Construction,visualization, and analysis of biological network models in Dynetica

Mathematical modeling has become an increasingly important aspect of biological research. Computer simulations help to improve our understanding of complex systems by testing the validity of proposed mechanisms and generating experimentally testable hypotheses. However, significant overhead is generated by the creation, debugging, and perturbation of these computational models and their parameters, especially for researchers who are unfamiliar with programming or numerical methods. Dynetica 2.0 is a user-friendly dynamic network simulator designed to expedite this process. Models are created and visualized in an easy-to-use graphical interface, which displays all of the species and reactions involved in a graph layout. System inputs and outputs, indicators, and intermediate expressions may be incorporated into the model via the versatile “expression variable” entity. Models can also be modular, allowing for the quick construction of complex systems from simpler components. Dynetica 2.0 supports a number of deterministic and stochastic algorithms for performing time-course simulations. Additionally, Dynetica 2.0 provides built-in tools for performing sensitivity or dose response analysis for a number of different metrics. Its parameter searching tools can optimize specific objectives of the time course or dose response of the system. Systems can be translated from Dynetica 2.0 into MATLAB code or the Systems Biology Markup Language (SBML) format for further analysis or publication. Finally, since it is written in Java, Dynetica 2.0 is platform independent, allowing for easy sharing and collaboration between researchers.     

Structural systems identification of genetic regulatory networks

MOTIVATION: Reverse engineering of genetic regulatory networks from experimental data is the first step toward the modeling of genetic networks. Linear state-space models, also known as linear dynamical models, have been applied to model genetic networks from gene expression time series data, but existing works have not taken into account available structural information. Without structural constraints, estimated models may contradict biological knowledge and estimation methods may over-fit. RESULTS: In this report, we extended expectation-maximization (EM) algorithms to incorporate prior network structure and to estimate genetic regulatory networks that can track and predict gene expression profiles. We applied our method to synthetic data and to SOS data and showed that our method significantly outperforms the regular EM without structural constraints. AVAILABILITY: The Matlab code is available upon request and the SOS data can be downloaded from http://www.weizmann.ac.il/mcb/UriAlon/Papers/SOSData/, courtesy of Uri Alon. Zak's data is available from his website, http://www.che.udel.edu/systems/people/zak.     

Comparative evaluation of reverse engineering gene regulatory networks with relevance networks, graphical gaussian models and bayesian networks

MOTIVATION: An important problem in systems biology is the inference of biochemical pathways and regulatory networks from postgenomic data. Various reverse engineering methods have been proposed in the literature, and it is important to understand their relative merits and shortcomings. In the present paper, we compare the accuracy of reconstructing gene regulatory networks with three different modelling and inference paradigms: (1) Relevance networks (RNs): pairwise association scores independent of the remaining network; (2) graphical Gaussian models (GGMs): undirected graphical models with constraint-based inference, and (3) Bayesian networks (BNs): directed graphical models with score-based inference. The evaluation is carried out on the Raf pathway, a cellular signalling network describing the interaction of 11 phosphorylated proteins and phospholipids in human immune system cells. We use both laboratory data from cytometry experiments as well as data simulated from the gold-standard network. We also compare passive observations with active interventions. RESULTS: On Gaussian observational data, BNs and GGMs were found to outperform RNs. The difference in performance was not significant for the non-linear simulated data and the cytoflow data, though. Also, we did not observe a significant difference between BNs and GGMs on observational data in general. However, for interventional data, BNs outperform GGMs and RNs, especially when taking the edge directions rather than just the skeletons of the graphs into account. This suggests that the higher computational costs of inference with BNs over GGMs and RNs are not justified when using only passive observations, but that active interventions in the form of gene knockouts and over-expressions are required to exploit the full potential of BNs. AVAILABILITY: Data, software and supplementary material are available from http://www.bioss.sari.ac.uk/staff/adriano/research.html     

