Model-based deconvolution of cell cycle time-series data reveals gene expression details at high resolution

Detecting cognizable trends of gene expression in a time series RNA-sequencing experiment: a bootstrap approach

Study of temporal trajectory of gene expression is important. RNA sequencing is popular in genome-scale studies of transcription. Because of high expenses involved, many time-course RNA sequencing studies are challenged by inadequacy of sample sizes. This poses difficulties in conducting formal statistical tests of significance of null hypotheses. We propose a bootstrap algorithm to identify 'cognizable' 'time-trends' of gene expression. Properties of the proposed algorithm are derived using a simulation study. The proposed algorithm captured known 'time-trends' in the simulated data with a high probability of success, even when sample sizes were small (n < 10). The proposed statistical method is efficient and robust to capture 'cognizable' 'time-trends' in RNA sequencing data.

The effects of cell asynchrony on gene expression levels: analysis and application to Plasmodium falciparum

To investigate the intraerythrocytic developmental cycle of Plasmodium falciparum, time-series gene expression data is commonly measured of infected red blood cells. However, the observed data are usually blurred due to cell asynchrony during experiments. In this paper, the effect of cell asynchrony is investigated by conducting numerical experiments. The simulation results suggest that cell asynchrony has varying effects on different intrinsic expression patterns. Specifically, the intrinsic patterns with high expression around the late life stage are more likely to be affected by cell asynchrony. It is also investigated how the effect of cell asynchrony depends on the experimental conditions. From this analysis, the burst rate r% in infection period and the standard deviation σ of growth rate are identified to have a strong impact on the blurring due to cell asynchrony. Consequently, it is important to measure these two parameters during biological experiments in order to deblur time-series gene expression data.

The effects of cell asynchrony on time-series data: an analysis on gene expression level of Plasmodium falciparum

To investigate the intraerythrocytic cycle of Plasmodium falciparum, time-series gene expression data are measured of infected red blood cells. However, the observed data is blurred due to cell asynchrony during experiments. In this paper, the effects of cell asynchrony are investigated by conducting numerical experiments. The simulation results suggest that cell asynchrony has varying effects on different intrinsic expression patterns. Specifically, the intrinsic patterns with high expression around the late life stage are more likely to be affected by cell asynchrony. It is also investigated how the effects of cell asynchrony are influenced by the experimental conditions. Certain parameters are identified that have a strong effects on cell asynchrony, and these parameters should be measured during biological experiments in order to deblur time-series gene expression data.

A stochastic model dissects cell states in biological transition processes

Many biological processes, including differentiation, reprogramming, and disease transformations, involve transitions of cells through distinct states. Direct, unbiased investigation of cell states and their transitions is challenging due to several factors, including limitations of single-cell assays. Here we present a stochastic model of cellular transitions that allows underlying single-cell information, including cell-state-specific parameters and rates governing transitions between states, to be estimated from genome-wide, population-averaged time-course data. The key novelty of our approach lies in specifying latent stochastic models at the single-cell level, and then aggregating these models to give a likelihood that links parameters at the single-cell level to observables at the population level. We apply our approach in the context of reprogramming to pluripotency. This yields new insights, including profiles of two intermediate cell states, that are supported by independent single-cell studies. Our model provides a general conceptual framework for the study of cell transitions, including epigenetic transformations.

Shrinkage regression-based methods for microarray missing value imputation

Background

Missing values commonly occur in the microarray data, which usually contain more than 5% missing values with up to 90% of genes affected. Inaccurate missing value estimation results in reducing the power of downstream microarray data analyses. Many types of methods have been developed to estimate missing values. Among them, the regression-based methods are very popular and have been shown to perform better than the other types of methods in many testing microarray datasets.

Results

To further improve the performances of the regression-based methods, we propose shrinkage regression-based methods. Our methods take the advantage of the correlation structure in the microarray data and select similar genes for the target gene by Pearson correlation coefficients. Besides, our methods incorporate the least squares principle, utilize a shrinkage estimation approach to adjust the coefficients of the regression model, and then use the new coefficients to estimate missing values. Simulation results show that the proposed methods provide more accurate missing value estimation in six testing microarray datasets than the existing regression-based methods do.

Conclusions

Imputation of missing values is a very important aspect of microarray data analyses because most of the downstream analyses require a complete dataset. Therefore, exploring accurate and efficient methods for estimating missing values has become an essential issue. Since our proposed shrinkage regression-based methods can provide accurate missing value estimation, they are competitive alternatives to the existing regression-based methods.

Missing value imputation for microarray data: a comprehensive comparison study and a web tool

BACKGROUND

Microarray data are usually peppered with missing values due to various reasons. However, most of the downstream analyses for microarray data require complete datasets. Therefore, accurate algorithms for missing value estimation are needed for improving the performance of microarray data analyses. Although many algorithms have been developed, there are many debates on the selection of the optimal algorithm. The studies about the performance comparison of different algorithms are still incomprehensive, especially in the number of benchmark datasets used, the number of algorithms compared, the rounds of simulation conducted, and the performance measures used.

