Modeling genetic regulatory dynamics in neural development.

We model genetic regulatory networks in the framework of continuous-time recurrent networks. The network parameters are determined from gene expression level time series data using genetic algorithms. We have applied the method to expression data from the development of rat central nervous system, where the active genes cluster into four groups, within which the temporal expression patterns are similar. The data permit us to identify approximately the interactions between these groups of genes. We find that generally a single time series is of limited value in determining the interactions in the network, but multiple time series collected in related tissues or under treatment with different drugs can fix their values much more precisely.     

On construction of stochastic genetic networks based on gene expression sequences

Reconstruction of genetic regulatory networks from time series data of gene expression patterns is an important research topic in bioinformatics. Probabilistic Boolean Networks (PBNs) have been proposed as an effective model for gene regulatory networks. PBNs are able to cope with uncertainty, corporate rule-based dependencies between genes and discover the sensitivity of genes in their interactions with other genes. However, PBNs are unlikely to use directly in practice because of huge amount of computational cost for obtaining predictors and their corresponding probabilities. In this paper, we propose a multivariate Markov model for approximating PBNs and describing the dynamics of a genetic network for gene expression sequences. The main contribution of the new model is to preserve the strength of PBNs and reduce the complexity of the networks. The number of parameters of our proposed model is O(n2) where n is the number of genes involved. We also develop efficient estimation methods for solving the model parameters. Numerical examples on synthetic data sets and practical yeast data sequences are given to demonstrate the effectiveness of the proposed model.     

Gene regulatory networks modelling using a dynamic evolutionary hybrid

Background  

Inference of gene regulatory networks is a key goal in the quest for understanding fundamental cellular processes and revealing underlying relations among genes. With the availability of gene expression data, computational methods aiming at regulatory networks reconstruction are facing challenges posed by the data's high dimensionality, temporal dynamics or measurement noise. We propose an approach based on a novel multi-layer evolutionary trained neuro-fuzzy recurrent network (ENFRN) that is able to select potential regulators of target genes and describe their regulation type.     

Inference of biological pathway from gene expression profiles by time delay boolean networks

One great challenge of genomic research is to efficiently and accurately identify complex gene regulatory networks. The development of high-throughput technologies provides numerous experimental data such as DNA sequences, protein sequence, and RNA expression profiles makes it possible to study interactions and regulations among genes or other substance in an organism. However, it is crucial to make inference of genetic regulatory networks from gene expression profiles and protein interaction data for systems biology. This study will develop a new approach to reconstruct time delay Boolean networks as a tool for exploring biological pathways. In the inference strategy, we will compare all pairs of input genes in those basic relationships by their corresponding [Formula: see text]-scores for every output gene. Then, we will combine those consistent relationships to reveal the most probable relationship and reconstruct the genetic network. Specifically, we will prove that [Formula: see text] state transition pairs are sufficient and necessary to reconstruct the time delay Boolean network of [Formula: see text] nodes with high accuracy if the number of input genes to each gene is bounded. We also have implemented this method on simulated and empirical yeast gene expression data sets. The test results show that this proposed method is extensible for realistic networks.     

An integer optimization algorithm for robust identification of non-linear gene regulatory networks

ABSTRACT: BACKGROUND: Reverse engineering gene networks and identifying regulatory interactions are integral to understanding cellular decision making processes. Advancement in high throughput experimental techniques has initiated innovative data driven analysis of gene regulatory networks. However, inherent noise associated with biological systems requires numerous experimental replicates for reliable conclusions. Furthermore, evidence of robust algorithms directly exploiting basic biological traits are few. Such algorithms are expected to be efficient in their performance and robust in their prediction. RESULTS: We have developed a network identification algorithm to accurately infer both the topology and strength of regulatory interactions from time series gene expression data in the presence of significant experimental noise and non-linear behavior. In this novel formulism, we have addressed data variability in biological systems by integrating network identification with the bootstrap resampling technique, hence predicting robust interactions from limited experimental replicates subjected to noise. Furthermore, we have incorporated non-linearity in gene dynamics using the S-system formulation. The basic network identification formulation exploits the trait of sparsity of biological interactions. Towards that, the identification algorithm is formulated as an integer-programming problem by introducing binary variables for each network component. The objective function is targeted to minimize the network connections subjected to the constraint of maximal agreement between the experimental and predicted gene dynamics. The developed algorithm is validated using both in-silico and experimental data-sets. These studies show that the algorithm can accurately predict the topology and connection strength of the in silico networks, as quantified by high precision and recall, and small discrepancy between the actual and predicted kinetic parameters. Furthermore, in both the in silico and experimental case studies, the predicted gene expression profiles are in very close agreement with the dynamics of the input data. CONCLUSIONS: Our integer programming algorithm effectively utilizes bootstrapping to identify robust gene regulatory networks from noisy, non-linear time-series gene expression data. With significant noise and non-linearities being inherent to biological systems, the present formulism, with the incorporation of network sparsity, is extremely relevant to gene regulatory networks, and while the formulation has been validated against in silico and E. Coli data, it can be applied to any biological system.     

A Markov-blanket-based model for gene regulatory network inference

An efficient two-step Markov blanket method for modeling and inferring complex regulatory networks from large-scale microarray data sets is presented. The inferred gene regulatory network (GRN) is based on the time series gene expression data capturing the underlying gene interactions. For constructing a highly accurate GRN, the proposed method performs: 1) discovery of a gene's Markov Blanket (MB), 2) formulation of a flexible measure to determine the network's quality, 3) efficient searching with the aid of a guided genetic algorithm, and 4) pruning to obtain a minimal set of correct interactions. Investigations are carried out using both synthetic as well as yeast cell cycle gene expression data sets. The realistic synthetic data sets validate the robustness of the method by varying topology, sample size, time delay, noise, vertex in-degree, and the presence of hidden nodes. It is shown that the proposed approach has excellent inferential capabilities and high accuracy even in the presence of noise. The gene network inferred from yeast cell cycle data is investigated for its biological relevance using well-known interactions, sequence analysis, motif patterns, and GO data. Further, novel interactions are predicted for the unknown genes of the network and their influence on other genes is also discussed.     

Novel recurrent neural network for modelling biological networks: Oscillatory p53 interaction dynamics

Understanding the control of cellular networks consisting of gene and protein interactions and their emergent properties is a central activity of Systems Biology research. For this, continuous, discrete, hybrid, and stochastic methods have been proposed. Currently, the most common approach to modelling accurate temporal dynamics of networks is ordinary differential equations (ODE). However, critical limitations of ODE models are difficulty in kinetic parameter estimation and numerical solution of a large number of equations, making them more suited to smaller systems. In this article, we introduce a novel recurrent artificial neural network (RNN) that addresses above limitations and produces a continuous model that easily estimates parameters from data, can handle a large number of molecular interactions and quantifies temporal dynamics and emergent systems properties. This RNN is based on a system of ODEs representing molecular interactions in a signalling network. Each neuron represents concentration change of one molecule represented by an ODE. Weights of the RNN correspond to kinetic parameters in the system and can be adjusted incrementally during network training. The method is applied to the p53-Mdm2 oscillation system – a crucial component of the DNA damage response pathways activated by a damage signal. Simulation results indicate that the proposed RNN can successfully represent the behaviour of the p53-Mdm2 oscillation system and solve the parameter estimation problem with high accuracy. Furthermore, we presented a modified form of the RNN that estimates parameters and captures systems dynamics from sparse data collected over relatively large time steps. We also investigate the robustness of the p53-Mdm2 system using the trained RNN under various levels of parameter perturbation to gain a greater understanding of the control of the p53-Mdm2 system. Its outcomes on robustness are consistent with the current biological knowledge of this system. As more quantitative data become available on individual proteins, the RNN would be able to refine parameter estimation and mapping of temporal dynamics of individual signalling molecules as well as signalling networks as a system. Moreover, RNN can be used to modularise large signalling networks.     

Boolean dynamics of genetic regulatory networks inferred from microarray time series data

MOTIVATION: Methods available for the inference of genetic regulatory networks strive to produce a single network, usually by optimizing some quantity to fit the experimental observations. In this article we investigate the possibility that multiple networks can be inferred, all resulting in similar dynamics. This idea is motivated by theoretical work which suggests that biological networks are robust and adaptable to change, and that the overall behavior of a genetic regulatory network might be captured in terms of dynamical basins of attraction. RESULTS: We have developed and implemented a method for inferring genetic regulatory networks for time series microarray data. Our method first clusters and discretizes the gene expression data using k-means and support vector regression. We then enumerate Boolean activation-inhibition networks to match the discretized data. Finally, the dynamics of the Boolean networks are examined. We have tested our method on two immunology microarray datasets: an IL-2-stimulated T cell response dataset and a LPS-stimulated macrophage response dataset. In both cases, we discovered that many networks matched the data, and that most of these networks had similar dynamics. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Inferring models of gene expression dynamics

