Substitution Matrix - Background

Background

In the process of evolution, from one generation to the next the amino acid sequences of an organism's proteins are gradually altered through the action of DNA mutations. For example, the sequence

could mutate into the sequence

in one step, and possibly

over a longer period of evolutionary time. Each amino acid is more or less likely to mutate into various other amino acids. For instance, a hydrophilic residue such as arginine is more likely to be replaced another hydrophilic residue such as glutamine, than it is to be mutated into a hydrophobic residue such as leucine. This is primarily due to redundancy in the genetic code, which translates similar codons into similar amino acids. Furthermore, mutating an amino acid to a residue with significantly different properties could affect the folding and/or activity of the protein. There is therefore usually strong selective pressure to remove such mutations quickly from a population.

If we have two amino acid sequences in front of us, we should be able to say something about how likely they are to be derived from a common ancestor, or homologous. If we can line up the two sequences using a sequence alignment algorithm such that the mutations required to transform a hypothetical ancestor sequence into both of the current sequences would be evolutionarily plausible, then we'd like to assign a high score to the comparison of the sequences.

To this end, we will construct a 20x20 matrix where the th entry is equal to the probability of the th amino acid being transformed into the th amino acid in a certain amount of evolutionary time. There are many different ways to construct such a matrix, called a substitution matrix. Here are the most commonly used ones: