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Integrated Pipelines for Inferring Gene Regulatory Networks from Single-Cell Data
Abstract
Background
Single-cell technologies provide unprecedented opportunities to study heterogeneity of molecular mechanisms. In particular, single-cell RNA-sequence data have been successfully used to infer gene regulatory networks with stochastic expressions. However, there are still substantial challenges in measuring the relationships between genes and selecting the important genetic regulations.
Objective
This prospective provides a brief review of effective methods for the inference of gene regulatory networks.
Methods
We concentrate on two types of inference methods, namely the model-free methods and mechanistic methods for constructing gene networks.
Results
For the model-free methods, we mainly discuss two issues, namely the measures for quantifying gene relationship and criteria for selecting significant connections between genes. The issue for mechanistic methods is different mathematical models to describe genetic regulations accurately.
Conclusions
We and advocates the development of ensemble methods that combine two or more methods together.
The mitogen-activated protein kinase (MAPK) pathway is an important intracellular signaling cascade that plays a key role in various cellular processes. Understanding the regulatory mechanisms of this pathway is essential for developing effective interventions and targeted therapies for related diseases. Recent advances in single-cell proteomic technologies have provided unprecedented opportunities to investigate the heterogeneity and noise within complex, multi-signaling networks across diverse cells and cell types. Mathematical modeling has become a powerful interdisciplinary tool that bridges mathematics and experimental biology, providing valuable insights into these intricate cellular processes. In addition, statistical methods have been developed to infer pathway topologies and estimate unknown parameters within dynamic models. This review presents a comprehensive analysis of how mathematical modeling of the MAPK pathway deepens our understanding of its regulatory mechanisms, enhances the prediction of system behavior, and informs experimental research, with a particular focus on recent advances in modeling and inference using single-cell proteomic data.
Background
Cancer is a leading cause of human death worldwide. Drug resistance, mainly caused by gene mutation, is a key obstacle to tumour treatment. Therefore, studying the mechanisms of drug resistance in cancer is extremely valuable for clinical applications.
Objective
This paper aims to review bioinformatics approaches and mathematical models for determining the evolutionary mechanisms of drug resistance and investigating their functions in designing therapy schemes for cancer diseases. We focus on the models with drug resistance based on genetic mutations for cancer therapy and bioinformatics approaches to study drug resistance involving gene co-expression networks and machine learning algorithms.
Results
We first review mathematical models with single-drug resistance and multidrug resistance. The resistance probability of a drug is different from the order of drug administration in a multidrug resistance model. Then, we discuss bioinformatics methods and machine learning algorithms that are designed to develop gene co-expression networks and explore the functions of gene mutations in drug resistance using multi-omics datasets of cancer cells, which can be used to predict individual drug response and prognostic biomarkers.
Conclusion
It was found that the resistance probability and expected number of drug-resistant tumour cells increase with the increase in the net reproductive rate of resistant tumour cells. Constrained models, such as logistical growth resistance models, can be used to identify more clinically realistic treatment strategies for cancer therapy. In addition, bioinformatics methods and machine learning algorithms can also lead to the development of effective therapy schemes.
Gene regulatory networks (GRNs) encode the complex molecular interactions that govern cell identity. Here we propose DeepSEM, a deep generative model that can jointly infer GRNs and biologically meaningful representation of single-cell RNA sequencing (scRNA-seq) data. In particular, we developed a neural network version of the structural equation model (SEM) to explicitly model the regulatory relationships among genes. Benchmark results show that DeepSEM achieves comparable or better performance on a variety of single-cell computational tasks, such as GRN inference, scRNA-seq data visualization, clustering and simulation, compared with the state-of-the-art methods. In addition, the gene regulations predicted by DeepSEM on cell-type marker genes in the mouse cortex can be validated by epigenetic data, which further demonstrates the accuracy and efficiency of our method. DeepSEM can provide a useful and powerful tool to analyze scRNA-seq data and infer a GRN.
One of the major challenges in single-cell data analysis is the determination of cellular developmental trajectories using single-cell data. Although substantial studies have been conducted in recent years, more effective methods are still strongly needed to infer the developmental processes accurately. This work devises a new method, named DTFLOW, for determining the pseudo-temporal trajectories with multiple branches. DTFLOW consists of two major steps: namely, a new method called Bhattacharyya kernel feature decomposition (BKFD) to reduce the data dimensions, and a novel approach, named reverse searching on k-nearest neighbor graph (RSKG), to identify the multi-branching processes of cellular differentiation. In BKFD we first establish a stationary distribution for each cell to represent the transition of cellular developmental states based on the random walk with restart algorithm, and then propose a new distance metric for calculating pseudotime of single cells by introducing the Bhattacharyya kernel matrix. The effectiveness of DTFLOW is rigorously examined by using four single-cell datasets. We compare the efficiency of DTFLOW with the published state-of-the-art methods. Simulation results suggest that DTFLOW has superior accuracy and strong robustness properties for constructing pseudotime trajectories. The Python source code of DTFLOW can be freely accessed at https://github.com/statway/DTFLOW.
