3D structure generation and PCA analysis for Anion transporters

Summary Aim:

To generate 3D co-ordinates for the Gale group compounds. Regenerate DRAGON descriptors (2D and 3D)

Use descriptors to carry out PCA (Principal component analysis) and possibly PLS (partial least squares) - which is a supervised version of PCA. Examine if the PCA output can be clustered in any form - how do these clusters/ distribution change between the 2D and 3D descriptors?

PAG Group compounds - Original Set

131 compounds in file, does contain some duplicates

Generation of 3D co-ordinates:

OpenBabel - Gen3D

This operation (invoked using –gen3d at the commandline) generates 3D structures for 0D or 2D structures using the following series of steps:

1. Use the OBBuilder to create a 3D structure using rules and ring templates
2. Do 250 steps of a steepest descent geometry optimization with the MMFF94 forcefield
3. Do 200 iterations of a Weighted Rotor conformational search (optimizing each conformer with 25 steps of a steepest descent)
4. Do 250 steps of a conjugate gradient geometry optimization (from open-babel.readthedocs.io/en/latest/3DStructureGen/SingleConformer.html)

Tried single molecule (101002_anie201200729-1.mol) - used Gen3D in OpenBabel. 3D co-ordinates were generated and saved to a new mol file. Also can see a comparison of the 2D and 3D structures.

When trying to process multiple molecules at one go - try sdf output format. (append input filename to title, generate 3D co-ordinates)

Appears to correctly generate multi structures in a single sdf file output - however the output appears to number 9 - 1 rather than 1 - 9 as OpenBabel pulls them in in reverse order.

All original PAG compounds selected (131 compounds) and 3D structures generated - output sdf format (3D_Structures_PAG_Originalset.sdf) - appears to give slight differences in the structures each time it is run - how would this affect the descriptors and PCA analysis etc? Second generated file - 3D_Structures_PAG_Originalset2.sdf is the same compounds.

Some of these are duplicates, would it be beneficial to remove all the duplicates before the generation of new descriptors?

Generation of descriptors:

Using DRAGON 6.0

File: 3D_Structures_PAG_Originalset

Output: 3D_Structures_PAG_Originalset_output1
No of descriptors: 4870? (all 2D & 3D - excluding Charge descriptors)
Exclude descriptors with constant values
Exclude descriptors with at least one missing value
3100 descriptors exported

Output: 3D_Structures_PAG_Originalset_output2
No of descriptors: 4870? (all 2D & 3D - excluding Charge descriptors)
Exclude descriptors with constant values
Exclude descriptors with constant and near-constant values
Exclude descriptors with stanard deviation < 0.0001
Exclude descriptors with at least one missing value
2996 descriptors exported

---

File: 3D_Structures_PAG_Originalset2

Output: 3D_Structures_PAG_Originalset2_output1
No of descriptors: 4870 (all 2D & 3D - excluding Charge descriptors)
Exclude descriptors with constant values
Exclude descriptors with at least one missing value
3100 descriptors exported

Output: 3D_Structures_PAG_Originalset2_output2
No of descriptors: 4870 (all 2D & 3D - excluding Charge descriptors)
Exclude descriptors with constant values
Exclude descriptors with constant and near-constant values
Exclude descriptors with stanard deviation < 0.0001
Exclude descriptors with at least one missing value
2996 descriptors exported

Same number of descriptors for the 1st and 2nd sets of molecules.

---

File: 2D_Structures_PAG_Originalset

Output: 2D_Structures_PAG_Originalset_output1
No of descriptors: 4870 (all 2D & 3D - excluding Charge descriptors)
Exclude descriptors with constant values
Exclude descriptors with at least one missing value
2013 descriptors exported

Output: 2D_Structures_PAG_Originalset_output2
No of descriptors: 4870 (all 2D & 3D - excluding Charge descriptors)
Exclude descriptors with constant values
Exclude descriptors with constant and near-constant values
Exclude descriptors with stanard deviation < 0.0001
Exclude descriptors with at least one missing value
1914 descriptors exported ***

PCA

PCA is pricinipal components analysis - this is a dimensionality reduction technique that is widely used in data analysis.

https://www.analyticsvidhya.com/blog/2016/03/practical-guide-principal-component-analysis-python/

Some general advice - from https://tgmstat.wordpress.com/2013/11/21/introduction-to-principal-component-analysis-pca/

PCA is not scale invariant, so it is highly recommended to standardize all the {p} variables before applying PCA. Singular Value Decomposition (SVD) is more numerically stable than eigendecomposition and is usually used in practice. How many principal components to retain will depend on the specific application. Plotting {(1-R^2)} versus the number of components can be useful to visualize the number of principal components that retain most of the variability contained in the original data. Two or three principal components can be used for visualization purposes.

