Protein Evolution with Dependence Among Codons Due to Tertiary Structure

[edit] 1 Abstract

• By allowing a general dependence structure among sites, models of evolution can reflect attributes of tertiary structure
• Amino acid replacement rates are higher when replacements lead to energetically favorable proteins than when they destabalize proteins

[edit] 2 Intro

• Rates of amino acid replacement can vary among protein positions and among the types of amino acids involved
• Rates of aa replacement at a site likely depend on aas found at other positions in the protein

[edit] 3 Modeling

• Markov model to describe the evolution of proteins under structural constraints

• Instantaneous rate matrix Failed to parse (Cannot write to or create math temp directory): R

• Entry in row i and column Failed to parse (Cannot write to or create math temp directory): j

represents rate of change frome one sequence to another

• A DNA sequence of length Failed to parse (Cannot write to or create math temp directory): N

nucleotides and ignoring stop codons gives a dimension to rate matrix Failed to parse (Cannot write to or create math temp directory): R
of Failed to parse (Cannot write to or create math temp directory): 4^N \times 4^N

• Assumption: each substitution event changes only a single nucleotide residue
• Reduces maximum number of nonzero elements in each row of Failed to parse (Cannot write to or create math temp directory): R

to Failed to parse (Cannot write to or create math temp directory): 3N + 1

, which comprise the diagonal entry representing no change and one entry for each of the three possible substitutions at each of the Failed to parse (Cannot write to or create math temp directory): N

nucleotide sites

• Assume: protein tertiary structure is known and fixed