Accelerating, hyperaccelerating, and decelerating networks

Many growing networks possess accelerating statistics where the number of links added with each new node is an increasing function of network size so the total number of links increases faster than linearly with network size. In particular, biological networks can display a quadratic growth in regulator number with genome size even while remaining sparsely connected. These features are mutually incompatible in standard treatments of network theory which typically require that every new network node possesses at least one connection. To model sparsely connected networks, we generalize existing approaches and add each new node with a probabilistic number of links to generate either accelerating, hyperaccelerating, or even decelerating network statistics in different regimes. Under preferential attachment for example, slowly accelerating networks display stationary scale-free statistics relatively independent of network size while more rapidly accelerating networks display a transition from scale-free to exponential statistics with network growth. Such transitions explain, for instance, the evolutionary record of single-celled organisms which display strict size and complexity limits.

Temporal and spatial transcriptional programs in murine kidney development

We have performed a systematic temporal and spatial expression profiling of the developing mouse kidney using Compugen long-oligonucleotide microarrays. The activity of 18,000 genes was monitored at 24-h intervals from 10.5-day-postcoitum (dpc) metanephric mesenchyme (MM) through to neonatal kidney, and a cohort of 3,600 dynamically expressed genes was identified. Early metanephric development was further surveyed by directly comparing RNA from 10.5 vs. 11.5 vs. 13.5dpc kidneys. These data showed high concordance with the previously published dynamic profile of rat kidney development (Stuart RO, Bush KT, and Nigam SK. Proc Natl Acad Sci USA 98: 5649-5654, 2001) and our own temporal data. Cluster analyses were used to identify gene ontological terms, functional annotations, and pathways associated with temporal expression profiles. Genetic network analysis was also used to identify biological networks that have maximal transcriptional activity during early metanephric development, highlighting the involvement of proliferation and differentiation. Differential gene expression was validated using whole mount and section in situ hybridization of staged embryonic kidneys. Two spatial profiling experiments were also undertaken. MM (10.5dpc) was compared with adjacent intermediate mesenchyme to further define metanephric commitment. To define the genes involved in branching and in the induction of nephrogenesis, expression profiling was performed on ureteric bud (GFP+) FACS sorted from HoxB7-GFP transgenic mice at 15.5dpc vs. the GFP- mesenchymal derivatives. Comparisons between temporal and spatial data enhanced the ability to predict function for genes and networks. This study provides the most comprehensive temporal and spatial survey of kidney development to date, and the compilation of these transcriptional surveys provides important insights into metanephric development that can now be functionally tested.

The applicability of recurrent neural networks for biological sequence analysis

Selection of machine learning techniques requires a certain sensitivity to the requirements of the problem. In particular, the problem can be made more tractable by deliberately using algorithms that are biased toward solutions of the requisite kind. In this paper, we argue that recurrent neural networks have a natural bias toward a problem domain of which biological sequence analysis tasks are a subset. We use experiments with synthetic data to illustrate this bias. We then demonstrate that this bias can be exploitable using a data set of protein sequences containing several classes of subcellular localization targeting peptides. The results show that, compared with feed forward, recurrent neural networks will generally perform better on sequence analysis tasks. Furthermore, as the patterns within the sequence become more ambiguous, the choice of specific recurrent architecture becomes more critical.

Gene duplication and hierarchical modularity in intracellular interaction networks

Networks of interactions evolve in many different domains. They tend to have topological characteristics in common, possibly due to common factors in the way the networks grow and develop. It has been recently suggested that one such common characteristic is the presence of a hierarchically modular organization. In this paper, we describe a new algorithm for the detection and quantification of hierarchical modularity, and demonstrate that the yeast protein-protein interaction network does have a hierarchically modular organization. We further show that such organization is evident in artificial networks produced by computational evolution using a gene duplication operator, but not in those developing via preferential attachment of new nodes to highly connected existing nodes. (C) 2004 Elsevier Ireland Ltd. All rights reserved.

Intertidal habitat conservation: identifying conservation targets in the absence of detailed biological information

1. Growing concern associated with threats to the marine environment has resulted in an increased demand for marine reserves that conserve representative and adequate examples of biodiversity. Often, the decisions about where to locate reserves must be made in the absence of detailed information on the patterns of distribution of the biota. Alternative approaches are required that include defining habitats using surrogates for biodiversity. Surrogate measures of biodiversity enable decisions about where to locate marine reserves to be made more reliably in the absence of detailed data on the distribution of species. 2. Intertidal habitat types derived using physical properties of the shoreline were used as a surrogate for intertidal biodiversity to assist with the identification of sites for inclusion in a candidate system of intertidal marine reserves for 17 463 km of the mainland coast of Queensland, Australia. This represents the first systematic approach, on essentially one-dimensional data, using fine-scale (tens to hundreds of metres) intertidal habitats to identify a system of marine reserves for such a large length of coast. A range of solutions would provide for the protection of a representative example of intertidal habitats in Queensland. 3. The design and planning of marine and terrestrial protected areas systems should not be undertaken independently of each other because it is likely to lead to inadequate representation of intertidal habitats in either system. The development of reserve systems specially designed to protect intertidal habitats should be integrated into the design of terrestrial and marine protected area systems. Copyright (c) 2005 John Wiley & Sons, Ltd.

