Probabilistic Boolean Networks (PBNs) comprise a graphical model based on uncertain rule-based dependencies between nodes and have been proposed as a model for genetic regulatory networks. As with any algebraic strucicf theckxx--zkfjx#[xk of important mappings between PBNs isckT--#G for both theory andapplic-kfjj This paper treats the ckxjH[[kfjj of mappings to alter PBNstruc-#V while at the same time maintaining cintaining with the original probability strucilit It ctkx[[jH projecHkfj onto sub-networks, adjuncwork of new nodes, resolution reducuti mappings formed by merging nodes, and morphological mappings on the graph structure of the PBN. It places PBNs in the framework of many-sorted algebras and in that context defines homomorphisms between PBNs.

Cluster analysis of gene-wide expression data from DNA microarray hybridization studies has proved to be a useful tool for identifying biologically relevant groupings of genes and constructing gene regulatory networks. The motivation for considering mutual information is its capacity to measure a general dependence among gene random variables. We propose a novel clustering strategy based on minimizing mutual information among gene clusters. Simulated annealing is employed to solve the optimization problem. Bootstrap techniques are employed to get more accurate estimates of mutual information when the data sample size is small. Moreover, we propose to combine the mutual information criterion and traditional distance criteria such as the Euclidean distance and the fuzzy membership metric in designing the clustering algorithm. The performances of the new clustering methods are compared with those of some existing methods, using both synthesized data and experimental data. It is seen that the clustering algorithm based on a combined metric of mutual information and fuzzy membership achieves the best performance. The supplemental material is available at www.gspsnap.tamu.edu/gspweb/zxb/glioma_zxb.

Motivation: Bayesian network methods have shown promise in gene regulatory network reconstruction because of their capability of capturing causal relationships between genes and handling data with noises found in biological experiments. The problem of learning network structures, however, is NP hard. Consequently, heuristic methods such as hill climbing are used for structure learning. For networks of a moderate size, hill climbing methods are not computationally efficient. Furthermore, relatively low accuracy of the learned structures may be observed. The purpose of this paper is to present a novel structure learning method for gene network discovery.. Results: In this paper, we present a novel structure learning method to reconstruct the underlying gene networks from the observational gene expression data. Unlike hill climbing approaches, the proposed method first constructs an undirected network based on mutual information between two nodes and then split the structure into substructures. The directional orientations for the edges that connect two nodes are then obtained by optimizing a scoring function for each substructure. Our method is evaluated using two benchmark network datasets with known structures. The results show that the proposed method can identify networks that are close to the optimal structures. It outperforms hill climbing methods in terms of both computation time and predicted structure accuracy. We also apply the method to gene expression data measured during the yeast cycle and show the effectiveness of the proposed method for network reconstruction.

In this paper, we propose to construct the networks according to the following stages. Firstly, we determine the number of possible parent gene sets and the input sets of gene variables corresponding to each gene, and this is done by using a novel clustering technique based on mutual information minimization. Simulated annealing is employed to solve the optimization problem. After such initial gene clustering, we restrict our attention to the class of different functions from the possible parent gene sets to each target gene. Secondly, each function is then modelled by a perceptron consisting of a linear term and a nonlinear term. A reversible jump Markov chain Monte Carlo (MCMC) technique is used to calculate the model order and the parameters. Finally, coefficient of determination (CoD) is employed to compute the probability of selecting different predictors for each gene. To test this approach for constructing gene regulatory networks, we have carried out computational experiments using data from known gene response pathways including ionizing radiation and downstream targets of inactivating gene mutations.

The most fundamental problem in genetic network modeling is generally known as the dimensionality problem. Typical gene expression matrices contain measurements of thousands of genes taken over fewer than twenty time-steps. A large dynamic network cannot be learned from data with such a limited number of time-steps without the use of additional constraints, preferably derived from biological knowledge. In this paper, we present an approach that can find rough estimates of the underlying genetic network based on limited time-course gene expression data by employing the fact that gene expression measurements are relatively noisy and genetic networks are thought to be robust. The method expands the data-set by adding noisy duplicates, thereby simultaneously tackling the dimensionality problem and making the solutions more robust against (the already large) noise in the data. This simple concept is similar to adding a Tikhonov regularization term in the optimization process. In the case of linear models, the addition of noisy duplicates is equivalent to ridge regression, i.e. the sum of the squared weights is minimized as well as the prediction error. In the limiting case, it becomes even equivalent to the application of the Moore-Penrose Pseudo-Inverse to the original data. The strength of the proposed concept of adding noisy duplicates lies in the fact that it can be employed to all modelling approaches, including non-linear models. 1

In this study we propose a novel model for the representation of biological networks and provide algorithms for learning model parameters from experimental data. Our approach is to build an initial model based on extant biological knowledge, and refine it to increase the consistency between model predictions and experimental data. Our model encompasses networks which contain heterogeneous biological entities (mRNA, proteins, metabolites) and aims to capture diverse regulatory circuitry on several levels (metabolism, transcription, translation, post-translation and feedback loops among them).

