Rearrangement Events on Circular Genomes.

Early literature on genome rearrangement modelling views the problem of computing evolutionary distances as an inherently combinatorial one. In particular, attention is given to estimating distances using the minimum number of events required to transform one genome into another. In hindsight, this approach is analogous to early methods for inferring phylogenetic trees from DNA sequences such as maximum parsimony-both are motivated by the principle that the true distance minimises evolutionary change, and both are effective if this principle is a true reflection of reality. Recent literature considers genome rearrangement under statistical models, continuing this parallel with DNA-based methods, with the goal of using model-based methods (for example maximum likelihood techniques) to compute distance estimates that incorporate the large number of rearrangement paths that can transform one genome into another. Crucially, this approach requires one to decide upon a set of feasible rearrangement events and, in this paper, we focus on characterising well-motivated models for signed, uni-chromosomal circular genomes, where the number of regions remains fixed. Since rearrangements are often mathematically described using permutations, we isolate the sets of permutations representing rearrangements that are biologically reasonable in this context, for example inversions and transpositions. We provide precise mathematical expressions for these rearrangements, and then describe them in terms of the set of cuts made in the genome when they are applied. We directly compare cuts to breakpoints, and use this concept to count the distinct rearrangement actions which apply a given number of cuts. Finally, we provide some examples of rearrangement models, and include a discussion of some questions that arise when defining plausible models.

Evaluation of the Relative Performance of the Subflattenings Method for Phylogenetic Inference.

The algebraic properties of flattenings and subflattenings provide direct methods for identifying edges in the true phylogeny-and by extension the complete tree-using pattern counts from a sequence alignment. The relatively small number of possible internal edges among a set of taxa (compared to the number of binary trees) makes these methods attractive; however, more could be done to evaluate their effectiveness for inferring phylogenetic trees. This is the case particularly for subflattenings, and the work we present here makes progress in this area. We introduce software for constructing and evaluating subflattenings for splits, utilising a number of methods to make computing subflattenings more tractable. We then present the results of simulations we have performed in order to compare the effectiveness of subflattenings to that of flattenings in terms of split score distributions, and susceptibility to possible biases. We find that subflattenings perform similarly to flattenings in terms of the distribution of split scores on the trees we examined, but may be less affected by bias arising from both split size/balance and long branch attraction. These insights are useful for developing effective algorithms to utilise these tools for the purpose of inferring phylogenetic trees.

A symmetry-inclusive algebraic approach to genome rearrangement.

Of the many modern approaches to calculating evolutionary distance via models of genome rearrangement, most are tied to a particular set of genomic modeling assumptions and to a restricted class of allowed rearrangements. The "position paradigm", in which genomes are represented as permutations signifying the position (and orientation) of each region, enables a refined model-based approach, where one can select biologically plausible rearrangements and assign to them relative probabilities/costs. Here, one must further incorporate any underlying structural symmetry of the genomes into the calculations and ensure that this symmetry is reflected in the model. In our recently-introduced framework of genome algebras, each genome corresponds to an element that simultaneously incorporates all of its inherent physical symmetries. The representation theory of these algebras then provides a natural model of evolution via rearrangement as a Markov chain. Whilst the implementation of this framework to calculate distances for genomes with "practical" numbers of regions is currently computationally infeasible, we consider it to be a significant theoretical advance: one can incorporate different genomic modeling assumptions, calculate various genomic distances, and compare the results under different rearrangement models. The aim of this paper is to demonstrate some of these features.

The structure of xylem vessels in grapevine (Vitaceae) and a possible passive mechanism for the systemic spread of bacterial disease.

Xylem-dwelling pathogens become systemic, suggesting that microorganisms move efficiently in the xylem. To better understand xylem pathways and how bacteria move within the xylem, vessel connectivity between stems and leaves of Vitis vinifera cv. Chardonnay and Muscadinia rotundifolia cv. Cowart was studied. Three methods were used: (1) the light-producing bacterium, Yersinia enterocolitica, (Ye) strain GY5232 was loaded into petioles and followed using X-ray film, (2) fluorescent beads were loaded and followed by microscopy, and (3) low-pressure air was pumped into leaves and extruded bubbles from cuts in submerged leaves were followed. Bacteria, beads, and air moved through long and branched xylem vessels from the petiole into the veins in leaves of both varieties. From the stem, bacteria and air traveled into primary and secondary veins of leaves one, two, and three nodes above the loading point of the bacteria or air. Particles and air could move unimpeded through single xylem vessels or multiple vessels (conduits) connected possibly through broken pit membranes from within the stem axis into leaf blades. Bacteria were also able to move long distances within minutes from stem to leaf passively without having to cross pit membranes. Such complex, open xylem conduits have not been well documented before; these findings will help elucidate mechanisms involved in the systemic spread of pathogens.

The Developmental Anatomy of Pierce's Disease Symptoms in Grapevines: Green Islands and Matchsticks.

Symptoms of Pierce's disease were studied in an anatomical context from infected grapevines (Vitis species) collected from field sites within Napa Valley, CA. Two symptoms, green islands and matchsticks, are reported in this study. Green islands formed as a result of incomplete initiation of the phellogen. In regions of the stem where a phellogen and subsequent periderm arose, immediately exterior tissue was cut off, causing it to brown. In regions of the stem where no periderm is formed, the exterior tissues remained green. Consequently, the stem is mottled with both green living epidermis and brown dying epidermis as determined by the presence or absence of an underlying periderm. Matchsticks formed when the leaf lamina separated from the petiole, and the petiole remained attached to the stem. Lamina broke off from the petioles consistently in a fracture zone where xylem from the petiole anastomoses into the five major veins of the leaf. No separation layer was found to explain this pseudoabscission.