PCA is an unsupervised technique - the response variable is not used to determine the direction of the component. Principal components are orthogonal.

---

loading packages in R

These packages may be required to be loaded in order for the system to function correctly.

rr library() #otherwise ggplot2 errors - required reinstallation

package 㤼㸱lazyeval㤼㸲 was built under R version 3.4.4

rr library(2)

package 㤼㸱ggplot2㤼㸲 was built under R version 3.4.4

rr library() #to work with ggplot2? library() #to work with ggplot2? library() #this is a package that is removed from CRAN - had to be downloaded from the archive - requires tidyr and gridExtra to be installed as well library()

Loading required package: magrittr
package 㤼㸱magrittr㤼㸲 was built under R version 3.4.4

rr library()

Attaching package: 㤼㸱dplyr㤼㸲

The following object is masked from 㤼㸱package:gridExtra㤼㸲:

    combine

The following objects are masked from 㤼㸱package:stats㤼㸲:

    filter, lag

The following objects are masked from 㤼㸱package:base㤼㸲:

    intersect, setdiff, setequal, union

rr library()

package 㤼㸱yaml㤼㸲 was built under R version 3.4.4

Getting data into R

DRAGON output files were converted to .csv file format. The number field (first column) was removed.

3D Descriptors

`3D_Structures_PAG_Originalset_output2`<- read.table("C:/Users/nk1g09/Dropbox/PAG_group/PCA/DRAGON/3D_Structures_PAG_Originalset_output2.csv", header=TRUE, sep=",", row.names="NAME")
# this brings in the csv file containing descriptors for the 3D structures as a dataframe

2D Descriptors

`2D_Structures_PAG_Originalset_output2`<- read.table("C:/Users/nk1g09/Dropbox/PAG_group/PCA/DRAGON/2D_Structures_PAG_Originalset_output2.csv", header=TRUE, sep=",", row.names="NAME")
# this brings in the csv file containing descriptors for the 2D structures as a dataframe

To colour the PCA plots by EC50 or compounds groupings it is necessary to merge the DRAGON descriptors with those compound identifiers which are not generated through DRAGON. This includes the experimental descriptors and identifiers such as compound names and molecular formulas.

Compound_Identifiers

Compound_Identifiers_classification<-read.table("C:/Users/nk1g09/Dropbox/PAG_group/PCA/PAG_compounds_chemical_values_duplicates.csv", header=TRUE, sep=",", row.names="NAME")
#brings in the compound identifers and experimental descriptors. 
joined_3D_PAG_Originalset_output2 <- merge(Compound_Identifiers_classification, `3D_Structures_PAG_Originalset_output2`, by='row.names')
#merges the two datasets by row-names (which are the compound filenames), this gives a 131 by 3007 dataframe
joined_2D_PAG_Originalset_output2 <- merge(Compound_Identifiers_classification, `2D_Structures_PAG_Originalset_output2`, by='row.names')

Running PCA - 3D

The PCA can now be run on the DRAGON descriptors, and coloured by various different options.

PCA no scaling

#need to run the PCA on all columns after the 11th column?
'3D_PAG_Original_output2_PCA2'<- prcomp(joined_3D_PAG_Originalset_output2[,12:3007])
plot(`3D_PAG_Original_output2_PCA2`$x[,1:2])

plot(`3D_PAG_Original_output2_PCA2`$x[,1:2], col=joined_3D_PAG_Originalset_output2$EC50_Cl.NO3.)
legend("topright", pch=20, col=unique(joined_3D_PAG_Originalset_output2$EC50_Cl.NO3.), legend=unique(joined_3D_PAG_Originalset_output2$EC50_Cl.NO3.))

#34 compounds are missing EC50 values, but there seems to be even more missing from this plot, doesn't plot correctly as there are too many values? need to group the EC50 values into bands. in some fashion.
plot(`3D_PAG_Original_output2_PCA2`$x[,1:2], col=joined_3D_PAG_Originalset_output2$Compound_Type, pch=20)
legend("topright", pch=20, col=unique(joined_3D_PAG_Originalset_output2$Compound_Type), legend=unique(joined_3D_PAG_Originalset_output2$Compound_Type))

What about if it is taken by Subtype instead of Type. If there are too many groups then the colour function cannot handle it properly and the colours are repeated. If using >8 groups for the colours then repeated colours will appear. Possibly able to use a different package to generate more colours, or could it use different symbols?

plot(`3D_PAG_Original_output2_PCA2`$x[,1:2], col=joined_3D_PAG_Originalset_output2$Compound_subtype, pch=20)
legend("topright", pch=20, col=unique(joined_3D_PAG_Originalset_output2$Compound_subtype), legend=unique(joined_3D_PAG_Originalset_output2$Compound_subtype))

#too many groups for the colours to work properly.