Gene regulatory network inference is essential to uncover complex relationships among gene pathways and inform downstream experiments, ultimately enabling regulatory network re-engineering. Network inference from transcriptional time-series data requires accurate, interpretable, and efficient determination of causal relationships among thousands of genes. Here, we develop Bootstrap Elastic net regression from Time Series (BETS), a statistical framework based on Granger causality for the recovery of a directed gene network from transcriptional time-series data. BETS uses elastic net regression and stability selection from bootstrapped samples to infer causal relationships among genes. BETS is highly parallelized, enabling efficient analysis of large transcriptional data sets. We show competitive accuracy on a community benchmark, the DREAM4 100-gene network inference challenge, where BETS is one of the fastest among methods of similar performance and additionally infers whether causal effects are activating or inhibitory. We apply BETS to transcriptional time-series data of differentially-expressed genes from A549 cells exposed to glucocorticoids over a period of 12 hours. We identify a network of 2768 genes and 31,945 directed edges (FDR ≤ 0.2). We validate inferred causal network edges using two external data sources: Overexpression experiments on the same glucocorticoid system, and genetic variants associated with inferred edges in primary lung tissue in the Genotype-Tissue Expression (GTEx) v6 project. BETS is available as an open source software package at https://github.com/lujonathanh/BETS.
Gene regulatory network is a complicated set of interactions between genetic materials, which dictates how cells develop in living organisms and react to their surrounding environment. Robust comprehension of these interactions would help explain how cells function as well as predict their reactions to external factors. This knowledge can benefit both developmental biology and clinical research such as drug development or epidemiology research. Recently, the rapid advance of single-cell sequencing technologies, which pushed the limit of transcriptomic profiling to the individual cell level, opens up an entirely new area for regulatory network research. To exploit this new abundant source of data and take advantage of data in single-cell resolution, a number of computational methods have been proposed to uncover the interactions hidden by the averaging process in standard bulk sequencing. In this article, we review 15 such network inference methods developed for single-cell data. We discuss their underlying assumptions, inference techniques, usability, and pros and cons. In an extensive analysis using simulation, we also assess the methods' performance, sensitivity to dropout and time complexity. The main objective of this survey is to assist not only life scientists in selecting suitable methods for their data and analysis purposes but also computational scientists in developing new methods by highlighting outstanding challenges in the field that remain to be addressed in the future development.
The advancement of single-cell sequencing technology in recent years has provided an opportunity to reconstruct gene regulatory networks (GRNs) with the data from thousands of single cells in one sample. This uncovers regulatory interactions in cells and speeds up the discoveries of regulatory mechanisms in diseases and biological processes. Therefore, more methods have been proposed to reconstruct GRNs using single-cell sequencing data. In this review, we introduce technologies for sequencing single-cell genome, transcriptome, and epigenome. At the same time, we present an overview of current GRN reconstruction strategies utilizing different single-cell sequencing data. Bioinformatics tools were grouped by their input data and mathematical principles for readers' convenience, and the fundamental mathematics inherent in each group will be discussed. Furthermore, the adaptabilities and limitations of these different methods will also be summarized and compared, with the hope to facilitate researchers recognizing the most suitable tools for them.
Hematopoiesis is a highly complex developmental process that produces various types of blood cells. This process is regulated by different genetic networks that control the proliferation, differentiation, and maturation of hematopoietic stem cells (HSCs). Although substantial progress has been made for understanding hematopoiesis, the detailed regulatory mechanisms for the fate determination of HSCs are still unraveled. In this study, we propose a novel approach to infer the detailed regulatory mechanisms. This work is designed to develop a mathematical framework that is able to realize nonlinear gene expression dynamics accurately. In particular, we intended to investigate the effect of possible protein heterodimers and/or synergistic effect in genetic regulation. This approach includes the Extended Forward Search Algorithm to infer network structure (top-down approach) and a non-linear mathematical model to infer dynamical property (bottom-up approach). Based on the published experimental data, we study two regulatory networks of 11 genes for regulating the erythrocyte differentiation pathway and the neutrophil differentiation pathway. The proposed algorithm is first applied to predict the network topologies among 11 genes and 55 non-linear terms which may be for heterodimers and/or synergistic effect. Then, the unknown model parameters are estimated by fitting simulations to the expression data of two different differentiation pathways. In addition, the edge deletion test is conducted to remove possible insignificant regulations from the inferred networks. Furthermore, the robustness property of the mathematical model is employed as an additional criterion to choose better network reconstruction results. Our simulation results successfully realized experimental data for two different differentiation pathways, which suggests that the proposed approach is an effective method to infer the topological structure and dynamic property of genetic regulations.
The recent boom in microfluidics and combinatorial indexing strategies, combined with low sequencing costs, has empowered single-cell sequencing technology. Thousands-or even millions-of cells analyzed in a single experiment amount to a data revolution in single-cell biology and pose unique data science problems. Here, we outline eleven challenges that will be central to bringing this emerging field of single-cell data science forward. For each challenge, we highlight motivating research questions, review prior work, and formulate open problems. This compendium is for established researchers, newcomers, and students alike, highlighting interesting and rewarding problems for the coming years.
We present a systematic evaluation of state-of-the-art algorithms for inferring gene regulatory networks from single-cell transcriptional data. As the ground truth for assessing accuracy, we use synthetic networks with predictable trajectories, literature-curated Boolean models and diverse transcriptional regulatory networks. We develop a strategy to simulate single-cell transcriptional data from synthetic and Boolean networks that avoids pitfalls of previously used methods. Furthermore, we collect networks from multiple experimental single-cell RNA-seq datasets. We develop an evaluation framework called BEELINE. We find that the area under the precision-recall curve and early precision of the algorithms are moderate. The methods are better in recovering interactions in synthetic networks than Boolean models. The algorithms with the best early precision values for Boolean models also perform well on experimental datasets. Techniques that do not require pseudotime-ordered cells are generally more accurate. Based on these results, we present recommendations to end users. BEELINE will aid the development of gene regulatory network inference algorithms. Comprehensive evaluation of algorithms for inferring gene regulatory networks using synthetic and experimental single-cell RNA-seq datasets finds heterogeneous performance and suggests recommendations to users.
Background
Inference of gene regulatory networks from gene expression data has been a long-standing and notoriously difficult task in systems biology. Recently, single-cell transcriptomic data have been massively used for gene regulatory network inference, with both successes and limitations.