Genetic Network Analyzer: qualitative simulation of genetic regulatory networks

MOTIVATION: The study of genetic regulatory networks has received a major impetus from the recent development of experimental techniques allowing the measurement of patterns of gene expression in a massively parallel way. This experimental progress calls for the development of appropriate computer tools for the modeling and simulation of gene regulation processes. RESULTS: We present Genetic Network Analyzer (GNA), a computer tool for the modeling and simulation of genetic regulatory networks. The tool is based on a qualitative simulation method that employs coarse-grained models of regulatory networks. The use of GNA is illustrated by a case study of the network of genes and interactions regulating the initiation of sporulation in Bacillus subtilis. AVAILABILITY: GNA and the model of the sporulation network are available at http://www-helix.inrialpes.fr/gna.     

Use with caution: Developmental systems divergence and potential pitfalls of animal models

Transgenic animal models have played an important role in elucidating gene functions and the molecular basis development, physiology, behavior, and pathogenesis. Transgenic models have been so successful that they have become a standard tool in molecular genetics and biomedical studies and are being used to fulfill one of the main goals of the post-genomic era: to assign functions to each gene in the genome. However, the assumption that gene functions and genetic systems are conserved between models and humans is taken for granted, often in spite of evidence that gene functions and networks diverge during evolution. In this review, I discuss some mechanisms that generate functional divergence and highlight recent examples demonstrating that gene functions and regulatory networks diverge through time. These examples suggest that annotation of gene functions based solely on mutant phenotypes in animal models, as well as assumptions of conserved functions between species, can be wrong. Therefore, animal models of gene function and human disease may not provide appropriate information, particularly for rapidly evolving genes and systems.     

An empirical Bayes approach to inferring large-scale gene association networks

MOTIVATION: Genetic networks are often described statistically using graphical models (e.g. Bayesian networks). However, inferring the network structure offers a serious challenge in microarray analysis where the sample size is small compared to the number of considered genes. This renders many standard algorithms for graphical models inapplicable, and inferring genetic networks an 'ill-posed' inverse problem. METHODS: We introduce a novel framework for small-sample inference of graphical models from gene expression data. Specifically, we focus on the so-called graphical Gaussian models (GGMs) that are now frequently used to describe gene association networks and to detect conditionally dependent genes. Our new approach is based on (1) improved (regularized) small-sample point estimates of partial correlation, (2) an exact test of edge inclusion with adaptive estimation of the degree of freedom and (3) a heuristic network search based on false discovery rate multiple testing. Steps (2) and (3) correspond to an empirical Bayes estimate of the network topology. RESULTS: Using computer simulations, we investigate the sensitivity (power) and specificity (true negative rate) of the proposed framework to estimate GGMs from microarray data. This shows that it is possible to recover the true network topology with high accuracy even for small-sample datasets. Subsequently, we analyze gene expression data from a breast cancer tumor study and illustrate our approach by inferring a corresponding large-scale gene association network for 3883 genes.     

The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models

MOTIVATION: Molecular biotechnology now makes it possible to build elaborate systems models, but the systems biology community needs information standards if models are to be shared, evaluated and developed cooperatively. RESULTS: We summarize the Systems Biology Markup Language (SBML) Level 1, a free, open, XML-based format for representing biochemical reaction networks. SBML is a software-independent language for describing models common to research in many areas of computational biology, including cell signaling pathways, metabolic pathways, gene regulation, and others. AVAILABILITY: The specification of SBML Level 1 is freely available from http://www.sbml.org/     

Stochastic Models and Numerical Algorithms for a Class of Regulatory Gene Networks

Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856–860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops.     

