TedSim: temporal dynamics simulation of single-cell RNA sequencing data and cell division history

Recently, lineage tracing technology using CRISPR/Cas9 genome editing has enabled simultaneous readouts of gene expressions and lineage barcodes, which allows for the reconstruction of the cell division tree and makes it possible to reconstruct ancestral cell types and trace the origin of each cell type. Meanwhile, trajectory inference methods are widely used to infer cell trajectories and pseudotime in a dynamic process using gene expression data of present-day cells. Here, we present TedSim (single-cell temporal dynamics simulator), which simulates the cell division events from the root cell to present-day cells, simultaneously generating two data modalities for each single cell: the lineage barcode and gene expression data. TedSim is a framework that connects the two problems: lineage tracing and trajectory inference. Using TedSim, we conducted analysis to show that (i) TedSim generates realistic gene expression and barcode data, as well as realistic relationships between these two data modalities; (ii) trajectory inference methods can recover the underlying cell state transition mechanism with balanced cell type compositions; and (iii) integrating gene expression and barcode data can provide more insights into the temporal dynamics in cell differentiation compared to using only one type of data, but better integration methods need to be developed.     

Modes and clustering for time-warped gene expression profile data

MOTIVATION: The study of the dynamics of regulatory processes has led to increased interest for the analysis of temporal gene expression level data. To address the dynamics of regulation, expression data are collected repeatedly over time. It is difficult to statistically represent the resulting high-dimensional data. When regulatory processes determine gene expression, time-warping is likely to be present, i.e. the sample of gene expression trajectories reflects variation not only in terms of the expression amplitudes, but also in terms of the temporal structure of gene expression. RESULTS: A non-parametric time-synchronized iterative mean updating technique is proposed to find an overall representation that corresponds to a mode of a sample of expression profiles, viewed as a random sample in function space. The proposed algorithm explores the application of previous work of Hall and Heckman to genome-wide expression data and provides an extension that includes random time-warping with the aim to synchronize timescales across genes. The proposed algorithm is universally applicable for the construction of modes for functional data with time-warping. We demonstrate the construction of mode functions for a sample of Drosophila gene expression data. The algorithm can be applied to define clusters among the observed trajectories of gene expression, without any kind of prior non-time-warped clustering, as illustrated in the numerical example.     

Tuning in the transcriptome: basins of attraction in the yeast cell cycle

Image processing techniques and wavelet analyses have been applied to the yeast cell cycle expression microchip data to reveal large-scale temporally coherent structures and high frequency oscillations in mRNA levels through the cycle. Because transitions in expression frequently occur in phase, they appear as peaks or troughs in colour maps and contour plots of expression levels. Although apparent in the untreated data, these transitions were identified and enhanced by convolution of a Laplacian kernel with the expression arrays of the first 4096 genes. Transitions associated with maximum up- or down-regulation of mRNA levels appear as bands at 30–40 min intervals through two cell cycles. Time-frequency analyses using wavelet transforms support these visualization techniques and lead to the conclusion that, with respect to gene expression, the dominant period is not the cell cycle (90–120 min) but, more commonly, the higher frequency 30–40 minute submultiple of the cycle period.     

Studying and modelling dynamic biological processes using time-series gene expression data

Biological processes are often dynamic, thus researchers must monitor their activity at multiple time points. The most abundant source of information regarding such dynamic activity is time-series gene expression data. These data are used to identify the complete set of activated genes in a biological process, to infer their rates of change, their order and their causal effects and to model dynamic systems in the cell. In this Review we discuss the basic patterns that have been observed in time-series experiments, how these patterns are combined to form expression programs, and the computational analysis, visualization and integration of these data to infer models of dynamic biological systems.     

Interactive Data Visualization for HIV Cohorts: Leveraging Data Exchange Standards to Share and Reuse Research Tools

Objective

To develop and disseminate tools for interactive visualization of HIV cohort data.

