Data based identification and prediction of nonlinear and complex dynamical systems

We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin

A mechanistic model of connector hubs, modularity, and cognition

The human brain network is modular--comprised of communities of tightly interconnected nodes. This network contains local hubs, which have many connections within their own communities, and connector hubs, which have connections diversely distributed across communities. A mechanistic understanding of these hubs and how they support cognition has not been demonstrated. Here, we leveraged individual differences in hub connectivity and cognition. We show that a model of hub connectivity accurately predicts the cognitive performance of 476 individuals in four distinct tasks. Moreover, there is a general optimal network structure for cognitive performance--individuals with diversely connected hubs and consequent modular brain networks exhibit increased cognitive performance, regardless of the task. Critically, we find evidence consistent with a mechanistic model in which connector hubs tune the connectivity of their neighbors to be more modular while allowing for task appropriate information integration across communities, which increases global modularity and cognitive performance

Correlation analysis of the transcriptome of growing leaves with mature leaf parameters in a maize RIL population

Background: To sustain the global requirements for food and renewable resources, unraveling the molecular networks underlying plant growth is becoming pivotal. Although several approaches to identify genes and networks involved in final organ size have been proven successful, our understanding remains fragmentary. Results: Here, we assessed variation in 103 lines of the Zea mays B73xH99 RIL population for a set of final leaf size and whole shoot traits at the seedling stage, complemented with measurements capturing growth dynamics, and cellular measurements. Most traits correlated well with the size of the division zone, implying that the molecular basis of final leaf size is already defined in dividing cells of growing leaves. Therefore, we searched for association between the transcriptional variation in dividing cells of the growing leaf and final leaf size and seedling biomass, allowing us to identify genes and processes correlated with the specific traits. A number of these genes have a known function in leaf development. Additionally, we illustrated that two independent mechanisms contribute to final leaf size, maximal growth rate and the duration of growth. Conclusions: Untangling complex traits such as leaf size by applying in-depth phenotyping allows us to define the relative contributions of the components and their mutual associations, facilitating dissection of the biological processes and regulatory networks underneath

Bayesian Inference for Genomic Data Analysis

High-throughput genomic data contain gazillion of information that are influenced by the complex biological processes in the cell. As such, appropriate mathematical modeling frameworks are required to understand the data and the data generating processes. This dissertation focuses on the formulation of mathematical models and the description of appropriate computational algorithms to obtain insights from genomic data. Specifically, characterization of intra-tumor heterogeneity is studied. Based on the total number of allele copies at the genomic locations in the tumor subclones, the problem is viewed from two perspectives: the presence or absence of copy-neutrality assumption. With the presence of copy-neutrality, it is assumed that the genome contains mutational variability and the three possible genotypes may be present at each genomic location. As such, the genotypes of all the genomic locations in the tumor subclones are modeled by a ternary matrix. In the second case, in addition to mutational variability, it is assumed that the genomic locations may be affected by structural variabilities such as copy number variation (CNV). Thus, the genotypes are modeled with a pair of (Q + 1)-ary matrices. Using the categorical Indian buffet process (cIBP), state-space modeling framework is employed in describing the two processes and the sequential Monte Carlo (SMC) methods for dynamic models are applied to perform inference on important model parameters. Moreover, the problem of estimating gene regulatory network (GRN) from measurement with missing values is presented. Specifically, gene expression time series data may contain missing values for entire expression values of a single point or some set of consecutive time points. However, complete data is often needed to make inference on the underlying GRN. Using the missing measurement, a dynamic stochastic model is used to describe the evolution of gene expression and point-based Gaussian approximation (PBGA) filters with one-step or two-step missing measurements are applied for the inference. Finally, the problem of deconvolving gene expression data from complex heterogeneous biological samples is examined, where the observed data are a mixture of different cell types. A statistical description of the problem is used and the SMC method for static models is applied to estimate the cell-type specific expressions and the cell type proportions in the heterogeneous samples

Gene expression data analysis using novel methods: Predicting time delayed correlations and evolutionarily conserved functional modules

