, but, in this study, is frequently rounded to the nearest whole number. Effective rotors take into account the flexibility of rings as well as rotatable bonds. Figure 1 shows the distributions of the non-hydrogen atom counts and the effective rotor counts (binned by whole numbers) for the experimental structures in the Molecular Modeling Database (MMDB) [21, 22] ligand dataset as downloaded from the PubChem Substance database (the MMDB contains only experimentally determined data found in the PDB). On average, the molecules in the MMDB ligand set have 17.1 non-hydrogen atoms and 4.9 effective rotors. Although molecules with up to 50 non-hydrogen atoms are considered in the present study, ~90% of them have 30 or less non-hydrogen atoms. In addition, as shown in panel (b) of Figure 1, molecules with greater than 16 effective rotors rarely occur, due to limiting the MMDB dataset to 15 rotatable bonds.

2. Parameter validation for conformer generation

OMEGA [19] was used in the present study. It is known to be among the fastest and most accurate conformer generation programs [17] available. In addition to high quality, it was the only commercially available program that had a non-windows-only C++ application programming interface (API) at the time of project initiation, a critical consideration given the computing environments at the National Center for Biotechnology Information (NCBI). A brief overview of the conformer generation algorithm of OMEGA is given in the Materials and Methods section. A more detailed explanation can be found elsewhere [11, 23].

where V _AA and V _BB are the self-overlap volume of A and B, respectively, and V _AB is the overlap volume between A and B [24–26]. Note that the ST score is a molecular similarity measure ranging from 0 (for no similarity) to 1 (for identical molecules), whereas the RMSD value is a molecular dissimilarity measure ranging from 0 (for identical molecules) to infinity. Among all theoretical 3-D conformers generated for a given molecule, the one with the least RMSD and the one with the greatest ST to the experimental 3-D coordinates were considered to be the most similar to the "bioactive" conformation. Therefore, the accuracy of a conformer model generated by OMEGA was evaluated using the minimum RMSD and the maximum ST values between the experimental conformation and a single theoretical 3-D conformation in the conformer model. In further discussion, the RMSD and ST values for a conformer model indicates the RMSD and ST values between the corresponding experimental structure and the most similar theoretical conformer in the conformer model, respectively.

2.1. Effects of fragment sampling rate

Fragment sampling in the OMEGA model building stage helps to ensure that flexible ring systems are appropriately examined to find all unique ring conformations. In OMEGA, a float-point value for the "-startfact" option determines the fragment sampling rate, using the following equation [23]:

$N_{samples}=\left[\text{1}0+\right[\Sigma \left(nrb=\text{3}\right)-\Sigma \left(nrb=\text{4}\right)]\times \mathtt{\text{startfact}}]$

(3)

where N _samples is the number of samples, and Σ(nrb = 3) and Σ(nrb = 4) are the sums of the number of atoms in the molecule that have three and four ring bonds, respectively. To investigate effects of the fragment sampling rate upon conformer generation, the conformer models generated using the default value of 20.0 for the "-startfact" option were compared with those generated using the value of 50.0, and the results were summarized in Table 2. In general, using the value of 50.0 rather than the default (= 20.0) was found not to have any significant effect on the overall average RMSD and ST values between the computationally generated conformers and the experimentally determined structures. There were also no significant effects of the increased sampling rate upon the number of conformers generated and the 100-k limit counts. A similar insensitiveness to the fragment sampling rate was observed in Figure 2, which shows the average RMSD as a function of the non-hydrogen atom count and the binned effective rotor count. Thus, the default fragment sampling rate was deemed to be sufficient and the default value of 20.0 was used in the remainder of this study.

