amino acids substitution probability I'm looking for the probabilities of amino acid substitutions in protein sequences.
A matrix of probabilities for every combination of amino acids (something like BLOSUM or PAM matrices but more universal and with raw probability values, not scores) is sought but alternatively, any method to ascertain this will be appreciated.
[EXTRA] If all diagonal values in such a matrix would be equal to 1, or you know any way to achieve that I'd be blessed.
The LG model is here:
0.425093 
0.276818 0.751878 
0.395144 0.123954 5.076149 
2.489084 0.534551 0.528768 0.062556 
0.969894 2.807908 1.695752 0.523386 0.084808 
1.038545 0.363970 0.541712 5.243870 0.003499 4.128591 
2.066040 0.390192 1.437645 0.844926 0.569265 0.267959 0.348847 
0.358858 2.426601 4.509238 0.927114 0.640543 4.813505 0.423881 0.311484 
0.149830 0.126991 0.191503 0.010690 0.320627 0.072854 0.044265 0.008705 0.108882 
0.395337 0.301848 0.068427 0.015076 0.594007 0.582457 0.069673 0.044261 0.366317 4.145067 
0.536518 6.326067 2.145078 0.282959 0.013266 3.234294 1.807177 0.296636 0.697264 0.159069 0.137500 
1.124035 0.484133 0.371004 0.025548 0.893680 1.672569 0.173735 0.139538 0.442472 4.273607 6.312358 0.656604 
0.253701 0.052722 0.089525 0.017416 1.105251 0.035855 0.018811 0.089586 0.682139 1.112727 2.592692 0.023918 1.798853 
1.177651 0.332533 0.161787 0.394456 0.075382 0.624294 0.419409 0.196961 0.508851 0.078281 0.249060 0.390322 0.099849 0.094464 
4.727182 0.858151 4.008358 1.240275 2.784478 1.223828 0.611973 1.739990 0.990012 0.064105 0.182287 0.748683 0.346960 0.361819 1.338132 
2.139501 0.578987 2.000679 0.425860 1.143480 1.080136 0.604545 0.129836 0.584262 1.033739 0.302936 1.136863 2.020366 0.165001 0.571468 6.472279 
0.180717 0.593607 0.045376 0.029890 0.670128 0.236199 0.077852 0.268491 0.597054 0.111660 0.619632 0.049906 0.696175 2.457121 0.095131 0.248862 0.140825 
0.218959 0.314440 0.612025 0.135107 1.165532 0.257336 0.120037 0.054679 5.306834 0.232523 0.299648 0.131932 0.481306 7.803902 0.089613 0.400547 0.245841 3.151815 
2.547870 0.170887 0.083688 0.037967 1.959291 0.210332 0.245034 0.076701 0.119013 10.649107 1.702745 0.185202 1.898718 0.654683 0.296501 0.098369 2.188158 0.189510 0.249313 

Where the amino acid frequencies are:
0.079066 0.055941 0.041977 0.053052 0.012937 0.040767 0.071586 0.057337 0.022355 0.062157 0.099081 0.064600 0.022951 0.042302 0.044040 0.061197 0.053287 0.012066 0.034155 0.069147
Amino acid order (matrix and frequencies)
A R N D C Q E G H I L K M F P S T W Y V
Reference
Le S.Q., Gascuel O. Molecular Biology and Evolution. 2008 25(7):1307-20.