Tree-based unrooted nonbinary phylogenetic networks

Genome-Wide Identification of Proline Transporter Gene Family in Non-Heading Chinese Cabbage and Functional Analysis of BchProT1 under Heat Stress

Non-heading Chinese cabbage prefers cool temperatures, and heat stress has become a major factor for reduced yield. The proline transporter protein (ProT) is highly selective for proline transport, contributing to the heat tolerance of non-heading Chinese cabbage. However, there has been no systematic study on the identification and potential functions of the ProT gene family in response to heat stress in non-heading Chinese cabbage. We identified six BchProT genes containing 11-12 transmembrane helices characteristic of membrane proteins through whole-genome sequencing. These genes diverged into three evolutionary branches and exhibited similarity in motifs and intron/exon numbers. Segmental duplication is the primary driving force for the amplification of BchProT. Notably, many stress-related elements have been identified in the promoters of BchProT using cis-acting element analysis. The expression level of BchProT6 was the highest in petioles, and the expression level of BchProT1 was the highest under high-temperature stress. Subcellular localization indicated their function at cell membranes. Heterologous expression of BchProT1 in Arabidopsis plants increased proline transport synthesis under heat-stress conditions. This study provides valuable information for exploring the molecular mechanisms underlying heat tolerance mediated by members of the BchProT family.

Maximum Covering Subtrees for Phylogenetic Networks

Tree-based phylogenetic networks, which may be roughly defined as leaf-labeled networks built by adding arcs only between the original tree edges, have elegant properties for modeling evolutionary histories. We answer an open question of Francis, Semple, and Steel about the complexity of determining how far a phylogenetic network is from being tree-based, including non-binary phylogenetic networks. We show that finding a phylogenetic tree covering the maximum number of nodes in a phylogenetic network can be computed in polynomial time via an encoding into a minimum-cost flow problem.

The Space of Tree-Based Phylogenetic Networks

Phylogenetic networks are generalizations of phylogenetic trees that allow the representation of reticulation events such as horizontal gene transfer or hybridization, and can also represent uncertainty in inference. A subclass of these, tree-based phylogenetic networks, have been introduced to capture the extent to which reticulate evolution nevertheless broadly follows tree-like patterns. Several important operations that change a general phylogenetic network have been developed in recent years and are important for allowing algorithms to move around spaces of networks; a vital ingredient in finding an optimal network given some biological data. A key such operation is the nearest neighbour interchange, or NNI. While it is already known that the space of unrooted phylogenetic networks is connected under NNI, it has been unclear whether this also holds for the subspace of tree-based networks. In this paper, we show that the space of unrooted tree-based phylogenetic networks is indeed connected under the NNI operation. We do so by explicitly showing how to get from one such network to another one without losing tree-basedness along the way. Moreover, we introduce some new concepts, for instance "shoat networks", and derive some interesting aspects concerning tree-basedness. Last, we use our results to derive an upper bound on the size of the space of tree-based networks.

Classes of tree-based networks

Recently, so-called tree-based phylogenetic networks have attracted considerable attention. These networks can be constructed from a phylogenetic tree, called the base tree, by adding additional edges. The primary aim of this study is to provide sufficient criteria for tree-basedness by reducing phylogenetic networks to related graph structures. Even though it is generally known that determining whether a network is tree-based is an NP-complete problem, one of these criteria, namely edge-basedness, can be verified in linear time. Surprisingly, the class of edge-based networks is closely related to a well-known family of graphs, namely, the class of generalized series-parallel graphs, and we explore this relationship in full detail. Additionally, we introduce further classes of tree-based networks and analyze their relationships.