概率级联布尔网络的集镇定及其应用

随着系统生物学和医学的迅速发展,基因调控网络已经成为一个热点研究领域.布尔网络作为研究生物系统和基因调控网络的一种重要模型,近年来引起了包括生物学家和系统科学家在内的很多学者的广泛关注.本文利用代数状态空间方法,研究了概率级联布尔网络的集镇定问题.首先给出概率级联布尔网络集镇定的定义,并利用矩阵的半张量积给出了概率级联布尔网络的代数表示.其次基于该代数表示,定义了一组合适的概率能达集,并给出了概率级联布尔网络集镇定问题可解的充要条件.最后将所得的理论结果应用于概率级联布尔网络的同步分析及n人随机级联演化布尔博弈的策略一致演化行为分析.     

An efficient top-down search algorithm for learning Boolean networks of gene expression

Boolean networks provide a simple and intuitive model for gene regulatory networks, but a critical defect is the time required to learn the networks. In recent years, efficient network search algorithms have been developed for a noise-free case and for a limited function class. In general, the conventional algorithm has the high time complexity of O(2^{2k mn k+1}) where m is the number of measurements, n is the number of nodes (genes), and k is the number of input parents. Here, we suggest a simple and new approach to Boolean networks, and provide a randomized network search algorithm with average time complexity O ^{(mn k+1}/ (log m)^(k−1)). We show the efficiency of our algorithm via computational experiments, and present optimal parameters. Additionally, we provide tests for yeast expression data. Editor: David Page     

Generating probabilistic Boolean networks from a prescribed stationary distribution

Modeling gene regulation is an important problem in genomic research. Boolean networks (BN) and its generalization probabilistic Boolean networks (PBNs) have been proposed to model genetic regulatory interactions. BN is a deterministic model while PBN is a stochastic model. In a PBN, on one hand, its stationary distribution gives important information about the long-run behavior of the network. On the other hand, one may be interested in system synthesis which requires the construction of networks from the observed stationary distribution. This results in an inverse problem which is ill-posed and challenging. Because there may be many networks or no network having the given properties and the size of the inverse problem is huge. In this paper, we consider the problem of constructing PBNs from a given stationary distribution and a set of given Boolean Networks (BNs). We first formulate the inverse problem as a constrained least squares problem. We then propose a heuristic method based on Conjugate Gradient (CG) algorithm, an iterative method, to solve the resulting least squares problem. We also introduce an estimation method for the parameters of the PBNs. Numerical examples are then given to demonstrate the effectiveness of the proposed methods.     

关于布尔控制网络的能观性和能检性的研究现状

布尔(控制)网络是模拟基因调控网络有效的数学模型.该模型将细胞内(或特定一个基因组内)基因与基因之间的相互作用关系量化,系统的状态和函数直接反应基因表达、复制、转录等生命活动,在新的数学工具矩阵半张量积的帮助下,取得了许多优秀成果.近些年,国内外病毒疫情频发,对全球各个方面造成巨大的冲击和损失,病毒检测技术是战“疫”中非常重要的一个环节.鉴于此,总结近年来矩阵半张量积在布尔(控制)网络的能观性和能检性方面取得的一些成果,以便更多学者关注这类问题和方法.首先回顾能观性和能检性的发展历程;然后,从理论角度分析并用网络图呈现4种能观性与3种能检性之间的关系,整理在布尔网络和布尔控制网络中相关的一些重要成果,包括状态反馈、输出反馈、含干扰、含切换等多种情形;最后通过简述能观性和能检性的应用现状展望其未来发展.     

具有少量基本回路布尔网络的不动点

近来作为自然和人造非线性动态网络的一种紧凑模型,布尔网络的研究受到广泛关注.不动点和吸引子是预测布尔网络长期行为的关键.本文针对具有少量基本回路的布尔网络,提出了确定不动点的算法.我们的方法是基于构成反馈顶点集的变量所满足的一组方程.作为应用,我们还给出了检验这类布尔网络全局稳定性的充要条件.     