RESULTS

In this paper, we performed a comprehensive comparison by using (I) thirteen datasets, (II) nine algorithms, (III) 110 independent runs of simulation, and (IV) three types of measures to evaluate the performance of each imputation algorithm fairly. First, the effects of different types of microarray datasets on the performance of each imputation algorithm were evaluated. Second, we discussed whether the datasets from different species have different impact on the performance of different algorithms. To assess the performance of each algorithm fairly, all evaluations were performed using three types of measures. Our results indicate that the performance of an imputation algorithm mainly depends on the type of a dataset but not on the species where the samples come from. In addition to the statistical measure, two other measures with biological meanings are useful to reflect the impact of missing value imputation on the downstream data analyses. Our study suggests that local-least-squares-based methods are good choices to handle missing values for most of the microarray datasets.

CONCLUSIONS

In this work, we carried out a comprehensive comparison of the algorithms for microarray missing value imputation. Based on such a comprehensive comparison, researchers could choose the optimal algorithm for their datasets easily. Moreover, new imputation algorithms could be compared with the existing algorithms using this comparison strategy as a standard protocol. In addition, to assist researchers in dealing with missing values easily, we built a web-based and easy-to-use imputation tool, MissVIA (http://cosbi.ee.ncku.edu.tw/MissVIA), which supports many imputation algorithms. Once users upload a real microarray dataset and choose the imputation algorithms, MissVIA will determine the optimal algorithm for the users' data through a series of simulations, and then the imputed results can be downloaded for the downstream data analyses.

Deconvolution of gene expression from cell populations across the C. elegans lineage

Background

Knowledge of when and in which cells each gene is expressed across multicellular organisms is critical in understanding both gene function and regulation of cell type diversity. However, methods for measuring expression typically involve a trade-off between imaging-based methods, which give the precise location of a limited number of genes, and higher throughput methods such as RNA-seq, which include all genes, but are more limited in their resolution to apply to many tissues. We propose an intermediate method, which estimates expression in individual cells, based on high-throughput measurements of expression from multiple overlapping groups of cells. This approach has particular benefits in organisms such as C. elegans where invariant developmental patterns make it possible to define these overlapping populations of cells at single-cell resolution.

Result

We implement several methods to deconvolve the gene expression in individual cells from population-level data and determine the accuracy of these estimates on simulated data from the C. elegans embryo.

Conclusion

These simulations suggest that a high-resolution map of expression in the C. elegans embryo may be possible with expression data from as few as 30 cell populations.

Branching process deconvolution algorithm reveals a detailed cell-cycle transcription program

Due to cell-to-cell variability and asymmetric cell division, cells in a synchronized population lose synchrony over time. As a result, time-series measurements from synchronized cell populations do not reflect the underlying dynamics of cell-cycle processes. Here, we present a branching process deconvolution algorithm that learns a more accurate view of dynamic cell-cycle processes, free from the convolution effects associated with imperfect cell synchronization. Through wavelet-basis regularization, our method sharpens signal without sharpening noise and can remarkably increase both the dynamic range and the temporal resolution of time-series data. Although applicable to any such data, we demonstrate the utility of our method by applying it to a recent cell-cycle transcription time course in the eukaryote Saccharomyces cerevisiae. Our method more sensitively detects cell-cycle-regulated transcription and reveals subtle timing differences that are masked in the original population measurements. Our algorithm also explicitly learns distinct transcription programs for mother and daughter cells, enabling us to identify 82 genes transcribed almost entirely in early G1 in a daughter-specific manner.

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.

Single-gene tuning of Caulobacter cell cycle period and noise, swarming motility, and surface adhesion

We established that the sensor histidine kinase DivJ has an important role in the regulation of C. crescentus cell cycle period and noise. This was accomplished by designing and conducting single-cell experiments to probe the dependence of cell cycle noise on divJ expression and constructing a simplified cell cycle model that captures the dependence of cell cycle noise on DivJ with molecular details.

In addition to its role in regulating the cell cycle, DivJ also affects polar cell development in C. crescentus, regulating swarming motility and surface adhesion. We propose that pleiotropic control of polar cell development by the DivJ–DivK–PleC signaling pathway underlies divJ-dependent tuning of cell swarming and adhesion behaviors.

We have integrated the study of single-cell fluorescence dynamics with a kinetic model simulation to provide direct quantitative evidence that the DivJ histidine kinase is localized to the cell pole through a dynamic diffusion-and-capture mechanism during the C. crescentus cell cycle.

