LGL: creating a map of protein function with an algorithm for visualizing very large biological networks

Networks are proving to be central to the study of gene function, protein-protein interaction, and biochemical pathway data. Visualization of networks is important for their study, but visualization tools are often inadequate for working with very large biological networks. Here, we present an algorithm, called large graph layout (LGL), which can be used to dynamically visualize large networks on the order of hundreds of thousands of vertices and millions of edges. LGL applies a force-directed iterative layout guided by a minimal spanning tree of the network in order to generate coordinates for the vertices in two or three dimensions, which are subsequently visualized and interactively navigated with companion programs. We demonstrate the use of LGL in visualizing an extensive protein map summarizing the results of approximately 21 billion sequence comparisons between 145579 proteins from 50 genomes. Proteins are positioned in the map according to sequence homology and gene fusions, with the map ultimately serving as a theoretical framework that integrates inferences about gene function derived from sequence homology, remote homology, gene fusions, and higher-order fusions. We confirm that protein neighbors in the resulting map are functionally related, and that distinct map regions correspond to distinct cellular systems, enabling a computational strategy for discovering proteins' functions on the basis of the proteins' map positions. Using the map produced by LGL, we infer general functions for 23 uncharacterized protein families.     

The incorporation of epigenetics in artificial gene regulatory networks

Artificial gene regulatory networks are computational models that draw inspiration from biological networks of gene regulation. Since their inception they have been used to infer knowledge about gene regulation and as methods of computation. These computational models have been shown to possess properties typically found in the biological world, such as robustness and self organisation. Recently, it has become apparent that epigenetic mechanisms play an important role in gene regulation. This paper describes a new model, the Artificial Epigenetic Regulatory Network (AERN) which builds upon existing models by adding an epigenetic control layer. Our results demonstrate that AERNs are more adept at controlling multiple opposing trajectories when applied to a chaos control task within a conservative dynamical system, suggesting that AERNs are an interesting area for further investigation.     

Gene Circuit Analysis of the Terminal Gap Gene huckebein

The early embryo of Drosophila melanogaster provides a powerful model system to study the role of genes in pattern formation. The gap gene network constitutes the first zygotic regulatory tier in the hierarchy of the segmentation genes involved in specifying the position of body segments. Here, we use an integrative, systems-level approach to investigate the regulatory effect of the terminal gap gene huckebein (hkb) on gap gene expression. We present quantitative expression data for the Hkb protein, which enable us to include hkb in gap gene circuit models. Gap gene circuits are mathematical models of gene networks used as computational tools to extract regulatory information from spatial expression data. This is achieved by fitting the model to gap gene expression patterns, in order to obtain estimates for regulatory parameters which predict a specific network topology. We show how considering variability in the data combined with analysis of parameter determinability significantly improves the biological relevance and consistency of the approach. Our models are in agreement with earlier results, which they extend in two important respects: First, we show that Hkb is involved in the regulation of the posterior hunchback (hb) domain, but does not have any other essential function. Specifically, Hkb is required for the anterior shift in the posterior border of this domain, which is now reproduced correctly in our models. Second, gap gene circuits presented here are able to reproduce mutants of terminal gap genes, while previously published models were unable to reproduce any null mutants correctly. As a consequence, our models now capture the expression dynamics of all posterior gap genes and some variational properties of the system correctly. This is an important step towards a better, quantitative understanding of the developmental and evolutionary dynamics of the gap gene network.     

Visualization, documentation, analysis, and communication of large-scale gene regulatory networks

Genetic regulatory networks (GRNs) are complex, large-scale, and spatially and temporally distributed. These characteristics impose challenging demands on software tools for building GRN models, and so there is a need for custom tools. In this paper, we report on our ongoing development of BioTapestry, an open source, freely available computational tool designed specifically for building GRN models. We also outline our future development plans, and give some examples of current applications of BioTapestry.     

Gene Regulatory Network Inferences Using a Maximum-Relevance and Maximum-Significance Strategy

Recovering gene regulatory networks from expression data is a challenging problem in systems biology that provides valuable information on the regulatory mechanisms of cells. A number of algorithms based on computational models are currently used to recover network topology. However, most of these algorithms have limitations. For example, many models tend to be complicated because of the “large p, small n” problem. In this paper, we propose a novel regulatory network inference method called the maximum-relevance and maximum-significance network (MRMSn) method, which converts the problem of recovering networks into a problem of how to select the regulator genes for each gene. To solve the latter problem, we present an algorithm that is based on information theory and selects the regulator genes for a specific gene by maximizing the relevance and significance. A first-order incremental search algorithm is used to search for regulator genes. Eventually, a strict constraint is adopted to adjust all of the regulatory relationships according to the obtained regulator genes and thus obtain the complete network structure. We performed our method on five different datasets and compared our method to five state-of-the-art methods for network inference based on information theory. The results confirm the effectiveness of our method.     