使用模型检测解决概率布尔网络优化控制

系统生物学期望对复杂生物系统建立一个真实的、可计算的模型,以便于以系统的角度去理解生物系统的演变过程。在系统生物学中,一个重要的主题是通过外部的干预控制发展关于基因调控网络的控制理论,以作为未来基因治疗技术。目前,布尔网络及其扩展的概率布尔网络已经被广泛用于对基因调控网络进行建模。在控制问题的研究中,概率布尔控制网络的状态迁移本质上构成一条有限状态空间的离散时间马尔科夫决策过程。依据马尔科夫决策过程的理论,通过概率模型检测方法解决网络中有限范围优化控制问题和无限范围优化控制问题。针对带有随机干扰且上下文相关的概率布尔控制网络,使用概率模型检测器PRISM对其进行形式化建模,然后将两类优化控制问题描述为相应的时序逻辑公式,最后通过模型检测寻找出最优解。实验结果表明,提出的方法可以有效地用于生物网络的分析和优化控制。     

Promoter analysis of co-regulated genes in the yeast genome.

The use of high density DNA arrays to monitor gene expression at a genome-wide scale constitutes a fundamental advance in biology. In particular, the expression pattern of all genes in Saccharomyces cerevisiae can be interrogated using microarray analysis where cDNAs are hybridized to an array of more than 6000 genes in the yeast genome. In an effort to build a comprehensive Yeast Promoter Database and to develop new computational methods for mapping upstream regulatory elements, we started recently in an on going collaboration with experimental biologists on analysis of large-scale expression data. It is well known that complex gene expression patterns result from dynamic interacting networks of genes in the genetic regulatory circuitry. Hierarchical and modular organization of regulatory DNA sequence elements are important information for our understanding of combinatorial control of gene expression. As a bioinformatics attempt in this new direction, we have done some computational exploration of various initial experimental data. We will use cell-cycle regulated gene expression as a specific example to demonstrate how one may extract promoter information computationally from such genome-wide screening. Full report of the experiments and of the complete analysis will be published elsewhere when all the experiments are to be finished later in this year (Spellman, P.T., et al. 1998. Mol. Biol. Cell 9, 3273-3297).     

The Discrete Basis Problem

Matrix decomposition methods represent a data matrix as a product of two factor matrices: one containing basis vectors that represent meaningful concepts in the data, and another describing how the observed data can be expressed as combinations of the basis vectors. Decomposition methods have been studied extensively, but many methods return real-valued matrices. Interpreting real-valued factor matrices is hard if the original data is Boolean. In this paper, we describe a matrix decomposition formulation for Boolean data, the Discrete Basis Problem. The problem seeks for a Boolean decomposition of a binary matrix, thus allowing the user to easily interpret the basis vectors. We also describe a variation of the problem, the Discrete Basis Partitioning Problem. We show that both problems are NP-hard. For the Discrete Basis Problem, we give a simple greedy algorithm for solving it; for the Discrete Basis Partitioning Problem we show how it can be solved using existing methods. We present experimental results for the greedy algorithm and compare it against other, well known methods. Our algorithm gives intuitive basis vectors, but its reconstruction error is usually larger than with the real-valued methods. We discuss about the reasons for this behavior.     

使用稳态系统和粒群优化算法进行基因调控网络推断

基因调控网络模型试图从海量的时序基因表达数据中研究基因的功能,推断基因之间的调控关系,从而揭示复杂的病理现象和生命现象.通过利用时序基因表达数据来推断一个基于稳态系统(S-system)模型的基因网络,提出使用粒群优化算法(PSO)来优化模型参数,从而捕捉基因表达数据中的动力学特性.实验结果表明,该方法能够使模型参数快速得到收敛,配置参数后模型仿真能力好,可以较好地识别基因调控关系.     

