Quantitative Structure-Activity Relationships (QSARs) Tutorial
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1 Quantitative Structure-Activity Relationships (QSARs) Tutorial Single and Multi Linear Regression This tutorial will show you how to perform a QSAR with MLR and PLS statistical tools
2 In the Gnumerics file enclosed (Tutorial Data) you will find 29 sugars with different sucrose relative power and 8 different descriptors as reported in the publication. The objective of this tutorial is to make you use of simple informatics tools to establish QSAR models. QSAR Pagina 2 The tutorial rely on the data available from Singh s paper. You can fine the publication in elearning website
3 Gnumeric QSAR Pagina 3 The gnumeric program will be used. The program can be searched in the net as it is freely available. Anyway it is also available from elarning. Download it and install by double click on the file.
4 Gnumeric QSAR Pagina 4 Answer to the question during the installation as shown in the slides
5 Gnumeric QSAR Pagina 5
6 Gnumeric QSAR Pagina 6
7 Gnumeric QSAR Pagina 7 Look for the folder where gnumeric has been installed and open up it
8 Open the file QSAR Pagina 8 By mean of the «file» menu
9 Open the file QSAR Pagina 9 From elearning download the file Rajesh.Student.gnumeric and open it with gnumeric
10 Initial Table QSAR Pagina 10 The opened file should appear as in the slide. There is a dependent variable (RS = relative sweetness) and 8 descriptors
11 Descriptors DH in the table W in the table EA and IP in the table SE in the table QSAR Pagina 11 Here are described the 8 used descriptors
12 Check dependent variable (RS) QSAR Pagina 12 The first thing to do is to check the linear distribution of the dependent variable RS. So copy the column of data belonging to RS it in the memory.
13 Check dependent variable (RS) QSAR Pagina 13. and paste it the into a new sheet
14 Check dependent variable (RS) QSAR Pagina 14
15 Check dependent variable (RS) QSAR Pagina 15 To check for linearity, just insert a column type chart
16 Check dependent variable (RS) QSAR Pagina 16 As you can see, the preview is showing the plot
17 Check dependent variable (RS) QSAR Pagina 17 Then click in the area of the sheet grid and the plot will appear. Clearly there is no linear distribution of the dependent variable
18 Check dependent variable (RS) QSAR Pagina 18 Let s transform it in the logarithm scale as shown in the slide
19 Check dependent variable (RS) QSAR Pagina 19
20 Check dependent variable (RS) QSAR Pagina 20 Then apply the formula for the cell «I2» to the other cells just grabbing the small square in the cell right bottom corner
21 Check dependent variable (RS) QSAR Pagina 21 And all the data will be transformed
22 Check dependent variable (RS) QSAR Pagina 22 Make the plot as shown before and now the linearity is present.
23 QSAR Pagina 23 Duplicate the sheet by right clicking on the sheet name.
24 Check dependent variable (RS) QSAR Pagina 24 Rename the sheet into «New Table»
25 Check dependent variable (RS) QSAR Pagina 25 Highlight the transformed RS variable and copy into the memory with the right click
26 Check dependent variable (RS) QSAR Pagina 26 Then paste it to the «New Table» sheet. Use the «paste special» option
27 Check dependent variable (RS) QSAR Pagina 27 and select «as value»
28 Check dependent variable (RS) QSAR Pagina 28 Now you have the dependent variable fixed
29 Independent variables analysis Notice that the 8 molecular descriptors have very different magnitudes. To guarantee the comparability of the MLR coefficients (see previous lesson on QSAR), proceed to the normalization of all the descriptors (for instance for the interval [0; 1] ). The first step is to calculate the MAX and MIN values of each descriptor with the functions =MAX(range) and =MIN(range) as described in the following slides QSAR Pagina 29 Once we have checked the dependent variable (RS) we need to analyse the independent variables (descriptors).
30 Independent variables analysis QSAR Pagina 30 First we calculate the maximum and the minimum values for each colum
31 Independent variables analysis QSAR Pagina 31 The method is similar to that already shown. Just do the same as displayed in the slide.
32 Independent variables analysis QSAR Pagina 32
33 Independent variables analysis QSAR Pagina 33
34 Independent variables analysis QSAR Pagina 34 And all the min and max values are promptly calculated
35 Independent variables analysis QSAR Pagina 35 In a new sheet.
36 Independent variables analysis QSAR Pagina 36 renamed «Normalized»
37 Independent variables analysis QSAR Pagina 37 Copy the ID and labels from «New Table» and also the descriptors labels
38 Independent variables analysis QSAR Pagina 38 paste everything in the «Normalized» sheet
39 Independent variables analysis QSAR Pagina 39 Make sure you have the same values for RS
40 Independent variables analysis QSAR Pagina 40 Now apply the normalization as described in the lesson. (see also the formula in the slide). Here the MinMax normalization is being applied: Normalized valued = (original value min) / (max min)
41 Independent variables analysis QSAR Pagina 41 And let s obtain the normalized matrix, that can be checked by calculating min and max. Their values should range all between 0 and 1.
