Oscillatory and anti-oscillatory motifs in genetic regulatory networks

Recently, self-sustained oscillatory genetic regulatory networks （GRNs） have attracted significant attention in the biological field. Given a GRN, it is important to anticipate whether the network could generate oscillation with proper parameters, and what the key ingredients for the oscillation are. In this paper the ranges of some function-related parameters which are favorable to sustained oscillations are considered. In particular, some oscillatory motifs appearing with high-frequency in most of the oscillatory GRNs are observed. Moreover, there are some anti-oscillatory motifs which have a strong oscillation repressing effect. Some conclusions analyzing these motif effects and constructing oscillatory GRNs are provided.

Dynamics of network motifs in genetic regulatory networks

Network motifs hold a very important status in genetic regulatory networks. This paper aims to analyse the dynamical property of the network motifs in genetic regulatory networks. The main result we obtained is that the dynamical property of a single motif is very simple with only an asymptotically stable equilibrium point, but the combination of several motifs can make more complicated dynamical properties emerge such as limit cycles. The above-mentioned result shows that network motif is a stable substructure in genetic regulatory networks while their combinations make the genetic regulatory network more complicated.

Stability of piecewise-linear models of genetic regulatory networks

This paper investigates the stability of the equilibria of the piecewise-linear models of genetic regulatory networks on the intersection of the thresholds of all variables. It first studies circling trajectories and derives some stability conditions by quantitative analysis in the state transition graph. Then it proposes a common Lyapunov function for convergence analysis of the piecewise-linear models and gives a simple sign condition. All the obtained conditions are only related to the constant terms on the right-hand side of the differential equation after bringing the equilibrium to zero.

Designing Genetic Regulatory Networks Using Fuzzy Petri Nets Approach

In this paper, we have successfully presented a fuzzy Petri net （FPN） model to design the genetic regulatory network. Based on the FPN model, an efficient algorithm is proposed to automatically reason about imprecise and fuzzy information. By using the reasoning algorithm for the FPN, we present an alternative approach that is more promising than the fuzzy logic. The proposed FPN approach offers more flexible reasoning capability because it is able to obtain results with fuzzy intervals rather than point values. In this paper, a novel model with a new concept of hidden fuzzy transition （HFT） to design the genetic regulatory network is developed. We have built the FPN model and classified the input data in terms of time point and obtained the output data, so the system can be viewed as the two-input and one output system. This method eliminates possible false predictions from the classical fuzzy model thereby allowing a wider search space for inferring regulatory relationship. The experimental results show the proposed approach is feasible and acceptable to design the genetic regulatory network and investigate the dynamical behaviors of gene network.

The application of hidden markov model in building genetic regulatory network

The research hotspot in post-genomic era is from sequence to function. Building genetic regulatory network (GRN) can help to understand the regulatory mechanism between genes and the function of organisms. Probabilistic GRN has been paid more attention recently. This paper discusses the Hidden Markov Model (HMM) approach served as a tool to build GRN. Different genes with similar expression levels are considered as different states during training HMM. The probable regulatory genes of target genes can be found out through the resulting states transition matrix and the determinate regulatory functions can be predicted using nonlinear regression algorithm. The experiments on artificial and real-life datasets show the effectiveness of HMM in building GRN.

Structure and Dynamics of Artificial Regulatory Networks Evolved by Segmental Duplication and Divergence Model

Based on a model of network encoding and dynamics called the artificial genome, we propose a segmental duplication and divergence model for evolving artificial regulatory networks. We find that this class of networks share structural properties with natural transcriptional regulatory networks. Specifically, these networks can display scale-free and small-world structures. We also find that these networks have a higher probability to operate in the ordered regimen, and a lower probability to operate in the chaotic regimen. That is, the dynamics of these networks is similar to that of natural networks. The results show that the structure and dynamics inherent in natural networks may be in part due to their method of generation rather than being exclusively shaped by subsequent evolution under natural selection.

