This paper is concerned with the problem of stochastic control of gene regulatory networks (GRNs) observed indirectly through noisy measurements and with uncertainty in the intervention inputs. The partial observability of the gene states and uncertainty in the intervention process are accounted for by modeling GRNs using the partially-observed Boolean dynamical system (POBDS) signal model with noisy gene expression measurements. Obtaining the optimal infinite-horizon control strategy for this problem is not attainable in general, and we apply reinforcement learning and Gaussian process techniques to find a near-optimal solution. The POBDS is first transformed to a directly-observed Markov Decision Process in a continuous belief space, and the Gaussian process is used for modeling the cost function over the belief and intervention spaces. Reinforcement learning then is used to learn the cost function from the available gene expression data. In addition, we employ sparsification, which enables the control of large partially-observed GRNs. The performance of the resulting algorithm is studied through a comprehensive set of numerical experiments using synthetic gene expression data generated from a melanoma gene regulatory network.
Single-cell gene expression measurements offer opportunities in deriving mechanistic understanding of complex diseases, including cancer. However, due to the complex regulatory machinery of the cell, gene regulatory network (GRN) model inference based on such data still manifests significant uncertainty. The goal of this paper is to develop optimal classification of single-cell trajectories accounting for potential model uncertainty. Partially-observed Boolean dynamical systems (POBDS) are used for modeling gene regulatory networks observed through noisy gene-expression data. We derive the exa…
Gene regulatory networks play a crucial role in controlling an organism's biological processes, which is why there is significant interest in developing computational methods that are able to extract their structure from high-throughput genetic data. A typical approach consists of a series of conditional independence tests on the covariance structure meant to progressively reduce the space of possible causal models. We propose a novel efficient Bayesian method for discovering the local causal relationships among triplets of (normally distributed) variables. In our approach, we score the patter…
Memorial Sloan Kettering Cancer Center（纪念斯隆凯特琳癌症中心）
We present a Bayesian hierarchical multi-view mixture model termed Symphony that simultaneously learns clusters of cells representing cell types and their underlying gene regulatory networks by integrating data from two views: single-cell gene expression data and paired epigenetic data, which is informative of gene-gene interactions. This model improves interpretation of clusters as cell types with similar expression patterns as well as regulatory networks driving expression, by explaining gene-gene covariances with the biological machinery regulating gene expression. We show the theoretical a…
Constructing gene regulatory networks is a fundamental task in systems biology. We introduce a Gaussian reciprocal graphical model for inference about gene regulatory relationships by integrating mRNA gene expression and DNA level information including copy number and methylation. Data integration allows for inference on the directionality of certain regulatory relationships, which would be otherwise indistinguishable due to Markov equivalence. Efficient inference is developed based on simultaneous equation models. Bayesian model selection techniques are adopted to estimate the graph structure…
Inferring gene regulatory networks is an important problem in systems biology. However, these networks can be hard to infer from experimental data because of the inherent variability in biological data as well as the large number of genes involved. We propose a fast, simple method for inferring regulatory relationships between genes from knockdown experiments in the NIH LINCS dataset by calculating posterior probabilities, incorporating prior information. We show that the method is able to find previously identified edges from TRANSFAC and JASPAR and discuss the merits and limitations of this …
Motivated by the need to study the molecular mechanism underlying Type 1 Diabetes (T1D) with the gene expression data collected from both the patients and healthy controls at multiple time points, we propose an innovative method for jointly estimating multiple dependent Gaussian graphical models. Compared to the existing methods, the proposed method has a few significant advantages. First, it includes a meta-analysis procedure to explicitly integrate information across distinct conditions. In contrast, the existing methods often integrate information through prior distributions or penalty func…
In this work we addressed the problem of stability analysis for an uncertain piecewise affine model of a genetic regulatory network. In particular we considered polytopic parameter uncertainties on the proteins production rate functions, giving conditions for the existence of a piecewise quadratic Lyapunov function for any possible realization of the system. In the spirit of other works in literature, the resulting conditions will be given on the vertices of the parameter polytope, while still taking into consideration the piecewise nature of the Lyapunov function and the presence, in general,…