We study the problem of identifying genetic networks in which expression dynamics are modeled by a differential equation that uses logical rules to specify time derivatives. We make three main contributions. First, we describe computationally efficient procedures for identifying the structure and dynamics of such networks from expression time series. Second, we derive predictions for the expected amount of data needed to identify randomly generated networks. Third, if expression values are available for only some of the genes, we show that the structure of the network for these "visible" genes can be identified and that the size and overall complexity of the network can be estimated. We validate these procedures and predictions using simulation experiments based on randomly generated networks with up to 30,000 genes and 17 distinct regulators per gene and on a network that models floral morphogenesis in Arabidopsis thaliana.     

A multiorganism based method for Bayesian gene network estimation

The primary goal of this article is to infer genetic interactions based on gene expression data. A new method for multiorganism Bayesian gene network estimation is presented based on multitask learning. When the input datasets are sparse, as is the case in microarray gene expression data, it becomes difficult to separate random correlations from true correlations that would lead to actual edges when modeling the gene interactions as a Bayesian network. Multitask learning takes advantage of the similarity between related tasks, in order to construct a more accurate model of the underlying relationships represented by the Bayesian networks. The proposed method is tested on synthetic data to illustrate its validity. Then it is iteratively applied on real gene expression data to learn the genetic regulatory networks of two organisms with homologous genes.     

A Boolean Model of the Gene Regulatory Network Underlying Mammalian Cortical Area Development

The cerebral cortex is divided into many functionally distinct areas. The emergence of these areas during neural development is dependent on the expression patterns of several genes. Along the anterior-posterior axis, gradients of Fgf8, Emx2, Pax6, Coup-tfi, and Sp8 play a particularly strong role in specifying areal identity. However, our understanding of the regulatory interactions between these genes that lead to their confinement to particular spatial patterns is currently qualitative and incomplete. We therefore used a computational model of the interactions between these five genes to determine which interactions, and combinations of interactions, occur in networks that reproduce the anterior-posterior expression patterns observed experimentally. The model treats expression levels as Boolean, reflecting the qualitative nature of the expression data currently available. We simulated gene expression patterns created by all possible networks containing the five genes of interest. We found that only of these networks were able to reproduce the experimentally observed expression patterns. These networks all lacked certain interactions and combinations of interactions including auto-regulation and inductive loops. Many higher order combinations of interactions also never appeared in networks that satisfied our criteria for good performance. While there was remarkable diversity in the structure of the networks that perform well, an analysis of the probability of each interaction gave an indication of which interactions are most likely to be present in the gene network regulating cortical area development. We found that in general, repressive interactions are much more likely than inductive ones, but that mutually repressive loops are not critical for correct network functioning. Overall, our model illuminates the design principles of the gene network regulating cortical area development, and makes novel predictions that can be tested experimentally.     

Statistical epistasis is a generic feature of gene regulatory networks

Functional dependencies between genes are a defining characteristic of gene networks underlying quantitative traits. However, recent studies show that the proportion of the genetic variation that can be attributed to statistical epistasis varies from almost zero to very high. It is thus of fundamental as well as instrumental importance to better understand whether different functional dependency patterns among polymorphic genes give rise to distinct statistical interaction patterns or not. Here we address this issue by combining a quantitative genetic model approach with genotype-phenotype models capable of translating allelic variation and regulatory principles into phenotypic variation at the level of gene expression. We show that gene regulatory networks with and without feedback motifs can exhibit a wide range of possible statistical genetic architectures with regard to both type of effect explaining phenotypic variance and number of apparent loci underlying the observed phenotypic effect. Although all motifs are capable of harboring significant interactions, positive feedback gives rise to higher amounts and more types of statistical epistasis. The results also suggest that the inclusion of statistical interaction terms in genetic models will increase the chance to detect additional QTL as well as functional dependencies between genetic loci over a broad range of regulatory regimes. This article illustrates how statistical genetic methods can fruitfully be combined with nonlinear systems dynamics to elucidate biological issues beyond reach of each methodology in isolation.     