Computing a Predictor Set Influence Zone through a Multi-Layer Genetic Network to Explore the Role of Estrogen in Breast Cancer

Modeling inter-relationships of genes over a specific genetic network is one of the most challenging studies in systems biology. Among the families of models proposed one commonly used is the discrete stochastic, based on conditionally independent Markov chains. In practice, this model is estimated from time sequential sampling, usually obtained by microarray experiments. In order to improve the accuracy of the estimation method, we can use biological knowledge. In this paper, we decided to apply this idea to study the role of estrogen in breast cancer proliferation. The n-influence zone of a set S of genes in a given multi-layer genetic network is a set L of genes regulated, directly or indirectly, by genes in S, after at most n-1 layers. In this manuscript we describe a new approach for computing the n-influence zone of S through the estimation of a multi-layer genetic network from gene expression time series, measured by microarrays, and biological knowledge. Using seed genes related to cell proliferation, our method was able to add to the third layer of the network other genes related to this biological function and validated in the literature. Using a set of genes directly influenced by estrogen, we could find a new role for cell adhesion genes estrogen dependent. Our pipeline is user-friendly and does not have high system requirements. We believe this paper could contribute to improve the data mining for biologists in microarray time series.

Dissecting the molecular basis of spike traits by integrating gene regulatory networks and genetic variation in wheat

Spike architecture influences both grain weight and grain number per spike,which are the two major components of grain yield in bread wheat(Triticum aestivum L.).However,the complex wheat genome and the influence of various environmental factors pose challenges in mapping the causal genes that affect spike traits.Here,we systematically identified genes involved in spike trait formation by integrating information on genomic variation and gene regulatory networks controlling young spike development in wheat.We identified 170 loci that are responsible for variations in spike length,spikelet number per spike,and grain number per spike through genome-wide association study and meta-QTL analyses.We constructed gene regulatory networks for young inflorescences at the double ridge stage and thefloret primordium stage,in which the spikelet meristem and thefloret meristem are predominant,respec-tively,by integrating transcriptome,histone modification,chromatin accessibility,eQTL,and protein–pro-tein interactome data.From these networks,we identified 169 hub genes located in 76 of the 170 QTL regions whose polymorphisms are significantly associated with variation in spike traits.The functions of TaZF-B1,VRT-B2,and TaSPL15-A/D in establishment of wheat spike architecture were verified.This study provides valuable molecular resources for understanding spike traits and demonstrates that combining genetic analysis and developmental regulatory networks is a robust approach for dissection of complex traits.

Efficient Numerical Optimization Algorithm Based on New Real-Coded Genetic Algorithm, AREX + JGG, and Application to the Inverse Problem in Systems Biology

In Systems Biology, system identification, which infers regulatory network in genetic system and metabolic pathways using experimentally observed time-course data, is one of the hottest issues. The efficient numerical optimization algorithm to estimate more than 100 real-coded parameters should be developed for this purpose. New real-coded genetic algorithm (RCGA), the combination of AREX (adaptive real-coded ensemble crossover) with JGG (just generation gap), have applied to the inference of genetic interactions involving more than 100 parameters related to the interactions with using experimentally observed time-course data. Compared with conventional RCGA, the combination of UNDX (unimodal normal distribution crossover) with MGG (minimal generation gap), new algorithm has shown the superiority with improving early convergence in the first stage of search and suppressing evolutionary stagnation in the last stage of search.

A Vertex Network Model of Arabidopsis Leaf Growth

Biology provides many examples of complex systems whose properties allow organisms to develop in a highly reproducible,or robust,manner.One such system is the growth and development of flat leaves in Arabidopsis thaliana.This mechanistically challenging process results from multiple inputs including gene interactions,cellular geometry,growth rates,and coordinated cell divisions.To better understand how this complex genetic and cellular information controls leaf growth,we developed a mathematical model of flat leaf production.This two-dimensional model describes the gene interactions in a vertex network of cells which grow and divide according to physical forces and genetic information.Interestingly,the model predicts the presence of an unknown additional factor required for the formation of biologically realistic gene expression domains and iterative cell division.This two-dimensional model will form the basis for future studies into robustness of adaxial-abaxial patterning.