Design and Methods

If a picture is worth a thousand words, then an interactive video, composed of a long string of pictures, can produce an even richer presentation of HIV population dynamics. We developed an HIV cohort data visualization tool using open-source software (R statistical language). The tool requires that the data structure conform to the HIV Cohort Data Exchange Protocol (HICDEP), and our implementation utilized Caribbean, Central and South America network (CCASAnet) data.

Results

This tool currently presents patient-level data in three classes of plots: (1) Longitudinal plots showing changes in measurements viewed alongside event probability curves allowing for simultaneous inspection of outcomes by relevant patient classes. (2) Bubble plots showing changes in indicators over time allowing for observation of group level dynamics. (3) Heat maps of levels of indicators changing over time allowing for observation of spatial-temporal dynamics. Examples of each class of plot are given using CCASAnet data investigating trends in CD4 count and AIDS at antiretroviral therapy (ART) initiation, CD4 trajectories after ART initiation, and mortality.

Conclusions

We invite researchers interested in this data visualization effort to use these tools and to suggest new classes of data visualization. We aim to contribute additional shareable tools in the spirit of open scientific collaboration and hope that these tools further the participation in open data standards like HICDEP by the HIV research community.     

Model-Based Deconvolution of Cell Cycle Time-Series Data Reveals Gene Expression Details at High Resolution

In both prokaryotic and eukaryotic cells, gene expression is regulated across the cell cycle to ensure “just-in-time” assembly of select cellular structures and molecular machines. However, present in all time-series gene expression measurements is variability that arises from both systematic error in the cell synchrony process and variance in the timing of cell division at the level of the single cell. Thus, gene or protein expression data collected from a population of synchronized cells is an inaccurate measure of what occurs in the average single-cell across a cell cycle. Here, we present a general computational method to extract “single-cell”-like information from population-level time-series expression data. This method removes the effects of 1) variance in growth rate and 2) variance in the physiological and developmental state of the cell. Moreover, this method represents an advance in the deconvolution of molecular expression data in its flexibility, minimal assumptions, and the use of a cross-validation analysis to determine the appropriate level of regularization. Applying our deconvolution algorithm to cell cycle gene expression data from the dimorphic bacterium Caulobacter crescentus, we recovered critical features of cell cycle regulation in essential genes, including ctrA and ftsZ, that were obscured in population-based measurements. In doing so, we highlight the problem with using population data alone to decipher cellular regulatory mechanisms and demonstrate how our deconvolution algorithm can be applied to produce a more realistic picture of temporal regulation in a cell.     

A dynamically growing self-organizing tree (DGSOT) for hierarchical clustering gene expression profiles

MOTIVATION: The increasing use of microarray technologies is generating large amounts of data that must be processed in order to extract useful and rational fundamental patterns of gene expression. Hierarchical clustering technology is one method used to analyze gene expression data, but traditional hierarchical clustering algorithms suffer from several drawbacks (e.g. fixed topology structure; mis-clustered data which cannot be reevaluated). In this paper, we introduce a new hierarchical clustering algorithm that overcomes some of these drawbacks. RESULT: We propose a new tree-structure self-organizing neural network, called dynamically growing self-organizing tree (DGSOT) algorithm for hierarchical clustering. The DGSOT constructs a hierarchy from top to bottom by division. At each hierarchical level, the DGSOT optimizes the number of clusters, from which the proper hierarchical structure of the underlying dataset can be found. In addition, we propose a new cluster validation criterion based on the geometric property of the Voronoi partition of the dataset in order to find the proper number of clusters at each hierarchical level. This criterion uses the Minimum Spanning Tree (MST) concept of graph theory and is computationally inexpensive for large datasets. A K-level up distribution (KLD) mechanism, which increases the scope of data distribution in the hierarchy construction, was used to improve the clustering accuracy. The KLD mechanism allows the data misclustered in the early stages to be reevaluated at a later stage and increases the accuracy of the final clustering result. The clustering result of the DGSOT is easily displayed as a dendrogram for visualization. Based on a yeast cell cycle microarray expression dataset, we found that our algorithm extracts gene expression patterns at different levels. Furthermore, the biological functionality enrichment in the clusters is considerably high and the hierarchical structure of the clusters is more reasonable. AVAILABILITY: DGSOT is available upon request from the authors.     

