Fifty-five sets were included into analysis, cumulating an amount of one-hundred and ninety-five models. One hundred fifty-six models were for activities estimation and prediction (95%CI [144 - 166]) and thirty-eight models for properties estimation and prediction (95%CI [28 - 50]).
Seventy-three models reported estimation and prediction of activity (95%CI [64 - 80]) and nineteen models (95%CI [12 - 27]) estimation and prediction ability of property. The number of MDF SAR models varied from two to eleven (for the set no. 40, Table 1) and for MDF SPR models varied from two to eight (for the set no. 48, table 1). The statistical characteristics of all models, and of the best performing models (in terms of closest squared correlation coefficient and cross-validation score to one) are presented in Table 3.
Table 3. Statistical characteristics of the MDF SAR/SPR models
| | | nv | Mean [95%CI] | Median | Min | Max | StDev
| | All models
| | Activity | r2 | 156 | 0.9023 [0.8783 - 0.9263] | 0.9489 | 0.0122 | 1.0000 | 0.1514
| | v | 2 [2 - 2] | 2 | 1 | 5 | 1.1003
| | nsample | 28 [24 - 31] | 23 | 5 | 69 | 21.468
| | Property | r2 | 38 | 0.8698 [0.8077 - 0.9319] | 0.9772 | 0.1208 | 1.0000 | 0.1889
| | v | 4 [2 - 6] | 2 | 1 | 24 | 6.0663
| | nsample | 77 [48 - 105] | 24 | 10 | 209 | 86.220
| | Best performing models
| | Activity | r2 | 45 | 0.9807 [0.9714 - 0.9900] | 0.9992 | 0.9037 | 1.0000 | 0.0310
| | v | 3 [2 - 3] | 2 | 2 | 5 | 1.0288
| | nsample | 19 [13 - 24] | 8 | 5 | 69 | 17.945
| | Property | r2 | 10 | 0.9572 [0.8993 - 1.0000] | 0.9883 | 0.7368 | 1.0000 | 0.0808
| | v | 3 [2 - 4] | 2.5 | 2 | 6 | 1.3703
| | nsample | 80 [16 - 144] | 27 | 10 | 209 | 90.120
|
r2 = squared correlation coefficient; v = number of descriptors used in models;
nsample = sample size; nv = number of valid samples; 95% CI = 95% confidence interval;
Min= minimum; Max = maximum, StDev = standard deviation
|
The MDF SAR/SPR models stored into database used two hundred and eighty-four molecular descriptors. Almost sixty-nine percent of them were used just by one model (one hundred and ninety-six descriptors, 95%CI [180 - 211]). The distribution of the descriptors used by MDF SAR/SPR models was:
Two descriptors were used by six models (imDrkQt, and lPMDVQg)
Four by five models (ASPrVQg, IiMMWHt, IMPrkQg, and iSMMWHg)
Sixteen descriptors were used by four models (AHMMVQg, aHPMwQt, aIDmjQg, iAMrVQg, iBMmwHg, iHDdFHg, iHMMtHg, IiDrQHg, iIPmWHt, ImmRDCg, imMrFHt, inDmwHg, INPRJQg, inPRlQg, isMdTHg, iSMmEQt)
Twenty one descriptors were used by three models (ABDmtQg, ASMmVQt, AsPmVQt, aSPRtQg, IADRSHg, IBPMWQt, iGPrfHt, iIMdLGg, iIMdTMg, iImrKHt, InMdTHg, isDRTCg, isDRtHg, ismRSEg, iSPRtQg, lfDdOQg, LHDmjQg, lIDrFEg, lIMdLGg, liMDWHg, LsDMpQg)
Forty-five descriptors were used by two models (ABmrtQg, AHDmEQg, aHMmjQt, AiMrKQt, AIPmVQt, AiPmVQt, aIPMwQt, anDRJQt, aSMMjQg, iAPmEQg, ibDMFHt, IbMmjHg, IBMrkGg, IBMRQCg, IbPdPHg, iFmRFMt, iFPMECg, IHDRKEg, iHMMTQt, IIDDKGg, IiMMSGg, imDdSCg, ImDmEEt, IMDMtQt, ImDrFEt, iMMMjQg, IMmrKQg, imMrtCg, inMRkQt, InPdJQg, inPRjQt, isDDkGg, IsMRKQg, ISPdlMg, IsPdOQg, lFDMwEt, lfDMWHt, lFMMKQg, LHDROQg, LIDmjQg, lImrKHt, lmMrsGg, lNPmfQt, LSPmEQg, LsPrDQt).
