This study quantitatively validates the principle that the biological properties associated with a given genotype are determined by the distribution of amino acids. In order to visualize this central law of molecular biology, each protein was represented by a point in 250-dimensional space based on its amino acid distribution. Proteins from the same family are found to cluster together, leading to the principle that the convex hull surrounding protein points from the same family do not intersect with the convex hulls of other protein families. This principle was verified computationally for all available and reliable protein kinases and human proteins. In addition, we generated 2,328,761 figures to show that the convex hulls of different families were disjoint from each other. The classification performs well with high and robust accuracy (95.75% and 97.5%) together with reasonable phylogenetic trees validate our methods further.

Herein we describe new frontiers in mathematical modeling and statistical analysis of oscillatory biomedical signals, motivated by our recent studies of network formation in the human brain during the early stages of life and studies forty years ago on cardiorespiratory patterns during sleep in infants and animal models. The frontiers involve new nonlinear-type time-frequency analysis of signals with multiple oscillatory components, and efficient particle filters for joint state and parameter estimators together with uncertainty quantification in hidden Markov models and empirical Bayes inference.

High-throughput biological technologies (e.g. ChIPseq, RNA-seq and single-cell RNA-seq) rapidly accelerate the accumulation of genome-wide omics data in diverse interrelated biological scenarios (e.g. cells, tissues and conditions). Integration and differential analysis are two common paradigms for exploring and analyzing such data. However, current integrative methods usually ignore the differential part, and typical differential analysis methods either fail to identify combinatorial patterns of difference or require matched dimensions of the data. Here, we propose a flexible framework CSMF to combine them into one paradigm to simultaneously reveal Common and Specific patterns via Matrix Factorization from data generated under interrelated biological scenarios. We demonstrate the effectiveness of CSMF with four representative applications including pairwise ChIP-seq data describing the chromatin modification map between K562 and Huvec cell lines; pairwise RNA-seq data representing the expression profiles of two different cancers; RNA-seq data of three breast cancer subtypes; and single-cell RNA-seq data of human embryonic stem cell differentiation at six time points. Extensive analysis yields novel insights into hidden combinatorial patterns in these multi-modal data. Results demonstrate that CSMF is a powerful tool to uncover common and specific patterns with significant biological implications from data of interrelated biological scenarios.

HIV-1 is the most common and pathogenic strain of human immunodeficiency virus consisting of many subtypes. To study the difference among HIV-1 subtypes in infection, diagnosis and drug design, it is important to identify HIV-1 subtypes from clinical HIV-1 samples. In this work, we propose an effective numeric representation called Subsequence Natural Vector (SNV) to encode HIV-1 sequences. Using the representation, we introduce an improved linear discriminant analysis method to classify HIV-1 viruses correctly. SNV is based on distribution of nucleotides in HIV-1 viral sequences. It not only computes the number of nucleotides, but also describes the position and variance of nucleotides in viruses. To validate our alignment-free method, 6902 complete genomes and 11,668 pol gene sequences of HIV-1 subtypes were collected from the up-to-date Los Alamos HIV database. SNV outperforms the three popular methods, Kameris, Comet and REGA, with almost 100% Sensitivity and Specificity, also with much less time. Our subtyping algorithm especially works better for circulating recombinant forms (CRFs) consisting of a few sequences. Our approach is also powerful to separate unique recombinant forms (URFs) from other subtypes with 100% Sensitivity and Specificity. Moreover, phylogenetic trees based on SNV representation are constructed using full-length HIV-1 genomes and pol genes respectively, where viruses from the same subtype are clustered together correctly.

Prochlorococcus marinus, one of the most abundant marine cyanobacteria in the global ocean, is classified into low-light (LL) and high-light (HL) adapted ecotypes. These two adapted ecotypes differ in their ecophysiological characteristics, especially whether adapted for growth at high-light or low-light intensities. However, some evolutionary relationships of Prochlorococcus phylogeny remain to be resolved, such as whether the strains SS120 and MIT9211 form a monophyletic group. We use the Natural Vector (NV) method to represent the sequence in order to identify the phylogeny of the Prochlorococcus. The natural vector method is alignment free without any model assumptions. This study added the covariances of amino acids in protein sequence to the natural vector method. Based on these new natural vectors, we can compute the Hausdorff distance between the two clades which represents the dissimilarity. This method enables us to systematically analyze both the dataset of ribosomal proteomes and the dataset of 16s-23s rRNA sequences in order to reconstruct the phylogeny of Prochlorococcus. Furthermore, we apply classification to inspect the relationship of SS120 and MIT9211. From the reconstructed phylogenetic trees and classification results, we may conclude that the SS120 does not cluster with MIT9211. This study demonstrates a new method for performing phylogenetic analysis. The results confirm that these two strains do not form a monophyletic clade in the phylogeny of Prochlorococcus.