Results
In the present work we propose an iterative algorithm called WASABI, dedicated to inferring a causal dynamical network from time-stamped single-cell data, which tackles some of the limitations associated with current approaches. We first introduce the concept of waves, which posits that the information provided by an external stimulus will affect genes one-by-one through a cascade, like waves spreading through a network. This concept allows us to infer the network one gene at a time, after genes have been ordered regarding their time of regulation. We then demonstrate the ability of WASABI to correctly infer small networks, which have been simulated in silico using a mechanistic model consisting of coupled piecewise-deterministic Markov processes for the proper description of gene expression at the single-cell level. We finally apply WASABI on in vitro generated data on an avian model of erythroid differentiation. The structure of the resulting gene regulatory network sheds a new light on the molecular mechanisms controlling this process. In particular, we find no evidence for hub genes and a much more distributed network structure than expected. Interestingly, we find that a majority of genes are under the direct control of the differentiation-inducing stimulus.
Conclusions
Together, these results demonstrate WASABI versatility and ability to tackle some general gene regulatory networks inference issues. It is our hope that WASABI will prove useful in helping biologists to fully exploit the power of time-stamped single-cell data.
Single-cell transcriptomics provides an opportunity to characterize cell-type-specific transcriptional networks, intercellular signaling pathways and cellular diversity with unprecedented resolution by profiling thousands of cells in a single experiment. However, owing to the unique statistical properties of scRNA-seq data, the optimal measures of association for identifying gene–gene and cell–cell relationships from single-cell transcriptomics remain unclear. Here, we conducted a large-scale evaluation of 17 measures of association for their ability to reconstruct cellular networks, cluster cells of the same type and link cell-type-specific transcriptional programs to disease. Measures of proportionality were consistently among the best-performing methods across datasets and tasks. Our analysis provides data-driven guidance for gene and cell network analysis in single-cell transcriptomics.
Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterizing stochastic effects in biochemical systems is essential to understand the complex dynamics of living things. Mathematical idealizations of biochemically reacting systems must be able to capture stochastic phenomena. While robust theory exists to describe such stochastic models, the computational challenges in exploring these models can be a significant burden in practice since realistic models are analytically intractable. Determining the expected behaviour and variability of a stochastic biochemical reaction network requires many probabilistic simulations of its evolution. Using a biochemical reaction network model to assist in the interpretation of time-course data from a biological experiment is an even greater challenge due to the intractability of the likelihood function for determining observation probabilities. These computational challenges have been subjects of active research for over four decades. In this review, we present an accessible discussion of the major historical developments and state-of-the-art computational techniques relevant to simulation and inference problems for stochastic biochemical reaction network models. Detailed algorithms for particularly important methods are described and complemented with Matlab w implementations. As a result, this review provides a practical and accessible introduction to computational methods for stochastic models within the life sciences community. © 2019 The Author(s) Published by the Royal Society. All rights reserved.
Advances in single-cell transcriptomics enable measuring the gene expression of individual cells, allowing cells to be ordered by their state in a dynamic biological process. Many algorithms assign 'pseudotimes' to each cell, representing the progress along the biological process. Ordering the expression data according to such pseudotimes can be valuable for understanding the underlying regulator-gene interactions in a biological process, such as differentiation. However, the distribution of cells sampled along a transitional process, and hence that of the pseudotimes assigned to them, is not uniform. This prevents using many standard mathematical methods for analyzing the ordered gene expression states. We present Single-Cell Inference of Networks using Granger Ensembles (SCINGE), an algorithm for gene regulatory network inference from single-cell gene expression data. Given ordered single-cell data, SCINGE uses kernel-based Granger Causality regression, which smooths the irregular pseudotimes and missing expression values. It then aggregates the predictions from an ensemble of regression analyses with a modified Borda method to compile a ranked list of candidate interactions between transcriptional regulators and their target genes. In two mouse embryonic stem cell differentiation case studies, SCINGE outperforms other contemporary algorithms for gene network reconstruction. However, a more detailed examination reveals caveats about transcriptional network reconstruction with single-cell RNA-seq data. Network inference methods, including SCINGE, may have near random performance for predicting the targets of many individual regulators even if the aggregate performance is good. In addition, in some cases including cells' pseudotime values can hurt the performance of network reconstruction methods. A MATLAB implementation of SCINGE is available at https://github.com/gitter-lab/SCINGE.
Background:
A fundamental fact in biology states that genes do not operate in isolation, and yet, methods that infer regulatory networks for single cell gene expression data have been slow to emerge. With single cell sequencing methods now becoming accessible, general network inference algorithms that were initially developed for data collected from bulk samples may not be suitable for single cells. Meanwhile, although methods that are specific for single cell data are now emerging, whether they have improved performance over general methods is unknown. In this study, we evaluate the applicability of five general methods and three single cell methods for inferring gene regulatory networks from both experimental single cell gene expression data and in silico simulated data.
Results:
Standard evaluation metrics using ROC curves and Precision-Recall curves against reference sets sourced from the literature demonstrated that most of the methods performed poorly when they were applied to either experimental single cell data, or simulated single cell data, which demonstrates their lack of performance for this task. Using default settings, network methods were applied to the same datasets. Comparisons of the learned networks highlighted the uniqueness of some predicted edges for each method. The fact that different methods infer networks that vary substantially reflects the underlying mathematical rationale and assumptions that distinguish network methods from each other.
