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1.  Rate and breadth of protein evolution are only weakly correlated 
Biology Direct  2012;7:8.
Background
Evolution at a protein site can be characterized from two different perspectives, by its rate and by the breadth of the set of acceptable amino acids.
Results
There is a weak positive correlation between rates and breadths of evolution, both across individual amino acid sites and across proteins.
Conclusions
Rate and breadth are two distinct, and only weakly correlated, characteristics of protein evolution. The most likely explanation of their positive correlation is heterogeneity of selective constraint, such that less functionally important sites evolve faster and can accept more amino acids.
Reviewers
This article was reviewed by Eugene V. Koonin, Arcady R. Mushegyan, and Eugene I. Shakhnovich.
doi:10.1186/1745-6150-7-8
PMCID: PMC3331848  PMID: 22336199
2.  On the relationship between the load and the variance of relative fitness 
Biology Direct  2011;6:20.
Background
Operation of natural selection can be characterized by a variety of quantities. Among them, variance of relative fitness V and load L are the most fundamental.
Results
Among all modes of selection that produce a particular value V of the variance of relative fitness, the minimal value Lmin of load L is produced by a mode under which fitness takes only two values, 0 and some positive value, and is equal to V/(1+V).
Conclusions
Although it is impossible to deduce the load from knowledge of the variance of relative fitness alone, it is possible to determine the minimal load consistent with a particular variance of relative fitness. The concept of minimal load consistent with a particular biological phenomenon may be applicable to studying several aspects of natural selection.
Reviewers
The manuscript was reviewed by Sergei Maslov, Alexander Gordon, and Eugene Koonin.
doi:10.1186/1745-6150-6-20
PMCID: PMC3094333  PMID: 21492441
3.  Rate of sequence divergence under constant selection 
Biology Direct  2010;5:5.
Background
Divergence of two independently evolving sequences that originated from a common ancestor can be described by two parameters, the asymptotic level of divergence E and the rate r at which this level of divergence is approached. Constant negative selection impedes allele replacements and, therefore, is routinely assumed to decelerate sequence divergence. However, its impact on E and on r has not been formally investigated.
Results
Strong selection that favors only one allele can make E arbitrarily small and r arbitrarily large. In contrast, in the case of 4 possible alleles and equal mutation rates, the lowest value of r, attained when two alleles confer equal fitnesses and the other two are strongly deleterious, is only two times lower than its value under selective neutrality.
Conclusions
Constant selection can strongly constrain the level of sequence divergence, but cannot reduce substantially the rate at which this level is approached. In particular, under any constant selection the divergence of sequences that accumulated one substitution per neutral site since their origin from the common ancestor must already constitute at least one half of the asymptotic divergence at sites under such selection.
Reviewers
This article was reviewed by Drs. Nicolas Galtier, Sergei Maslov, and Nick Grishin.
doi:10.1186/1745-6150-5-5
PMCID: PMC2835663  PMID: 20092641
4.  Extensive parallelism in protein evolution 
Biology Direct  2007;2:20.
Background
Independently evolving lineages mostly accumulate different changes, which leads to their gradual divergence. However, parallel accumulation of identical changes is also common, especially in traits with only a small number of possible states.
Results
We characterize parallelism in evolution of coding sequences in three four-species sets of genomes of mammals, Drosophila, and yeasts. Each such set contains two independent evolutionary paths, which we call paths I and II. An amino acid replacement which occurred along path I also occurs along path II with the probability 50–80% of that expected under selective neutrality. Thus, the per site rate of parallel evolution of proteins is several times higher than their average rate of evolution, but still lower than the rate of evolution of neutral sequences. This deficit may be caused by changes in the fitness landscape, leading to a replacement being possible along path I but not along path II. However, constant, weak selection assumed by the nearly neutral model of evolution appears to be a more likely explanation. Then, the average coefficient of selection associated with an amino acid replacement, in the units of the effective population size, must exceed ~0.4, and the fraction of effectively neutral replacements must be below ~30%. At a majority of evolvable amino acid sites, only a relatively small number of different amino acids is permitted.
Conclusion
High, but below-neutral, rates of parallel amino acid replacements suggest that a majority of amino acid replacements that occur in evolution are subject to weak, but non-trivial, selection, as predicted by Ohta's nearly-neutral theory.
Reviewers
This article was reviewed by John McDonald (nominated by Laura Landweber), Sarah Teichmann and Subhajyoti De, and Chris Adami.
doi:10.1186/1745-6150-2-20
PMCID: PMC2020468  PMID: 17705846

Results 1-4 (4)