Modelling the evolution of genetic regulatory networks

An evolutionary model of genetic regulatory networks is developed, based on a model of network encoding and dynamics called the Artificial Genome (AG). This model derives a number of specific genes and their interactions from a string of (initially random) bases in an idealized manner analogous to that employed by natural DNA. The gene expression dynamics are determined by updating the gene network as if it were a simple Boolean network. The generic behaviour of the AG model is investigated in detail. In particular, we explore the characteristic network topologies generated by the model, their dynamical behaviours, and the typical variance of network connectivities and network structures. These properties are demonstrated to agree with a probabilistic analysis of the model, and the typical network structures generated by the model are shown to lie between those of random networks and scale-free networks in terms of their degree distribution. Evolutionary processes are simulated using a genetic algorithm, with selection acting on a range of properties from gene number and degree of connectivity through periodic behaviour to specific patterns of gene expression. The evolvability of increasingly complex patterns of gene expression is examined in detail. When a degree of redundancy is introduced, the average number of generations required to evolve given targets is reduced, but limits on evolution of complex gene expression patterns remain. In addition, cyclic gene expression patterns with periods that are multiples of shorter expression patterns are shown to be inherently easier to evolve than others. Constraints imposed by the template-matching nature of the AG model generate similar biases towards such expression patterns in networks in initial populations, in addition to the somewhat scale-free nature of these networks. The significance of these results on current understanding of biological evolution is discussed.     

Learning Gene Networks under SNP Perturbations Using eQTL Datasets

The standard approach for identifying gene networks is based on experimental perturbations of gene regulatory systems such as gene knock-out experiments, followed by a genome-wide profiling of differential gene expressions. However, this approach is significantly limited in that it is not possible to perturb more than one or two genes simultaneously to discover complex gene interactions or to distinguish between direct and indirect downstream regulations of the differentially-expressed genes. As an alternative, genetical genomics study has been proposed to treat naturally-occurring genetic variants as potential perturbants of gene regulatory system and to recover gene networks via analysis of population gene-expression and genotype data. Despite many advantages of genetical genomics data analysis, the computational challenge that the effects of multifactorial genetic perturbations should be decoded simultaneously from data has prevented a widespread application of genetical genomics analysis. In this article, we propose a statistical framework for learning gene networks that overcomes the limitations of experimental perturbation methods and addresses the challenges of genetical genomics analysis. We introduce a new statistical model, called a sparse conditional Gaussian graphical model, and describe an efficient learning algorithm that simultaneously decodes the perturbations of gene regulatory system by a large number of SNPs to identify a gene network along with expression quantitative trait loci (eQTLs) that perturb this network. While our statistical model captures direct genetic perturbations of gene network, by performing inference on the probabilistic graphical model, we obtain detailed characterizations of how the direct SNP perturbation effects propagate through the gene network to perturb other genes indirectly. We demonstrate our statistical method using HapMap-simulated and yeast eQTL datasets. In particular, the yeast gene network identified computationally by our method under SNP perturbations is well supported by the results from experimental perturbation studies related to DNA replication stress response.     

Relevance of systems biological approach in the differential diagnosis of invasive lobular carcinoma & invasive ductal carcinoma

Breast cancer is a malignant neoplasm originating from breast tissue, most commonly from the inner lining of milk ducts or the lobules that supply the ducts with milk. ILCs and IDCs vary from each other with respect to various histological, biological and clinical features. Remarkably, ductal tumors tending to form glandular structures, whereas lobular tumors are less cohesive and tends to invade in single file. The high degree of similarity in the prognoses of IDC and ILC makes it beneficial to develop a differential diagnostic protocol to classify the two conditions. The main goal of the study is to construct the genetic regulatory network from the microarray data using biological knowledge and constraint-based inferences, in order to explore the potential significant gene regulatory networks that can differentiate IDC and ILC and thereby understand the complex interactions that are influenced by the genetic networks. Out of the 54676 genes present on the GPL570 platform- 29 genes exhibited 4 fold up regulation in case of IDC and 22 in the case of ILC. The ductal and lobular tumors displayed a striking difference in the expression of genes associated with cell adhesion, protein folding, and protein phosphorylation and invasion. Construction of separate gene regulation networks for IDC and ILC on the basis of gene expression altercation can be utilized in understanding the distinction in the possible mechanism that underlies the pathological differences between the two, which can be exploited in identifying diagnostic or therapeutic targets.