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In this blog post I offer a cash prize for computing a p-value [update June 9th: the winner has been announced!]. For details about the competition you can skip directly to the challenge. But context is important:

Background

I’ve recently been reading a bioRxiv posting by X. Lan and J. Pritchard, Long-term survival of duplicate genes despite absence of subfunctionalized expression (2015) that examines the question of whether gene expression data (from human and mouse tissues) supports a model of duplicate preservation by subfunctionalization.

The term subfunctionalization is a hypothesis for explaining the ubiquity of persistence of gene duplicates in extant genomes. The idea is that gene pairs arising from a duplication event evolve, via neutral mutation, different functions that are distinct from their common ancestral gene, yet together recapitulate the original function. It was introduced in 1999 an alternative to the older hypothesis of neofunctionalization, which posits that novel gene functions arise by virtue of “retention” of one copy of a gene after duplication, while the other copy morphs into a new gene with a new function. Neofunctionalization was first floated as an idea to explain gene duplicates in the context of evolutionary theory by Haldane and Fisher in the 1930s, and was popularized by Ohno in his book Evolution by Gene Duplication published in 1970. The cartoon below helps to understand the difference between the *functionalization hypotheses (adapted from wikipedia):

Lan and Pritchard examine the credibility of the sub- and neofunctionalization hypotheses using modern high-throughput gene expression (RNA-Seq) data: in their own words “Based on theoretical models and previous literature, we expected that–aside from the youngest duplicates–most duplicate pairs would be functionally distinct, and that the primary mechanism for this would be through divergent expression profiles. In particular, the sub- and neofunctionalization models suggest that, for each duplicate gene, there should be at least one tissue where that gene is more highly expressed than its partner.”

What they found was that, in their words, that “surprisingly few duplicate pairs show any evidence of sub-/neofunctionalization of expression.” The went further, stating that “the prevailing model for the evolution of gene duplicates holds that, to survive, duplicates must achieve non-redundant functions, and that this usually occurs by partitioning the expression space. However, we report here that sub-/neofunctionalization of expression occurs extremely slowly, and generally does not happen until the duplicates are separated by genomic rearrangements. Thus, in most cases long-term survival must rely on other factors.” They propose instead that “following duplication the expression levels of a gene pair evolve so that their combined expression matches the optimal level. Subsequently, the relative expression levels of the two genes evolve as a random walk, but do so slowly (33) due to constraint on their combined expression. If expression happens to become asymmetric, this reduces functional constraint on the minor gene. Subsequent accumulation of missense mutations in the minor gene may provide weak selective pressure to eventually eliminate expression of this gene, or may free the minor gene to evolve new functions.”

The Lan and Pritchard paper is the latest in a series of works that examine high-browed evolutionary theories with hard data, and that are finding reality to be far more complicated than the intuitively appealing, yet clearly inadequate, hypotheses of neo- and subfunctionalization. One of the excellent papers in the area is

Dean et al. Pervasive and Persistent Redundancy among Duplicated Genes in Yeast, PLoS Genetics, 2008.

where the authors argue that in yeast “duplicate genes do not often evolve to behave like singleton genes even after very long periods of time.” I mention this paper, from the Petrov lab, because its results are fundamentally at odds with what is arguably the first paper to provide genome-wide evidence for neofunctionalization (also in yeast):

M. Kellis, B.W. Birren and E.S. Lander, Proof and evolutionary analysis of ancient genome duplication in the yeast Saccharomyces cerevisae, Nature 2004.

At the time, the Kellis-Birren-Lander paper was hailed as containing “work that may lead to better understanding of genetic diseases” and in the press release Kellis stated that “understanding the dynamics of genome duplication has implications in understanding disease. In certain types of cancer, for instance, cells have twice as many chromosomes as they should, and there are many other diseases linked to gene dosage and misregulation.” He added that “these processes are not much different from what happened in yeast.” and the author of the press releases added that “whole genome duplication may have allowed other organisms besides yeast to achieve evolutionary innovations in one giant leap instead of baby steps. It may account for up to 80 percent (seen this number before?) of flowering plant species and could explain why fish are the most diverse of all vertebrates.”

This all brings me to:

The challenge

In the abstract of their paper, Kellis, Birren and Lander wrote that:

Strikingly, 95% of cases of accelerated evolution involve only one member of a gene pair, providing strong support for a specific model of evolution, and allowing us to distinguish ancestral and derived functions.” [boldface by authors]
In the main text of the paper, the authors expanded on this claim, writing:

Strikingly, in nearly every case (95%), accelerated evolution was confined to only one of the two paralogues. This strongly supports the model in which one of the paralogues retained an ancestral function while the other, relieved of this selective constraint, was free to evolve more rapidly”.

The word “strikingly” suggests a result that is surprising in its statistical significance with respect to some null model the authors have in mind. The data is as follows:

The authors identified 457 duplicated gene pairs that arose by whole genome duplication (for a total of 914 genes) in yeast. Of the 457 pairs 76 showed accelerated (protein) evolution in S. cerevisiae. The term “accelerated” was defined to relate to amino acid substitution rates in S. cerevisiae, which were required to be 50% faster than those in another yeast species, K. waltii. Of the 76 genes, only four pairs were accelerated in both paralogs. Therefore 72 gene pairs showed acceleration in only one paralog (72/76 = 95%).

So, is it indeed “striking” that “in nearly every case (95%), accelerated evolution was confined to only one of the two praralogues”? Well, the authors don’t provide a pvalue in their paper, nor do they propose a null model with respect to which the question makes sense. So I am offering a prize to help crowdsource what should have been an exercise undertaken by the authors, or if not a requirement demanded by the referees. To incentivize people in the right direction,

I will award ${\bf \frac{\100}{p}}$

to the person who can best justify a reasonable null model, together with a p-value (p) for the phrase “Strikingly, 95% of cases of accelerated evolution involve only one member of a gene pair” in the abstract of the Kellis-Birren-Lander paper. Notice the smaller the (justifiable) p-value someone can come up with, the larger the prize will be.

Bonus: explain in your own words how you think the paper was accepted to Nature without the authors having to justify their use of the word “strikingly” for a main result of the paper, and in a timeframe consisting of submission on December 17th 2003 (just three days before Hanukkah and one week before Christmas) and acceptance January 19th 2004 (Martin Luther King Jr. day).

Rules

To be eligible for the prize entries must be submitted as comments on this blog post by 11:59pm EST on Sunday May 31st June 7th, 2015 and they must be submitted with a valid e-mail address. I will keep the name (and e-mail address) of the winner anonymous if they wish (this can be ensured by using a pseudonym when submitting the entry as a comment). The prize, if awarded, will go to the person submitting the most complete, best explained solution that has a pvalue calculation that is correct according to the model proposed. Preference will be given to submission from students, especially undergraduates, but individuals in any stage of their career, and from anywhere in the world, are encouraged to submit solutions. I reserve the right to interpret the phrase “reasonable null model” in a way that is consistent with its use in the scientific community and I reserve the right to not award the prize if no good/correct solutions are offered. Participants do not have to answer the bonus question to win.

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