The topological analysis of biological networks has been a prolific topic in network science during the last decade. A persistent problem with this approach is the inherent uncertainty and noisy nature of the data. One of the cases in which this situation is more marked is that of transcriptional regulatory networks (TRNs) in bacteria. The datasets are incomplete because regulatory pathways associated to a relevant fraction of bacterial genes remain unknown. Furthermore, direction, strengths and signs of the links are sometimes unknown or simply overlooked. Finally, the experimental approaches…
University of Cambridge（剑桥大学）；Computer Laboratory（计算机实验室）
Delays in protein synthesis cause a confounding effect when constructing Gene Regulatory Networks (GRNs) from RNA-sequencing time-series data. Accurate GRNs can be very insightful when modelling development, disease pathways, and drug side-effects. We present a model which incorporates translation delays by combining mechanistic equations and Bayesian approaches to fit to experimental data. This enables greater biological interpretability, and the use of Gaussian processes enables non-linear expressivity through kernels as well as naturally accounting for biological variation.
Gene regulatory network (GRN) refers to the complex network formed by regulatory interactions between genes in living cells. In this paper, we consider inferring GRNs in single cells based on single cell RNA sequencing (scRNA-seq) data. In scRNA-seq, single cells are often profiled from mixed populations and their cell identities are unknown. A common practice for single cell GRN analysis is to first cluster the cells and infer GRNs for every cluster separately. However, this two-step procedure ignores uncertainty in the clustering step and thus could lead to inaccurate estimation of the netwo…
Timing is essential for many cellular processes, from cellular responses to external stimuli to the cell cycle and circadian clocks. Many of these processes are based on gene expression. For example, an activated gene may be required to reach in a precise time a threshold level of expression that triggers a specific downstream process. However, gene expression is subject to stochastic fluctuations, naturally inducing an uncertainty in this threshold-crossing time with potential consequences on biological functions and phenotypes. Here, we consider such "timing fluctuations", and we ask how the…
Regulatory interactions between genes show a large amount of cross-species variability, even when the underlying functions are conserved: There are many ways to achieve the same function. Here we investigate the ability of regulatory networks to reproduce given expression levels within a simple model of gene regulation. We find an exponentially large space of regulatory networks compatible with a given set of expression levels, giving rise to an extensive entropy of networks. Typical realisations of regulatory networks are found to share a bias towards symmetric interactions, in line with empi…
GeneNetMiner is standalone software which parses the sentences of iHOP and captures regulatory relations. The regulatory relations are either gene gene regulations or gene biological processes relations. Capturing of gene biological process relations is a unique feature for the tools of this kind. These relations can be used to build up gene regulatory networks for specific biological processes, diseases, or phenotypes. Users are able to search genes and biological processes to find the regulatory relationships between them. Each regulatory relationship has been assigned a confidence score, wh…
Reconstructing transcriptional regulatory networks is an important task in functional genomics. Data obtained from experiments that perturb genes by knockouts or RNA interference contain useful information for addressing this reconstruction problem. However, such data can be limited in size and/or are expensive to acquire. On the other hand, observational data of the organism in steady state (e.g. wild-type) are more readily available, but their informational content is inadequate for the task at hand. We develop a computational approach to appropriately utilize both data sources for estimatin…
Identification of genes that initiate cell anomalies and cause cancer in humans is among the important fields in the oncology researches. The mutation and development of anomalies in these genes are then transferred to other genes in the cell and therefore disrupt the normal functionality of the cell. These genes are known as cancer driver genes (CDGs). Various methods have been proposed for predicting CDGs, most of which based on genomic data and based on computational methods. Therefore, some researchers have developed novel bioinformatics approaches. In this study, we propose an algorithm, …
The biological processes of cellular decision making and differentiation involve a plethora of signalling pathways and gene regulatory circuits. These networks, in their turn, exhibit a multitude of motifs playing crucial parts in regulating network activity. Here, we compare the topological placement of motifs in gene regulatory and signalling networks and find that it suggests different evolutionary strategies in motif distribution for distinct cellular subnetworks.