One hundred and forty-seven descriptors have been used in the best performing models. The correspondences between using the descriptors in all models and in best performing models are presented in Table 4.
Table 4. Descriptors in all models versus best performing models
| Descriptors | Total
| | all models | best models
| | 1 | 1 | 89
| | 1 Total | 89
| | 2 | 1 | 24
| | 2 | 2
| | 3 | 1
| | 2 Total | 27
| | 3 | 1 | 11
| | 3 | 1
| | 3 Total | 12
| | 4 | 1 | 9
| | 2 | 4
| | 4 Total | 13
| | 5 | 1 | 3
| | 2 | 1
| | 5 Total | 4
| | 6 | 1 | 2
| | 6 Total | 2
| | Total | 147
|
The partial squared correlation coefficient (the squared correlation coefficient between each descriptor from the model and property or activity of interest) varied for the all models from 0.0001 to 0.9995 with an average of 0.3645. For the best performing models, the values of the partial squared correlation coefficients varied from 0.0001 to 0.9794 with an average of 0.2959. The average values of partial squared correlation coefficients for all models and for best performing model according with the activity or property of interest are summarized in Table 5. More, the descriptors that obtained greater value of partial squared correlation coefficients are not found in the best performing model.
Table 5. The average contribution of the descriptors to the model
| Set abb. | Avgr2-best | Avgr2-all | | Set abb. | Avgr2-best | Avgr2-all
| | MDF SARs | | MDF SPRs
| | DevMTOp00 | 0.8673 | 0.9113 | | 23159 | 0.0089 | 0.1685
| | DevMTOp01 | 0.6632 | 0.7753 | | 31572 | 0.2274 | 0.2581
| | DevMTOp02 | 0.4144 | 0.5866 | | 33504 | 0.5297 | 0.6416
| | DevMTOp03 | 0.0398 | 0.3232 | | 36638 | 0.2880 | 0.3051
| | DevMTOp04 | 0.2221 | 0.4454 | | IChr10 | 0.5998 | 0.4005
| | DevMTOp05 | 0.1355 | 0.3823 | | MR10 | 0.8971 | 0.9075
| | DevMTOp06 | 0.3040 | 0.5251 | | PCB_lkow | 0.2268 | 0.3327
| | DevMTOp07 | 0.4579 | 0.6160 | | PCB_rrf | 0.2712 | 0.2843
| | DevMTOp08 | 0.3384 | 0.5284 | | PCB_rrt | 0.4687 | 0.7021
| | DevMTOp09 | 0.4035 | 0.5883 | | RRC433_lkow | 0.2308 | 0.3011
| | DevMTOp10 | 0.4169 | 0.5941 | | Min | 0.0089 | 0.1685
| | DevMTOp11 | 0.1692 | 0.4368 | | Max | 0.8971 | 0.9075
| | DevMTOp12 | 0.0214 | 0.3060 | | Average | 0.3748 | 0.4302
| | DevMTOp14 | 0.1092 | 0.3786 |
| | DevMTOp15 | 0.1100 | 0.3905 |
| | DevMTOp16 | 0.2451 | 0.4669 |
| | DevMTOp17 | 0.1447 | 0.3694 |
| | DevMTOp18 | 0.5083 | 0.6717 |
| | DevMTOp19 | 0.2888 | 0.5032 |
| | DevMTOp20 | 0.1391 | 0.3846 |
| | DevMTOp21 | 0.0721 | 0.3492 |
| | DevMTOp22 | 0.1946 | 0.4475 |
| | DevMTOp23 | 0.1430 | 0.4033 |
| | DevMTOp24 | 0.4997 | 0.6464 |
| | DevMTOp25 | 0.0441 | 0.3559 |
| | DHFR | 0.1482 | 0.1680 |
| | Dipeptides | 0.5145 | 0.4603 |
| | RRC433_lbr | 0.1612 | 0.2329 |
| | RRC433_pka | 0.2623 | 0.2144 |
| | Ta395 | 0.1027 | 0.1002 |
| | Tox395 | 0.2053 | 0.2712 |
| | 19654 | 0.1360 | 0.3286 |
| | 22583 | 0.2288 | 0.1908 |
| | 26449 | 0.3874 | 0.5332 |
| | 3300 | 0.2408 | 0.2761 |
| | 41521 | 0.2407 | 0.4365 |
| | 52344 | 0.5083 | 0.4243 |
| | 52730 | 0.5806 | 0.7092 |
| | 23110 | 0.1298 | 0.2106 |
| | 23158 | 0.3011 | 0.2719 |
| | 23167 | 0.3546 | 0.3636 |
| | 40846_1 | 0.3264 | 0.4271 |
