A Model of Evolutionary Change in Proteins

Contents 1 Accepted point mutations 2 Data used 3 Characteristics of accepted point mutations 4 Mutation probability matrix 5 Simulating the mutational process 6 Relatedness Odds Matrix 7 Computing relationships 8 PDF Available

[edit] 1 Accepted point mutations

• Accepted point mutation: exchange of one amino acid for another that is accepted by natural selection

• What is the frequency of change between one amino acid and another? 20x20 = 400 possible substitutions

• Used mutation data from phylogenetic trees and a few pairs of related sequences

• Will assume that the likelihood of X replacing Y is the same as Y replacing X, making things symmetric; thus the frequency of amino acid occurrence in any large group of proteins will stay relatively constant with time

• The difference in comparing observed sequences with inferred ancestral sequences apparent in cases where A changes to D and A changes to C, but C does not directly change to D. Comparing the observed sequences would, however, infer the change of C to D.

[edit] 2 Data used

• Number of mutations in data set: 1814.

• Very distantly related sequences omitted, assuming that the changes on their branches would be produced by successive acceptive mutations

[edit] 3 Characteristics of accepted point mutations

• The matrices of accepted point mutations show a definite pattern, meaning that the amino acids have mutational properties that do not depend on the protein they are found in. Many single nucleotide changes are seldom observed even though they would be expected if random chance was the driving factor.

• Relative mutability of an amino acid: the probability that an amino acid will change in a given interval of time. Computed by counting the number of times each amino acid has changed in a time interval and how many times it has occured in the sequences and thus been subject to mutation. Relative mutability of the amino acid is proportional to the ratio of changes to occurrences.

• In most families:
  • S, I, M, N more mutable than A
  • D, E, Q, T, V somewhat more mutable than A in some families and less in others
  • All other amino acids usu. much less mutable than A

• Substitution of a larger amino acid with a distinctive shape/chemistry for any other uncommon

[edit] 4 Mutation probability matrix

• Mutation probability matrix: an element Failed to parse (Cannot write to or create math temp directory): M_{ij}

gives the probability that the amino acid in column Failed to parse (Cannot write to or create math temp directory): j
will be replaced by the amino acid in row i after a given evolutionary interval

• Nondiagonal elements have the values:

Failed to parse (Cannot write to or create math temp directory): M_{ij} = \frac{\lambda m_j A_{ij}}{\sum_i A_{ij}}

where Failed to parse (Cannot write to or create math temp directory): A_{ij}

is an element of the accepted point mutation matrix (ie, mutation counts), Failed to parse (Cannot write to or create math temp directory): m_j
is the mutability of the jth amino acid and Failed to parse (Cannot write to or create math temp directory): \lambda
is a proportionality constant.

• Diagonal elements have the values:

Failed to parse (Cannot write to or create math temp directory): M_{jj} = 1 - \lambda m_j

• A column's elements will sum to 1 as probabilities; the probability of observing a change in a site of that column's amino acid is proportional to the mutability of that amino acid.

[edit] 5 Simulating the mutational process

• Amino acids would be changes based on a random number uniformly distributed between 0 and 1, where certain percent brackets determine which amino acid is used as a substitution

• A period of evolution can be simulated by successive applications of matrix to the sequences resulting from the last application, or multiplying the matrix by itself repeatedly and then applying it to the sequence.

• At a great distance of simulated evolution (2000 PAMs), there is no information left in the amino acid mutational alternatives.

[edit] 6 Relatedness Odds Matrix

• How often do we expect a mutation from i to Failed to parse (Cannot write to or create math temp directory): j

to happen compared to random chance?

• Failed to parse (Cannot write to or create math temp directory): R_{ij} = M_{ij} / f_i

• Symmetrical -- Failed to parse (Cannot write to or create math temp directory): R_{ij} = R_{ji}

[edit] 7 Computing relationships

• Odds matrix can be used as a scoring matrix for detecting distant relationships, by discriminating between significant relationships and random chance

[edit] 8 PDF Available

• Dayhoff et al 1978