Molecular Evolutionwith an emphasis on substitution rates

Gavin JD SmithState Key Laboratory of Emerging Infectious Diseases

& Department of MicrobiologyThe University of Hong Kong

Bioinformatic and Comparative Genome Analysis CourseHKU-Pasteur Research Centre - Hong Kong

August 17 - August 29, 2009

Why?

“Understanding the selective pressures that have shaped genetic variation is a central goal in the study of evolutionary biology” Pond et al. 2007

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Dynamics of evolution

• The diversity exhibited by a population reflects the organisms natural history

• The genetic diversity of a population is a combination of:- biological properties (e.g. mutation rates, generation time)

- evolutionary forces (e.g. molecular adaptation, genetic drift)

• Three principal mechanisms are responsible for viral genetic variation- mutation

- selection

- recombination

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Mutations

As nonsynonymous (β) mutations directly alter proteins (& potentially their function) they are more likely to affect organism fitness than synonymous (α) mutations that leave the amino acid sequence unchanged

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Mutations

• Mutations that result in amino acid changes are non-synonymous

• Mutations that do not result in amino acid changes are silent or synonymous

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Selective pressures

• Selective pressure on coding sequences can be calculated by comparison of the relative rates of α & β mutations

• The ratio ω = β/α (also referred to as dN/dS or KA/KS) is a standard measure of selective pressure

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Selective pressures

• ω ≈ 1 indicates neutral evolution, ω < 1 negative (or purifying) selection, & ω > 1 positive (or diversifying) selection

• To infer selective pressures it is necessary to be able to accurately estimate nonsynonymous & synonymous rates– this is where models come in (discussed later)

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Evolutionary rates and Selection

• Mutations have evolutionary consequences ONLY if they are successfully transmitted to the next generation

MUTATION RATE:

Number of nucleotide alterations per round of replication

SUBSTITUTION (or EVOLUTION) RATE:

Number of nucleotide alterations fixed in a population per unit of time

• The rate of evolution of a virus reflects the relative proportion of advantageous, neutral or deleterious evolutionary forces exerted on it

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Selective pressures

• Under negative selection less ‘fit’ nonsynonymous subst. accumulate more slowly than synonymous subst.

• Alternatively expressed, negative selection exerts pressure to remove deleterious subst. from a population

• Positive selection acts to fix more ‘fit’ or advantageous subst. in a population

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Evolutionary models

• Necessary for accurate rate estimation• Current models either take the nucleotide or

the codon as the unit of evolution• The structure of the genetic code determines

that realistic models of evolution should consider triplets of nucleotides (i.e. codons) to be the basic unit of evolution

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Nucleotide based models

• Nucleotide substitution models– each nucleotide position of an alignment is

treated independently

• Codon position substitution models– partitions nucleotide data so that codon positions

1, 2 & 3 may have different parameters– SRD06 model has two categories 1+2 & 3

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Codon based models

• A model of DNA sequence evolution applicable to coding regions

• Uses the codon, as opposed to the nucleotide, as the unit of evolution

• Accounts for dependencies among nucleotides within a codon

• Most commonly used are GY94 (Goldman & Yang) and MG94 (Muse & Gaut)

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Nucleotide substitution modelsas an example

Models of nucleotide evolution

Several probabilistic models of evolution have been developed to convert observed nucleotide distances into measures of actual evolutionary distances

The relative complexity of these models is a function of the extent of the biological, biochemical ad evolutionary assumptions (i.e. parameters) they incorporate

Substitutions are usually described as probabilities of mutational events, mathematically modeled by matrices of relative rates:

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Jukes-Cantor (JC)

• First proposed model

• It assumes that the four bases have equal frequencies and all substitutions are equally likely

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Kimura’s 2 parameter

• Transitions are generally more frequent than transversions

• K2P model assumes that the rate of transitions per site (α) differs from the rate of transversions per site (β)

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• If some substitutions are more common in one sequence than others, some substitutions may be more frequent than others

• F81 model allows the frequency (π) of the four nucleotides to be different

Felsenstein (1981)

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Hasegawa, Kishino and Yano

• The HKY85 model allows rates of transitions and transversions to differ and base frequencies to vary

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General Time Reversible

• The GTR/REV model allows each possible substitution to have its own probability

• Substitutions are reversible (i.e. substitutions from i to j has the same probability as a substitution from j to i)

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After Whelan et al. 2001

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Rate heterogeneity

• Different regions of RNA/DNA may have different probabilities of change, and variable rates of substitution can have considerable impact on sequence divergence

• Typically, a gamma distribution is used to describe heterogeneity in nucleotide substitution rate across sequences

• The range of rate variation among sites is dictated by the shape parameter α of the distribution

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Beware of recombination!!

• Many phylogenetic methods implicitly assume that all sites in a sequence share a common evolutionary history

• However, recombination can violate this assumption by allowing sites to move freely between different genetic backgrounds

• This may cause different sections of an alignment to lead to contradictory estimates of the tree and subsequently confuse model inferences

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Global vs. Local ω models

• Global – fits a single model to a given alignment & tree (i.e. all branches are equal)

• Local – can a unique set of substitution rates to every branch in a tree

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Acknowledgements

• HKU: Vijaykrishna Dhanasekaran & Justin Bahl for help with preparing the presentation & practical component

• Estimating selection pressures on alignments of coding sequences: Analyses using HyPhy. Edited by Sergei L. Kosakovsky Pond, Art F.Y. Poon, and Simon D.W. Frost

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