Energy Window a					5/5					5/15		10/10	10/15	15/15
Conformer FF b		Full			NoEstat			Trunc		Trunc		NoEstat	NoEstat	NoEstat
Fragment FF b	Full	NoEstat	Trunc	Full	NoEstat	Trunc	Full	NoEstat	Trunc	Full	Trunc	Trunc	Trunc	Trunc
Sampling rate = 20
RMSD	0.69	0.69	0.71	0.48	0.48	0.48	0.467	0.467	0.462	0.41	0.41	0.42	0.40	0.42
ST	0.89	0.89	0.89	0.93	0.93	0.93	0.93	0.93	0.93	0.95	0.95	0.94	0.943	0.94
# Conformers	698	698	645	2827	2,814	2,870	5,369	5,352	5,852	12,957	13,012	10,794	13,118	10,794
# 100-k Limit cases	23	18	36	94	93	118	216	211	239	2,203	2,209	1,842	2,198	1,842
Sampling rate = 50
RMSD	0.69	0.69	0.71	0.48	0.48	0.48	0.466	0.467	0.462	0.41	0.41	0.42	0.40	0.42
ST	0.89	0.89	0.89	0.93	0.93	0.93	0.93	0.93	0.93	0.95	0.95	0.94	0.946	0.94
# Conformers	696	697	646	2,834	2,818	2,875	5,377	5,358	5,857	12,981	13,025	10,796	13,124	10,796
# 100-k Limit cases	21	18	36	96	96	119	217	211	239	2,203	2,210	1,841	2,196	1,841

^a The first and second numbers indicate the energy windows used for model building and torsion search, respectively.

^b Full = the 94s variant of the Merck molecular force field (MMFF94s); NoEstat = MMFF94s without coulombic interaction terms; Trunc = MMFF94s without coulombic and van der Waals attractive terms.

2.3. Effects of energy window

In the model building step, the energy window, specified with the "-ewindow" flag, primarily limits the ring conformations allowed in the torsion search step. If the strain energy of a ring conformation is greater than the least-energy ring conformation plus the value of the energy window, then the ring conformation is discarded. When this "-ewindow" parameter is used in the torsion search step, the energy window determines the maximum energy range of conformers, relative to the global-minimum conformer. Figure 3 shows the effect of energy windows on the overall average accuracy of the conformer models generated. When both the model building and torsion search energy windows were 1 kcal/mol, the overall average RMSD and ST of the conformer model generated were 0.69 and 0.885, respectively. On the other hand, the use of an energy window for both stages of 30 kcal/mol resulted in a substantially improved overall average RMSD of 0.39 and an ST of 0.945. This indicates that a larger energy window gives more accurate conformer models, consistent with the data in Table 3. The increased energy window allows more conformational diversity of a molecule to be considered, but also results in more conformers per molecule (and more 100-k limit cases), as shown in Table 4. Note in Figure 3 that a rapid near-convergence in the overall average RMSD and ST occurs at the energy windows of 10 and 15 kcal/mol for model building and torsion search, respectively. The overall average RMSD and ST at these energy windows were 0.40 and 0.944, respectively. Employing bigger energy windows provided only small improvements to the overall accuracy of the conformer models. Therefore, when looking at overall average results, it initially appears reasonable to use an energy window of 10 kcal/mol for model building and 15 kcal/mol for torsion search without significant reduction in overall accuracy.

3. Accuracy of conformer models and 100-k limit cases

Figures 4 and 5 show the average RMSD and the average ST values of the conformer models, respectively, as a function of the non-hydrogen atom count and the effective rotor count for different energy window values. An increase in the non-hydrogen atom count and the effective rotor count causes a linear increase in the RMSD and a linear decrease in the ST values, indicating that the accuracy of conformer model decreases as a function of both the molecular size and flexibility.

