Dirichlet mixture priors

III. APPLICATIONS IN MOLECULAR BIOLOGY A. Dirichlet Mixture Priors for Sequence Profiles... 

M Brown, R Hughey, A Krogh, IS Mian, K Sjolander, D Haussler. Using Dirichlet mixture priors to derive hidden Markov models for protein families. Intelligent Systems in Molecular Biology 1 47-55, 1993. 

A prior distribution for sequence profiles can be derived from mixtures of Dirichlet distributions [16,51-54]. The idea is simple Each position in a multiple alignment represents one of a limited number of possible distributions that reflect the important physical forces that determine protein structure and function. In certain core positions, we expect to get a distribution restricted to Val, He, Met, and Leu. Other core positions may include these amino acids plus the large hydrophobic aromatic amino acids Phe and Trp. There will also be positions that are completely conserved, including catalytic residues (often Lys, GIu, Asp, Arg, Ser, and other polar amino acids) and Gly and Pro residues that are important in achieving certain backbone conformations in coil regions. Cys residues that form disulfide bonds or coordinate metal ions are also usually well conserved. 

CX.0 = Z(=iCx.r represents the total number of counts that the prior distribution represents, and the a, the counts for each type of amino acid (not necessarily integers). Because different distributions will occur in multiple sequence alignments, the prior distribution for any position should be represented as a mixture of N Dirichlet distributions ... 

Sjdlander et al. [16] describe the process assumed in their model of sequence alignments, which is how the counts for a particular position in a multiple sequence alignment would arise from the mixture Dirichlet prior ... 

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