| | 40846_2 | 0.1319 | 0.2170 |
| | 40846_4 | 0.2529 | 0.2621 |
| | Triazines | 0.4323 | 0.4613 |
| | Min | 0.0214 | 0.1002 |
| | Max | 0.8673 | 0.9113 |
| | Average | 0.2800 | 0.4210 |
|
Avgr2-best = the average of the partial squared correlation coefficient on best performing model;
Avgr2-all = the average of the partial squared correlation coefficient on all models
|
Summarizing the characters that were included into the descriptors name it can be observed that, with a single exception, all characters for first, third, fourth, fifth, sixth and seven descriptor name letters appear in the descriptors names if all MDF SAR/SPR models. The same observation is valid for analysis of the best performing ones. There were identified that three characters out of nineteen from the second descriptor letter (the letters a, g and h, see Table 2) did not appear in any model. In order to applied cluster analysis techniques the frequency of the characters into the models according with the set name were transformed as qualitative variables (yes/no). The summaries of the results obtained by performing the two steps cluster analysis on all models as well as on the best performing models are presented in Table 6 (DescL = the letter in the descriptor name, Ch = character, Best model = the model that obtained the greatest squared correlation coefficient and cross-validation leave-one-out score). There were included into the Table 6 the absolute frequency of appearance of the character into the name of descriptors and the attribute importance into the cluster (‡ = significant importance in cluster at a significance level of 5%).
Table 6. Two steps cluster analysis: results
| DescL | Ch | All models | Best model
| | Cluster 1(41) | Cluster 2(14) | Total
| | 1st letter | I | 25 | 13 | 38 | 31
| | i | 30 | 14‡ | 44 | 38
| | A | 7 | 4 | 11 | 7
| | a | 10 | 3 | 13 | 5
| | L | 13 | 4 | 17 | 8
| | l | 28 | 10 | 38 | 31
| | 2nd letter | m | 10 | 7 | 17 | 9
| | M | 3 | 4 | 7 | 7
| | n | 12 | 7 | 19 | 13
| | N | 7 | 1 | 8 | 5
| | S | 11 | 8 | 19 | 12
| | P | 5 | 1 | 6 | 5
| | s | 19 | 7 | 26 | 18
| | A | 14 | 5 | 19 | 13
| | B | 6 | 7‡ | 13 | 9
| | b | 2 | 6‡ | 8 | 6
| | G | 7 | 2 | 9 | 8
| | F | 3 | 7‡ | 10 | 4
| | f | 2 | 1 | 3 | 2
| | H | 14 | 9 | 23 | 16
| | I | 17 | 8 | 25 | 11
| | i | 3 | 7‡ | 10 | 4
| | 3rd letter | m | 13 | 8 | 21 | 10
| | M | 29 | 14‡ | 43 | 36
| | D | 31 | 13 | 44 | 34
| | P | 31 | 11 | 42 | 34
| | 4th letter | R | 22 | 10 | 32 | 23
| | r | 26 | 13 | 39 | 32
| | M | 11‡ | 14‡ | 25 | 20
| | m | 28 | 13 | 41 | 25
| | D | 12 | 8 | 20 | 15
| | d | 10 | 10‡ | 20 | 14
| | 5th letter | D | 7 | 2 | 9 | 4
| | d | 4 | 2 | 6 | 3
| | O | 6 | 0 | 6 | 5
| | o | 3 | 2 | 5 | 2
| | P | 3 | 3 | 6 | 4
| | p | 5 | 2 | 7 | 4
| | Q | 1 | 3‡ | 4 | 3
| | q | 6 | 1 | 7 | 6
| | J | 7 | 6 | 13 | 6
| | j | 9 | 5 | 14 | 6
| | K | 3 | 7‡ | 10 | 5
| | k | 10 | 8‡ | 18 | 13
| | L | 7 | 2 | 9 | 6
| | l | 4 | 2 | 6 | 5
| | V | 8 | 6 | 14 | 10
| | E | 5‡ | 9‡ | 14 | 9
| | W | 1 | 4‡ | 5 | 5
| | w | 9 | 7 | 16 | 8
| | F | 4‡ | 10‡ | 14 | 7
| | f | 9 | 2 | 11 | 5
| | S | 7 | 5 | 12 | 8
| | s | 6 | 6 | 12 | 5
| | T | 6 | 6 | 12 | 9
