Identifying cell types with single cell sequencing data

Single-cell RNA sequencing (scRNA-seq) techniques, which examine the genetic information of individual cells, provide an unparalleled resolution to discern deeply into cellular heterogeneity. On the contrary, traditional RNA sequencing technologies (bulk RNA sequencing technologies), measure the average RNA expression level of a large number of input cells, which are insufficient for studying heterogeneous systems. Hence, scRNA-seq technologies make it possible to tackle many inaccessible problems, such as rare cell types identification, cancer evolution and cell lineage relationship inference. Cell population identification is the fundamental of the analysis of scRNA-seq data. Generally, the workflow of scRNA-seq analysis includes data processing, dropout imputation, feature selection, dimensionality reduction, similarity matrix construction and unsupervised clustering. Many single-cell clustering algorithms rely on similarity matrices of cells, but many existing studies have not received the expectant results. There are some unique challenges in analyzing scRNA-seq data sets, including a significant level of biological and technical noise, so similarity matrix construction still deserves further study. In my study, I present a new method, named Learning Sparse Similarity Matrices (LSSM), to construct cell-cell similarity matrices, and then several clustering methods are used to identify cell populations respectively with scRNA-seq data. Firstly, based on sparse subspace theory, the relationship between a cell and the other cells in the same cell type is expressed by a linear combination. Secondly, I construct a convex optimization objective function to find the similarity matrix, which is consist of the corresponding coefficients of the linear combinations mentioned above. Thirdly, I design an algorithm with column-wise learning and greedy algorithm to solve the objective function. As a result, the large optimization problem on the similarity matrix can be decomposed into a series of smaller optimization problems on the single column of the similarity matrix respectively, and the sparsity of the whole matrix can be ensured by the sparsity of each column. Fourthly, in order to pick an optimal clustering method for identifying cell populations based on the similarity matrix developed by LSSM, I use several clustering methods separately based on the similarity matrix calculated by LSSM from eight scRNA-seq data sets. The clustering results show that my method performs the best when combined with spectral clustering (Laplacian eigenmaps + k-means clustering). In addition, compared with five state-of-the-art methods, my method outperforms most competing methods on eight data sets. Finally, I combine LSSM with t-Distributed Stochastic Neighbor Embedding (t-SNE) to visualize the data points of scRNA-seq data in the two-dimensional space. The results show that for most data points, in the same cell types they are close, while from different cell clusters, they are separated

Predictive Pattern Discovery in Dynamic Data Systems

This dissertation presents novel methods for analyzing nonlinear time series in dynamic systems. The purpose of the newly developed methods is to address the event prediction problem through modeling of predictive patterns. Firstly, a novel categorization mechanism is introduced to characterize different underlying states in the system. A new hybrid method was developed utilizing both generative and discriminative models to address the event prediction problem through optimization in multivariate systems. Secondly, in addition to modeling temporal dynamics, a Bayesian approach is employed to model the first-order Markov behavior in the multivariate data sequences. Experimental evaluations demonstrated superior performance over conventional methods, especially when the underlying system is chaotic and has heterogeneous patterns during state transitions. Finally, the concept of adaptive parametric phase space is introduced. The equivalence between time-domain phase space and associated parametric space is theoretically analyzed

Understanding Recurrent Disease: A Dynamical Systems Approach

Recurrent disease, characterized by repeated alternations between acute relapse and long re- mission, can be a feature of both common diseases, like ear infections, and serious chronic diseases, such as HIV infection or multiple sclerosis. Due to their poorly understood etiology and the resultant challenge for medical treatment and patient management, recurrent diseases attract much attention in clinical research and biomathematics. Previous studies of recurrence by biomathematicians mainly focus on in-host models and generate recurrent patterns by in- corporating forcing functions or stochastic elements. In this study, we investigate deterministic in-host models through the qualitative analysis of dynamical systems, to reveal the possible intrinsic mechanisms underlying disease recurrence. Recurrence in HIV infection is referred to as “viral blips”, that is, transient periods of high viral replication separated by long periods of quiescence. A 4-dimensional HIV antioxidant- therapy model exhibiting viral blips is studied using bifurcation theory. Four conditions for the existence of viral blips in a deterministic in-host model are proposed. Guided by the four con- ditions, the simplest 2-dimensional infection model which shows recurrence is obtained. One key point for recurrence is identified, that is an increasing and saturating infectivity function. Furthermore, Hopf and generalized Hopf bifurcations, Bogdanov-Takens bifurcation, and ho- moclinic bifurcation are proved to exist in this 2-dimensional model. Bogdanov-Takens bifur- cation and homoclinic bifurcation provide a new mechanism for generating recurrence. From the viewpoint of modelling, the increasing and saturating infectivity function gives rise to a convex incidence rate, which further induces backward bifurcation and Hopf bifurcation, and allows the infection model to exhibit rich dynamical behavior, such as bistability, recurrence, and regular oscillation. The relapse-remission cycle in autoimmune disease is investigated based on a regulatory T cell model. By introducing a newly discovered class of regulatory T cells, Hopf bifurcation oc- curs in the autoimmune model with negative backward bifurcation, and gives rise to a recurrent pattern. The main insight of this thesis is that recurrent disease can arise naturally from the de- terministic dynamics of populations. It will provide a starting point for further research in dynamical systems theory, and recurrence in other physical systems