Conclusions:
This study provides a comprehensive evaluation of network modeling algorithms applied to experimental single cell gene expression data and in silico simulated datasets where the network structure is known. Comparisons demonstrate that most of these assessed network methods are not able to predict network structures from single cell expression data accurately, even if they are specifically developed for single cell methods. Also, single cell methods, which usually depend on more elaborative algorithms, in general have less similarity to each other in the sets of edges detected. The results from this study emphasize the importance for developing more accurate optimized network modeling methods that are compatible for single cell data. Newly-developed single cell methods may uniquely capture particular features of potential gene-gene relationships, and caution should be taken when we interpret these results.
Background:
Recent advances in omics technologies have raised great opportunities to study large-scale regulatory networks inside the cell. In addition, single-cell experiments have measured the gene and protein activities in a large number of cells under the same experimental conditions. However, a significant challenge in computational biology and bioinformatics is how to derive quantitative information from the single-cell observations and how to develop sophisticated mathematical models to describe the dynamic properties of regulatory networks using the derived quantitative information.
Methods:
This work designs an integrated approach to reverse-engineer gene networks for regulating early blood development based on singel-cell experimental observations. The wanderlust algorithm is initially used to develop the pseudo-trajectory for the activities of a number of genes. Since the gene expression data in the developed pseudo-trajectory show large fluctuations, we then use Gaussian process regression methods to smooth the gene express data in order to obtain pseudo-trajectories with much less fluctuations. The proposed integrated framework consists of both bioinformatics algorithms to reconstruct the regulatory network and mathematical models using differential equations to describe the dynamics of gene expression.
Results:
The developed approach is applied to study the network regulating early blood cell development. A graphic model is constructed for a regulatory network with forty genes and a dynamic model using differential equations is developed for a network of nine genes. Numerical results suggests that the proposed model is able to match experimental data very well. We also examine the networks with more regulatory relations and numerical results show that more regulations may exist. We test the possibility of auto-regulation but numerical simulations do not support the positive auto-regulation. In addition, robustness is used as an importantly additional criterion to select candidate networks.
Conclusion:
The research results in this work shows that the developed approach is an efficient and effective method to reverse-engineer gene networks using single-cell experimental observations.
In the life sciences, many assays measure only the relative abundances of components in each sample. Such data, called compositional data, require special treatment to avoid misleading conclusions. Awareness of the need for caution in analyzing compositional data is growing, including the understanding that correlation is not appropriate for relative data. Recently, researchers have proposed proportionality as a valid alternative to correlation for calculating pairwise association in relative data. Although the question of how to best measure proportionality remains open, we present here a computationally efficient R package that implements three measures of proportionality. In an effort to advance the understanding and application of proportionality analysis, we review the mathematics behind proportionality, demonstrate its application to genomic data, and discuss some ongoing challenges in the analysis of relative abundance data.
Motivation:
Single cell transcriptional profiling opens up a new avenue in studying the functional role of cell-to-cell variability in physiological processes. The analysis of single cell expression profiles creates new challenges due to the distributive nature of the data and the stochastic dynamics of gene transcription process. The reconstruction of gene regulatory networks (GRNs) using single cell transcriptional profiles is particularly challenging, especially when directed gene-gene relationships are desired.
Results:
We developed SINCERITIES (SINgle CEll Regularized Inference using TIme-stamped Expression profileS) for the inference of GRNs from single cell transcriptional profiles. We focused on time-stamped cross-sectional expression data, commonly generated from transcriptional profiling of single cells collected at multiple time points after cell stimulation. SINCERITIES recovers directed regulatory relationships among genes by employing regularized linear regression (ridge regression), using temporal changes in the distributions of gene expressions. Meanwhile, the modes of the gene regulations (activation and repression) come from partial correlation analyses between pairs of genes. We demonstrated the efficacy of SINCERITIES in inferring GRNs using in silico time-stamped single cell expression data and single cell transcriptional profiles of THP-1 monocytic human leukemia cells. The case studies showed that SINCERITIES could provide accurate GRN predictions, significantly better than other GRN inference algorithms such as TSNI, GENIE3 and JUMP3. Moreover, SINCERITIES has a low computational complexity and is amenable to problems of extremely large dimensionality. Finally, an application of SINCERITIES to single cell expression data of T2EC chicken erythrocytes pointed to BATF as a candidate novel regulator of erythroid development.
Availability:
The MATLAB and R version of SINCERITIES is freely available from the following websites: http://www.cabsel.ethz.ch/tools/sincerities.html and https://github.com/CABSEL/SINCERITIES .
Contact:
rudi.gunawan@chem.ethz.ch.
Supplementary information:
Supplementary file and material are available at Bioinformatics online.
While single-cell gene expression experiments present new challenges for data processing, the cell-to-cell variability observed also reveals statistical relationships that can be used by information theory. Here, we use multivariate information theory to explore the statistical dependencies between triplets of genes in single-cell gene expression datasets. We develop PIDC, a fast, efficient algorithm that uses partial information decomposition (PID) to identify regulatory relationships between genes. We thoroughly evaluate the performance of our algorithm and demonstrate that the higher-order information captured by PIDC allows it to outperform pairwise mutual information-based algorithms when recovering true relationships present in simulated data. We also infer gene regulatory networks from three experimental single-cell datasets and illustrate how network context, choices made during analysis, and sources of variability affect network inference. PIDC tutorials and open-source software for estimating PID are available. PIDC should facilitate the identification of putative functional relationships and mechanistic hypotheses from single-cell transcriptomic data.