| | t | 10 | 7 | 17 | 8
| | 6th letter | C | 10 | 7 | 17 | 6
| | H | 9‡ | 14‡ | 23 | 20
| | M | 17 | 7 | 24 | 16
| | E | 10 | 5 | 15 | 12
| | G | 12 | 8 | 20 | 11
| | Q | 40 | 14 | 54 | 44
| | 7th letter | g | 40 | 14 | 54 | 41
| | t | 31 | 13 | 44 | 51
| DescL = the letter in the descriptor name
Ch = character
Best model = the model that obtained
the greatest squared correlation coefficient
and cross-validation leave-one-out score
‡ = significant importance in cluster
at a significance level of 5%
|
The hierarchical cluster technique was applied in order to analyze the best performing models. The Icile plot is presented in Figure 1 and the associated dendrogram in Figure 2.
Figure 1. Best performing MDF SAR/SPR models analysis: icile plot
Figure 2. Best performing MDF SAR/SPR models analysis: dendrogram
| Discussion | #29 | Abstract | Intro | Material | Method | Results | + | Conclusion | Ref
| Searching the information regarding the MDF SAR/SPR models for patterns revealed important information for activity/property characterization of compounds classes by applying the molecular descriptors family methodology.
As it can be observed from Table 3, the average of the correlation coefficient obtained by MDF SARs is greater comparing with the value obtained by the MDF SPRs, while the number of variables is less for MDF SARs than for MDF SPRs when all models are considered. When the best performing models are analyzed it can be observed that the squared correlation coefficient average obtained by the MDF SAR models is very closed to the squared correlation coefficient average obtained by MDF SPR models, and the average of the descriptors is the same.
Just forty-five percent of the molecular descriptors that were used in one model on completely sample of models could be found in the best performing models (see Table 4). Sixty percent of the molecular descriptors used by two models on whole samples were found again on the best performing models (see Table 4). Fifty-seven percent of the molecular descriptors used by three models on whole samples were found again on the best performing models; almost eighty-one percent of the molecular descriptors used by four models on whole samples were found again on the best performing models. All molecular descriptors used by five, and respectively six models on whole samples were found as being used on the best performing models too (see Table 4). These observations sustained the stability and consistency of the MDF SAR/SPR method in identification of the molecular descriptors that are able to identify the strongest relationships between compounds structure and associated activity or property.
Analyzing the data presented in Table 4 it can be observed that the average, minimum and maximum values of average contribution of descriptors are smaller values for the best performing models than the values obtained on all models. This observation leads to the conclusion that the best performing models are obtained by combination of descriptors, and the molecular descriptors that had a value of the partial correlation coefficient closest to one are not always found in the best performing model.
