On the robustness of update schedules in Boolean networks

Deterministic Boolean networks have been used as models of gene regulation and other biological networks. One key element in these models is the update schedule, which indicates the order in which states are to be updated. We study the robustness of the dynamical behavior of a Boolean network with respect to different update schedules (synchronous, block-sequential, sequential), which can provide modelers with a better understanding of the consequences of changes in this aspect of the model. For a given Boolean network, we define equivalence classes of update schedules with the same dynamical behavior, introducing a labeled graph which helps to understand the dependence of the dynamics with respect to the update, and to identify interactions whose timing may be crucial for the presence of a particular attractor of the system. Several other results on the robustness of update schedules and of dynamical cycles with respect to update schedules are presented. Finally, we prove that our equivalence classes generalize those found in sequential dynamical systems.     

Intrinsic properties of Boolean dynamics in complex networks

We study intrinsic properties of attractor in Boolean dynamics of complex networks with scale-free topology, comparing with those of the so-called Kauffman's random Boolean networks. We numerically study both frozen and relevant nodes in each attractor in the dynamics of relatively small networks (20?N?200). We investigate numerically robustness of an attractor to a perturbation. An attractor with cycle length of ?_c in a network of size N consists of ?_c states in the state space of 2^N states; each attractor has the arrangement of N nodes, where the cycle of attractor sweeps ?_c states. We define a perturbation as a flip of the state on a single node in the attractor state at a given time step. We show that the rate between unfrozen and relevant nodes in the dynamics of a complex network with scale-free topology is larger than that in Kauffman's random Boolean network model. Furthermore, we find that in a complex scale-free network with fluctuation of the in-degree number, attractors are more sensitive to a state flip for a highly connected node (i.e. input-hub node) than to that for a less connected node. By some numerical examples, we show that the number of relevant nodes increases, when an input-hub node is coincident with and/or connected with an output-hub node (i.e. a node with large output-degree) one another.     

使用线性微分方程构建初步的乳腺癌转移相关基因网络模型

随着基因芯片的技术的推广,越来越多的表达数据需要被处理和分析．利用这些表达数据提取基因调控矩阵从而构建基因网络是一个重要的问题．通过线性微分方程模型可以初步构建基因网络,了解网络结构,提取最显著的信息．然而由于分子生物学的条件限制或者数据来源的限制,导致实验数据不充分,使方程组无解．本文使用三次样条方法,对26例临床、病理资料完备的具有淋巴结转移的乳腺癌基因表达数据进行插值处理,使表达数据满秩,从而使用最小二乘法解出加权矩阵,构建初步的表达基因调控网络．通过对构建的基因网络的初步分析表明:乳腺癌转移的形成是由多基因异常引起多条传导通路异常,致使细胞恶性转化的结果,这与生物学上公认的看法是相一致的．因此,利用此线性模型方法对基因表达谱进行分析兵有一定可行性,在认识乳腺癌转移机制,乳腺癌诊断和治疗方面具有一定的理论和应用价值．     

Pathway analysis identifies perturbation of genetic networks induced by butyrate in a bovine kidney epithelial cell line

Ruminant species have evolved to metabolize the short-chain volatile fatty acids (VFA), acetate, propionate, and butyrate, to fulfill up to 70% of their nutrient energy requirements. The inherent VFA dependence of ruminant cells was exploited to add a level of increased sensitivity to the study of the role of butyrate gene-response elements in regulatory biochemical pathways. Global gene expression profiles of the bovine kidney epithelial cells regulated by sodium butyrate were investigated with high-density oligonucleotide microarrays. The detailed mechanisms by which butyrate induces cell growth arrest and apoptosis were analyzed using the Ingenuity Pathways Knowledge Base. The functional category and pathway analyses of the microarray data revealed that four canonical pathways (Cell cycles: G2/M DNA damage checkpoint, and pyrimidine metabolism; G1/S checkpoint regulation and purine metabolism) were significantly perturbed. The biologically relevant networks and pathways of these genes were also identified. IGF2, TGFB1, TP53, E2F4, and CDC2 were established as being centered in these genomic networks. The present findings provide a basis for understanding the full range of the biological roles and the molecular mechanisms that butyrate may play in animal cell growth, proliferation, and energy metabolisms. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users. Mention of trade names or commercial products in this publication is solely for providing specific information and does not imply recommendation or endorsement by the US Department of Agriculture.     

一类微生物连续培养竞争模型的定性分析

研究一类微生物连续培养竞争模型的解的结构,分析了平衡点的稳定性及平衡点附近极限环存在唯一性,证明系统存在正向不变集。     

Genetically-designed Neural Networks for Error Reduction in an Optimized Biomechanical Model of the Human Elbow Joint Complex

A real time dynamic biomechanical model of the human elbow joint has been used as the first step in the process of calculating time varying joint position from the electromyograms (EMGs) of eight muscles crossing the joint. Since calculation of position has a high sensitivity to errors in the model torque calculation, a genetic algorithm (GA) neural network (NN) has been developed for automatic error reduction in the dynamic model. Genetic algorithms are used to design many neural network structures during a preliminary trial effort, and then each network's performance is ranked to choose a trained network that represents the most accurate result. Experimental results from three subjects have shown model error reduction in 84.2% of the data sets from a subject on which the model had been trained, and 52.6% of the data sets from the subjects on which the model had not been trained. Furthermore, the GA networks reduced the error standard deviation across all subjects, showing that progress in error reduction was made evenly across all data sets.