Gene regulatory networks play a crucial role in controlling an organism's biological processes, which is why there is significant interest in developing computational methods that are able to extract their structure from high-throughput genetic data. Many of these computational methods are designed to infer individual regulatory relationships among genes from data on gene expression. We propose a novel efficient Bayesian method for discovering local causal relationships among triplets of (normally distributed) variables. In our approach, we score covariance structures for each triplet in one g…
College of Mathematics and Statistics, Shenzhen University（深圳大学数学与统计学院）
In this paper, we tested several sparse optimization algorithms based on the public dataset of the DREAM5 Gene Regulatory Network Inference Challenge. And we find that introducing 20% of the regulatory network as a priori known data can provide a basis for parameter selection of inference algorithms, thus improving prediction efficiency and accuracy. In addition to testing common sparse optimization methods, we also developed voting algorithms by bagging them. Experiments on the DREAM5 dataset show that the sparse optimization-based inference of the moderation relation works well, achieving be…
Developing and maintaining life requires a lot of computation. This is done by gene regulatory networks. But we have little understanding of how this computation is organized. I show that there is a direct correspondence between the structural and functional building blocks of regulatory networks, which I call regulatory motifs. I derive a simple bound on the range of function that these motifs can perform, in terms of the local network structure. I prove that this range is a small fraction of all possible functions, which severely constrains global network behavior. Part of this restriction i…
Inference of gene regulatory networks has been an active area of research for around 20 years, leading to the development of sophisticated inference algorithms based on a variety of assumptions and approaches. With the always increasing demand for more accurate and powerful models, the inference problem remains of broad scientific interest. The abstract representation of biological systems through gene regulatory networks represents a powerful method to study such systems, encoding different amounts and types of information. In this review, we summarize the different types of inference algorit…
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 expression data. The results reveal very low prediction accuracies for unsupervised techniques with the notable exception of the z-score method on knock-out data. In all other cases the supervised approach achieved the highest accura…
Genes are connected in regulatory networks, often modelled by ordinary differential equations. Changes in expression of a gene propagate to other genes along paths in the network. At a stable state, the system's Jacobian matrix confers information about network connectivity. To disclose the functional properties of genes, knowledge of network connections is essential. We present a new method to reconstruct the Jacobian matrix of models for gene regulatory systems from equilibrium protein concentrations. In a recent paper we defined propagation and feedback functions describing how genetic vari…
Increased biological complexity is generally associated with the addition of new genetic information, which must be integrated into the existing regulatory network that operates within the cell. General arguments on network control, as well as several recent genomic observations, indicate that regulatory gene number grows disproportionally fast with increasing genome size. We present two models for the growth of regulatory networks. Both predict that the number of transcriptional regulators will scale quadratically with total gene number. This appears to be in good quantitative agreement with …
We study the oscillatory behaviour of a gene regulatory network with interlinked positive and negative feedback loop. Frequency and amplitude are two important properties of oscillation. Studied network produces two different modes of oscillation. In one mode (mode 1) frequency remains constant over a wide range amplitude and in other mode (mode 2) the amplitude of oscillation remains constant over a wide range of frequency. Our study reproduces both features of oscillations in a single gene regulatory network and show that the negative plus positive feedback loops in gene regulatory network o…
