Inference on the structure of gene regulatory networks

Gene regulatory network inference with covariance dynamics

Determining gene regulatory network (GRN) structure is a central problem in biology, with a variety of inference methods available for different types of data. For a widely prevalent and challenging use case, namely single-cell gene expression data measured after intervention at multiple time points with unknown joint distributions, there is only one known specifically developed method, which does not fully utilize the rich information contained in this data type. We develop an inference method for the GRN in this case, netWork infErence by covariaNce DYnamics, dubbed WENDY. The core idea of WENDY is to model the dynamics of the covariance matrix, and solve this dynamics as an optimization problem to determine the regulatory relationships. To evaluate its effectiveness, we compare WENDY with other inference methods using synthetic data and experimental data. Our results demonstrate that WENDY performs well across different data sets.

Order-of-Mutation Effects on Cancer Progression: Models for Myeloproliferative Neoplasm

In some patients with myeloproliferative neoplasms (MPN), two genetic mutations are often found: JAK2 V617F and one in the TET2 gene. Whether one mutation is present influences how the other subsequent mutation will affect the regulation of gene expression. In other words, when a patient carries both mutations, the order of when they first arose has been shown to influence disease progression and prognosis. We propose a nonlinear ordinary differential equation, the Moran process, and Markov chain models to explain the non-additive and non-commutative mutation effects on recent clinical observations of gene expression patterns, proportions of cells with different mutations, and ages at diagnosis of MPN. Combined, these observations are used to shape our modeling framework. Our key proposal is that bistability in gene expression provides a natural explanation for many observed order-of-mutation effects. We also propose potential experimental measurements that can be used to confirm or refute predictions of our models.

Algorithms for the Uniqueness of the Longest Common Subsequence

Given several number sequences, determining the longest common subsequence is a classical problem in computer science. This problem has applications in bioinformatics, especially determining transposable genes. Nevertheless, related works only consider how to find one longest common subsequence. In this paper, we consider how to determine the uniqueness of the longest common subsequence. If there are multiple longest common subsequences, we also determine which number appears in all/some/none of the longest common subsequences. We focus on four scenarios: (1) linear sequences without duplicated numbers; (2) circular sequences without duplicated numbers; (3) linear sequences with duplicated numbers; (4) circular sequences with duplicated numbers. We develop corresponding algorithms and apply them to gene sequencing data.

Order-of-mutation effects on cancer progression: models for myeloproliferative neoplasm

In some patients with myeloproliferative neoplasms (MPN), two genetic mutations are often found, JAK2 V617F and one in the TET2 gene. Whether or not one mutation is present will influence how the other subsequent mutation affects the regulation of gene expression. When both mutations are present, the order of their occurrence has been shown to influence disease progression and prognosis. We propose a nonlinear ordinary differential equation (ODE), Moran process, and Markov chain models to explain the non-additive and non-commutative mutation effects on recent clinical observations of gene expression patterns, proportions of cells with different mutations, and ages at diagnosis of MPN. These observations consistently shape our modeling framework. Our key proposal is that bistability in gene expression provides a natural explanation for many observed order-of-mutation effects. We also propose potential experimental measurements that can be used to confirm or refute predictions of our models.

Inference on autoregulation in gene expression with variance-to-mean ratio

Some genes can promote or repress their own expressions, which is called autoregulation. Although gene regulation is a central topic in biology, autoregulation is much less studied. In general, it is extremely difficult to determine the existence of autoregulation with direct biochemical approaches. Nevertheless, some papers have observed that certain types of autoregulations are linked to noise levels in gene expression. We generalize these results by two propositions on discrete-state continuous-time Markov chains. These two propositions form a simple but robust method to infer the existence of autoregulation from gene expression data. This method only needs to compare the mean and variance of the gene expression level. Compared to other methods for inferring autoregulation, our method only requires non-interventional one-time data, and does not need to estimate parameters. Besides, our method has few restrictions on the model. We apply this method to four groups of experimental data and find some genes that might have autoregulation. Some inferred autoregulations have been verified by experiments or other theoretical works.

Mathematical modeling of regulatory networks of intracellular processes - Aims and selected methods

Regulatory networks structure and signaling pathways dynamics are uncovered in time- and resource consuming experimental work. However, it is increasingly supported by modeling, analytical and computational techniques as well as discrete mathematics and artificial intelligence applied to to extract knowledge from existing databases. This review is focused on mathematical modeling used to analyze dynamics and robustness of these networks. This paper presents a review of selected modeling methods that facilitate advances in molecular biology.

spliceJAC: transition genes and state-specific gene regulation from single-cell transcriptome data

Extracting dynamical information from single-cell transcriptomics is a novel task with the promise to advance our understanding of cell state transition and interactions between genes. Yet, theory-oriented, bottom-up approaches that consider differences among cell states are largely lacking. Here, we present spliceJAC, a method to quantify the multivariate mRNA splicing from single-cell RNA sequencing (scRNA-seq). spliceJAC utilizes the unspliced and spliced mRNA count matrices to constructs cell state-specific gene-gene regulatory interactions and applies stability analysis to predict putative driver genes critical to the transitions between cell states. By applying spliceJAC to biological systems including pancreas endothelium development and epithelial-mesenchymal transition (EMT) in A549 lung cancer cells, we predict genes that serve specific signaling roles in different cell states, recover important differentially expressed genes in agreement with pre-existing analysis, and predict new transition genes that are either exclusive or shared between different cell state transitions.