Assessing the Discordance of Multiple Sequence Alignments

Multiple sequence alignments have wide applicability in many areas of computational biology, including comparative genomics, functional annotation of proteins, gene finding, and modeling evolutionary processes. Because of the computational difficulty of multiple sequence alignment and the availability of numerous tools, it is critical to be able to assess the reliability of multiple alignments. We present a tool called StatSigMA to assess whether multiple alignments of nucleotide or amino acid sequences are contaminated with one or more unrelated sequences. There are numerous applications for which StatSigMA can be used. Two such applications are to distinguish homologous sequences from nonhomologous ones and to compare alignments produced by various multiple alignment tools. We present examples of both types of applications.     

A structured approach for the engineering of biochemical network models, illustrated for signalling pathways

Quantitative models of biochemical networks (signal transduction cascades, metabolic pathways, gene regulatory circuits) are a central component of modern systems biology. Building and managing these complex models is a major challenge that can benefit from the application of formal methods adopted from theoretical computing science. Here we provide a general introduction to the field of formal modelling, which emphasizes the intuitive biochemical basis of the modelling process, but is also accessible for an audience with a background in computing science and/or model engineering. We show how signal transduction cascades can be modelled in a modular fashion, using both a qualitative approach--qualitative Petri nets, and quantitative approaches--continuous Petri nets and ordinary differential equations (ODEs). We review the major elementary building blocks of a cellular signalling model, discuss which critical design decisions have to be made during model building, and present a number of novel computational tools that can help to explore alternative modular models in an easy and intuitive manner. These tools, which are based on Petri net theory, offer convenient ways of composing hierarchical ODE models, and permit a qualitative analysis of their behaviour. We illustrate the central concepts using signal transduction as our main example. The ultimate aim is to introduce a general approach that provides the foundations for a structured formal engineering of large-scale models of biochemical networks.     

RNIE: genome-wide prediction of bacterial intrinsic terminators

Bacterial Rho-independent terminators (RITs) are important genomic landmarks involved in gene regulation and terminating gene expression. In this investigation we present RNIE, a probabilistic approach for predicting RITs. The method is based upon covariance models which have been known for many years to be the most accurate computational tools for predicting homology in structural non-coding RNAs. We show that RNIE has superior performance in model species from a spectrum of bacterial phyla. Further analysis of species where a low number of RITs were predicted revealed a highly conserved structural sequence motif enriched near the genic termini of the pathogenic Actinobacteria, Mycobacterium tuberculosis. This motif, together with classical RITs, account for up to 90% of all the significantly structured regions from the termini of M. tuberculosis genic elements. The software, predictions and alignments described below are available from http://github.com/ppgardne/RNIE.     

Neural networks for perceptual processing: from simulation tools to theories

Neural networks are modelling tools that are, in principle, able to capture the input-output behaviour of arbitrary systems that may include the dynamics of animal populations or brain circuits. While a neural network model is useful if it captures phenomenologically the behaviour of the target system in this way, its utility is amplified if key mechanisms of the model can be discovered, and identified with those of the underlying system. In this review, we first describe, at a fairly high level with minimal mathematics, some of the tools used in constructing neural network models. We then go on to discuss the implications of network models for our understanding of the system they are supposed to describe, paying special attention to those models that deal with neural circuits and brain systems. We propose that neural nets are useful for brain modelling if they are viewed in a wider computational framework originally devised by Marr. Here, neural networks are viewed as an intermediate mechanistic abstraction between 'algorithm' and 'implementation', which can provide insights into biological neural representations and their putative supporting architectures.     

Prediction of protein functions with gene ontology and interspecies protein homology data

Accurate computational prediction of protein functions increasingly relies on network-inspired models for the protein function transfer. This task can become challenging for proteins isolated in their own network or those with poor or uncharacterized neighborhoods. Here, we present a novel probabilistic chain-graph-based approach for predicting protein functions that builds on connecting networks of two (or more) different species by links of high interspecies sequence homology. In this way, proteins are able to "exchange" functional information with their neighbors-homologs from a different species. The knowledge of interspecies relationships, such as the sequence homology, can become crucial in cases of limited information from other sources of data, including the protein-protein interactions or cellular locations of proteins. We further enhance our model to account for the Gene Ontology dependencies by linking multiple but related functional ontology categories within and across multiple species. The resulting networks are of significantly higher complexity than most traditional protein network models. We comprehensively benchmark our method by applying it to two largest protein networks, the Yeast and the Fly. The joint Fly-Yeast network provides substantial improvements in precision, accuracy, and false positive rate over networks that consider either of the sources in isolation. At the same time, the new model retains the computational efficiency similar to that of the simpler networks.     