PCA with scaling

scale function

Need to try the PCA with scaling included in it and see how this changes the plot. in addition how the 2D and 3D plots differ.

#using the scale function to scale the data prior to PCA
#need to run the PCA on all columns after the 11th column?
'3D_PAG_Original_output2_PCA3'<- prcomp(scale(joined_3D_PAG_Originalset_output2[,12:3007]))
plot(`3D_PAG_Original_output2_PCA3`$x[,1:2], col=joined_3D_PAG_Originalset_output2$Compound_Type, pch=20)
legend("topright", pch=20, col=unique(joined_3D_PAG_Originalset_output2$Compound_Type), legend=unique(joined_3D_PAG_Originalset_output2$Compound_Type))

scale. in prcomp

How does the scale() function compare to using scale. in the prcomp function?

#using scale. = TRUE to scale the data for PCA
#need to run the PCA on all columns after the 11th column?
'3D_PAG_Original_output2_PCA4'<- prcomp(joined_3D_PAG_Originalset_output2[,12:3007], scale. = TRUE)
plot(`3D_PAG_Original_output2_PCA4`$x[,1:2], col=joined_3D_PAG_Originalset_output2$Compound_Type, pch=20)
legend("topright", pch=20, col=unique(joined_3D_PAG_Originalset_output2$Compound_Type), legend=unique(joined_3D_PAG_Originalset_output2$Compound_Type))

The two outputs seem to generate the same plot for the PCA.

Running PCA - 2D

Follow the same structure for generating the 3D PCA plots, but for the 2D instead so they can be compared. This just used the Compound_Type as colouring as neither Ec50 or subtypes currently colour correctly.

PCA with scaling

'2D_PAG_Original_output2_PCA'<- prcomp(joined_2D_PAG_Originalset_output2[,12:1925], scale. = TRUE)
plot(`2D_PAG_Original_output2_PCA`$x[,1:2])

plot(`2D_PAG_Original_output2_PCA`$x[,1:2], col=joined_2D_PAG_Originalset_output2$Compound_Type, pch=20)

plot(`2D_PAG_Original_output2_PCA`$x[,1:2], col=joined_2D_PAG_Originalset_output2$Compound_Type, pch=20)
legend("topright", pch=20, col=unique(joined_2D_PAG_Originalset_output2$Compound_Type), legend=unique(joined_2D_PAG_Originalset_output2$Compound_Type), cex=0.75)

#legend was too large 

Legends and plotting

The legends on the existing plots are too large/misplaced so they cover up data that is plotted on the graph.

It is possible to move the legend when using the plot() function, using par() to create an area for the legend.

Using ggplot2 may be a better option if the package can be installed easily.

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Comparing plots: multiple plots can be displayed in a single area using the par() function or layout() function creating a plot with multiple subplots.

ggplot2 - 3D

If using ggplots how would it work to produce multiple plots in a single environment? and how does it get the colouration?

#join PCA output and compound types
PC3Di<-data.frame(`3D_PAG_Original_output2_PCA4`$x,Compound_Type=joined_3D_PAG_Originalset_output2$Compound_Type) # scaled PCA for the 3D structures, combined with the compound type column
PC3Dii<-data.frame(`3D_PAG_Original_output2_PCA4`$x,Compound_Type=joined_3D_PAG_Originalset_output2$Compound_Type, EC50=joined_3D_PAG_Originalset_output2$EC50_Cl.NO3.) #scaled PCA for the 3D structures, combined with the compound type and EC50 value columns
PC3Diii<-data.frame(`3D_PAG_Original_output2_PCA4`$x,Compound_Type=joined_3D_PAG_Originalset_output2$Compound_Type, Log.1.EC50.=joined_3D_PAG_Originalset_output2$Log.1.EC50.) #scaled PCA for the 3D structures, combined with the compound type and log EC50 values
#quick plot of the data
qplot(x=PC1, y=PC2, data=PC3Di, color=Compound_Type)

qplot(x=PC1, y=PC2, data=PC3Dii, color=Compound_Type, size=EC50) # do I need to scale the EC50 values?

