We construct a virus database called VirusDB (http://yaulab.math.tsinghua.edu.cn/VirusDB/) and an online inquiry system to serve people who are interested in viral classification and prediction. The database stores all viral genomes, their corresponding natural vectors, and the classification information of the single/multiple-segmented viral reference sequences downloaded from National Center for Biotechnology Information. The online inquiry system serves the purpose of computing natural vectors and their distances based on submitted genomes, providing an online interface for accessing and using the database for viral classification and prediction, and back-end processes for automatic and manual updating of database content to synchronize with GenBank. Submitted genomes data in FASTA format will be carried out and the prediction results with 5 closest neighbors and their classifications will be returned by email. Considering the one-to-one correspondence between sequence and natural vector, time efficiency, and high accuracy, natural vector is a significant advance compared with alignment methods, which makes VirusDB a useful database in further research.

Zika virus (ZIKV) is a mosquito-borne flavivirus. It was first isolated from Uganda in 1947 and has become an emergent event since 2007. However, because of the inconsistency of alignment methods, the evolution of ZIKV remains poorly understood. In this study, we first use the complete protein and an alignment-free method to build a phylogenetic tree of 87 Zika strains in which Asian, East African, and West African lineages are characterized. We also use the NS5 protein to construct the genetic relationship among 44 Zika strains. For the first time, these strains are divided into two clades: African 1 and African 2. This result suggests that ZIKV originates from Africa, then spread to Asia, Pacific islands, and throughout the Americas. We also perform the phylogeny analysis for 53 viruses in genus Flavivirus to which ZIKV belongs using complete proteins. Our conclusion is consistent with the classification by the hosts and transmission vectors.

Analyzing phylogenetic relationships using mathematical methods has always been of importance in bioinformatics. Quantitative research may interpret the raw biological data in a precise way. Multiple Sequence Alignment (MSA) is used frequently to analyze biological evolutions, but is very time-consuming. When the scale of data is large, alignment methods cannot finish calculation in reasonable time. Therefore, we present a new method using moments of cumulative Fourier power spectrum in clustering the DNA sequences. Each sequence is translated into a vector in Euclidean space. Distances between the vectors can reflect the relationships between sequences. The mapping between the spectra and moment vector is one-to-one, which means that no information is lost in the power spectra during the calculation. We cluster and classify several datasets including Influenza A, primates, and human rhinovirus (HRV) datasets to build up the phylogenetic trees. Results show that the new proposed cumulative Fourier power spectrum is much faster and more accurately than MSA and another alignment-free method known as k-mer. The research provides us new insights in the study of phylogeny, evolution, and efficient DNA comparison algorithms for large genomes. The computer programs of the cumulative Fourier power spectrum are available at GitHub (https://github.com/YaulabTsinghua/cumulative-Fourier-power-spectrum).

Comparing DNA and protein sequence groups plays an important role in biological evolutionary relationship research. Despite many methods available for sequence comparison, only a few can be used for group comparison. In this study, we propose a novel approach using convex hulls. We use statistical information contained within the sequences to represent each sequence as a point in high dimensional space. We find that the points belonging to one biological group are located in a different region of space than points belonging to other biological groups. To be more precise, the convex hull of the points from one group are disjoint from the convex hulls of points from other groups. This finding allows us to do phylogenetic analysis for groups in an efficient way. Five different theorems are presented for checking whether two convex hulls intersect or are disjoint. Test results for datasets related to HRV, HPV, Ebolavirus, PKC and protein phosphatase domains demonstrate that our method performs well and provides a new tool for studying group phylogeny. More significantly, the convex analysis presents a new way to search for sequences belonging to a biological group by examining points within the group’s convex hull.

Laser scanning is an effective tool for acquiring geometric attributes of trees and vegetation, which lays a solid foundation for 3-dimensional tree modelling. Existing studies on tree modelling from laser scanning data are vast. However, some works cannot guarantee sufficient modelling accuracy, while some other works are mainly rule-based and therefore highly depend on user inputs. In this paper, we propose a novel method to accurately and automatically reconstruct detailed 3D tree models from laser scans. We first extract an initial tree skeleton from the input point cloud by establishing a minimum spanning tree using the Dijkstra shortest-path algorithm. Then, the initial tree skeleton is pruned by iteratively removing redundant components. After that, an optimization-based approach is performed to fit a sequence of cylinders to approximate the geometry of the tree branches. Experiments on various types of trees from different data sources demonstrate the effectiveness and robustness of our method. The overall fitting error (i.e., the distance between the input points and the output model) is less than 10 cm. The reconstructed tree models can be further applied in the precise estimation of tree attributes, urban landscape visualization, etc. The source code of this work is freely available at https://github.com/tudelft3d/adtree