What’s in a Likelihood? Simple Models of Protein Evolution and the Contribution of Structurally Viable Reconstructions to the Likelihood
Issue Date
2011Author
Holder, Mark T.
Publisher
Oxford University Press
Type
Article
Article Version
Scholarly/refereed, publisher version
Metadata
Show full item recordAbstract
Most phylogenetic models of protein evolution assume that sites are independent and identically distributed.
Interactions between sites are ignored, and the likelihood can be conveniently calculated as the product of the individual
site likelihoods. The calculation considers all possible transition paths (also called substitution histories or mappings) that
are consistent with the observed states at the terminals, and the probability density of any particular reconstruction depends
on the substitution model. The likelihood is the integral of the probability density of each substitution history taken over
all possible histories that are consistent with the observed data. We investigated the extent to which transition paths that
are incompatible with a protein’s three-dimensional structure contribute to the likelihood. Several empirical amino acid
models were tested for sequence pairs of different degrees of divergence. When simulating substitutional histories starting
from a real sequence, the structural integrity of the simulated sequences quickly disintegrated. This result indicates that
simple models are clearly unable to capture the constraints on sequence evolution. However, when we sampled transition
paths between real sequences from the posterior probability distribution according to these same models, we found that
the sampled histories were largely consistent with the tertiary structure. This suggests that simple empirical substitution
models may be adequate for interpolating changes between observed sequences during phylogenetic inference despite
the fact that the models cannot predict the effects of structural constraints from first principles. This study is significant
because it provides a quantitative assessment of the biological realism of substitution models from the perspective of protein
structure, and it provides insight on the prospects for improving models of protein sequence evolution. [Ancestral state
reconstruction; empirical amino acid models; maximum likelihood; phylogenetics; protein structure.]
Description
This is an electronic version of an article published in Systematic Biology [Lakner C, Holder MT, Goldman N, Naylor GJP. 2011. What's in a Likelihood? Simple Models of Protein Evolution and the Contribution of Structurally Viable Reconstructions to the Likelihood Systematic Biology. 60(2):161-174.
]. Systematic Biology is available online at informaworld http://dx.doi.org/10.1093/sysbio/syq088.
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Citation
Lakner C, Holder MT, Goldman N, Naylor GJP. 2011. What's in a Likelihood? Simple Models of Protein Evolution and the Contribution of Structurally Viable Reconstructions to the Likelihood Systematic Biology. 60(2):161-174.
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