#if EC50 equals NA then it should be some different marking, otherwise some form of scale of binned sizes?
qplot(x=PC1, y=PC2, data=PC3Diii, color=Compound_Type, size=Log.1.EC50.) #logec50 values

Check the EC50 values - are these sized correctly? LogEC50 values aren’t very clear for differentiation

ggfortify

Could use autoplot through ggfortify (now outdated?) But this would require extra modification to use scaling and colours from the compound types.

ggplot2 - 2D

colour the plots for the 2D PCA - by compound type and do size by EC50

#join PCA output and compound types
PC2Di<-data.frame(`2D_PAG_Original_output2_PCA`$x,Compound_Type=joined_2D_PAG_Originalset_output2$Compound_Type) # scaled PCA for the 2D structures, combined with the compound type column
PC2Dii<-data.frame(`2D_PAG_Original_output2_PCA`$x,Compound_Type=joined_2D_PAG_Originalset_output2$Compound_Type, EC50=joined_2D_PAG_Originalset_output2$EC50_Cl.NO3.) #scaled PCA for the 2D structures, combined with the compound type and EC50 value columns
PC2Diii<-data.frame(`2D_PAG_Original_output2_PCA`$x,Compound_Type=joined_2D_PAG_Originalset_output2$Compound_Type, Log.1.EC50.=joined_2D_PAG_Originalset_output2$Log.1.EC50.) #scaled PCA for the 2D structures, combined with compound type and logEC50 values
#quick plot of the data
qplot(x=PC1, y=PC2, data=PC2Di, color=Compound_Type)

qplot(x=PC1, y=PC2, data=PC2Dii, color=Compound_Type, size=EC50) 

qplot(x=PC1, y=PC2, data=PC2Diii, color=Compound_Type, size=Log.1.EC50.)

qplot(x=PC1, y=PC2, data=PC2Diii, color=Log.1.EC50., pch = Compound_Type) # not very easy to differentiate

Comparison Plots

Want a comparison of the 2D PCA and the 3D PCA. Attempting to get two plots to display on the same image. This cannot be done using pa or layout for ggplots however this may be feasible through the use of ggpubr package.

plot2D<- ggplot(PC3Di, aes(x=PC1, y=PC2, color=Compound_Type)) +
    geom_point() + ggtitle("PCA of Anion transporter compounds - 3D descriptors")
plot3D<- ggplot(PC2Di, aes(x=PC1, y=PC2, color=Compound_Type)) +
    geom_point() + ggtitle("PCA of Anion transporter compounds - 2D descriptors")
par(mfrow=c(2,1))  
ggplot(PC3Di, aes(x=PC1, y=PC2, color=Compound_Type)) +
    geom_point() + ggtitle("PCA of Anion transporter compounds - 3D descriptors")

ggplot(PC2Di, aes(x=PC1, y=PC2, color=Compound_Type)) +
    geom_point() + ggtitle("PCA of Anion transporter compounds - 2D descriptors")

#how to get two ggplot plots to plot together on a single plot?
#can put two normal plots together on a single plot, but what about the ggplots. 
#plot(PC3Di$PC1, PC3Di$PC2, col=PC3Di$Compound_Type)
#plot(PC2Di$PC1, PC2Di$PC2, col=PC2Di$Compound_Type)

ggpubr function can be used to arrange multiple plots on a single layout and create extra text, annotations etc. Installation of ggpubr installs gridExtra and cowplot which give extra functionality.

#requires ggpubr package
plot3D<- ggplot(PC3Di, aes(x=PC1, y=PC2, color=Compound_Type)) +
    geom_point() + ggtitle("PCA of Anion transporter compounds \n 3D descriptors") +theme(plot.title = element_text(size=10, hjust=0.5))
plot2D<- ggplot(PC2Di, aes(x=PC1, y=PC2, color=Compound_Type)) +
    geom_point() + ggtitle("PCA of Anion transporter compounds \n 2D descriptors") +theme(plot.title = element_text(size=10, hjust=0.5))
comparison_plot<- ggarrange(plot2D, plot3D, 
          labels = c("A", "B"), common.legend=TRUE, legend="bottom" , label.x = 0, label.y = 0, hjust=-0.5, vjust=-0.2)
comparison_plot

ggsave("C:/Users/nk1g09/Dropbox/PAG_group/PCA/R_coding/PCA_Comparison.png", width=6, height=4)

Comparing the 3D and 2D scaled PCA does not produce a large difference in the presence of clusters.