Bifurcation and Turing instability for genetic regulatory networks with diffusion

In this paper,a diffusive genetic regulatory network under Neumann boundary conditions is considered.First,the criteria for the local stability and diffusion-driven instability of the positive stationary solution without and with diffusion are investigated,respectively.Moreover,Turing regions and pattern formation are obtained in the plane of diffusion coeficients.Second,the existence and multiplicity of spatially homogeneous/nonhomogeneous non-constant steady-states are studied by using the Lyapunov-Schmidt reduction.Finally,some numerical simulations are carried out to illustrate the theoretical results.

MODELING GENETIC REGULATORY NETWORKS:A DELAY DISCRETE DYNAMICAL MODEL APPROACH

Modeling genetic regulatory networks is an important research topic in genomic research and computationM systems biology. This paper considers the problem of constructing a genetic regula- tory network （GRN） using the discrete dynamic system （DDS） model approach. Although considerable research has been devoted to building GRNs, many of the works did not consider the time-delay effect. Here, the authors propose a time-delay DDS model composed of linear difference equations to represent temporal interactions among significantly expressed genes. The authors also introduce interpolation scheme and re-sampling method for equalizing the non-uniformity of sampling time points. Statistical significance plays an active role in obtaining the optimal interaction matrix of GRNs. The constructed genetic network using linear multiple regression matches with the original data very well. Simulation results are given to demonstrate the effectiveness of the proposed method and model.

Existence and exponential stability of weighted pseudo-almost periodic solutions for genetic regulatory networks with time-varying delays

The importance of prediction for genetic regulatory network(GRNs)makes mathematical modeling a prominent tool.In this paper,we consider weighted pseudo-almost periodic solutions for a class of GRNs with time-varying delays.We establish the existence,uniqueness,and global exponential stability by employing the theory of dichotomy,the fixed point theorem,and differential inequality.A numerical example along with a graphical illustration are presented to support our main results.Our results extend existing GRNs models using almost periodic functions to support a wider range of regulatory processes.

Delayed fuzzy genetic regulatory networks:Novel results

In this manuscript, we studied a class of delayed Fuzzy Genetic Regulatory Networks (FGRNs) with Stepanov-like weighted pseudo almost automorphic coefficients. New criteria for the existence, uniqueness and global exponential stability of its weighted pseudo almost automorphic solution are established. Our approach is based on Banach fixed point theorem and novel analysis techniques. Moreover, a numerical example is given to illustrate the validity of the obtained results.

基于t检验和逐步网络搜索的有向基因调控网络推断算法

为了克服基于条件互信息的路径一致算法(PCA-CMI)无法识别调控方向的缺陷,并进一步提高网络推断准确率,提出了一种基于t检验和逐步网络搜索的有向网络推断算法(DNI-T-SRS)。首先,对不同实验条件下的表达数据进行t检验以辨别基因调控的上下游关系,指导路径一致(Path Consensus)算法中条件基因的选取,根据CMI2(Conditional Mutual Inclusive Information)剔除网络中的冗余边,得到了基于t检验的有向调控关系推断算法CMI2NI-T(CMI2-based Network Inference guided by t-Test);然后,建立有向调控关系对应的米氏微分方程模型对数据进行拟合,根据贝叶斯信息准则进行逐步网络搜索以修正网络推断结果。利用CMI2NI-T推断DREAM6挑战中的两个测试网络,所得到的曲线下面积(AUC)分别为0.7679和0.9796,相较于PCA-CMI分别提高了16.23%和11.62%;通过进一步的数据拟合后DNI-T-SRS的推断准确率分别达到了86.67%和100.00%,相较于PCA-CMI分别提高了18.19%和10.52%。实验结果表明,所提DNI-T-SRS算法能够有效剔除间接调控关系并保留直接调控连接,得到精确的基因调控网络推断结果。

