PAM matrix calculation

Question

[cedrichermansakaspomlol]

Hi everyone,

I've been working on a personal project in PHP, namely an alignment algoritm using Needlemann-Wunsh. I've added some fixed PAM and BLOSSUM matrices however I wanted to add the option to use a variable PAM matrix. For instance PAM65 would be (PAM1)^65. After implementing everything in PHP and running it, I get the correct PAM250 matrix when compared to the official PAM250 matrix of NCBI (some rounding errors probably). However when testing the PAM30 and comparing that one I get totally different results.

My matrix multiplication code looks like this:

function matrixmult($m1,$m2){
      $r=count($m1);
      $c=count($m2[0]);
      $p=count($m2);
      if(count($m1[0])!=$p){throw new Exception('Incompatible matrixes');}
      $m3=array();
      for ($i=0;$i< $r;$i++){
          for($j=0;$j<$c;$j++){
              $m3[$i][$j]=0;
              for($k=0;$k<$p;$k++){
                  $m3[$i][$j]+=$m1[$i][$k]*$m2[$k][$j];
              }
          }
      }

      for ($i = 0; $i < $r; $i++) {
         $sum=0;
         for ($j = 0; $j < $c; $j++) {
            $sum+=$m3[$j][$i];
         }
         $sum-=$m3[$i][$i];
         echo $sum;
         $m3[$i][$i]=1-$sum;
      }
      return($m3);
  }

This would then be run N-1 times with m1 being PAM(i) and m2 being PAM1.

The second part of the function makes sure that the sum of each column = 1

Next I would calculate the Log-odds scoring matrix as following:

foreach ($PAMN2 as $key => $line) {
        foreach ($line as $key2 => $word) {
           $scomat[$key][$key2]=round(10*log(($word/($rm[$key])),10));
        }
  }

With the keys being amino acid 1 letter codes and rm being the relative frequencies of the amino acids.

I did not really understand how the log odds are symmetric so I just copied the lower half of the scoring matrix to the upper half:

$allkeys = array_keys($scomat);
  for ($i = 0; $i < 20; $i++) {
     for ($j = 0; $j < $i; $j++) {
        $scomat[$allkeys[$j]][$allkeys[$i]]=$scomat[$allkeys[$i]][$allkeys[$j]];
     }
  }

I wondered if anyone knows why the scoring matrix is wrong? The PAM1 that I use is the standard one as well as the amino acid frequencies.

Best regards

Cedric