Analysis of a mechanistic Markov model for gene duplicates evolving under subfunctionalization

A Rigorous Framework to Classify the Postduplication Fate of Paralogous Genes

Gene duplication has a central role in evolution; still, little is known on the fates of the duplicated copies, their relative frequency, and on how environmental conditions affect them. Moreover, the lack of rigorous definitions concerning the fate of duplicated genes hinders the development of a global vision of this process. In this paper, we present a new framework aiming at characterizing and formally differentiating the fate of duplicated genes. Our framework has been tested via simulations, where the evolution of populations has been simulated using aevol, an in silico experimental evolution platform. Our results show several patterns that confirm some of the conclusions from previous studies, while also exhibiting new tendencies; this may open up new avenues to better understand the role of duplications as a driver of evolution.

Models for the retention of duplicate genes and their biological underpinnings

Gene content in genomes changes through several different processes, with gene duplication being an important contributor to such changes. Gene duplication occurs over a range of scales from individual genes to whole genomes, and the dynamics of this process can be context dependent. Still, there are rules by which genes are retained or lost from genomes after duplication, and probabilistic modeling has enabled characterization of these rules, including their context-dependence. Here, we describe the biology and corresponding mathematical models that are used to understand duplicate gene retention and its contribution to the set of biochemical functions encoded in a genome.

Expectations of duplicate gene retention under the gene duplicability hypothesis

BACKGROUND

Gene duplication is an important process in evolution. What causes some genes to be retained after duplication and others to be lost is a process not well understood. The most prevalent theory is the gene duplicability hypothesis, that something about the function and number of interacting partners (number of subunits of protein complex, etc.), determines whether copies have more opportunity to be retained for long evolutionary periods. Some genes are also more susceptible to dosage balance effects following WGD events, making them more likely to be retained for longer periods of time. One would expect these processes that affect the retention of duplicate copies to affect the conditional probability ratio after consecutive whole genome duplication events. The probability that a gene will be retained after a second whole genome duplication event (WGD2), given that it was retained after the first whole genome duplication event (WGD1) versus the probability a gene will be retained after WGD2, given it was lost after WGD1 defines the probability ratio that is calculated.

RESULTS

Since duplicate gene retention is a time heterogeneous process, the time between the events (t1) and the time since the most recent event (t2) are relevant factors in calculating the expectation for observation in any genome. Here, we use a survival analysis framework to predict the probability ratio for genomes with different values of t1 and t2 under the gene duplicability hypothesis, that some genes are more susceptible to selectable functional shifts, some more susceptible to dosage compensation, and others only drifting. We also predict the probability ratio with different values of t1 and t2 under the mutational opportunity hypothesis, that probability of retention for certain genes changes in subsequent events depending upon how they were previously retained. These models are nested such that the mutational opportunity model encompasses the gene duplicability model with shifting duplicability over time. Here we present a formalization of the gene duplicability and mutational opportunity hypotheses to characterize evolutionary dynamics and explanatory power in a recently developed statistical framework.

CONCLUSIONS

This work presents expectations of the gene duplicability and mutational opportunity hypotheses over time under different sets of assumptions. This expectation will enable formal testing of processes leading to duplicate gene retention.

Dosage balance acts as a time-dependent selective barrier to subfunctionalization

BACKGROUND

Gene duplication is an important process for genome expansion, sometimes allowing for new gene functions to develop. Duplicate genes can be retained through multiple processes, either for intermediate periods of time through processes such as dosage balance, or over extended periods of time through processes such as subfunctionalization and neofunctionalization.

RESULTS

Here, we built upon an existing subfunctionalization Markov model by incorporating dosage balance to describe the interplay between subfunctionalization and dosage balance to explore selective pressures on duplicate copies. Our model incorporates dosage balance using a biophysical framework that penalizes the fitness of genetic states with stoichiometrically imbalanced proteins. These imbalanced states cause increased concentrations of exposed hydrophobic surface areas, which cause deleterious mis-interactions. We draw comparison between our Subfunctionalization + Dosage-Balance Model (Sub + Dos) and the previous Subfunctionalization-Only (Sub-Only) Model. This comparison includes how the retention probabilities change over time, dependent upon the effective population size and the selective cost associated with spurious interaction of dosage-imbalanced partners. We show comparison between Sub-Only and Sub + Dos models for both whole-genome duplication and small-scale duplication events.