In this work, we provide a comparative study of the main available association measures for characterizing gene regulatory strengths. Detecting the association between genes (as well as RNAs, proteins, and other molecules) is very important to decipher their functional relationship from genomic data in bioinformatics. With the availability of more and more high-throughput datasets, the quantification of meaningful relationships by employing association measures will make great sense of the data. There are various quantitative measures have been proposed for identifying molecular associations. They are depended on different statistical assumptions, for different intentions, as well as with different computational costs in calculating the associations in thousands of genes. Here, we comprehensively summarize these association measures employed and developed for describing gene regulatory relationships. We compare these measures in their consistency and specificity of detecting gene regulations from both simulation and real gene expression profiling data. Obviously, these measures used in genes can be easily extended in other biological molecules or across them.
Motivation: The analysis of RNA-Seq data from individual differentiating cells enables us to reconstruct the differentiation process and the degree of differentiation (in pseudo-time) of each cell. Such analyses can reveal detailed expression dynamics and functional relationships for differentiation. To further elucidate differentiation processes, more insight into gene regulatory networks is required. The pseudo-time can be regarded as time information and, therefore, single-cell RNA-Seq data are time-course data with high time resolution. Although time-course data are useful for inferring networks, conventional inference algorithms for such data suffer from high time complexity when the number of samples and genes is large. Therefore, a novel algorithm is necessary to infer networks from single-cell RNA-Seq during differentiation.
Results: In this study, we developed the novel and efficient algorithm SCODE to infer regulatory networks, based on ordinary differential equations. We applied SCODE to three single-cell RNA-Seq datasets and confirmed that SCODE can reconstruct observed expression dynamics. We evaluated SCODE by comparing its inferred networks with use of a DNaseI-footprint based network. The performance of SCODE was best for two of the datasets and nearly best for the remaining dataset. We also compared the runtimes and showed that the runtimes for SCODE are significantly shorter than for alternatives. Thus, our algorithm provides a promising approach for further single-cell differentiation analyses.
Availability: The R source code of SCODE is available at https://github.com/hmatsu1226/SCODE.
Contact:hirotaka.matsumoto@riken.jp
Supplementary information
:
Supplementary data
are available at Bioinformatics online.
Background
Single-cell technologies make it possible to quantify the comprehensive states of individual cells, and have the power to shed light on cellular differentiation in particular. Although several methods have been developed to fully analyze the single-cell expression data, there is still room for improvement in the analysis of differentiation.
Results
In this paper, we propose a novel method SCOUP to elucidate differentiation process. Unlike previous dimension reduction-based approaches, SCOUP describes the dynamics of gene expression throughout differentiation directly, including the degree of differentiation of a cell (in pseudo-time) and cell fate. SCOUP is superior to previous methods with respect to pseudo-time estimation, especially for single-cell RNA-seq. SCOUP also successfully estimates cell lineage more accurately than previous method, especially for cells at an early stage of bifurcation. In addition, SCOUP can be applied to various downstream analyses. As an example, we propose a novel correlation calculation method for elucidating regulatory relationships among genes. We apply this method to a single-cell RNA-seq data and detect a candidate of key regulator for differentiation and clusters in a correlation network which are not detected with conventional correlation analysis.
Conclusions
We develop a stochastic process-based method SCOUP to analyze single-cell expression data throughout differentiation. SCOUP can estimate pseudo-time and cell lineage more accurately than previous methods. We also propose a novel correlation calculation method based on SCOUP. SCOUP is a promising approach for further single-cell analysis and available at https://github.com/hmatsu1226/SCOUP.
Electronic supplementary material
The online version of this article (doi:10.1186/s12859-016-1109-3) contains supplementary material, which is available to authorized users.
Devising computational methods to accurately reconstruct gene regulatory networks given gene expression data is key to systems biology applications. Here we propose a method for reconstructing gene regulatory networks by simultaneous consideration of data sets from different perturbation experiments and corresponding controls. The method imposes three biologically meaningful constraints: (1) expression levels of each gene should be explained by the expression levels of a small number of transcription factor coding genes, (2) networks inferred from different data sets should be similar with respect to the type and number of regulatory interactions, and (3) relationships between genes which exhibit similar differential behavior over the considered perturbations should be favored. We demonstrate that these constraints can be transformed in a fused LASSO formulation for the proposed method. The comparative analysis on transcriptomics time-series data from prokaryotic species, Escherichia coli and Mycobacterium tuberculosis, as well as a eukaryotic species, mouse, demonstrated that the proposed method has the advantages of the most recent approaches for regulatory network inference, while obtaining better performance and assigning higher scores to the true regulatory links. The study indicates that the combination of sparse regression techniques with other biologically meaningful constraints is a promising framework for gene regulatory network reconstructions.
The ability to discover physical laws and governing equations from data is
one of humankind's greatest intellectual achievements. A quantitative
understanding of dynamic constraints and balances in nature has facilitated
rapid development of knowledge and enabled advanced technological achievements,
including aircraft, combustion engines, satellites, and electrical power. In
this work, we combine sparsity-promoting techniques and machine learning with
nonlinear dynamical systems to discover governing physical equations from
measurement data. The only assumption about the structure of the model is that
there are only a few important terms that govern the dynamics, so that the
equations are sparse in the space of possible functions; this assumption holds
for many physical systems. In particular, we use sparse regression to determine
the fewest terms in the dynamic governing equations required to accurately
represent the data. The resulting models are parsimonious, balancing model
complexity with descriptive ability while avoiding overfitting. We demonstrate
the algorithm on a wide range of problems, from simple canonical systems,
including linear and nonlinear oscillators and the chaotic Lorenz system, to
the fluid vortex shedding behind an obstacle. The fluid example illustrates the
ability of this method to discover the underlying dynamics of a system that
took experts in the community nearly 30 years to resolve. We also show that
this method generalizes to parameterized, time-varying, or externally forced
systems.
High-dimensional single-cell snapshot data are becoming widespread in the systems biology community, as a mean to understand biological processes at the cellular level. However, as temporal information is lost with such data, mathematical models have been limited to capture only static features of the underlying cellular mechanisms.