Does the clustering change if it is coloured by Log(1/EC50) instead?

plot3D_2<- ggplot(PC3Diii, aes(x=PC1, y=PC2, color=Log.1.EC50.)) +
    geom_point() + ggtitle("PCA of Anion transporter compounds \n 3D descriptors") +theme(plot.title = element_text(size=10, hjust=0.5))
#this colouration is the straight LogEC50 (not Log(1/EC50)) - it also appears to be the ln and not base 10 log. need to check if this is correct. 
plot2D_2<- ggplot(PC2Diii, aes(x=PC1, y=PC2, color=Log.1.EC50.)) +
    geom_point() + ggtitle("PCA of Anion transporter compounds \n 2D descriptors") +theme(plot.title = element_text(size=10, hjust=0.5))
comparison_plot_2<- ggarrange(plot2D_2, plot3D_2, 
          labels = c("A", "B"), common.legend=TRUE, legend="bottom" , label.x = 0, label.y = 0, hjust=-0.5, vjust=-0.2)
comparison_plot_2

ggsave("C:/Users/nk1g09/Dropbox/PAG_group/PCA/R_coding/PCA_Comparison_2.png", width=6, height=4)

How much variance do the first two PC values account for in the dataset?

PCA variance

Determining the proportion of variance that is contained within the first 2 PCs for the 2D and 3D descriptors.

The 3D scaled PCA is - 3D_PAG_Original_output2_PCA4 the 2D scaled PCA is - 2D_PAG_Original_output2_PCA

summary(`3D_PAG_Original_output2_PCA4`)

Importance of components:
                           PC1     PC2      PC3      PC4     PC5     PC6   PC7     PC8     PC9    PC10   PC11    PC12    PC13    PC14    PC15   PC16
Standard deviation     37.7003 18.3958 14.70963 10.07133 9.83226 8.69800 8.301 7.79434 6.81213 6.64735 6.4309 5.76033 5.40156 5.29806 4.79419 4.6444
Proportion of Variance  0.4744  0.1129  0.07222  0.03386 0.03227 0.02525 0.023 0.02028 0.01549 0.01475 0.0138 0.01108 0.00974 0.00937 0.00767 0.0072
Cumulative Proportion   0.4744  0.5874  0.65958  0.69343 0.72570 0.75095 0.774 0.79423 0.80972 0.82447 0.8383 0.84935 0.85908 0.86845 0.87612 0.8833
                          PC17    PC18    PC19    PC20    PC21    PC22    PC23    PC24    PC25    PC26    PC27    PC28    PC29   PC30    PC31    PC32
Standard deviation     4.32512 4.25001 4.03990 3.89068 3.72504 3.65501 3.45202 3.36349 3.27503 3.24721 3.12952 3.02677 2.99266 2.8468 2.69681 2.66057
Proportion of Variance 0.00624 0.00603 0.00545 0.00505 0.00463 0.00446 0.00398 0.00378 0.00358 0.00352 0.00327 0.00306 0.00299 0.0027 0.00243 0.00236
Cumulative Proportion  0.88957 0.89560 0.90104 0.90610 0.91073 0.91519 0.91917 0.92294 0.92652 0.93004 0.93331 0.93637 0.93936 0.9421 0.94449 0.94685
                          PC33    PC34   PC35    PC36    PC37    PC38    PC39    PC40    PC41    PC42    PC43   PC44    PC45    PC46    PC47    PC48
Standard deviation     2.60026 2.54154 2.3870 2.36021 2.30247 2.25027 2.22005 2.20094 2.14324 2.13068 2.05753 1.9757 1.94799 1.86588 1.84947 1.81973
Proportion of Variance 0.00226 0.00216 0.0019 0.00186 0.00177 0.00169 0.00165 0.00162 0.00153 0.00152 0.00141 0.0013 0.00127 0.00116 0.00114 0.00111
Cumulative Proportion  0.94911 0.95127 0.9532 0.95503 0.95680 0.95849 0.96013 0.96175 0.96328 0.96480 0.96621 0.9675 0.96878 0.96994 0.97108 0.97219