Gene interaction in DNA microarray data is decomposed by information geometric measure

MOTIVATION: Given the vast amount of gene expression data, it is essential to develop a simple and reliable method of investigating the fine structure of gene interaction. We show how an information geometric measure achieves this. RESULTS: We introduce an information geometric measure of binary random vectors and show how this measure reveals the fine structure of gene interaction. In particular, we propose an iterative procedure by using this measure (called IPIG). The procedure finds higher-order dependencies which may underlie the interaction between two genes of interest. To demonstrate the method, we investigate the interaction between the two genes of interest in the data from human acute lymphoblastic leukemia cells. The method successfully discovered biologically known findings and also selected other genes as hidden causes that constitute the interaction. AVAILABILITY: Softwares are currently not available but are possibly made available in future at http://www.mns.brain.riken.go.jp/~nakahara/DNA_pub.html where all the related information is also linked.     

Cluster analysis of dynamic parameters of gene expression

Cluster analysis has proven to be a valuable statistical method for analyzing whole genome expression data. Although clustering methods have great utility, they do represent a lower level statistical analysis that is not directly tied to a specific model. To extend such methods and to allow for more sophisticated lines of inference, we use cluster analysis in conjunction with a specific model of gene expression dynamics. This model provides phenomenological dynamic parameters on both linear and non-linear responses of the system. This analysis determines the parameters of two different transition matrices (linear and nonlinear) that describe the influence of one gene expression level on another. Using yeast cell cycle microarray data as test set, we calculated the transition matrices and used these dynamic parameters as a metric for cluster analysis. Hierarchical cluster analysis of this transition matrix reveals how a set of genes influence the expression of other genes activated during different cell cycle phases. Most strikingly, genes in different stages of cell cycle preferentially activate or inactivate genes in other stages of cell cycle, and this relationship can be readily visualized in a two-way clustering image. The observation is prior to any knowledge of the chronological characteristics of the cell cycle process. This method shows the utility of using model parameters as a metric in cluster analysis.     

Cyclin E expression during development in Caenorhabditis elegans

Our interest in the coordination of cell cycle control and differentiation has led us to investigate the Caenorhabditis elegans cye-1 gene encoding the G(1) cell cycle regulator cyclin E. We have studied the expression and function of cye-1 by using monoclonal antibodies directed against CYE-1 protein, cye-1::GFP reporter genes, and a cye-1 chromosomal deletion mutation. We show that a ubiquitous embryonic pattern of expression becomes restricted and dynamic during postembryonic development. Promoter analysis reveals a relatively small region of cis-acting sequences that are necessary for the complex pattern of expression of this gene. Our studies demonstrate that two other G(1) cell cycle genes, encoding cyclin D and CDK4/6, have similarly compact promoter requirements. This suggests that a relatively simple mechanism of regulation may underlie the dynamic developmental patterns of expression exhibited by these three G(1) cell cycle genes. Our analysis of a new cye-1 deletion allele confirms and extends previous studies of two point mutations in the gene.     

Mathematical Models for Cell Migration with Real-Time Cell Cycle Dynamics

The fluorescent ubiquitination-based cell cycle indicator, also known as FUCCI, allows the visualization of the G1 and S/G2/M cell cycle phases of individual cells. FUCCI consists of two fluorescent probes, so that cells in the G1 phase fluoresce red and cells in the S/G2/M phase fluoresce green. FUCCI reveals real-time information about cell cycle dynamics of individual cells, and can be used to explore how the cell cycle relates to the location of individual cells, local cell density, and different cellular microenvironments. In particular, FUCCI is used in experimental studies examining cell migration, such as malignant invasion and wound healing. Here we present, to our knowledge, new mathematical models that can describe cell migration and cell cycle dynamics as indicated by FUCCI. The fundamental model describes the two cell cycle phases, G1 and S/G2/M, which FUCCI directly labels. The extended model includes a third phase, early S, which FUCCI indirectly labels. We present experimental data from scratch assays using FUCCI-transduced melanoma cells, and show that the predictions of spatial and temporal patterns of cell density in the experiments can be described by the fundamental model. We obtain numerical solutions of both the fundamental and extended models, which can take the form of traveling waves. These solutions are mathematically interesting because they are a combination of moving wavefronts and moving pulses. We derive and confirm a simple analytical expression for the minimum wave speed, as well as exploring how the wave speed depends on the spatial decay rate of the initial condition.     