Superiority of network motifs over optimal networks and an application to the revelation of gene network evolution

MOTIVATION: Estimating the network of regulative interactions between genes from gene expression measurements is a major challenge. Recently, we have shown that for gene networks of up to around 35 genes, optimal network models can be computed. However, even optimal gene network models will in general contain false edges, since the expression data will not unambiguously point to a single network. RESULTS: In order to overcome this problem, we present a computational method to enumerate the most likely m networks and to extract a widely common subgraph (denoted as gene network motif) from these. We apply the method to bacterial gene expression data and extensively compare estimation results to knowledge. Our results reveal that gene network motifs are in significantly better agreement to biological knowledge than optimal network models. We also confirm this observation in a series of estimations using synthetic microarray data and compare estimations by our method with previous estimations for yeast. Furthermore, we use our method to estimate similarities and differences of the gene networks that regulate tryptophan metabolism in two related species and thereby demonstrate the analysis of gene network evolution. AVAILABILITY: Commercial license negotiable with Gene Networks Inc. (cherkis@gene-networks.com) CONTACT: sascha-ott@gmx.net     

On Parametric Stability of Gene Networks Controlling Ontogenetic Processes

The problem of evaluation of parametric stability of three models of pro- and eukaryotic gene networks controlling ontogenetic processes has been defined and solved. Experimental schemes of testing gene networks for parametric stability based on the method of generalized threshold models were developed and realized as a software application. We studied the sensitivity of the functioning modes to random variations of the parameters in three model systems: phage development control system, Arabidopsis thaliana flower morphogenesis control subsystem, and gene subnetwork controlling early ontogeny of Drosophila melanogaster. The parametric stability was quantitatively assessed for these models.     

SiBIC: A Web Server for Generating Gene Set Networks Based on Biclusters Obtained by Maximal Frequent Itemset Mining

Detecting biclusters from expression data is useful, since biclusters are coexpressed genes under only part of all given experimental conditions. We present a software called SiBIC, which from a given expression dataset, first exhaustively enumerates biclusters, which are then merged into rather independent biclusters, which finally are used to generate gene set networks, in which a gene set assigned to one node has coexpressed genes. We evaluated each step of this procedure: 1) significance of the generated biclusters biologically and statistically, 2) biological quality of merged biclusters, and 3) biological significance of gene set networks. We emphasize that gene set networks, in which nodes are not genes but gene sets, can be more compact than usual gene networks, meaning that gene set networks are more comprehensible. SiBIC is available at http://utrecht.kuicr.kyoto-u.ac.jp:8080/miami/faces/index.jsp.     

Efficient parametric analysis of the chemical master equation through model order reduction

ABSTRACT: BACKGROUND: Stochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state space dimension of these equations, numerical simulations are computationally expensive. This is a particular problem for analysis tasks requiring repeated simulations for different parameter values. Such tasks are computationally expensive to the point of infeasibility with the chemical master equation. RESULTS: In this article, we apply parametric model order reduction techniques in order to construct accurate low-dimensional parametric models of the chemical master equation. These surrogate models can be used in various parametric analysis task such as identifiability analysis, parameter estimation, or sensitivity analysis. As biological examples, we consider two models for gene regulation networks, a bistable switch and a network displaying stochastic oscillations. CONCLUSIONS: The results show that the parametric model reduction yields efficient models of stochastic biochemical reaction networks, and that these models can be useful for systems biology applications involving parametric analysis problems such as parameter exploration, optimization, estimation or sensitivity analysis.     

New computational approaches for analysis of cis-regulatory networks

The investigation and modeling of gene regulatory networks requires computational tools specific to the task. We present several locally developed software tools that have been used in support of our ongoing research into the embryogenesis of the sea urchin. These tools are especially well suited to iterative refinement of models through experimental and computational investigation. They include: BioArray, a macroarray spot processing program; SUGAR, a system to display and correlate large-BAC sequence analyses; SeqComp and FamilyRelations, programs for comparative sequence analysis; and NetBuilder, an environment for creating and analyzing models of gene networks. We also present an overview of the process used to build our model of the Strongylocentrotus purpuratus endomesoderm gene network. Several of the tools discussed in this paper are still in active development and some are available as open source.