CONCLUSION

These comparisons show that following whole-genome duplication, dosage balance serves as a time-dependent selective barrier to the subfunctionalization process, by causing an overall delay but ultimately leading to a larger portion of the genome retained through subfunctionalization. This higher percentage of the genome that is ultimately retained is caused by the alternative competing process, nonfunctionalization, being selectively blocked to a greater extent. In small-scale duplication, the reverse pattern is seen, where dosage balance drives faster rates of subfunctionalization, but ultimately leads to a smaller portion of the genome retained as duplicates. This faster rate of subfunctionalization is because the dosage balance of interacting gene products is negatively affected immediately after duplication and the loss of a duplicate restores the stoichiometric balance. Our findings provide support that the subfunctionalization of genes that are susceptible to dosage balance effects, such as proteins involved in complexes, is not a purely neutral process. With stronger selection against stoichiometrically imbalanced gene partners, the rates of subfunctionalization and nonfunctionalization slow; however, this ultimately leads to a greater proportion of subfunctionalized gene pairs.

WGDTree: a phylogenetic software tool to examine conditional probabilities of retention following whole genome duplication events

BACKGROUND

Multiple processes impact the probability of retention of individual genes following whole genome duplication (WGD) events. In analyzing two consecutive whole genome duplication events that occurred in the lineage leading to Atlantic salmon, a new phylogenetic statistical analysis was developed to examine the contingency of retention in one event based upon retention in a previous event. This analysis is intended to evaluate mechanisms of duplicate gene retention and to provide software to generate the test statistic for any genome with pairs of WGDs in its history.

RESULTS

Here a software package written in Python, 'WGDTree' for the analysis of duplicate gene retention following whole genome duplication events is presented. Using gene tree-species tree reconciliation to label gene duplicate nodes and differentiate between WGD and SSD duplicates, the tool calculates a statistic based upon the conditional probability of a gene duplicate being retained after a second whole genome duplication dependent upon the retention status after the first event. The package also contains methods for the simulation of gene trees with WGD events. After running simulations, the accuracy of the placement of events has been determined to be high. The conditional probability statistic has been calculated for Phalaenopsis equestris on a monocot species tree with a pair of consecutive WGD events on its lineage, showing the applicability of the method.

CONCLUSIONS

A new software tool has been created for the analysis of duplicate genes in examination of retention mechanisms. The software tool has been made available on the Python package index and the source code can be found on GitHub here: https://github.com/cnickh/wgdtree .

A Simple Evolutionary Model of Genetic Robustness After Gene Duplication

When a dispensable gene is duplicated (referred to the ancestral dispensability denoted by O⁺), genetic buffering and duplicate compensation together maintain the duplicate redundancy, whereas duplicate compensation is the only mechanism when an essential gene is duplicated (referred to the ancestral essentiality denoted by O^-). To investigate these evolutionary scenarios of genetic robustness, I formulated a simple mixture model for analyzing duplicate pairs with one of the following states: double dispensable (DD), semi-dispensable (one dispensable one essential, DE), or double essential (EE). This model was applied to the yeast duplicate pairs from a whole-genome duplication (WGD) occurred about 100 million years ago (mya), and the mouse duplicate pairs from a WGD occurred about more than 500 mya. Both case studies revealed that the proportion of essentiality for those duplicates with ancestral essentiality [P_E(O^-)] was much higher than that for those with ancestral dispensability [P_E(O⁺)]. While it was negligible in the yeast duplicate pairs, P_E(O⁺) (about 20%) was shown statistically significant in the mouse duplicate pairs. These findings, together, support the hypothesis that both sub-functionalization and neo-functionalization may play some roles after gene duplication, though the former may be much faster than the later.

A subfunctionalisation model of gene family evolution predicts balanced tree shapes

We consider a subfunctionalisation model of gene family evolution. A family of n genes that perform z functions is represented by an n×z binary matrix Y_t where a 1 in the ijth position indicates that gene i can perform function j. Y_t evolves according to a continuous time Markov chain (CTMC) that represents the processes of gene duplication, coding region loss and regulatory region loss with the restriction that each function is protected by selection, meaning that each column in the matrix must contain at least one 1. We generate gene trees based on the CTMC {Y_t,t⩾0}. We analyse the long-run behaviour of the model and specify the conditions where we expect gene trees to continue to grow and where we expect them to have a stable number of genes. We show that different choices of rate parameters for the processes of duplication and loss lead to different tree shapes as measured by two common tree-shape statistics: the β-statistic for measuring tree balance and the γ-statistic for assessing diversification rate. We use an extension of β that is estimated from sets of trees. This extension is less biased compared to using the average β value for individual trees. When the rate of gene duplication dominates the rate of gene loss, the process is unstable and the distribution of tree shapes is close to following the uniform ranked tree shape (URT) distribution. However, when the process is stable, gene trees are predicted to have positive values of β indicating balanced trees and negative values of γ indicating that diversification occurs more towards the root of the tree. The results of our analyses suggest that comparing the tree-shape statistics of empirical gene-trees to the predictions presented here will provide a test of the subfunctionalisation model.