Single-cell transcriptome analysis dissects lncRNA-associated gene networks in Arabidopsis

The plant genome produces an extremely large collection of long noncoding RNAs(lncRNAs)that are generally expressed in a context-specific manner and have pivotal roles in regulation of diverse biological processes.Here,we mapped the transcriptional heterogeneity of lncRNAs and their associated gene reg-ulatory networks at single-cell resolution.We generated a comprehensive cell atlas at the whole-organism level by integrative analysis of 28 published single-cell RNA sequencing(scRNA-seq)datasets from juvenile Arabidopsis seedlings.We then provided an in-depth analysis of cell-type-related lncRNA signatures that show expression patterns consistent with canonical protein-coding gene markers.We further demon-strated that the cell-type-specific expression of lncRNAs largely explains their tissue specificity.In addi-tion,we predicted gene regulatory networks on the basis of motif enrichment and co-expression analysis of lncRNAs and mRNAs,and we identified putative transcription factors orchestrating cell-type-specific expression of lncRNAs.The analysis results are available at the single-cell-based plant lncRNA atlas data-base(scPLAD;https://biobigdata.nju.edu.cn/scPLAD/).Overall,this work demonstrates the power of inte-grative single-cell data analysis applied to plant lncRNA biology and provides fundamental insights into lncRNA expression specificity and associated gene regulation.

基因调控网络的控制:机遇与挑战

众所周知,基因调控网络(Genetic regulatory networks,GRNs)是一类基本且重要的生物网络.基因调控网络可以通过输入、噪声、参数以及正负反馈等进行功能的鲁棒性调节与控制.本文首先简要回顾了基因调控网络控制方面的若干研究进展,然后提出了一些与控制相关的基因调控网络的基本科学问题.基因调控网络的控制以生命科学为背景,以控制理论为理论基础.过去几十年,控制论的基本思想与方法逐步渗透到基因调控网络的研究中.同时,来源于生命科学的控制问题也为我们提出了新的机遇与挑战.基因调控网络的控制对生命科学中困扰人类的基本问题,如延长寿命、治愈癌症、糖尿病等顽疾有着非常重要的现实意义.此外,基因调控网络控制研究对合成生物学、网络医学、个性化医学等相关学科的发展具有潜在的应用价值.

具有区间时滞的离散时间基因调控网络稳定性研究

针对具有随机干扰和区间时滞的离散时间基因调控网络(GRNs),基于Lyapunov稳定性定理,利用改进型自由权矩阵方法研究其时滞相关稳定问题.通过考虑时变时滞、时滞上界及它们的差三者之间的关系,同时保留增广Lyapunov-Krasovskii泛函差分中的所有有用项,获得一种更低保守性的时滞相关渐近稳定新判据.最后,给出仿真实例验证本文方法的有效性及相比已有方法的优越性.

产品基因调控网络模型及其对设计过程的辅助

基于图论建立一种描述该映射关系的模型,借用基因调控网络的部分概念,以设计要素为节点、以要素间的相关关系为边,建立产品的基因调控网络模型并绘制其基因调控网络图。通过基因调控网络图对产品中的众多设计要素进行分类,并识别其节点类型与节点集团,作为析出知识供设计师规划设计活动。基于交互式遗传算法开发了产品方案优化设计原型系统,并利用基因调控网络的知识发现辅助安排优化程序,制订优化搜索策略。基于纯净水瓶的参数化模型对基因调控网络的设计辅助作用进行了验证。

不确定基因调控网络的保成本控制（英文）

针对一类含常数时滞的不确定基因调控网络,设计了状态反馈控制器,使得闭环系统鲁棒渐近稳定,并且其线性二次性能指标有上界。基于李雅普诺夫稳定性理论和线性不等式技术,给出保成本控制器存在的充分条件,进而通过求解一个线性矩阵不等式约束的凸优化问题,得到最优保成本控制器。数值实例结果表明,所设计的保成本控制器是有效的。