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## Point Accepted Mutations

The definition of matrix M describes mutation over a given period of evolution. In order to procede, we must quantify this change in a mathematically meaningful way. Dayhoff et. al. introduced the term PAM (point accepted mutation) unit. A 1-PAM unit is the amount of evolution which will change, on average, of the amino acids. In mathematical terms, this is expressed as a matrix M such that where fi is the frequency of the ith amino acid. (Recall that Mii represents the probability amino acid i does not change.)

If we have a probability or frequency vector p, the product gives the probability vector (or the expected frequency of p) after an evolution equivalent to 1-PAM unit.

Alternatively, if we start with amino acid i (a probability vector which contains a 1 in position i and 0s in all others), (the ith column of M) is the corresponding probability vector after one unit of random evolution.

After k units of evolution (a k-PAM evolution), a frequency vector p will be changed into the frequency vector .

Note that PAM distance does not correlate in any immediate way to chronological time. Evolutionary rates may be very different between species and proteins.    Next: Dayhoff Matrices Up: Modeling Evolution Previous: Modeling Evolution
Gaston Gonnet
1998-09-15