The role of humanin in natural stress tolerance: An underexplored therapeutic avenue

BACKGROUND

The discovery of humanin (HN/MTRNR2) 20 years ago blazed a trail to identifying mitochondrial derived peptides with biological function.

SCOPE

Humanin is associated with pro-survival, cytoprotective, anti-inflammatory, and anti-oxidative properties and may play a role in reducing neurodegenerative and metabolic disease progression. Although the role of humanin in vitro and in vivo laboratory models is well characterized, the regulation of humanin in natural models that encounter lethal cytotoxic and oxidative insults, as part of their natural history, require immediate research. In this review, we discuss the conservation of humanin-homologues across champion hibernators, anoxia and freeze-tolerant vertebrates and postulate on the putative roles of humanin in non-model species.

SIGNIFICANCE

We hope characterization of humanin in animals that are naturally immune to cellular insults, that are otherwise lethal for non-tolerant species, will elucidate key biomarkers and cytoprotective pathways with therapeutic potential and help differentiate pro-survival mechanisms from cellular consequences of stress.

Detecting Selection on Segregating Gene Duplicates in a Population

Gene duplication is a fundamental process that has the potential to drive phenotypic differences between populations and species. While evolutionarily neutral changes have the potential to affect phenotypes, detecting selection acting on gene duplicates can uncover cases of adaptive diversification. Existing methods to detect selection on duplicates work mostly inter-specifically and are based upon selection on coding sequence changes, here we present a method to detect selection directly on a copy number variant segregating in a population. The method relies upon expected relationships between allele (new duplication) age and frequency in the population dependent upon the effective population size. Using both a haploid and a diploid population with a Moran Model under several population sizes, the neutral baseline for copy number variants is established. The ability of the method to reject neutrality for duplicates with known age (measured in pairwise dS value) and frequency in the population is established through mathematical analysis and through simulations. Power is particularly good in the diploid case and with larger effective population sizes, as expected. With extension of this method to larger population sizes, this is a tool to analyze selection on copy number variants in any natural or experimentally evolving population. We have made an R package available at https://github.com/peterbchi/CNVSelectR/ which implements the method introduced here.

Genome-wide identification and expression analysis of the VQ gene family in soybean (Glycine max)

Background

VQ proteins, the plant-specific transcription factors, are involved in plant development and multiple stresses; however, only few articles systematic reported the VQ genes in soybean.

Methods

In total, we identified 75 GmVQ genes, which were classified into 7 groups (I-VII). Conserved domain analysis indicated that VQ gene family members all contain the VQ domains. VQ genes from the same evolutionary branches of soybean shared similar motifs and structures. Promoter analysis revealed that cis-elements related to stress responses, phytohormone responses and controlling physical as well as reproductive growth. Based on the RNA-seq and qRT-PCR analysis, GmVQ genes were showed expressing in nine tissues, suggesting their putative function in many aspects of plant growth and development as well as response to stress in Glycine max.

Results

This study aims to understand the roles of VQ genes in various development processes and their expression patterns in responses to stimuli. Our results provide basic information in identification and classification of GmVQ genes. Further experimental analysis will allows us to know the functions of GmVQs participation in plant growth and stress responses.

Pseudogenization of the Humanin gene is common in the mitochondrial DNA of many vertebrates

In the human the peptide Humanin is produced from the small Humanin gene which is embedded as a gene-within-a-gene in the 16S ribosomal molecule of the mitochondrial DNA (mtDNA). The peptide itself appears to be significant in the prevention of cell death in many tissues and improve cognition in animal models. By using simple data mining techniques, it is possible to show that 99.4% of the human Humanin sequences in the GenBank database are unaffected by mutations. However, in other vertebrates, pseudogenization of the Humanin gene is a common feature; occurring apparently randomly in some species and not others. The persistence, or loss, of a functional Humanin gene may be an important factor in laboratory animals, especially if they are being used as animal models in studies of Alzheimer's disease (AD). The exact reason why Humanin underwent pseudogenization in some vertebrate species during their evolution remains to be determined. This study was originally planned to review the available information about Humanin and it was a surprise to be able to show that pseudogenization has occurred in a gene in the mtDNA and is not restricted solely to chromosomal genes.