                          PC49   PC50    PC51    PC52    PC53    PC54    PC55    PC56    PC57    PC58    PC59   PC60    PC61    PC62    PC63    PC64
Standard deviation     1.77329 1.7271 1.70627 1.68954 1.65833 1.62603 1.56789 1.54263 1.51130 1.49830 1.46513 1.4517 1.40944 1.38904 1.35564 1.33189
Proportion of Variance 0.00105 0.0010 0.00097 0.00095 0.00092 0.00088 0.00082 0.00079 0.00076 0.00075 0.00072 0.0007 0.00066 0.00064 0.00061 0.00059
Cumulative Proportion  0.97324 0.9742 0.97520 0.97616 0.97708 0.97796 0.97878 0.97957 0.98034 0.98108 0.98180 0.9825 0.98317 0.98381 0.98442 0.98502
                          PC65    PC66    PC67    PC68    PC69    PC70    PC71    PC72    PC73    PC74    PC75   PC76    PC77    PC78    PC79    PC80
Standard deviation     1.31853 1.30024 1.27195 1.23138 1.21421 1.20425 1.18943 1.15265 1.14850 1.12618 1.11179 1.0900 1.08026 1.05284 1.04709 1.01764
Proportion of Variance 0.00058 0.00056 0.00054 0.00051 0.00049 0.00048 0.00047 0.00044 0.00044 0.00042 0.00041 0.0004 0.00039 0.00037 0.00037 0.00035
Cumulative Proportion  0.98560 0.98616 0.98670 0.98721 0.98770 0.98818 0.98866 0.98910 0.98954 0.98996 0.99038 0.9908 0.99116 0.99153 0.99190 0.99224
                          PC81    PC82    PC83    PC84   PC85    PC86    PC87    PC88    PC89    PC90    PC91    PC92    PC93    PC94    PC95   PC96
Standard deviation     1.00689 0.98558 0.97437 0.95802 0.9457 0.92739 0.92070 0.88670 0.87714 0.85761 0.85316 0.83535 0.81963 0.81142 0.80028 0.7743
Proportion of Variance 0.00034 0.00032 0.00032 0.00031 0.0003 0.00029 0.00028 0.00026 0.00026 0.00025 0.00024 0.00023 0.00022 0.00022 0.00021 0.0002
Cumulative Proportion  0.99258 0.99291 0.99322 0.99353 0.9938 0.99411 0.99440 0.99466 0.99492 0.99516 0.99541 0.99564 0.99586 0.99608 0.99630 0.9965
                         PC97    PC98    PC99   PC100   PC101   PC102   PC103   PC104   PC105   PC106   PC107   PC108   PC109   PC110   PC111   PC112
Standard deviation     0.7649 0.76021 0.75273 0.74718 0.73183 0.72181 0.70196 0.68991 0.67465 0.64963 0.64358 0.62706 0.62222 0.60842 0.59032 0.58577
Proportion of Variance 0.0002 0.00019 0.00019 0.00019 0.00018 0.00017 0.00016 0.00016 0.00015 0.00014 0.00014 0.00013 0.00013 0.00012 0.00012 0.00011
Cumulative Proportion  0.9967 0.99688 0.99707 0.99726 0.99744 0.99761 0.99778 0.99794 0.99809 0.99823 0.99837 0.99850 0.99863 0.99875 0.99887 0.99898
                         PC113   PC114  PC115   PC116   PC117   PC118   PC119   PC120   PC121   PC122   PC123   PC124   PC125   PC126     PC127     PC128
Standard deviation     0.57533 0.56329 0.5438 0.52257 0.50533 0.48740 0.47769 0.45341 0.44488 0.42188 0.39742 0.38655 0.34996 0.31899 7.295e-14 2.588e-15
Proportion of Variance 0.00011 0.00011 0.0001 0.00009 0.00009 0.00008 0.00008 0.00007 0.00007 0.00006 0.00005 0.00005 0.00004 0.00003 0.000e+00 0.000e+00
Cumulative Proportion  0.99909 0.99920 0.9993 0.99939 0.99947 0.99955 0.99963 0.99970 0.99976 0.99982 0.99988 0.99993 0.99997 1.00000 1.000e+00 1.000e+00
                           PC129     PC130     PC131
Standard deviation     2.588e-15 2.588e-15 2.588e-15
Proportion of Variance 0.000e+00 0.000e+00 0.000e+00
Cumulative Proportion  1.000e+00 1.000e+00 1.000e+00