Here, we present a modular framework which allows to recover the temporal behaviour from single-cell snapshot data and reverse engineer the dynamics of gene expression. The framework combines a dimensionality reduction method with a cell time-ordering algorithm to generate pseudo time-series observations. These are in turn used to learn transcriptional ODE models and do model selection on structural network features. We apply it on synthetic data and then on real hematopoietic stem cells data, to reconstruct gene expression dynamics during differentiation pathways and infer the structure of a key gene regulatory network.
C++ and Matlab code available at https://www.helmholtz-muenchen.de/fileadmin/ICB/software/inferenceSnapshot.zip.
fabian.theis@helmholtz-muenchen.deSupplementary information: Supplementary data are available at Bioinformatics online.
© The Author 2015. Published by Oxford University Press.
Reconstruction of the molecular pathways controlling organ development has been hampered by a lack of methods to resolve embryonic progenitor cells. Here we describe a strategy to address this problem that combines gene expression profiling of large numbers of single cells with data analysis based on diffusion maps for dimensionality reduction and network synthesis from state transition graphs. Applying the approach to hematopoietic development in the mouse embryo, we map the progression of mesoderm toward blood using single-cell gene expression analysis of 3,934 cells with blood-forming potential captured at four time points between E7.0 and E8.5. Transitions between individual cellular states are then used as input to develop a single-cell network synthesis toolkit to generate a computationally executable transcriptional regulatory network model of blood development. Several model predictions concerning the roles of Sox and Hox factors are validated experimentally. Our results demonstrate that single-cell analysis of a developing organ coupled with computational approaches can reveal the transcriptional programs that underpin organogenesis.
Inference of gene regulatory network from expression data is a challenging task. Many methods have been developed to this purpose but a comprehensive evaluation that covers unsupervised, semi-supervised and supervised methods, and provides guidelines for their practical application, is lacking.
We performed an extensive evaluation of inference methods on simulated and experimental expression data. The results reveal low prediction accuracies for unsupervised techniques with the notable exception of the Z-SCORE method on knockout data. In all other cases, the supervised approach achieved the highest accuracies and even in a semi-supervised setting with small numbers of only positive samples, outperformed the unsupervised techniques.
Background
Inferring the structure of gene regulatory networks (GRN) from a collection of gene expression data has many potential applications, from the elucidation of complex biological processes to the identification of potential drug targets. It is however a notoriously difficult problem, for which the many existing methods reach limited accuracy.
Results
In this paper, we formulate GRN inference as a sparse regression problem and investigate the performance of a popular feature selection method, least angle regression (LARS) combined with stability selection, for that purpose. We introduce a novel, robust and accurate scoring technique for stability selection, which improves the performance of feature selection with LARS. The resulting method, which we call TIGRESS (for Trustful Inference of Gene REgulation with Stability Selection), was ranked among the top GRN inference methods in the DREAM5 gene network inference challenge. In particular, TIGRESS was evaluated to be the best linear regression-based method in the challenge. We investigate in depth the influence of the various parameters of the method, and show that a fine parameter tuning can lead to significant improvements and state-of-the-art performance for GRN inference, in both directed and undirected settings.
Conclusions
TIGRESS reaches state-of-the-art performance on benchmark data, including both in silico and in vivo (E. coli and S. cerevisiae) networks. This study confirms the potential of feature selection techniques for GRN inference. Code and data are available on http://cbio.ensmp.fr/tigress. Moreover, TIGRESS can be run online through the GenePattern platform (GP-DREAM, http://dream.broadinstitute.org).
Motivation: When analysing gene expression time series data, an often overlooked but crucial aspect of the model is that the regulatory network structure may change over time. Although some approaches have addressed this problem previously in the literature, many are not well suited to the sequential nature of the data.
Results: Here, we present a method that allows us to infer regulatory network structures that may vary between time points, using a set of hidden states that describe the network structure at a given time point. To model the distribution of the hidden states, we have applied the Hierarchical Dirichlet Process Hidden Markov Model, a non-parametric extension of the traditional Hidden Markov Model, which does not require us to fix the number of hidden states in advance. We apply our method to existing microarray expression data as well as demonstrating is efficacy on simulated test data.
Contact:
thomas.thorne@imperial.ac.uk
Reconstructing gene regulatory networks from high-throughput data is a long-standing challenge. Through the Dialogue on Reverse Engineering Assessment and Methods (DREAM) project, we performed a comprehensive blind assessment of over 30 network inference methods on Escherichia coli, Staphylococcus aureus, Saccharomyces cerevisiae and in silico microarray data. We characterize the performance, data requirements and inherent biases of different inference approaches, and we provide guidelines for algorithm application and development. We observed that no single inference method performs optimally across all data sets. In contrast, integration of predictions from multiple inference methods shows robust and high performance across diverse data sets. We thereby constructed high-confidence networks for E. coli and S. aureus, each comprising ∼1,700 transcriptional interactions at a precision of ∼50%. We experimentally tested 53 previously unobserved regulatory interactions in E. coli, of which 23 (43%) were supported. Our results establish community-based methods as a powerful and robust tool for the inference of transcriptional gene regulatory networks.
Network inference, which is the reconstruction of biological networks from high-throughput data, can provide valuable information about the regulation of gene expression in cells. However, it is an underdetermined problem, as the number of interactions that can be inferred exceeds the number of independent measurements. Different state-of-the-art tools for network inference use specific assumptions and simplifications to deal with underdetermination, and these influence the inferences. The outcome of network inference therefore varies between tools and can be highly complementary. Here we categorize the available tools according to the strategies that they use to deal with the problem of underdetermination. Such categorization allows an insight into why a certain tool is more appropriate for the specific research question or data set at hand.