Temporally-coordinated localization of various structural and signaling proteins is critical for proper cell cycle regulation and polar cell development in the bacterium, Caulobacter crescentus. Included among these dynamically-localized regulatory proteins is the sensor histidine kinase, DivJ (Wheeler and Shapiro, 1999). Co-localized with DivJ in the early stalked phase is the phosphorylated response regulator DivK∼P (Jacobs et al, 2001), and the protease ClpXP (McGrath et al, 2006), which degrades the master cell cycle regulator, CtrA (Jenal and Fuchs, 1998). Recent single-cell measurements of surface attached C. crescentus cells have revealed an intriguing role for DivJ in the control of noise in cell division period (Siegal-Gaskins and Crosson, 2008). The noise of the cell cycle increases significantly upon disruption of the divJ gene, with a relatively small accompanying increase in the mean cell cycle time. The deterministic nature of the existing cell cycle models (Li et al, 2008, 2009; Shen et al, 2008) cannot explain the measured increase in cell cycle period and noise in a divJ null strain. Moreover, mechanistic descriptions of how DivJ and its signaling partners are localized and how these proteins underlie the control of polar cell development and cell adhesion in C. crescentus remain immature.

The single-cell experiments and analysis presented herein reveal that C. crescentus cell cycle period and noise can be tuned by DivJ (Figure 2). Specifically, in the case of low (or no) divJ expression the cell cycle is perturbed, and this is quantified by way of the (measured) noise in the cell cycle period. The level of noise is readily controlled through regulated expression of the divJ gene (Figure 2B). A simplified protein interaction network of stalked C. crescentus cell cycle regulation involving minimal components (CtrA, CtrA∼P, DivK, DivK∼P, and DivJ) was constructed to explore such tunability at the molecular level. The agreement of our model with our (and other) experiments suggests this simplified protein regulatory network is sufficient to explain the major features of the C. crescentus cell cycle. Indeed, stochastic simulations of this model using the Gillespie method (Gillespie, 1976) establish the importance of robust DivJ-mediated phosphorylation of its cognate receiver protein, DivK, in regulating the variance of cell cycle oscillations. Increased variability in the concentration of DivK∼P at the single cell level under divJ depletion subsequently leads to increased noise in the regulation of CtrA phosphorylation and degradation. Our experiments and simulations provide evidence that the steady state level of DivK∼P at the single-cell level (as maintained by DivJ) is essential in maintaining regular timing of the cell division period in C. crescentus.

In addition to its role in regulating cell cycle, divJ expression also affects polar cell development in C. crescentus. Specifically, the capacity of swarmer cells to adhere to a glass surface is suppressed at high levels of divJ expression. The effect of elevated divJ expression on the adhesive capacity of the cell is reflected in a reduced rate of two-dimensional biofilm formation. This effect is quantitatively captured by our mathematical model that relates single-cell surface adhesion physiology and biofilm formation dynamics. This result, and our observation that divJ expression tunes swarming motility in semi-solid growth medium, suggests a model in which increased DivJ concentration in the swarmer compartment (due to constitutive overexpression) ultimately results in improper development of polar organelles that are required for adhesion of swarming motility.

Despite the appreciated significance of protein localization for bacterial physiological functions, the molecular mechanism of how polar protein localization is achieved has only been tested in a few cases (Shapiro et al, 2002; Thanbichler and Shapiro, 2008). Mechanisms such as the polar insertion model and diffusion-and-capture have been proposed but the community's knowledge is limited to very few examples (Charles et al, 2001; Rudner et al, 2002). We provide direct evidence from experiments and simulations that the DivJ histidine kinase becomes localized to the cell pole through a dynamic diffusion-and-capture mechanism during the C. crescentus cell cycle (Figure 7). We show that a kinetic model based on a Langmuir adsorption/desorption relationship (Figure 7D) is sufficient to explain the time evolution of the single cell fluorescence time traces (Figure 7C and E) and allows establishing quantitative correspondences between the simulated dynamics and experimentally determined DivJ–EGFP dynamics. This localization mechanism is consistent with a diffusion-and-capture model. In short, the model posits that proteins are randomly distributed and are freely diffusing until they are captured at the site where they ultimately reside (Rudner et al, 2002; Shapiro et al, 2002; Bardy and Maddock, 2007). With a diffusion-and-capture pathway, it has been argued that proteins can be adsorbed either dynamically or statically (Shapiro et al, 2009). Our analysis of DivJ–EGFP in single cells supports a dynamic diffuse-and-capture mechanism for DivJ localization.

Sensor histidine kinases underlie the regulation of a range of physiological processes in bacterial cells, from chemotaxis to cell division. In the gram-negative bacterium Caulobacter crescentus, the membrane-bound histidine kinase, DivJ, is a polar-localized regulator of cell cycle progression and development. We show that DivJ localizes to the cell pole through a dynamic diffusion and capture mechanism rather than by active localization. Analysis of single C. crescentus cells in microfluidic culture demonstrates that controlled expression of divJ permits facile tuning of both the mean and noise of the cell division period. Simulations of the cell cycle that use a simplified protein interaction network capture previously measured oscillatory protein profiles, and recapitulate the experimental observation that deletion of divJ increases the cell cycle period and noise. We further demonstrate that surface adhesion and swarming motility of C. crescentus in semi-solid media can also be tuned by divJ expression. We propose a model in which pleiotropic control of polar cell development by the DivJ–DivK–PleC signaling pathway underlies divJ-dependent tuning of cell swarming and adhesion behaviors.