Feasible prediction in S-system models of genetic networks

To construct the model of gene expression using microarray techniques can reveal the regulation rules from the gene expression profiles. From S-system model, it is able to analyze the regulatory system dynamics. However, with 2N(N + 1) parameters (called a set), an S-system model of N-gene genetic networks takes lots of iterations to have convergent gene expression profiles. To mining the association between the gene expression profiles and 2N(N + 1) parameters may provide information about the probability of the convergent gene expression profiles instead of trying to obtain the convergent gene expression profiles in lots of iteration. Based on this novel approach, higher accuracy of the binary classifier can be used to analyze and prediction the convergence of the gene expression profiles from an initial set to reduce the search time of the inference problem. This paper applies popular data mining algorithms to the classification tasks and compares their accuracy rates with a dataset (250 cases, including 176 training cases and 74 test cases). According to decision rules of the chosen classifier, we can provide a convergence prediction of time-series gene expression profiles on the given set of parameters.     

Modeling gene expression networks using fuzzy logic.

Gene regulatory networks model regulation in living organisms. Fuzzy logic can effectively model gene regulation and interaction to accurately reflect the underlying biology. A new multiscale fuzzy clustering method allows genes to interact between regulatory pathways and across different conditions at different levels of detail. Fuzzy cluster centers can be used to quickly discover causal relationships between groups of coregulated genes. Fuzzy measures weight expert knowledge and help quantify uncertainty about the functions of genes using annotations and the gene ontology database to confirm some of the interactions. The method is illustrated using gene expression data from an experiment on carbohydrate metabolism in the model plant Arabidopsis thaliana. Key gene regulatory relationships were evaluated using information from the gene ontology database. A new regulatory relationship concerning trehalose regulation of carbohydrate metabolism was also discovered in the extracted network.     

布尔网络的分析与控制——矩阵半张量积方法

布尔网络是描述基因调控网络的一个有力工具. 由于系统生物学的发展, 布尔网络的分析与控制成为生物学与系统控制学科的交叉热点. 本文综述作者用其原创的矩阵半张量积方法在布尔网络的分析与控制中得到的一系列结果. 内容包括: 布尔网络的拓扑结构, 布尔控制网络的能控、能观性与实现, 布尔网络的稳定性和布尔控制网络的镇定, 布尔控制网络的干扰解耦, 布尔 (控制) 网络的辨识,以及布尔网络的最优控制等.     

A two-stage methodology for gene regulatory network extraction from time–course gene expression data

The discovery of gene regulatory networks (GRN) from time–course gene expression data (gene trajectory data) is useful for (1) identifying important genes in relation to a disease or a biological function; (2) gaining an understanding on the dynamic interaction between genes; (3) predicting gene expression values at future time points and accordingly; (4) predicting drug effect over time.In this paper, we propose a two-stage methodology that is implemented in the software ‘Gene Network Explorer (GNetXP)’ for extracting GRNs from gene trajectory data. In the first stage, we apply a hybrid Genetic Algorithm and Expectation Maximization algorithm on clustering the large number of gene trajectories using the mixture of multiple linear regression models for fitting the trajectory data. In the second stage, we apply the Kalman Filter to identify a set of first-order differential equations that describe the dynamics of the representative trajectories, and use these equations for discovering important gene interactions and predicting gene expression values at future time points. The proposed method is demonstrated on the human fibroblast response gene expression data.     

Detecting reliable gene interactions by a hierarchy of Bayesian network classifiers

The main purpose of a gene interaction network is to map the relationships of the genes that are out of sight when a genomic study is tackled. DNA microarrays allow the measure of gene expression of thousands of genes at the same time. These data constitute the numeric seed for the induction of the gene networks. In this paper, we propose a new approach to build gene networks by means of Bayesian classifiers, variable selection and bootstrap resampling. The interactions induced by the Bayesian classifiers are based both on the expression levels and on the phenotype information of the supervised variable. Feature selection and bootstrap resampling add reliability and robustness to the overall process removing the false positive findings. The consensus among all the induced models produces a hierarchy of dependences and, thus, of variables. Biologists can define the depth level of the model hierarchy so the set of interactions and genes involved can vary from a sparse to a dense set. Experimental results show how these networks perform well on classification tasks. The biological validation matches previous biological findings and opens new hypothesis for future studies.     