Microarray technology enables the study of gene expression on a large scale. One of the main challenges has been to devise methods to cluster genes that share similar expression profiles. In gene expression time courses, a particular gene may encode transcription factor and thus controlling several genes downstream; in this case, the gene expression profiles may be staggered, indicating a time-delayed response in transcription of the later genes. The standard clustering algorithms consider gene expression profiles in a global way, thus often ignoring such local time-delayed correlations. We have developed novel methods to capture time-delayed correlations between expression profiles: (1) A method using dynamic programming and (2) CLARITY, an algorithm that uses a local shape based similarity measure to predict time-delayed correlations and local correlations. We used CLARITY on a dataset describing the change in gene expression during the mitotic cell cycle in Saccharomyces cerevisiae. The obtained clusters were significantly enriched with genes that share similar functions, reflecting the fact that genes with a similar function are often co-regulated and thus co-expressed. Time-shifted as well as local correlations could also be predicted using CLARITY. In datasets, where the expression profiles of independent experiments are compared, the standard clustering algorithms often cluster according to all conditions, considering all genes. This increases the background noise and can lead to the missing of genes that change the expression only under particular conditions. We have employed a genetic algorithm based module predictor that is capable to identify group of genes that change their expression only in a subset of conditions. With the aim of supplementing the Ustilago maydis genome annotation, we have used the module prediction algorithm on various independent datasets from Ustilago maydis. The predicted modules were cross-referenced in various Saccharomyces cerevisiae datasets to check its evolutionarily conservation between these two organisms. The key contributions of this thesis are novel methods that explore biological information from DNA microarray data

Unraveling gene regulatory networks from time-resolved gene expression data -- a measures comparison study

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Computational methods for analysis and modeling of time-course gene expression data

Genes encode proteins, some of which in turn regulate other genes. Such interactions make up gene regulatory relationships or (dynamic) gene regulatory networks. With advances in the measurement technology for gene expression and in genome sequencing, it has become possible to measure the expression level of thousands of genes simultaneously in a cell at a series of time points over a specific biological process. Such time-course gene expression data may provide a snapshot of most (if not all) of the interesting genes and may lead to a better understanding gene regulatory relationships and networks. However, inferring either gene regulatory relationships or networks puts a high demand on powerful computational methods that are capable of sufficiently mining the large quantities of time-course gene expression data, while reducing the complexity of the data to make them comprehensible. This dissertation presents several computational methods for inferring gene regulatory relationships and gene regulatory networks from time-course gene expression. These methods are the result of the author’s doctoral study. Cluster analysis plays an important role for inferring gene regulatory relationships, for example, uncovering new regulons (sets of co-regulated genes) and their putative cis-regulatory elements. Two dynamic model-based clustering methods, namely the Markov chain model (MCM)-based clustering and the autoregressive model (ARM)-based clustering, are developed for time-course gene expression data. However, gene regulatory relationships based on cluster analysis are static and thus do not describe the dynamic evolution of gene expression over an observation period. The gene regulatory network is believed to be a time-varying system. Consequently, a state-space model for dynamic gene regulatory networks from time-course gene expression data is developed. To account for the complex time-delayed relationships in gene regulatory networks, the state space model is extended to be the one with time delays. Finally, a method based on genetic algorithms is developed to infer the time-delayed relationships in gene regulatory networks. Validations of all these developed methods are based on the experimental data available from well-cited public databases

Gene expression data analysis using novel methods: Predicting time delayed correlations and evolutionarily conserved functional modules

Microarray technology enables the study of gene expression on a large scale. One of the main challenges has been to devise methods to cluster genes that share similar expression profiles. In gene expression time courses, a particular gene may encode transcription factor and thus controlling several genes downstream; in this case, the gene expression profiles may be staggered, indicating a time-delayed response in transcription of the later genes. The standard clustering algorithms consider gene expression profiles in a global way, thus often ignoring such local time-delayed correlations. We have developed novel methods to capture time-delayed correlations between expression profiles: (1) A method using dynamic programming and (2) CLARITY, an algorithm that uses a local shape based similarity measure to predict time-delayed correlations and local correlations. We used CLARITY on a dataset describing the change in gene expression during the mitotic cell cycle in Saccharomyces cerevisiae. The obtained clusters were significantly enriched with genes that share similar functions, reflecting the fact that genes with a similar function are often co-regulated and thus co-expressed. Time-shifted as well as local correlations could also be predicted using CLARITY. In datasets, where the expression profiles of independent experiments are compared, the standard clustering algorithms often cluster according to all conditions, considering all genes. This increases the background noise and can lead to the missing of genes that change the expression only under particular conditions. We have employed a genetic algorithm based module predictor that is capable to identify group of genes that change their expression only in a subset of conditions. With the aim of supplementing the Ustilago maydis genome annotation, we have used the module prediction algorithm on various independent datasets from Ustilago maydis. The predicted modules were cross-referenced in various Saccharomyces cerevisiae datasets to check its evolutionarily conservation between these two organisms. The key contributions of this thesis are novel methods that explore biological information from DNA microarray data