Lie Markov models with purine/pyrimidine symmetry

Continuous-time Markov chains are a standard tool in phylogenetic inference. If homogeneity is assumed, the chain is formulated by specifying time-independent rates of substitutions between states in the chain. In applications, there are usually extra constraints on the rates, depending on the situation. If a model is formulated in this way, it is possible to generalise it and allow for an inhomogeneous process, with time-dependent rates satisfying the same constraints. It is then useful to require that there exists a homogeneous average of this inhomogeneous process within the same model. This leads to the definition of "Lie Markov models", which are precisely the class of models where such an average exists. These models form Lie algebras and hence concepts from Lie group theory are central to their derivation. In this paper, we concentrate on applications to phylogenetics and nucleotide evolution, and derive the complete hierarchy of Lie Markov models that respect the grouping of nucleotides into purines and pyrimidines -- that is, models with purine/pyrimidine symmetry. We also discuss how to handle the subtleties of applying Lie group methods, most naturally defined over the complex field, to the stochastic case of a Markov process, where parameter values are restricted to be real and positive. In particular, we explore the geometric embedding of the cone of stochastic rate matrices within the ambient space of the associated complex Lie algebra. The whole list of Lie Markov models with purine/pyrimidine symmetry is available at http://www.pagines.ma1.upc.edu/~jfernandez/LMNR.pdf.Comment: 32 page

Modelling mitochondrial site polymorphisms to infer the number of segregating units and mutation rate

We present a mathematical model of mitochondrial inheritance evolving under neutral evolution to interpret the heteroplasmies observed at some sites. A comparison of the levels of heteroplasmies transmitted from mother to her offspring allows us to estimate the number Nx of inherited mitochondrial genomes (segregating units). The model demonstrates the necessity of accounting for both the multiplicity of an unknown number Nx, and the threshold θ, below which heteroplasmy cannot be detected reliably, in order to estimate the mitochondrial mutation rate μm in the maternal line of descent. Our model is applicable to pedigree studies of any eukaryotic species where site heteroplasmies are observed in regions of the mitochondria, provided neutrality can be assumed. The model is illustrated with an analysis of site heteroplasmies in the first hypervariable region of mitochondrial sequence data sampled from Adélie penguin families, providing an estimate Nx and μm. This estimate of μm was found to be consistent with earlier estimates from ancient DNA analysis

RNase MRP and the RNA processing cascade in the eukaryotic ancestor

BACKGROUND: Within eukaryotes there is a complex cascade of RNA-based macromolecules that process other RNA molecules, especially mRNA, tRNA and rRNA. An example is RNase MRP processing ribosomal RNA (rRNA) in ribosome biogenesis. One hypothesis is that this complexity was present early in eukaryotic evolution; an alternative is that an initial simpler network later gained complexity by gene duplication in lineages that led to animals, fungi and plants. Recently there has been a rapid increase in support for the complexity-early theory because the vast majority of these RNA-processing reactions are found throughout eukaryotes, and thus were likely to be present in the last common ancestor of living eukaryotes, herein called the Eukaryotic Ancestor. RESULTS: We present an overview of the RNA processing cascade in the Eukaryotic Ancestor and investigate in particular, RNase MRP which was previously thought to have evolved later in eukaryotes due to its apparent limited distribution in fungi and animals and plants. Recent publications, as well as our own genomic searches, find previously unknown RNase MRP RNAs, indicating that RNase MRP has a wide distribution in eukaryotes. Combining secondary structure and promoter region analysis of RNAs for RNase MRP, along with analysis of the target substrate (rRNA), allows us to discuss this distribution in the light of eukaryotic evolution. CONCLUSION: We conclude that RNase MRP can now be placed in the RNA-processing cascade of the Eukaryotic Ancestor, highlighting the complexity of RNA-processing in early eukaryotes. Promoter analyses of MRP-RNA suggest that regulation of the critical processes of rRNA cleavage can vary, showing that even these key cellular processes (for which we expect high conservation) show some species-specific variability. We present our consensus MRP-RNA secondary structure as a useful model for further searches