Fuzzy logic and related methods as a screening tool for detecting gene regulatory networks

The analysis of gene expression microarrays plays an important role in elucidating the functionality of genes, including the discovery of genetic interactions that regulate gene expression. Several methods for modeling such gene regulatory networks exist, including a variety of continuous and discrete models. Methods based on fuzzy logic provide an interesting alternative. However, the guidelines for modeling gene expression with fuzzy logic are fairly open, and the need arises to investigate how adjustments in the modeling scheme will affect the results. In this work, we modify an existing fuzzy logic algorithm to involve an arbitrary number of classification states, and investigate the limiting behavior as the number of states tends to infinity. We also propose a probabilistic model as an alternative to the fuzzy logic model. We investigate the behavior of both models using yeast cell-cycle data and the simulated data of Werhli et al. [A.V. Werhli, M. Grzegorczyk, D. Husmeier, Comparative evaluation of reverse engineering gene regulatory networks with relevance networks, graphical Gaussian models, and Bayesian networks, Bioinformatics 22 (2006) 2523–2531]. We found that altering the number of classification states in both the fuzzy logic and probability models can influence which networks are predicted by both models. As the number of states tends to infinity, the predictions made by both models converge to those of a regression model. Models with a small to moderate number of classification states produced better results from a biological standpoint, compared to models with higher numbers of states. In simulated data, models with differing numbers of classification states produced similar overall results. Thus, increasing the complexity of the models has no apparent benefit, and models with smaller numbers of classification states are therefore preferred based on their ease of linguistic interpretation. The software used in this paper is freely available for non-commercial use at http://louisville.edu/~g0broc01.     

Testing the significance of cell-cycle patterns in time-course microarray data using nonparametric quadratic inference functions

We develop an approach to analyze time-course microarray data which are obtained from a single sample at multiple time points and to identify which genes are cell-cycle regulated. Since some genes have similar gene expression patterns, to reduce the amount of hypothesis testing, we first perform a clustering analysis to group genes into classes with similar cell-cycle patterns, including a class with no cell-cycle phenomena at all. Then we build a statistical model and an inference function assuming that genes within a cluster share the same mean model. A varying coefficient nonparametric approach is employed to be more flexible to fit the time-course data. In order to incorporate the correlation of longitudinal measurements, the quadratic inference function method is applied to obtain more efficient estimators and more powerful tests. Furthermore, this method allows us to perform chi-squared tests to determine whether certain genes are cell-cycle regulated. A data example on cell-cycle microarray data as well as simulations are illustrated.     

Gene interaction – An evolutionary biclustering approach

DNA Microarray experiments form a powerful tool for studying gene expression patterns, in large scale. Sharing of the regulatory mechanism among genes, in an organism, is predominantly responsible for their co-expression. Biclustering aims at finding a subset of similarly expressed genes under a subset of experimental conditions. A small number of genes participate in a cellular process of interest. Again, a gene may be simultaneously involved in a number of cellular processes. In cellular environment, genes interact among themselves to produce enzymes, metabolites, proteins, etc. responsible for a particular function(s).In this study, a simple and novel correlation-based approach is proposed to extract gene interaction networks from biclusters in microarray data. Local search strategy is employed to add (remove) relevant (irrelevant) genes for finer tuning, in multi-objective biclustering framework. Preprocessing is done to preserve strongly correlated gene interaction pairs. Experimental results on time-series gene expression data from Yeast are biologically validated using benchmark databases and literature.