Recent advances in gene-expression profiling technologies provide large amounts of gene expression data. This raises the possibility for a functional understanding of genome dynamics by means of mathematical modelling. As gene expression involves intrinsic noise, stochastic models are essential for better descriptions of gene regulatory networks. However, stochastic modelling for large scale gene expression data sets is still in the very early developmental stage. In this paper we present some stochastic models by introducing stochastic processes into neural network models that can describe intermediate regulation for large scale gene networks. Poisson random variables are used to represent chance events in the processes of synthesis and degradation. For expression data with normalized concentrations, exponential or normal random variables are used to realize fluctuations. Using a network with three genes, we show how to use stochastic simulations for studying robustness and stability properties of gene expression patterns under the influence of noise, and how to use stochastic models to predict statistical distributions of expression levels in a population of cells. The discussion suggests that stochastic neural network models can give better descriptions of gene regulatory networks and provide criteria for measuring the reasonableness of mathematical models. 1

Introduction The complex functions of a living cell are carried out through the concerted activity of many genes and gene products. This activity is often coordinated by the organization of Computer Science Department, Stanford University, Stanford, California, 94305, USA. Department of Genetics, Stanford University School of Medicine, Stanford, California, 94305, USA. Dept. of Cell Research and Immunology, Tel Aviv U. & Computer Science Dept., Weizmann Inst., Israel. School of Computer Science & Engineering, Hebrew University, Jerusalem, 91904, Israel. * These authors contributed equally to this manuscript. # Correspondence should be addressed to E.S. (eran@cs.stanford.edu) or D.K. (koller@cs.stanford.edu). Supplementary information: attached pdf and http://www.cs.stanford.edu/~eran/module_nets/ (username: modnet, password: modnet-review). the genome into regulatory modules, or sets of co-regulated genes that share a common function. Such is the case for most of the m

ABSTRACT: The overexpression of recombinant proteins in microorganisms may lead to a metabolic depression or collapse of the cell factory. In order to understand this process and to optimize the cellular productivity the stress response was investigated. The expression of the recombinant human superoxide dismutase (SOD) was induced under steady state conditions and the expression of all 4289 protein coding genes of the microorganism Escherichia coli was monitored using microarrays. After normalization by the LOWESS method 102 differentially expressed genes were selected by a novel criterion that includes the measurement error. These differentially expressed genes were clustered using the EcoCyc database and the fuzzy-c-means clustering method. The results from clustering were interpreted in terms of dynamic models, which have been constructed either via Singular Value Decomposition (SVD) or a novel heuristic algorithm for dynamic model structure optimization.

The inference of regulatory interactions between genes from time-course micro-array data is one of the most challenging tasks in the field of functional genomics. The multitude of genes that can now be measured using micro-array technology requires analysis tools that can easily scale-up with respect to the number of genes. This scalability is especially important when inferring genetic interactions, because this task is complicated by the combinatorial nature of gene interaction and because the high cost of micro-array measurements still severely limits the number of measured timepoints. Because of this limitation of the data, it is essential to incorporate as much additional information as possible. This can be achieved by applying constraints based on general biological knowledge and by including specific knowledge about known interactions. In this paper we employ the fact that genetic networks are believed to exhibit limited connectivity. We propose a general approach in which we separate the task of finding the structure of the networks from the task of finding the best parameters of the model, given the structure. The second task can be solved e#ciently for most models, but the first task amounts to a search problem which requires the choice of a suitable evaluation function and search strategy. Experimental investigations determined that the best evaluation function is simply the mean squared error on the training data. Through further extensive experimental investigation of several search strategies, it was found that the best search strategy is based on an approach of greedily increasing the number of connections. The strength of the proposed approach lies in the fact that it can be employed to all genetic network models and allows genetic network models to sca...