var_explained_3D = `3D_PAG_Original_output2_PCA4`$sdev^2 / sum(`3D_PAG_Original_output2_PCA4`$sdev^2)
barplot(100*var_explained_3D, xlab = '', ylab = '% variance explained')

summary(`2D_PAG_Original_output2_PCA`)

Importance of components:
                           PC1      PC2      PC3     PC4     PC5     PC6     PC7     PC8     PC9    PC10   PC11    PC12    PC13    PC14    PC15    PC16
Standard deviation     31.3992 12.85031 12.35032 8.70017 7.37012 6.75793 6.47591 6.38635 5.57640 5.51096 5.2134 4.50857 4.29606 4.02713 3.85259 3.50995
Proportion of Variance  0.5151  0.08628  0.07969 0.03955 0.02838 0.02386 0.02191 0.02131 0.01625 0.01587 0.0142 0.01062 0.00964 0.00847 0.00775 0.00644
Cumulative Proportion   0.5151  0.60138  0.68107 0.72062 0.74900 0.77286 0.79477 0.81608 0.83233 0.84819 0.8624 0.87302 0.88266 0.89113 0.89889 0.90532
                          PC17    PC18    PC19    PC20    PC21    PC22    PC23    PC24    PC25    PC26    PC27    PC28    PC29    PC30    PC31    PC32
Standard deviation     3.43901 3.17394 3.14350 3.04224 2.91319 2.87702 2.80798 2.71491 2.57654 2.49217 2.41036 2.39006 2.23801 2.15965 2.11663 2.03740
Proportion of Variance 0.00618 0.00526 0.00516 0.00484 0.00443 0.00432 0.00412 0.00385 0.00347 0.00324 0.00304 0.00298 0.00262 0.00244 0.00234 0.00217
Cumulative Proportion  0.91150 0.91676 0.92193 0.92676 0.93120 0.93552 0.93964 0.94349 0.94696 0.95021 0.95324 0.95623 0.95884 0.96128 0.96362 0.96579
                         PC33    PC34    PC35    PC36    PC37    PC38   PC39    PC40    PC41    PC42    PC43    PC44    PC45    PC46    PC47    PC48
Standard deviation     2.0064 1.92025 1.85173 1.82552 1.76628 1.70281 1.6396 1.56201 1.48288 1.45666 1.43162 1.37913 1.34851 1.30427 1.27947 1.24312
Proportion of Variance 0.0021 0.00193 0.00179 0.00174 0.00163 0.00151 0.0014 0.00127 0.00115 0.00111 0.00107 0.00099 0.00095 0.00089 0.00086 0.00081
Cumulative Proportion  0.9679 0.96982 0.97161 0.97335 0.97498 0.97650 0.9779 0.97918 0.98032 0.98143 0.98250 0.98350 0.98445 0.98534 0.98619 0.98700
                          PC49    PC50    PC51    PC52    PC53    PC54    PC55    PC56    PC57   PC58    PC59    PC60    PC61    PC62    PC63    PC64
Standard deviation     1.20682 1.13871 1.09202 1.08727 1.06053 1.02809 1.00146 0.95743 0.92966 0.8798 0.86526 0.84728 0.83606 0.81846 0.79825 0.78372
Proportion of Variance 0.00076 0.00068 0.00062 0.00062 0.00059 0.00055 0.00052 0.00048 0.00045 0.0004 0.00039 0.00038 0.00037 0.00035 0.00033 0.00032
Cumulative Proportion  0.98776 0.98844 0.98906 0.98968 0.99027 0.99082 0.99134 0.99182 0.99227 0.9927 0.99307 0.99344 0.99381 0.99416 0.99449 0.99481
                          PC65    PC66    PC67    PC68    PC69    PC70    PC71    PC72    PC73   PC74    PC75    PC76    PC77    PC78    PC79    PC80
Standard deviation     0.76540 0.73324 0.70956 0.69792 0.68822 0.67484 0.65748 0.64724 0.62961 0.6237 0.58493 0.56889 0.55998 0.53690 0.52693 0.51915
Proportion of Variance 0.00031 0.00028 0.00026 0.00025 0.00025 0.00024 0.00023 0.00022 0.00021 0.0002 0.00018 0.00017 0.00016 0.00015 0.00015 0.00014
Cumulative Proportion  0.99512 0.99540 0.99566 0.99592 0.99616 0.99640 0.99663 0.99685 0.99705 0.9973 0.99744 0.99760 0.99777 0.99792 0.99806 0.99820
                          PC81    PC82    PC83    PC84    PC85    PC86    PC87    PC88    PC89    PC90    PC91    PC92    PC93    PC94    PC95    PC96
Standard deviation     0.49638 0.48909 0.48244 0.47718 0.46388 0.46104 0.42638 0.41543 0.40873 0.37717 0.37270 0.35784 0.34475 0.33545 0.32007 0.31214
Proportion of Variance 0.00013 0.00012 0.00012 0.00012 0.00011 0.00011 0.00009 0.00009 0.00009 0.00007 0.00007 0.00007 0.00006 0.00006 0.00005 0.00005
Cumulative Proportion  0.99833 0.99846 0.99858 0.99870 0.99881 0.99892 0.99902 0.99911 0.99920 0.99927 0.99934 0.99941 0.99947 0.99953 0.99958 0.99963
                          PC97    PC98    PC99   PC100   PC101   PC102   PC103   PC104   PC105   PC106   PC107   PC108   PC109   PC110   PC111     PC112
Standard deviation     0.29791 0.27967 0.27474 0.27118 0.24296 0.23394 0.21947 0.21312 0.20249 0.19064 0.17617 0.15936 0.13919 0.12900 0.08422 0.0007454
Proportion of Variance 0.00005 0.00004 0.00004 0.00004 0.00003 0.00003 0.00003 0.00002 0.00002 0.00002 0.00002 0.00001 0.00001 0.00001 0.00000 0.0000000
Cumulative Proportion  0.99968 0.99972 0.99976 0.99980 0.99983 0.99986 0.99988 0.99991 0.99993 0.99995 0.99996 0.99998 0.99999 1.00000 1.00000 1.0000000
                           PC113     PC114     PC115     PC116     PC117     PC118     PC119     PC120     PC121     PC122     PC123     PC124     PC125
Standard deviation     7.069e-14 9.439e-15 3.652e-15 3.319e-15 2.267e-15 2.267e-15 2.267e-15 2.267e-15 2.267e-15 2.267e-15 2.267e-15 2.267e-15 2.267e-15
Proportion of Variance 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00
Cumulative Proportion  1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00
                           PC126     PC127     PC128     PC129     PC130     PC131
Standard deviation     2.267e-15 2.267e-15 2.267e-15 2.267e-15 2.267e-15 1.768e-15
Proportion of Variance 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00 0.000e+00
Cumulative Proportion  1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00