Genetic regulatory networks enable cells to respond to the changes in internal and external conditions by dynamically coordinating their gene expression profiles. Our ability to make quantitative measurements in these biochemical circuits has deepened our understanding of what kinds of computations genetic regulatory networks can perform and with what reliability. These advances have motivated researchers to look for connections between the architecture and function of genetic regulatory networks. Transmitting information between network's inputs and its outputs has been proposed as one such p…
Cancer disease occurs because of a disorder in the cellular regulatory mechanism, Which causes cellular malformation. The genes that start the malformation are called Cancer driver genes (CDGs) . Numerous computational methods have been introduced to identify cancer driver genes that use the concept of mutation.Regarding abnormalities spread in human cell and tumor development, CDGs are likely to be the potential types of gene with high influence in the network. This increases the importance of influence diffusion concept for the identification of CDGs.recently developed a method based on infl…
Genes are frequently regulated in complex manners, necessitating modelling approaches which go beyond simple (linear) gene-to-gene interactions and address the modularity of cis-regulatory regions and alternate transcription initiation sites. In particular, sharp expression patterns (peaks or stripes) indicate that gene regulation involves nonlinear transcription factor kinetics (beyond first-order). We propose a methodology for approaching this problem, using the example of the multiple cis-regulatory modules (CRMs) and two transcripts (P1 and P2) found in the Drosophila hunchback (hb) and (C…
In this review we discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternative modelling approaches, we use a paradigmatic two-gene network to focus on the role played by time delays in the dynamics of gene regulatory networks. We contrast the dynamics of the reduced model arising in the limit of fast mRNA dynamics with that of the full model. The review concludes with the discussion of some open problems.
The study of fluctuations in gene regulatory networks is extended to the case of Gaussian colored noise. Firstly, the solution of the corresponding Langevin equation with colored noise is expressed in terms of an Ito integral. Then, two important lemmas concerning the variance of an Ito integral and the covariance of two Ito integrals are shown. Based on the lemmas, we give the general formulae for the variances and covariance of molecular concentrations for a regulatory network near a stable equilibrium explicitly. Two examples, the gene auto-regulatory network and the toggle switch, are pres…
Cardiac development is complex, multiscale process encompassing cell fate adoption, differentiation and morphogenesis. To elucidate pathways underlying this process, a recently developed algorithm to reverse engineer gene regulatory networks was applied to time-course microarray data obtained from the developing mouse heart. The algorithm generates many different putative network topologies that are capable of explaining the experimental data via model simulation. To cull specious network interactions, thousands of topologies are merged and filtered to generate a scale-free, hierarchical netwo…
The time taken for gene expression varies not least because proteins vary in length considerably. This paper uses an abstract, tuneable Boolean regulatory network model to explore gene expression time variation. In particular, it is shown how non-uniform expression times can emerge under certain conditions through simulated evolution. That is, gene expression time variance appears beneficial in the shaping of the dynamical behaviour of the regulatory network without explicit consideration of protein function.
Background:Gene regulations often change over time rather than being constant. But many of gene regulatory networks extracted from databases are static. The tumor suppressor gene $P53$ is involved in the pathogenesis of many tumors, and its inhibition effects occur after a certain period. Therefore, it is of great significance to elucidate the regulation mechanism over time points. Result:A qualitative method for representing dynamic gene regulatory network is developed, called CdtGRN. It adopts the combination of convolutional neural networks(CNN) and fully connected networks(DNN) as the core…
New approach to design a dynamic model of genes with multiple autonomous regulatory modules by evolution in silico is proposed. The approach is based on Genetic Algorithms, enforced by new crossover operators, especially worked out for these purposes. The approach exploits the subbasin-portal architecture of the fitness functions suitable for this kind of evolutionary modeling. The effectiveness of the approach is demonstrated on a series of benchmark tests.
