Bailin Hao

Applied symbolic dynamics and chaos

Symbolic dynamics of unimodal maps maps with multiple critical points symbolic dynamics of circle maps symbolic dynamics of two-dimensional maps application to ordinary differential equations counting the number of periodic orbits symbolic dynamics and grammatical complexity symbolic dynamics and knot theory.

A fungal phylogeny based on 82 complete genomes using the composition vector method

BackgroundMolecular phylogenetics and phylogenomics have greatly revised and enriched the fungal systematics in the last two decades. Most of the analyses have been performed by comparing single or multiple orthologous gene regions. Sequence alignment has always been an essential element in tree construction. These alignment-based methods (to be called the standard methods hereafter) need independent verification in order to put the fungal Tree of Life (TOL) on a secure footing. The ever-increasing number of sequenced fungal genomes and the recent success of our newly proposed alignment-free composition vector tree (CVTree, see Methods) approach have made the verification feasible.ResultsIn all, 82 fungal genomes covering 5 phyla were obtained from the relevant genome sequencing centers. An unscaled phylogenetic tree with 3 outgroup species was constructed by using the CVTree method. Overall, the resultant phylogeny infers all major groups in accordance with standard methods. Furthermore, the CVTree provides information on the placement of several currently unsettled groups. Within the sub-phylum Pezizomycotina, our phylogeny places the Dothideomycetes and Eurotiomycetes as sister taxa. Within the Sordariomycetes, it infers that Magnaporthe grisea and the Plectosphaerellaceae are closely related to the Sordariales and Hypocreales, respectively. Within the Eurotiales, it supports that Aspergillus nidulans is the early-branching species among the 8 aspergilli. Within the Onygenales, it groups Histoplasma and Paracoccidioides together, supporting that the Ajellomycetaceae is a distinct clade from Onygenaceae. Within the sub-phylum Saccharomycotina, the CVTree clearly resolves two clades: (1) species that translate CTG as serine instead of leucine (the CTG clade) and (2) species that have undergone whole-genome duplication (the WGD clade). It places Candida glabrata at the base of the WGD clade.ConclusionUsing different input data and methodology, the CVTree approach is a good complement to the standard methods. The remarkable consistency between them has brought about more confidence to the current understanding of the fungal branch of TOL.

CVTree update: a newly designed phylogenetic study platform using composition vectors and whole genomes

The CVTree web server (http://tlife.fudan.edu.cn/cvtree) presented here is a new implementation of the whole genome-based, alignment-free composition vector (CV) method for phylogenetic analysis. It is more efficient and user-friendly than the previously published version in the 2004 web server issue of Nucleic Acids Research. The development of whole genome-based alignment-free CV method has provided an independent verification to the traditional phylogenetic analysis based on a single gene or a few genes. This new implementation attempts to meet the challenge of ever increasing amount of genome data and includes in its database more than 850 prokaryotic genomes which will be updated monthly from NCBI, and more than 80 fungal genomes collected manually from several sequencing centers. This new CVTree web server provides a faster and stable research platform. Users can upload their own sequences to find their phylogenetic position among genomes selected from the servers; inbuilt database. All sequence data used in a session may be downloaded as a compressed file. In addition to standard phylogenetic trees, users can also choose to output trees whose monophyletic branches are collapsed to various taxonomic levels. This feature is particularly useful for comparing phylogeny with taxonomy when dealing with thousands of genomes.

Symbolic dynamics and characterization of complexity

Abstract Symbolic dynamics deals with robust properties of dynamics without digging into numbers. For one-dimensional maps there have been some new results (periodic window theorem, generalized composition rule, construction of median words without using harmonics and antiharmonics, incorporation of discrete symmetry to analyze symmetry breaking and symmetry restoration, etc.) This new understanding has been applied to ordinary differential equations, in particular, the systematics of stable periodic solutions in the Lorenz model has been shown to be given basically by symbolic dynamics of the cubic map. Symbolic dynamics may be used to extract invariant characteristics from time series. Its relation with grammatical complexity will also be commented on.