The conformer models that reach the 100-k limit cases may exclude important conformational diversity due to the truncated description of the molecule. Indeed, as Figures 4 and 5 show better accuracy of reproduction when truncated conformer models are excluded. Figure 6 shows effects of the 100-k limit cases upon the distributions of the non-hydrogen atom count and the effective rotor counts, and Figure 7 displays effects of the 100-k limit cases upon the average number of conformers for a molecule as a function of energy window. As one can see in Figure 6, the 100-k limit cases begin appearing for molecules with moderate size and flexibility (e.g., with ~15 non-hydrogen atoms and ~7 effective rotors). As a molecule becomes bigger and more flexible, the OMEGA conformer generation hits the 100-k limit more frequently. Therefore, removal of these cases from the dataset of 25,972 3-D reference structures leaves only a relatively small number of "non-100-k cases" for >30 non-hydrogen atoms and >10 effective rotors, causing a greater variability in the average RMSD and ST in these regions of panels (b) and (d) of Figures 4 and 5. Despite the increased variability, one can still see a slightly noticeable trend of improved accuracy in panel (d) of Figures 4 and 5. One can also see in all panels of Figures 4 and 5 that the energy window for torsion search of 25 kcal/mol gives a clear improvement over 15 kcal/mol for larger values of non-hydrogen atoms and, to a lesser extent, effective rotors. As such, for the remainder of the study 25 kcal/mol will be used for both fragment model and torsion search.

4. Prediction of RMSD accuracy of the conformer ensemble

So far, we have found ways to get the best average RMSD and ST accuracy using OMEGA as the conformer generator. Now we are faced with the problem of data reduction, as it is not practical to store or use all conformers produced when considering millions of chemical structures. Naturally, one would like to maximally reduce the conformer count without significantly sacrificing accuracy, e.g., by a minimum RMSD separation between conformers. The lower the separation RMSD used, the greater the count of conformers that must be kept. Conversely, too large of an RMSD separation may reduce the ensemble accuracy. In an ideal world, one would know a priori precisely which conformers are needed and discard the rest. In the real world, this is not possible to know; however, if one can reliably predict the RMSD accuracy of a conformer model, then one can devise an RMSD separation value that could be used as a sampling threshold with some statistical assurances that the sampled conformer model should have at least one conformer within the sampling RMSD some significantly large percentage of the time.

where RMSD _pred is the predicted RMSD of a theoretical conformer ensemble for a molecule, and N _NHA and N _ER are its non-hydrogen atom and effective rotor counts, respectively. The R² value of the regression equation for all 25,972 chemical structures was 0.65 and the standard deviation of RMSD _pred was 0.19. The correlation between the RMSD _pred and the actual RMSD (RMSD _actual ) is shown in Figure 8.

To highlight this, we plotted in Figure 9 the distribution of the difference between RMSD _actual and RMSD _pred using Eq. (5), binned in 0.1 increments. Figure 9 shows that Eq. (5) yields an RMSD _pred that is greater than or equal to RMSD _actual more than 90% of the time.

The R² values of the regression formula Eqs. (6) and (7) were 0.52 and 0.33, respectively, and the standard deviation of RMSD _pred was 0.17 and 0.29 for Eqs. (6) and (7), respectively. (Attempts to partition N _ER and N _NHA values using different partitioning schemes had similar R² results.) In the same manner as used to derive Eq. (5), one can add these first standard deviations to Eqs. (6) and (7) to get RMSD sampling formulas Eqs. (8) and (9), respectively, for the two individual groups. As shown in Figure 8, the RMSD _pred values from Eqs. (6) and (7) are comparable with those from Eq. (4), despite the poor R² values for Eqs. (6) and (7). As shown in Figure 9, where the RMSD sampling values from Eq. (5) are compared with those from Eqs. (8) and (9), the frequency distributions of the difference between RMSD _pred and RMSD _actual are similar to each other. The RMSD _pred value is greater than or equal to RMSD _actual for ~91.0% of the time when Eq. (5) is used, and for ~91.6% of the time when Eqs. (8) and (9) are used.

In the recent study of Hawkins et al. [11], the quality of theoretical conformations from OMEGA was evaluated by comparing a set of 197 high-quality PDB ligand structures with corresponding OMEGA-generated theoretical conformers. They used the MMFF94_Trunc force field to generate conformers and then reduced their count to a maximum of 200 by sampling. The mean RMSD between the 197 ligand set and their corresponding theoretical conformers was 0.67 Å. According to their bootstrapping tests, the OMEGA-generated conformers are expected 90% of the time to have an RMSD value between 0.647-0.688 Å for chemical structures with similar properties to those tested. The average rotatable bond count and non-hydrogen atom count of this 197 ligand set were 6.3 and 24.4, respectively, indicating that they are, on average, slightly bigger and flexible than the 25,972 set used in our study (4.9 rotatable bonds and 17.1 non-hydrogen atoms on average). With these average counts as the N _NHA and N _ER values in Eq. (5), RMSD_pred is predicted to be 0.71 Å, which is comparable to 0.67 Å, the mean RMSD between the 197 ligand set and the corresponding theoretical conformers. Considering that the OMEGA parameters used in both studies were not exactly identical and that we used their reported rotatable bond count rather than effective rotor count, this may suggest that Eq (5) may have applicability beyond the parameter sets used in this study.

