Proportional matrix

This document shows the proportional matrix. For all 57 amino acids and secondary structures combinations, we further analysis the overlaping of each combination against the rest of 56, and we structured a \(57\times57\) matrix to representation the proportion.

Raw matrix

ProportionalMatrix <- data.frame()
for (i in 1:57) {
        aa = AA_SS_label[i,1]
        ss = AA_SS_label[i,2]
        cs <- pop.table %>% filter(Residue==aa & SS == ss)
        cacb <- data.frame(CA = subset(cs, Carbon == "CA")["Value"], 
                           CB = subset(cs, Carbon == "CB")["Value"])
        colnames(cacb) <- c("CA", "CB")
        sample500 = sample_n(na.omit(cacb), 500, replace = T)
        rowProbs = c()
        for (s in c("B", "C", "H")) {
                probilities <- apply(sample500, 1, function(CaCbCS.v){AaProb.f(ChiStr.f(CaCbCS.v, secondaryStructure = s, invCovMatList.l.D))} )
                rowProbs_ss <- apply(probilities, 1, mean)
                rowProbs_ss[3] <- rowProbs_ss[2]+rowProbs_ss[3]
                rowProbs_ss <- rowProbs_ss[-2]
                rowProbs = c(rowProbs, rowProbs_ss)
        }
                
        ProportionalMatrix <- rbind(ProportionalMatrix, rowProbs)
}

Normalize by row then by column

• Normalyze by row

Verify results

[1] 0.6615166155492859

• Normalize by column

verify Results

[1] 0.6121114647280311
[1] 0.6121114647280311

Final matrix Bill

Save the proportional matrix

Moseley Matrix

[1] 0.5228722366992041
[1] 0.5228722366992041

Final matrix Moseley

Save the proportional matrix

Results

Normalize row and column:

     var.names                       vrange            
[1,] "glyCombNoPriorProMatrixBill"   "5.83673469387755"
[2,] "glyCombWithPriorProMatrixBill" "3.6734693877551" 
[3,] "glyRmNoPriorProMatrixBill"     "5.6734693877551" 
[4,] "glyRmWithPriorProMatrixBill"   "3.6734693877551" 

Normalize only the column

     var.names                          vrange            
[1,] "glyCombNoPriorProMatrixMoseley"   "4.40816326530612"
[2,] "glyCombWithPriorProMatrixMoseley" "1.30612244897959"
[3,] "glyRmNoPriorProMatrixMoseley"     "3.55102040816327"
[4,] "glyRmWithPriorProMatrixMoseley"   "1.30612244897959"