Networks can provide a graphical representation of complex systems, including gene regulation processes. They can also provide a basis for further quantitative and computational analysis and modelling of biological systems. Single cell technology is now allowing us to probe molecular mechanisms and processes at unprecedented detail, and there is hope that we can learn better, more detailed network models from such data, in order to help us understand the mechanisms underlying cellular processes. But learning the structure of networks is notoriously difficult for at least two reasons: (i) network inference is a statistically challenging problem; and (ii) the naive picture of static networks may be fundamentally inapplicable to the description of biological systems. Here I will give some overview of the basic problem; discuss a set of promising network inference methods and how to validate them; and outline how we can go beyond the limitations imposed by static network models.
Gene regulatory network (GRN) is the important mechanism of maintaining life process, controlling biochemical reaction and regulating compound level, which plays an important role in various organisms and systems. Reconstructing GRN can help us to understand the molecular mechanism of organisms and to reveal the essential rules of a large number of biological processes and reactions in organisms. Various outstanding network reconstruction algorithms use specific assumptions that affect prediction accuracy, in order to deal with the uncertainty of processing. In order to study why a certain method is more suitable for specific research problem or experimental data, we conduct research from model-based, information-based and machine learning-based method classifications. There are obviously different types of computational tools that can be generated to distinguish GRNs. Furthermore, we discuss several classical, representative and latest methods in each category to analyze core ideas, general steps, characteristics, etc. We compare the performance of state-of-the-art GRN reconstruction technologies on simulated networks and real networks under different scaling conditions. Through standardized performance metrics and common benchmarks, we quantitatively evaluate the stability of various methods and the sensitivity of the same algorithm applying to different scaling networks. The aim of this study is to explore the most appropriate method for a specific GRN, which helps biologists and medical scientists in discovering potential drug targets and identifying cancer biomarkers.
Motivation:
Single-cell RNA sequencing (scRNA-seq) offers new possibilities to infer gene regulatory network (GRNs) for biological processes involving a notion of time, such as cell differentiation or cell cycles. It also raises many challenges due to the destructive measurements inherent to the technology.
Results:
In this work, we propose a new method named GRISLI for de novo GRN inference from scRNA-seq data. GRISLI infers a velocity vector field in the space of scRNA-seq data from profiles of individual cells, and models the dynamics of cell trajectories with a linear ordinary differential equation to reconstruct the underlying GRN with a sparse regression procedure. We show on real data that GRISLI outperforms a recently proposed state-of-the-art method for GRN reconstruction from scRNA-seq data.
Availability and implementation:
The MATLAB code of GRISLI is available at: https://github.com/PCAubin/GRISLI.
Supplementary information:
Supplementary data are available at Bioinformatics online.
Here, we present Scribe (https://github.com/aristoteleo/Scribe-py), a toolkit for detecting and visualizing causal regulatory interactions between genes and explore the potential for single-cell experiments to power network reconstruction. Scribe employs restricted directed information to determine causality by estimating the strength of information transferred from a potential regulator to its downstream target. We apply Scribe and other leading approaches for causal network reconstruction to several types of single-cell measurements and show that there is a dramatic drop in performance for “pseudotime”-ordered single-cell data compared with true time-series data. We demonstrate that performing causal inference requires temporal coupling between measurements. We show that methods such as “RNA velocity” restore some degree of coupling through an analysis of chromaffin cell fate commitment. These analyses highlight a shortcoming in experimental and computational methods for analyzing gene regulation at single-cell resolution and suggest ways of overcoming it.
Several methods were developed to mine gene–gene relationships from expression data. Examples include correlation and mutual information methods for coexpression analysis, clustering and undirected graphical models for functional assignments, and directed graphical models for pathway reconstruction. Using an encoding for gene expression data, followed by deep neural networks analysis, we present a framework that can successfully address all of these diverse tasks. We show that our method, convolutional neural network for coexpression (CNNC), improves upon prior methods in tasks ranging from predicting transcription factor targets to identifying disease-related genes to causality inference. CNNC’s encoding provides insights about some of the decisions it makes and their biological basis. CNNC is flexible and can easily be extended to integrate additional types of genomics data, leading to further improvements in its performance.
Transcriptional regulation is a fundamental molecular mechanism involved in almost every aspect of life, from homeostasis to development, from metabolism to behavior, from reaction to stimuli to disease progression. In recent years, the concept of Gene Regulatory Networks (GRNs) has grown popular as an effective applied biology approach for describing the complex and highly dynamic set of transcriptional interactions, due to its easy-to-interpret features. Since cataloguing, predicting and understanding every GRN connection in all species and cellular contexts remains a great challenge for biology, researchers have developed numerous tools and methods to infer regulatory processes. In this review, we catalogue these methods in six major areas, based on the dominant underlying information leveraged to infer GRNs: Coexpression, Sequence Motifs, Chromatin Immunoprecipitation (ChIP), Orthology, Literature and Protein-Protein Interaction (PPI) specifically focused on transcriptional complexes. The methods described here cover a wide range of user-friendliness: from web tools that require no prior computational expertise to command line programs and algorithms for large scale GRN inferences. Each method for GRN inference described herein effectively illustrates a type of transcriptional relationship, with many methods being complementary to others. While a truly holistic approach for inferring and displaying GRNs remains one of the greatest challenges in the field of systems biology, we believe that the integration of multiple methods described herein provides an effective means with which experimental and computational biologists alike may obtain the most complete pictures of transcriptional relationships. This article is part of a Special Issue entitled: Transcriptional Profiles and Regulatory Gene Networks edited by Dr. Dr. Federico Manuel Giorgi and Dr. Shaun Mahony.