Two clusters were obtained by applying the two-step cluster analysis technique on the all models, showing that there exist some similarities between MDF models. One cluster used forty-one sets of compounds while the second cluster used fourteen compounds. Four characters had significant importance into the first cluster obtained on all models (see table 6):
Character M (the overlapping descriptors interaction on the maximal fragments) from fourth position on descriptors name
Characters E (interaction descriptor of the second atom property divided to the distance between the atoms) and F (interaction descriptor of the square first atom property divided to the square distance between atoms) as fifth position on descriptors name
Character H (number of directly bonded hydrogen's as atomic property) from sixth position on descriptors name
In the second cluster, the one that comprise fourteen sets of compounds, fourteen characters revealed to have significant importance in clustering:
Character i (the inverse linearization procedure applied in global molecular descriptor generation) from the first position on descriptors name
Characters B (as average mean by atom), b (average mean by bond), F (geometric mean by atom), i (harmonic mean by bond) from the second position on descriptors name (the cumulative method of fragmentation properties)
Character M (the maximal fragments criteria) from the third position on descriptors name
Characters M (the overlapping descriptors interaction on the maximal fragments) and d (the overlapping descriptors interaction on threat descriptors as Cartesian vectors) from the fourth position on descriptors name
Characters Q (the squared product between first and second atoms properties), K (the product between the first and second atoms properties and the distance between them), k (the inverse of K), E (interaction descriptor of the second atom property divided to the distance between the atoms), and W (the square of the first atom property divided to the distance between two atoms) from the fifth position on descriptors name
Character H (number of directly bonded hydrogen's as atomic property) from the sixth position on descriptors name:
On the sample of best performing MDF SAR/SPR models, the two-step cluster analysis was able to identify two clusters. This could be explained by the absence of similarities of descriptors characters used by the best performing models. The most frequently met characters on the descriptors name on the best performing models were:
i character for the first position on descriptors name (the inverse linearization procedure applied in global molecular descriptor generation)
s character for the second position on descriptors name (the product between the first and second atoms properties divided to the distance rice to power three)
M character for the third position on descriptors name (the maximal fragments criteria)
r character for the fourth position on descriptors name (the overlapping descriptors interaction obtained by treating descriptors as scalars and computing resultant relative to conventional origin)
k character for the fifth position on descriptors name (the inverse of the product between the first and second atoms properties and the distance between them)
Q character for the sixth position on descriptors name (semi-empirical Extended Hückel model, Single Point approach as atomic property)
t character for the first position on descriptors name (molecular topology)
Taking into account the above information, it can be concluding that there could not be identify similarities or patterns on the MDF SAR/SPR models even if the results of the analysis of all models say something else. Note that in the analysis of the all MDF SAR/SPR models were included for each set of compounds the univariate models that in most of the cases obtained weak performances in terms of estimation and prediction abilities.
The quantitative variables similarities of the best performing models were analyzed with hierarchical cluster technique. Looking at the icile plot (Figure 1) it can be analyzed what happen at each clusterization step. At the start step (the one that is not represented on icicle plot, Figure 1), each set of compounds was a cluster unto itself (the number of clusters at the start point being equal with fifty-five). Starting with the first step, the sets were ordered in the icicle plot according with their combination into clusters. The 15:DevMTOp15 set is linked first with 12:DevMTOp11 set, being follow by the 24:DevMTOp24 set, and so on until all the clusters are formed. From the dendrogram (see Figure 2) it can be observed that at a small distances three clusters are formed: one that comprised forty-seven sets, and other two that comprised five and respectively three sets. The differences between the obtained three clusters are at the level of sample size, and number of descriptors used by model. On the cluster that comprised forty-seven sets the sample sizes varied from five to forty, and the number of molecular descriptors from two to three. On the cluster that comprised five sets the sample seizes varied from fifty-seven to seventy-three and the number of descriptors from two to five, while on the cluster that comprised three sets the number of compounds were of two hundred and nine and the number of variables from two to six. At a short distance, two clusters are linked together (the one that comprised forty-seven and the other that comprised five sets). All the clusters are linked together at the maximum distance as possible.
The research reached its goal of searching the patterns on MDF SAR/SPR models. The results shown that on the studied sets of compounds the MDF SAR/SPR method identified models that are unique for each set do to the complex information obtained from compounds structure. Based on the obtained results the MDF SAR/SPR method will be updated by analyzing of the usefulness of the three characters from the second position descriptor name that were not identified in any model. The development of the MDF SAR/SPR database by analyzing and including of more compounds sets will be done in the future. Data mining techniques applied on larger sets of compounds could revealing important information for characterization of activities or properties of compound based on information obtained from the structure.
| Conclusion | #29 | Abstract | Intro | Material | Method | Results | Discussion | + | Ref
| The data mining techniques applied on MDF SAR/SPR models revealed that is not possible any classification of characters used on descriptors name and thus on their construction. This result sustains the ability of MDF SAR/SPR method on identification of those structure characteristics of compounds that are linked with the activity or property of interest.
The hierarchical cluster analysis is a useful technique in identification of similarities of MDF SAR/SPR models regarding the quantitative variables, in our case the squared correlation coefficient, the number of descriptors used by models and the sample sizes.
Data mining techniques applied on larger sets of compounds analyzed with MDF SAR/SPR method could reveal important information for characterization of activities or properties of compound based on information obtained from the structure.
| | Ref | #29 | Abstract | Intro | Material | Method | Results | Discussion | Conclusion | +
|
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