MarC-V: a spreadsheet-based tool for analysis, normalization, and visualization of single cDNA microarray experiments

The comprehensive analysis and visualization of data extracted from cDNA microarrays can be a time-consuming and error-prone process that becomes increasingly tedious with increased number of gene elements on a particular microarray. With the increasingly large number of gene elements on today's microarrays, analysis tools must be developed to meet this challenge. Here, we present MarC-V, a Microsoft Excel spreadsheet tool with Visual Basic macros to automate much of the visualization and calculation involved in the analysis process while providing the familiarity and flexibility of Excel. Automated features of this tool include (i) lower-bound thresholding, (ii) data normalization, (iii) generation of ratio frequency distribution plots, (iv) generation of scatter plots color-coded by expression level, (v) ratio scoring based on intensity measurements, (vi) filtering of data based on expression level or specific gene interests, and (vii) exporting data for subsequent multi-array analysis. MarC-V also has an importing function included for GenePix results (GPR) raw data files.     

Limits to convergence of vegetation during early primary succession

Questions: Primary succession, measured by changes in species composition, is slow, usually forcing a chronose‐quence approach. A unique data set is used to explore spatial and temporal changes in vegetation structure after a 1980 volcanic eruption. On the basis of data from a transect of 20 permanent plots with an altitudinal range of 250 m sampled through 2005, two questions are asked: Do changes along the transect recapitulate succession? Do plots converge to similar composition over time? Location: A ridge between 1218 and 1468 m on Mount St. Helens, Washington, USA. Methods: Repeat sampling of plots for species cover along a 1‐km transect. Floristic changes were characterized by techniques including DCA, clustering and similarity. Results: Species richness and cover increased with time at rates that decreased with increasing elevation. The establishment of Lupinus lepidus accelerated the rate of succession and may control its trajectory. Diversity (H) at first increased with richness, then declined as dominance hierarchies developed. Primary succession was characterized by overlapping phases of species assembly (richness), vegetation maturation (diversity peaks, cover expands) and inhibition (diversity declines). Each plot passed through several community classes, but by 2005, only four classes persisted. Succession trajectories (measured by DCA) became shorter with elevation. Similarity between groups of plots defined by their classification in 2005 did not increase with time. Similarity within plot groups converged slightly at the lower elevations. Despite similarities between temporal and spatial trends in composition, trajectories of higher plots do not recapitulate those of lower plots, apparently because Lupinus was not an early colonist. Any vegetation convergence has been limited to plots that are in close proximity.     

Application of Bayesian decomposition for analysing microarray data

MOTIVATION: Microarray and gene chip technology provide high throughput tools for measuring gene expression levels in a variety of circumstances, including cellular response to drug treatment, cellular growth and development, tumorigenesis, among many other processes. In order to interpret the large data sets generated in experiments, data analysis techniques that consider biological knowledge during analysis will be extremely useful. We present here results showing the application of such a tool to expression data from yeast cell cycle experiments. RESULTS: Originally developed for spectroscopic analysis, Bayesian Decomposition (BD) includes two features which make it useful for microarray data analysis: the ability to assign genes to multiple coexpression groups and the ability to encode biological knowledge into the system. Here we demonstrate the ability of the algorithm to provide insight into the yeast cell cycle, including identification of five temporal patterns tied to cell cycle phases as well as the identification of a pattern tied to an approximately 40 min cell cycle oscillator. The genes are simultaneously assigned to the patterns, including partial assignment to multiple patterns when this is required to explain the expression profile. AVAILABILITY: The application is available free to academic users under a material transfer agreement. Go to http://bioinformatics.fccc.edu/ for more details.