42 Independent variables analysis QSAR Pagina 42 At this point we can continue analysing the data.
43 Independent variables analysis QSAR Pagina 43 Prepare a new sheet «Intercorrelation» as in the slide
44 Independent variables analysis QSAR Pagina 44 And by the proper function calculate the squared pearson coefficients (r2)
45 Independent variables analysis QSAR Pagina 45 First RS vs RS. It should be = 1!
46 Independent variables analysis QSAR Pagina 46 Lock at the formula and define fixed variable (insert $ signs as in the slide)
47 Independent variables analysis QSAR Pagina 47 Then just by drugging the r2 is calculated for all the values in the first row. Make a similar operation in the others rows
48 Independent variables analysis QSAR Pagina 48 And the correlation matrix is obtained
49 Independent variables analysis QSAR Pagina 49 In the first row are reported the r2 values for each variable with the dependent variable, these are monoparametric regressions. The best one is IP that as the highest r^2 value.
50 Independent variables analysis QSAR Pagina 50 In the yellow area are highlighted the intercorrelations among the descriptors to check for any collinearity. As a limit an r2 greater than 0.5 means that two variable are correlated and should not used together.
51 Choice of the best descriptors (stepwise method) In order to get an overview of the uniparametric relationship between the various descriptors we use a linear regression analysis function built into Gnumeric (Statistics > Dependent Observations > Regression) QSAR Pagina 51 In the next slides we are going to make a stepwise building of the QSAR model
52 Choice of the best descriptors (stepwise method) QSAR Pagina 52
53 Choice of the best descriptors (stepwise method) QSAR Pagina 53 We start with the uniparametric regressions using the «Statistic Regression» menu. Then by clicking in the X and Y variable boxes we define the areas containing the values. While doing this operation select also the label of the variables. Then click on the OK button.
54 Choice of the best descriptors (stepwise method) QSAR Pagina 54 and a new sheet «Regression (1)» will be created with all the statistical values
55 Choice of the best descriptors (stepwise method) logrs = * EA QSAR Pagina 55 By analysing the new sheet we can observe the intercept and constant values of the line and thus we can write its equation
56 Choice of the best descriptors (stepwise method) QSAR Pagina 56 Reapeat for all the descriptors
57 Choice of the best descriptors (stepwise method) QSAR Pagina 57
58 Choice of the best descriptors (stepwise method) QSAR Pagina 58
59 Choice of the best descriptors (stepwise method) QSAR Pagina 59
60 Choice of the best descriptors (stepwise method) QSAR Pagina 60
61 Choice of the best descriptors (stepwise method) QSAR Pagina 61
62 Choice of the best descriptors (stepwise method) QSAR Pagina 62
63 Choice of the best descriptors (stepwise method) QSAR Pagina 63 And record the r^2 values in a new sheet «Regressions»
64 Choice of the best descriptors (stepwise method) QSAR Pagina 64
65 Choice of the best descriptors (stepwise method) QSAR Pagina 65 Compare the Regressions with the initial correlations and the they should be the same values.
66 MLR with all variables Overfitting! QSAR Pagina 66 Just to try, instead of highlighting one parameter, select all the 8 descriptors while doung the regressions, in the new sheet «Regression (9)» the values are clearlyindicating that 8 parameters give a perfect regression of r2 = 1! This is overfitting! We are using collinear parameters and the model is LYING!
67 No differences with unscaled data! QSAR Pagina 67 IF we repeated with unscaled data (without normalizing) we can observe that the results are the same, the only differences are the intercept and the variable coefficient values. Although it seems that scaling is not necessary, apply always a normalization in you matrix!
68 Step Forward Multi Linear Regressions QSAR Pagina 68 Going back to the intercorrelation data it is possible to see that the first parameter to use is «IP» and that we can associate with it only «W», «MR», «SASA», «TE» and «DH» values. The ones that display low correlation with «IP». At first glance we could expect a godd correlation by using atriparametric model including «IP»,
69 Step Forward Multi Linear Regressions QSAR Pagina 69 Let s prepare the biparametric combinations
70 Step Forward Multi Linear Regressions QSAR Pagina 70 And by using the «Statistic Regression» menu the five biparametric are easily build.
71 Step Forward Multi Linear Regressions QSAR Pagina 71
72 Step Forward Multi Linear Regressions QSAR Pagina 72
73 Step Forward Multi Linear Regressions QSAR Pagina 73
74 Step Forward Multi Linear Regressions QSAR Pagina 74
75 Biparametric models QSAR Pagina 75 The best combination resulted to be IP + W, but also IP + MR should be analyzed with other descriptor
76 Step Forward Multi Linear Regressions QSAR Pagina 76 So prepare the triparametric combination for IP + W
77 Step Forward Multi Linear Regressions QSAR Pagina 77 And the other threes for IP + MR
78 Step Forward Multi Linear Regressions QSAR Pagina 78 And build the seven triparametric models
79 Step Forward Multi Linear Regressions QSAR Pagina 79
80 Step Forward Multi Linear Regressions QSAR Pagina 80
81 Step Forward Multi Linear Regressions QSAR Pagina 81
82 Step Forward Multi Linear Regressions QSAR Pagina 82
83 Step Forward Multi Linear Regressions QSAR Pagina 83
84 Step Forward Multi Linear Regressions QSAR Pagina 84
85 Triparametric models QSAR Pagina 85 From the results the best triparametric model is that with «IP» + «MR» + «SASA»
86 Triparametric models QSAR Pagina 86 The fitting plot can be made by the «Insert Chart» menu
87 Compare result with those published Are the same! QSAR Pagina 87 Comparing the results with those reported in the publication the same results were obtained using data not normalized. The same results are obtained either with normalized or autoscaled data!
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