1. Datasets

The "experimental" 3-D coordinate data set of small molecules used in the present study was downloaded from the Molecular Modeling DataBase (MMDB) [21, 22] ligand dataset as available from the PubChem Substance database at NCBI on October 20, 2006. The data set was used to calibrate the parameters used when operating the software generation package OMEGA [19]. Ligands that were too small or too big were discarded by limiting the non-hydrogen atom count to 2 - 50. Ligands too flexible (with a rotatable bond count greater than 15) were also eliminated. This filtering stage resulted in an initial dataset that contained 25,972 non-unique organic 3-D experimental reference structures where a 3-D conformer model could be generated.

2. Conformer generation using OMEGA

Essentially, the OMEGA application performs conformer generation in two primary stages: model building and torsion search. In the model building stage, initial molecular structures are constructed by assembling fragment templates, which are generated from fragmentation of the input molecular graph along sigma bonds. In the torsion search stage, OMEGA generates a conformer ensemble using particular rule-based torsion angles that depend on the molecular environment between connecting fragments.

There are a number of adjustable parameters available when performing conformer generation. The effects of three primary parameters upon the accuracy of conformer models generated were evaluated:

(1) -startfact (20 or 50): the argument of this option determines the fragment sampling rate for determination of fragment conformations. Effects of this parameter were studied by trying two values, 20 (default) and 50.

(2) -buildff and -searchff (MMFF94s, MMFF94s_NoEstat, or MMFF94s_Trunc): these specify the type of molecular force field used in the model building and torsion search stages, respectively. The MMFF94s argument tells OMEGA to use the 94s variant of Merck molecular force field. The MMFF94s_NoStat excludes the coulombic terms from the MMFF94s force field and the MMFF94s_Trunc means the MMFF94s force field was truncated by removal of both the coulombic and van der Waals attractive terms.

(3) -ewindow (1-10, 15, 20, 25, or 30): the size of energy window in the model building and torsion search stages in units of kcal/mol. Different values may be specified for the two stages. Various combinations of integer values ranging from one to thirty (default is 10) were used. The energy window indicates the maximum allowed energetic separation from the lowest conformer energy. Higher energy conformers are discarded.

See Table 1 for all non-default parameters used. It is important to note that a maximum of 100,000 (100-k) conformers were generated per chemical structure. This limit is more than adequate for small or inflexible structures but for flexible compounds this limitation is of concern. For example, imagine a chemical structure with nine rotatable bonds where one systematically samples each rotatable bond four times; one would generate 4⁹ (= 262,144) conformations. Therefore, the effects of these 100-k limit cases upon the overall accuracy of the conformer models is analyzed as a function of the non-hydrogen atom counts and the effective rotor counts. While increasing this 100-k threshold to a larger value was not possible with earlier versions of OMEGA, one can see that increasing the total count of conformers considered by five or ten times would still not be sufficient for many flexible molecules.

To assess the accuracy of reproduction of experimental coordinates as a function of conformer generation parameters modification, two metrics were used: the RMSD of non-hydrogen atoms using the OEChem OERMSD function (with "automorph" detection turned on to allow proper treatment of symmetrically equivalent atoms and "overlay" turned on to allow rotation/translation to yield the lowest possible RMSD value) and the shape-optimized ST using the value reported by ROCS. For each conformer produced for a structure, an RMSD and ST determination were made. The lowest RMSD and greatest ST values per conformer model were used to assess "accuracy" of reproduction for the parameters used.