# Mutations

are a big theme in this course. We wouldn't be here without them - we're all mutants. We can use the idea of mutations to make an important point: the sum of the probabilities of mutually exclusive events, if these events account for everything that can happen, is 1 - the reason being that we are 100% positive SOMETHING will happen.

Over to the right are the first 3 columns of what is called a mutation probability matrix (there should be 20 columns in all, one for each amino acid codon). For example, follow the R column down to the K row, in which position you'll find the number 0.0037. This is the probability (about 1 chance out of 270) that an R amino acid codon will be replaced by a K amino acid codon during an evolutionary interval of 1 PAM (the meaning of this is immaterial right now). What else can happen to the initial R codon? Well, it may stay the same, or after 1 PAM we may find in substitution either a K or any of the other 18 amino acid codons. That gives us 20 possible outcomes, the most likely being no change (probability 0.9913). But one of these things will happen, Nature doesn't allow for anything else. Well, in general, the total probability that something/anything will happen is 1, since it is 100% certain that something/anything will happen as long as time continues to flow (staying the same is something, too). Therefore, the sum of all the probabilities in the R column should be 1, as each represents part of the probability of everything that can happen to R. Likewise, the sum of all the numbers in the A column should be 1, as they represent the probabilities of everything that can happen to A; and likewise for the N column, etc. And that about covers it for now. ### Matrix

 A R N etc... A 0.9867 0.0002 0.0009 R 0.0001 0.9913 0.0001 N 0.0004 0.0001 0.9822 D 0.0006 0.0000 0.0042 C 0.0001 0.0001 0.0000 Q 0.0003 0.0009 0.0004 E 0.0010 0.0000 0.0007 G 0.0021 0.0001 0.0012 H 0.0001 0.0008 0.0018 I 0.0002 0.0002 0.0003 L 0.0003 0.0001 0.0003 K--> 0.0002 0.0037 0.0025 M 0.0001 0.0001 0.0000 F 0.0001 0.0001 0.0001 P 0.0013 0.0005 0.0002 S 0.0028 0.0011 0.0034 T 0.0022 0.0002 0.0013 W 0.0000 0.0002 0.0000 Y 0.0001 0.0000 0.0003 V 0.0013 0.0002 0.0001