`R`

is a handy tool for modeling, so there must be some packages for Quantitative structure–activity relationship(QSPR) in Chemistry. Recently I wanted to summarize some papers for a presentation, then I found rcdk package, which is a useful tool for QSPR. However, little posts about this topic for beginner. As an absolutely beginner, I make this post as a note for the whole process and add comments for someone else to reproduce a QSPR model by their own.

First,you need the following knowledge:

Chemistry Development Kit(CDK) is powerful, we will use their function to read in the molecular and calculate some descriptor via

`rcdk`

package and no need to install CDK and their function has been included in the packageJust

`install.packages(c('rJava','rcdk'))`

is enough for a R userCopy the smiles files or the sdf files to your work directory or just use a demo data

`bpdata`

Then we begin

```
library(rcdk)
data(bpdata)
```

The first column is the SMILES vector of the molecular structures so we use parse.smiles to read it

`mols <- parse.smiles(bpdata[, 1])`

So rcdk will convert the smiles into a java object this object could be used to get the milecular descriptor. Also you need to know the class of mols is a list. rcdk has five ctegories of descriptor we think the topological descriptor may relate to the Boiling Point in this tests.

`desc.names <- get.desc.names("topological")`

Then we get the names of those topological descriptors.Up to now, we know the structures and the descriptors’ name. Then we will get the descriptors.

For the list we need to use lapply or sapply to apply the descriptors caculator function with the descriptors’ name in the desc.names.

`data <- lapply(mols, eval.desc, desc.names)`

This is also a list so we need to unlist and make a dataframe for QSPR model. Also we need to give the column a name.

```
df <- data.frame(matrix(unlist(data), nrow = 277, byrow = T))
colnames(df) <- colnames(data[[1]])
```

We need to remove some desciptors unchanged

`df2 <- df[, which(!apply(df, 2, sd) == 0)]`

OK, here we get a data frame contained the descriptors we needed. Then we will use those \(X\) to make a \(f(X) = Y\), which is a QSPR model.

Define the response

`Y <- bpdata[, 2]`

Get a train set and a test set

```
train <- sample(1:277, 200)
traindataX <- df2[train, ]
traindataY <- Y[train]
testdataX <- df2[-train, ]
testdataY <- Y[-train]
```

Build a regression model with the leaps packages

`library("leaps")`

Define a function to predict the test data

```
predict.regsubsets = function(object, newdata, id, ...) {
form = as.formula(~.)
mat = model.matrix(form, newdata)
coefi = coef(object, id)
xvars = names(coefi)
mat[, xvars] %*% coefi}
```

A 5-fold cross-validation

```
k = 5
folds = sample(1:k, nrow(traindataX), replace = TRUE)
cv.errors = matrix(NA, k, 50, dimnames = list(NULL, paste(1:50)))
for (j in 1:k) {
best.fit = regsubsets(y = traindataY[folds != j],
x = traindataX[folds != j, ],
nvmax = 50,
really.big = T,
method = "forward")
for (i in 1:50) {pred = predict.regsubsets(best.fit, traindataX[folds == j, ], id = i);
cv.errors[j, i] = mean((traindataY[folds == j] - pred)^2)
}
}
mean.cv.errors = apply(cv.errors, 2, mean)
which.min(mean.cv.errors)
#38
reg.fwd = regsubsets(x = traindataX,
y = traindataY,
nvmax = 44,
really.big = T,
method = "forward")
```

We got a model with many variables on the train dataset, and now we could see the results on the test dataset.

```
val.errors <- rep(NA, 50)
for (i in 1:50) {
pred = predict.regsubsets(reg.fwd, testdataX, id = i)
val.errors[i] = mean((testdataY - pred)^2)
}
which.min(val.errors)
#41
```

So if you want to see the names of selected variables for prediction the selected QSPR model, you may use `coef`

to get what you want. For example, we show the coef of the selected 15 variables models by the following code.

`coef(reg.fwd, 15)`

(Intercept) khs.dCH2 khs.sOH khs.dO HybRatio VP.2

310.981 -69.776 70.007 38.068 -61.738 58.648

SPC.4 SPC.6 SC.4 VC.3 ATSm5 ATSc2

-4.957 -3.223 -75.819 -42.528 1.890 35.852

ATSc4 khs.aaS khs.sI C4SP3

31.831 0.000 -8.693 10.937

From the results I find the topological descriptors might be not good for the prediction for that no clear overfit were found in train and test dataset.

OK, this is the whole process for using rcdk package for QSPR. Just modify the input, you will get what you want.