Reconstruction Of Gene Regulatory Network With Delayed Differential Equations Network Model

Advances in molecular biological, analytical and computational technologies are enabling us to investigate systematically the complex molecular processes underlying biological systems. In particular, using high-throughput gene expression assays, we are able to measure the output of the gene regulatory network. We aim here to review datamining and modeling approaches for conceptualizing and unraveling the functional relationships implicit in these datasets. Clustering of co-expression profiles allows us to infer shared regulatory inputs and functional pathways. We discuss various aspects of clustering, ranging from distance measures to clustering algorithms and multiple cluster memberships. More advanced analysis aims to infer causal connections between genes directly, i.e. who is regulating whom and how. We discuss several approaches to the problem of reverse engineering of genetic networks, from discrete Boolean networks, to continuous linear and non-linear models. We conclude that the combination of predictive modeling with systematic experimental verification will be required to gain deeper insight into living organisms, therapeutic targeting and bioengineering.There are four parts in the struction of network procedure. The author of this paper analyzes all of the parts. First of all, the data will be preprocessed; secondly, the model of struction methods, partically differential equation; what's more, the optimal algorithms were selected and created; last but not least, the topology of the gene regulatory networks and the scale-free proporties were researched.Naturally,the analysis of the clustering will be researched. All clustering algorithms assume the pre-existence of groupings of the objects to be clustered. Random noise and other uncertainties have obscured these groupings. The objectives of the clustering algorithm are to recover the original grouping among the data. Clustering algorithms can be divided into hierarchical and non-hierarchical methods. Non-hierarchical methods typically cluster objects into K groups in an iterative process until certain goodness criteria are optimized. Examples of non-hierarchical methods include K-means, expectation-maximization (EM) and autoclass. Hierarchical methods return an hierarchy of nested clusters, where each cluster typically consists of the union of two or more smaller clusters. The hierarchical methods can be further distinguished into agglomerative and divisive methods, depending on whether they start with single-object clusters and recursively merge them into larger clusters, or start with the cluster containing all objects and recursively divide it into smaller clusters. This paper proposes an improved parallel immune genetic algorithm. In the aspect of the population size, we introduce the islands concept, which can make the sizes of populations'variable; In the aspect of the fitness function, we introduce the immune operator, which can avoid the algorithm premature convergence. Hence,this method can prevent local convergence in the optimal algorithm in a great extent, and make the probability of approaching the global convergence bigger. The algorithm is used with the Yeast Saccharomyces cerevisiae cell cycle gene expression profile from SGD to cluster in the aspect of co-expression. Contrast to the experiment analyzed by Spellman for functional genomics, the efficiency of this algorithm in the functional genomics can be proved.After clustering, construction of the gene regulatory network is our next work. In network inference, the goal is to construct a coarse-scale model of the network of regulatory interactions between the genes. This requires inference of the causal relationships among genes, i.e. reverse engineering the network architecture from its activity profiles. As the molecular dynamics data we acquire becomes more copious and complex, we may need to routinely consult reverse engineering methods to provide the guiding hypotheses for experimental design. We propose a scheme to reverse-engineer gene networks on a genome-wide scale using a relatively big amount of gene expression data from microarray experiments. Our method is based on the empirical observation that such networks are typically large and sparse. It uses singular value decomposition to construct a family of candidate solutions and then uses robust regression to identify the solution with the smallest number of connections as the most likely solution. In this paper we generalize the additive regulation model by converting differential equations into integral equations with adjustable kernel functions. These kernel functions can be selected based on prior knowledge or defined through iterative improvement in data analysis. This makes the integral model very flexible and thus capable of covering a broad range of biological systems more adequately and specifically than previous models. As the number of the unknown parameters for even medium-sized networks may exceed the number of experimentally measured points, fitting algorithms for underdetermined problems have to be applied.P38 MAPK is one of the most important central regulatory proteins that can respond extra environmental stresses. It can activate or inhibit many other genes, which can lead some disease, such as cancers or inflammations etc. We proposed a new differential equation model using linear regression analysis to calculate the weight values of the Genetic Regulatory Networks to simulate the P38 MAPK pathway in Genetic level. The results of the network are reasonable. We can investigate the P38 MAPK pathway some extra hypotheses from the result model, and provide biologists optimal designs for further experiments of disease researches. After construction of the gene regulatory network, the analysis of proporties of the network is important. Scale-Free networks are complex networks which have a few highly connected nodes, while most nodes are poorly connected. More precisely, in such networks, the connectivity of the nodes follows a power law: the proportion P(k) of nodes with degree k (i.e. that are connected to k other nodes) is roughly proportional to k. In this paper, we use the reconnection method to new analysis of the topology of the network to hub regulatory function.Organization structure of this paper is as follows:ChapterⅠ: Introduction. We simply introduce what is the network and how is the research now.ChapterⅡ: Preprocess in gene dataset. This chapter introduces knowledge of data merging and cluster analysis with their function in gene regulatory network construction. And we introduce the proposed novel genetic algorithm clustering.ChapterⅢ: Construction of the gene regulatory network. This chapter introduces basic knowledge of differential equation with its ability and advantage for reconstructing gene regulatory network. And we proposed the novel construction of network algorithm.ChapterⅣ: Analysis of the topology of the network. We introduce the basis of the topology of network. And we proposed the novel reconnection of the topology genetic regulatory network.ChapterⅤ: Summary and Prospect. This chapter sums up my work and introduces some outlook for development of system biology and research of gene regulatory network.