The functional interpretation of single-cell RNA sequencing (scRNA-seq) data can be enhanced by integrating additional data types beyond RNA-based gene expression. In this Review, Stuart and Satija discuss diverse approaches for integrative single-cell analysis, including experimental methods for profiling multiple omics types from the same cells, analytical approaches for extracting additional layers of information directly from scRNA-seq data and computational integration of omics data collected across different cell samples.
Motivation:
Molecular profiling techniques have evolved to single-cell assays, where dense molecular profiles are screened simultaneously for each cell in a population. High-throughput single-cell experiments from a heterogeneous population of cells can be experimentally and computationally sorted as a sequence of samples pseudo-temporally ordered samples. The analysis of these data sets, comprising a large number of samples, has the potential to uncover the dynamics of the underlying regulatory programmes.
Results:
We present a novel approach for modelling and inferring gene regulatory networks from high-throughput time series and pseudo-temporally sorted single-cell data. Our method is based on a first-order autoregressive moving-average model and it infers the gene regulatory network within a variational Bayesian framework. We validate our method with synthetic data and we apply it to single cell qPCR and RNA-Seq data for mouse embryonic cells and hematopoietic cells in zebra fish.
Supplementary information:
The method presented in this paper is available at https://github.com/mscastillo/GRNVBEM.
Availability:
R package LEAP available on CRAN CONTACT: jun.li@nd.edu SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.
The availability of gene expression data at the single cell level makes it possible to probe the molecular underpinnings of complex biological processes such as differentiation and oncogenesis. Promising new methods have emerged for reconstructing a progression ’trajectory’ from static single-cell transcriptome measurements. However, it remains unclear how to adequately model the appreciable level of noise in these data to elucidate gene regulatory network rewiring. Here, we present a framework called Single Cell Inference of MorphIng Trajectories and their Associated Regulation (SCIMITAR) that infers progressions from static single-cell transcriptomes by employing a continuous parametrization of Gaussian mixtures in high-dimensional curves. SCIMITAR yields rich models from the data that highlight genes with expression and co-expression patterns that are associated with the inferred progression. Further, SCIMITAR extracts regulatory states from the implicated trajectory-evolvingco-expression networks. We benchmark the method on simulated data to show that it yields accurate cell ordering and gene network inferences. Applied to the interpretation of a single-cell human fetal neuron dataset, SCIMITAR finds progression-associated genes in cornerstone neural differentiation pathways missed by standard differential expression tests. Finally, by leveraging the rewiring of gene-gene co-expression relations across the progression, the method reveals the rise and fall of co-regulatory states and trajectory-dependent gene modules. These analyses implicate new transcription factors in neural differentiation including putative co-factors for the multi-functional NFAT pathway.
A quantitative model has been developed for processes in the bacteriophage lambda that control the switchover from lysogenic to lytic modes of growth. These processes include the interactions of cI repressor and cro proteins at the three DNA sites of the right operator, OR, the binding of RNA polymerase at promoters PR and PRM, the synthesis of cI repressor and cro proteins, and the degradative action of recA during induction of lysis. The model is comprised of two major physical-chemical components: (1) a statistical thermodynamic theory for relative probabilities of the various molecular configurations of the control system; and (2) a kinetic model for the coupling of these probabilities to functional events, including synthesis of regulatory proteins cI and cro. Using independently evaluated interaction constants and rate parameters, the model was found capable of predicting essential physiological characteristics of the system over an extended time. Sufficiency of the model to predict known physiological properties lends credence to the physical-chemical assumptions used in its construction.
This paper introduces two new probabilistic graphical models for reconstruction of genetic regulatory networks using DNA microarray data. One is an independence graph (IG) model with either a forward or a backward search algorithm and the other one is a Gaussian network (GN) model with a novel greedy search method. The performances of both models were evaluated on four MAPK pathways in yeast and three simulated data sets. Generally, an IG model provides a sparse graph but a GN model produces a dense graph where more information about gene-gene interactions may be preserved. The results of our proposed models were compared with several other commonly used models, and our models have shown to give superior performance. Additionally, we found the same common limitations in the prediction of genetic regulatory networks when using only DNA microarray data.
Mol Syst Biol. 3: 137
Robustness is one of the fundamental characteristics of biological systems. Numerous reports have been published on how robustness is involved in various biological processes and on mechanisms that give rise to robustness in living systems (Savageau, 1985a, 1985b, 1998; Barkai and Leibler, 1997; Alon et al , 1999; von Dassow et al , 2000; Bhalla and Iyengar, 2001; Csete and Doyle, 2002, 2004; Kitano et al , 2004, 2004a, 2004b; Stelling et al , 2004; Kitano and Oda, 2006; Kitano, 2007a). With increasing interest in systems biology, properties at the system level such as robustness have attracted serious scientific research. Nevertheless, a mathematical foundation that provides a unified perspective on robustness is yet to be established. For systems biology to mature into a solid scientific discipline, there must be a solid theoretical and methodological foundation. Often, systems biology is equated with computer simulation of cells and organs. Although computer simulation is a powerful technique for clarifying the complex dynamics of biological systems, it is also a useful tool for exploring the foundation of biological systems. While investigation on the dynamic properties of specific aspects of organisms is scientifically significant and can be widely applied, it is a study on specific instances of design within a design space that is shaped by fundamental principles, structural, environmental, and evolutionary constraints. The scientific goal of systems biology is not merely to create precision models of cells and organs, but also to discover fundamental and structural principles behind biological systems that define the possible design space of life (Figure 1). The value of understanding fundamental and structural theories is that they provide deeper insights into the governing principles that complex evolvable systems including biological …
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