Network Reconstruction Using Nonparametric Additive ODE Models

Network representations of biological systems are widespread and reconstructing unknown networks from data is a focal problem for computational biologists. For example, the series of biochemical reactions in a metabolic pathway can be represented as a network, with nodes corresponding to metabolites and edges linking reactants to products. In a different context, regulatory relationships among genes are commonly represented as directed networks with edges pointing from influential genes to their targets. Reconstructing such networks from data is a challenging problem receiving much attention in the literature. There is a particular need for approaches tailored to time-series data and not reliant on direct intervention experiments, as the former are often more readily available. In this paper, we introduce an approach to reconstructing directed networks based on dynamic systems models. Our approach generalizes commonly used ODE models based on linear or nonlinear dynamics by extending the functional class for the functions involved from parametric to nonparametric models. Concomitantly we limit the complexity by imposing an additive structure on the estimated slope functions. Thus the submodel associated with each node is a sum of univariate functions. These univariate component functions form the basis for a novel coupling metric that we define in order to quantify the strength of proposed relationships and hence rank potential edges. We show the utility of the method by reconstructing networks using simulated data from computational models for the glycolytic pathway of Lactocaccus Lactis and a gene network regulating the pluripotency of mouse embryonic stem cells. For purposes of comparison, we also assess reconstruction performance using gene networks from the DREAM challenges. We compare our method to those that similarly rely on dynamic systems models and use the results to attempt to disentangle the distinct roles of linearity, sparsity, and derivative estimation.     

Efficient reverse-engineering of a developmental gene regulatory network

Understanding the complex regulatory networks underlying development and evolution of multi-cellular organisms is a major problem in biology. Computational models can be used as tools to extract the regulatory structure and dynamics of such networks from gene expression data. This approach is called reverse engineering. It has been successfully applied to many gene networks in various biological systems. However, to reconstitute the structure and non-linear dynamics of a developmental gene network in its spatial context remains a considerable challenge. Here, we address this challenge using a case study: the gap gene network involved in segment determination during early development of Drosophila melanogaster. A major problem for reverse-engineering pattern-forming networks is the significant amount of time and effort required to acquire and quantify spatial gene expression data. We have developed a simplified data processing pipeline that considerably increases the throughput of the method, but results in data of reduced accuracy compared to those previously used for gap gene network inference. We demonstrate that we can infer the correct network structure using our reduced data set, and investigate minimal data requirements for successful reverse engineering. Our results show that timing and position of expression domain boundaries are the crucial features for determining regulatory network structure from data, while it is less important to precisely measure expression levels. Based on this, we define minimal data requirements for gap gene network inference. Our results demonstrate the feasibility of reverse-engineering with much reduced experimental effort. This enables more widespread use of the method in different developmental contexts and organisms. Such systematic application of data-driven models to real-world networks has enormous potential. Only the quantitative investigation of a large number of developmental gene regulatory networks will allow us to discover whether there are rules or regularities governing development and evolution of complex multi-cellular organisms.     

A model-based strategy to investigate the role of <Emphasis Type="Italic">microRNA</Emphasis> regulation in cancer signalling networks

In this paper we present and discuss a model-based approach to link miRNA translational control with cell signalling networks. MicroRNAs are small regulatory RNAs that are able to regulate the activity and the stability of specific messenger RNA and have been implicated in tumour progression due to their ability to translationally regulate critical oncogenes and tumour suppressors. In our approach, data on protein–protein interactions and miRNA regulation, obtained from bioinformatics databases, are integrated with quantitative experimental data using mathematical modelling. Predictive computational simulations and qualitative (bifurcation) analyses of those mathematical models are employed to further support the investigation of such multifactorial networks in the context of cancer progression. We illustrate our approach with the C-Myc/E2F signalling network, involved in the progression of several tumour subtypes, including colorectal cancer.     

An applications-focused review of comparative genomics tools: capabilities,limitations and future challenges

A team at the Lawrence Livermore National Laboratory (LLNL) was given the task of using computational tools to speed up the development of DNA diagnostics for pathogen detection. This work will be described in another paper in this issue (see pages 133-149). To achieve this goal it was necessary to understand the merits and limitations of the various available comparative genomics tools. A review of some recent tools for multisequence/genome alignment and substring comparison is presented, within the general framework of applicability to a large-scale application. We note that genome alignments are important for many things, only one of which is pathogen detection. Understanding gene function, gene regulation, gene networks, phylogenetic studies and other aspects of evolution all depend on accurate nucleic acid and protein sequence alignment. Selecting appropriate tools can make a large difference in the quality of results obtained and the effort required.     

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