CVTree3 Web Server for Whole-genome-based and Alignment-free Prokaryotic Phylogeny and Taxonomy

A faithful phylogeny and an objective taxonomy for prokaryotes should agree with each other and ultimately follow the genome data. With the number of sequenced genomes reaching tens of thousands, both tree inference and detailed comparison with taxonomy are great challenges. We now provide one solution in the latest Release 3.0 of the alignment-free and whole-genome-based web server CVTree3. The server resides in a cluster of 64 cores and is equipped with an interactive, collapsible, and expandable tree display. It is capable of comparing the tree branching order with prokaryotic classification at all taxonomic ranks from domains down to species and strains. CVTree3 allows for inquiry by taxon names and trial on lineage modifications. In addition, it reports a summary of monophyletic and non-monophyletic taxa at all ranks as well as produces print-quality subtree figures. After giving an overview of retrospective verification of the CVTree approach, the power of the new server is described for the mega-classification of prokaryotes and determination of taxonomic placement of some newly-sequenced genomes. A few discrepancies between CVTree and 16S rRNA analyses are also summarized with regard to possible taxonomic revisions. CVTree3 is freely accessible to all users at http://tlife.fudan.edu.cn/cvtree3/ without login requirements.

Mean-field HP model, designability and alpha-helices in protein structures

Analysis of the geometric properties of a mean-field HP model on a square lattice for protein structure shows that structures with a large number of switchbacks between surface and core sites are chosen favorably by peptides as unique ground states. Global comparison of model (binary) peptide sequences with concatenated (binary) protein sequences listed in the Protein Data Bank and the Dali Domain Dictionary indicates that the highest correlation occurs between model peptides choosing the favored structures and those portions of protein sequences containing alpha helices.

Composition vector approach to whole-genome-based prokaryotic phylogeny: Success and foundations

Composition vector approach to prokaryotic phylogeny provides an alignment-free and parameter-free method based on whole-genome data. It has also been applied to viruses and fungi. In all studied cases the inferred phylogenetic relationships agree well with taxonomic knowledge in major groupings and fine branchings. In this review article, after demonstrating its successful application to a collection of 892 genomes including 62 Archaea, 822 Bacteria and 8 Eukarya, we will outline some ongoing work towards the foundations of this new approach.

PROKARYOTIC PHYLOGENY BASED ON COMPLETE GENOMES WITHOUT SEQUENCE ALIGNMENT

We present a brief review of a series of on-going work on bacterial phylogeny. We propose a new method to infer relatedness of prokaryotes from their complete genome data without using sequence alignment, leading to results comparable with the bacteriologists systematics as reflected in the latest 2001 edition of Bergeys Manual of Systematic Bacteriology.1 We only touch on the mathematical aspects of the method. The biological implications of our results will be published elsewhere.

Hierarchy of Chaotic Bands

Results of a detailed numerical study on the structure of chaotic bands in a forced limit cycle oscillator (the Brusselator) are presented. Embedded in the chaotic bands of primary bifurcation sequence there are many secondary sequences with both direct and inverse segments. Within secondary chaotic bands tertiary sequences of similar structure exist. This has been shown by using subharmonic stroboscopic sampling combined with power spectra analysis.

Molecular phylogeny of coronaviruses including human SARS-CoV

Phylogenetic tree of coronaviruses (CoVs) including the human SARS-associated virus is reconstructed from complete genomes by using our newly developed K-string composition approach. The relation of the human SARS-CoV to other coronaviruses, i.e. the rooting of the tree is suggested by choosing an appropriate outgroup. SARS-CoV makes a separate group closer but still distant from G2 (CoVs in mammalian host). The relation between different isolates of the human SARS virus is inferred by first constructing an ultrametric distance matrix from counting sequence variations in the genomes. The resulting tree is consistent with clinic relations between the SARS-CoV isolates. In addition to a larger variety of coronavirus genomes these results provide phylogenetic knowledge based on independent novel methodology as compared to recent phylogenetic studies on SARS-CoV.