var_explained_2D = `2D_PAG_Original_output2_PCA`$sdev^2 / sum(`2D_PAG_Original_output2_PCA`$sdev^2)
barplot(100*var_explained_2D, xlab = '', ylab = '% variance explained')

For 3D descriptors - cummulative explained variance of 58.7% for PC1 and PC2, and 65.9% for PC1,2 & 3

For 2D descriptors - cummulative explained variance of 60.1% for PC1 and PC2, and 68.1% for PC1,2 & 3

Can we plot the 3D version, showing PC1, 2 & 3 together? scatterplot3d is a package that would do this - does ggplot2 do 3D plots?

Model against the Log(1/EC50)

Use PC1,2 & 3 in a model for Log(1/EC50) Use PC2Diii and PC3Diii as these contain the Log(1/ec50) values along with the PCs generated in the PCA.

#2D model
fit_2D_PCA <- lm(formula = Log.1.EC50. ~  PC1 + PC2 + PC3, data=PC2Diii) #fits the model
summary(fit_2D_PCA) # summary statistics

Call:
lm(formula = Log.1.EC50. ~ PC1 + PC2 + PC3, data = PC2Diii)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.9409 -0.5209 -0.0368  0.4921  2.7478 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.536152   0.092869   5.773 1.02e-07 ***
PC1          0.011330   0.003131   3.618 0.000482 ***
PC2         -0.005532   0.006986  -0.792 0.430493    
PC3          0.010618   0.007472   1.421 0.158623    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9069 on 93 degrees of freedom
  (34 observations deleted due to missingness)
Multiple R-squared:  0.1498,    Adjusted R-squared:  0.1224 
F-statistic: 5.463 on 3 and 93 DF,  p-value: 0.001674

This doesn’t produce a good model. R2 of only 0.1498 and R2adj of 0.1224, additionally only the PC1 variable appears to be statistically significant.

Plot a predicted against actual

Log1EC50_noNA<- na.omit(PC2Diii$Log.1.EC50.)
plot(Log1EC50_noNA, fitted(fit_2D_PCA))
abline(lm(formula = Log.1.EC50. ~  PC1 + PC2 + PC3, data=PC2Diii))

only using the first two of 4 regression coefficients

#2D model
fit_3D_PCA <- lm(formula = Log.1.EC50. ~  PC1 + PC2 + PC3, data=PC3Diii) #fits the model
summary(fit_3D_PCA) # summary statistics

Call:
lm(formula = Log.1.EC50. ~ PC1 + PC2 + PC3, data = PC3Diii)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.92300 -0.54886 -0.07387  0.51816  2.75523 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  0.540878   0.092366   5.856  7.1e-08 ***
PC1          0.008644   0.002601   3.324  0.00127 ** 
PC2         -0.008609   0.004795  -1.795  0.07587 .  
PC3          0.010095   0.006373   1.584  0.11656    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.9027 on 93 degrees of freedom
  (34 observations deleted due to missingness)
Multiple R-squared:  0.1578,    Adjusted R-squared:  0.1307 
F-statistic:  5.81 on 3 and 93 DF,  p-value: 0.001103

This also doesn’t produce a good model. R2 of only 0.1578 and R2adj of 0.1307, additionally only the PC1 variable appears to be statistically significant.

Plot a predicted against actual

#Log1EC50_noNA<- na.omit(PC3Diii$Log.1.EC50.)
plot(Log1EC50_noNA, fitted(fit_3D_PCA))
abline(lm(formula = Log.1.EC50. ~  PC1 + PC2 + PC3, data=PC3Diii))

only using the first two of 4 regression coefficients