RNase MRP and the RNA processing cascade in the eukaryotic ancestor

Background Within eukaryotes there is a complex cascade of RNA-based macromolecules that process other RNA molecules, especially mRNA, tRNA and rRNA. A simple example is the RNase MRP processing of ribosomal RNA (rRNA) in ribosome biogenesis. One hypothesis is that this complexity was present early in eukaryotic evolution; an alternative is that an initial simplified network later gained complexity by gene duplication in lineages that led to animals, fungi and plants. Recently there has been a rapid increase in support for the complexity-early theory because the vast majority of these RNA-processing reactions are found throughout eukaryotes, and thus were likely to be present in the last common ancestor of living eukaryotes, named here as the Eukaryotic Ancestor. Results We present an overview of the RNA processing cascade in the Eukaryotic Ancestor and investigate in particular, RNase MRP which was previously thought to have evolved later in eukaryotes due to its apparent limited distribution in fungi and animals and plants. Recent publications, as well as our own genomic searches have uncovered previously unknown RNase MRP RNAs, indicating that RNase MRP has a wide distribution in eukaryotes. Combining secondary structure and promoter region analysis of new and previously discovered RNase MRP RNAs along with analysis of the primary substrate (rRNA), allows us to discuss this distribution in the light of eukaryotic evolution. Conclusions We conclude that RNase MRP can now be placed in the RNA-processing cascade present in the Eukaryotic Ancestor. This highlights the complexity of RNAprocessing in early eukaryotes

IQ-TREE 2: New Models and Efficient Methods for Phylogenetic Inference in the Genomic Era

IQ-TREE (http://www.iqtree.org, last accessed February 6, 2020) is a user-friendly and widely used software package for phylogenetic inference using maximum likelihood. Since the release of version 1 in 2014, we have continuously expanded IQ-TREE to integrate a plethora of new models of sequence evolution and efficient computational approaches of phylogenetic inference to deal with genomic data. Here, we describe notable features of IQ-TREE version 2 and highlight the key advantages over other software.This work was supported by the Austrian Science Fund (Grant No. I-2805-B29) to A.v.H. and by the Australian National University Futures Scheme grant to R.L

Short hydrogen bonds enhance nonaromatic protein-related fluorescence.

Fluorescence in biological systems is usually associated with the presence of aromatic groups. Here, by employing a combined experimental and computational approach, we show that specific hydrogen bond networks can significantly affect fluorescence. In particular, we reveal that the single amino acid L-glutamine, by undergoing a chemical transformation leading to the formation of a short hydrogen bond, displays optical properties that are significantly enhanced compared with L-glutamine itself. Ab initio molecular dynamics simulations highlight that these short hydrogen bonds prevent the appearance of a conical intersection between the excited and the ground states and thereby significantly decrease nonradiative transition probabilities. Our findings open the door to the design of new photoactive materials with biophotonic applications

Short hydrogen bonds enhance nonaromatic protein-related fluorescence.

Fluorescence in biological systems is usually associated with the presence of aromatic groups. Here, by employing a combined experimental and computational approach, we show that specific hydrogen bond networks can significantly affect fluorescence. In particular, we reveal that the single amino acid L-glutamine, by undergoing a chemical transformation leading to the formation of a short hydrogen bond, displays optical properties that are significantly enhanced compared with L-glutamine itself. Ab initio molecular dynamics simulations highlight that these short hydrogen bonds prevent the appearance of a conical intersection between the excited and the ground states and thereby significantly decrease nonradiative transition probabilities. Our findings open the door to the design of new photoactive materials with biophotonic applications

Is the general time-reversible model bad for molecular phylogenetics?

The general time reversible model (GTR) is presently the most popular model used in phylogentic studies. However, GTR has an undesirable mathematical property that is potentially of significant concern. It is the purpose of this article to give examples that demonstrate why this deficit may pose a problem for phylogenetic analysis and interpretation.Comment: 10 pages, 2 figure