From the response to external stimuli to cell division and death, the dynamics of living cells is based on the expression of specific genes at specific times. The decision when to express a gene is implemented by the binding and unbinding of transcription factor molecules to regulatory DNA. Here, we construct stochastic models of gene expression dynamics and test them on experimental time-series data of messenger-RNA concentrations. The models are used to infer biophysical parameters of gene transcription, including the statistics of transcription factor-DNA binding and the target genes contro…
Biological systems and processes are networks of complex nonlinear regulatory interactions between nucleic acids, proteins, and metabolites. A natural way in which to represent these interaction networks is through the use of a graph. In this formulation, each node represents a nucleic acid, protein, or metabolite and edges represent intermolecular interactions (inhibition, regulation, promotion, coexpression, etc.). In this work, a novel algorithm for the discovery of latent graph structures given experimental data is presented.
Integrating expression data with gene interactions in a network is essential for understanding the functional organization of the cells. Consequently, knowledge of interaction types in biological networks is important for data interpretation. Signing of Regulatory Networks (SIREN) plugin for Cytoscape is an open-source Java tool for discrimination of interaction type (activatory or inhibitory) in gene regulatory networks. Utilizing an information theory based concept, SIREN seeks to identify the interaction type of pairs of genes by examining their corresponding gene expression profiles. We in…
Gene regulatory networks arise in all living cells, allowing the control of gene expression patterns. The study of their topology has revealed that certain subgraphs of interactions or "motifs" appear at anomalously high frequencies. We ask here whether this phenomenon may emerge because of the functions carried out by these networks. Given a framework for describing regulatory interactions and dynamics, we consider in the space of all regulatory networks those that have a prescribed function. Monte Carlo sampling is then used to determine how these functional networks lead to specific motif s…
A description for regulatory genetic network based on generalized potential energy is constructed. The potential energy is derived from the steady state solution of linearized Fokker-Plank equation, and the result is shown to be equivalent to the system of coupled oscillators. The correspondence between the quantities from the mechanical picture and the steady-state fluctuations is established. Explicit calculation is given for auto-regulatory networks in which, the force constant associated with the degree of protein is very weak. Negative feedback not only suppresses the fluctuations but als…
Regulatory networks describe the interactions between molecular or cellular regulators, like transcription factors and genes in gene regulatory networks, kinases and their receptors in signalling networks, or neurons in neural networks. A long-standing aim of quantitative biology is to reconstruct such networks on the basis of large-scale data. Our aim is to leverage fluctuations around the non-equilibrium steady state for network inference. To this end, we use a stochastic model of gene regulation or neural dynamics and solve it approximately within a Gaussian mean-field theory. We develop a …
The structure of a stochastic nonlinear gene regulatory network is uncovered by studying its response to input signal generators. Four applications are studied in detail: a nonlinear connection of two linear systems, the design of a logic pulse, a molecular amplifier and the interference of three signal generators in E2F1 regulatory element. The gene interactions are presented using molecular diagrams that have a precise mathematical structure and retain the biological meaning of the processes.
Modeling Dynamics, Cell Type Specificity, and Perturbations in Gene Regulatory Networks
Wisconsin Institute for Discovery, University of Wisconsin-Madison（威斯康星发现研究所，威斯康星大学麦迪逊分校）；Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison（威斯康星大学麦迪逊分校生物统计与医学信息学系）
In this paper, we conduct theoretical analyses on inferring the structure of gene regulatory networks. Depending on the experimental method and data type, the inference problem is classified into 20 different scenarios. For each scenario, we discuss the problem that with enough data, under what assumptions, what can be inferred about the structure. For scenarios that have been covered in the literature, we provide a brief review. For scenarios that have not been covered in literature, if the structure can be inferred, we propose new mathematical inference methods and evaluate them on simulated…
Interactions between genes and gene products give rise to complex circuits that enable cells to process information and respond to external signals. Theoretical studies often describe these interactions using continuous, stochastic, or logical approaches. We propose a new modeling framework for gene regulatory networks, that combines the intuitive appeal of a qualitative description of gene states with a high flexibility in incorporating stochasticity in the duration of cellular processes. We apply our methods to the regulatory network of the segment polarity genes, thus gaining novel insights…