Inherent size constraints on prokaryote gene networks due to "accelerating" growth

Networks exhibiting accelerating growth have total link numbers growing faster than linearly with network size and either reach a limit or exhibit graduated transitions from nonstationary-to-stationary statistics and from random to scale-free to regular statistics as the network size grows. However, if for any reason the network cannot tolerate such gross structural changes then accelerating networks are constrained to have sizes below some critical value. This is of interest as the regulatory gene networks of single-celled prokaryotes are characterized by an accelerating quadratic growth and are size constrained to be less than about 10,000 genes encoded in DNA sequence of less than about 10 megabases. This paper presents a probabilistic accelerating network model for prokaryotic gene regulation which closely matches observed statistics by employing two classes of network nodes (regulatory and non-regulatory) and directed links whose inbound heads are exponentially distributed over all nodes and whose outbound tails are preferentially attached to regulatory nodes and described by a scale-free distribution. This model explains the observed quadratic growth in regulator number with gene number and predicts an upper prokaryote size limit closely approximating the observed value. (c) 2005 Elsevier GmbH. All rights reserved.

GANN: Genetic algorithm neural networks for the detection of conserved combinations of features in DNA

Background: The multitude of motif detection algorithms developed to date have largely focused on the detection of patterns in primary sequence. Since sequence-dependent DNA structure and flexibility may also play a role in protein-DNA interactions, the simultaneous exploration of sequence-and structure-based hypotheses about the composition of binding sites and the ordering of features in a regulatory region should be considered as well. The consideration of structural features requires the development of new detection tools that can deal with data types other than primary sequence. Results: GANN ( available at http://bioinformatics.org.au/gann) is a machine learning tool for the detection of conserved features in DNA. The software suite contains programs to extract different regions of genomic DNA from flat files and convert these sequences to indices that reflect sequence and structural composition or the presence of specific protein binding sites. The machine learning component allows the classification of different types of sequences based on subsamples of these indices, and can identify the best combinations of indices and machine learning architecture for sequence discrimination. Another key feature of GANN is the replicated splitting of data into training and test sets, and the implementation of negative controls. In validation experiments, GANN successfully merged important sequence and structural features to yield good predictive models for synthetic and real regulatory regions. Conclusion: GANN is a flexible tool that can search through large sets of sequence and structural feature combinations to identify those that best characterize a set of sequences.

Stochastic models for regulatory networks of the genetic toggle switch

Bistability arises within a wide range of biological systems from the A phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. in this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.

Stochastic delay differential equations for genetic regulatory networks

Time delay is an important aspect in the modelling of genetic regulation due to slow biochemical reactions such as gene transcription and translation, and protein diffusion between the cytosol and nucleus. In this paper we introduce a general mathematical formalism via stochastic delay differential equations for describing time delays in genetic regulatory networks. Based on recent developments with the delay stochastic simulation algorithm, the delay chemical masterequation and the delay reaction rate equation are developed for describing biological reactions with time delay, which leads to stochastic delay differential equations derived from the Langevin approach. Two simple genetic regulatory networks are used to study the impact of' intrinsic noise on the system dynamics where there are delays. (c) 2006 Elsevier B.V. All rights reserved.

Evolving genetic regulatory networks using an artificial genome

Boolean models of genetic regulatory networks (GRNs) have been shown to exhibit many of the characteristic dynamics of real GRNs, with gene expression patterns settling to point attractors or limit cycles, or displaying chaotic behaviour, depending upon the connectivity of the network and the relative proportions of excitatory and inhibitory interactions. This range of behaviours is only apparent, however, when the nodes of the GRN are updated synchronously, a biologically implausible state of affairs. In this paper we demonstrate that evolution can produce GRNs with interesting dynamics under an asynchronous update scheme. We use an Artificial Genome to generate networks which exhibit limit cycle dynamics when updated synchronously, but collapse to a point attractor when updated asynchronously. Using a hill climbing algorithm the networks are then evolved using a fitness function which rewards patterns of gene expression which revisit as many previously seen states as possible. The final networks exhibit “fuzzy limit cycle” dynamics when updated asynchronously.

Multilevel modelling for inference of genetic regulatory networks

Time-course experiments with microarrays are often used to study dynamic biological systems and genetic regulatory networks (GRNs) that model how genes influence each other in cell-level development of organisms. The inference for GRNs provides important insights into the fundamental biological processes such as growth and is useful in disease diagnosis and genomic drug design. Due to the experimental design, multilevel data hierarchies are often present in time-course gene expression data. Most existing methods, however, ignore the dependency of the expression measurements over time and the correlation among gene expression profiles. Such independence assumptions violate regulatory interactions and can result in overlooking certain important subject effects and lead to spurious inference for regulatory networks or mechanisms. In this paper, a multilevel mixed-effects model is adopted to incorporate data hierarchies in the analysis of time-course data, where temporal and subject effects are both assumed to be random. The method starts with the clustering of genes by fitting the mixture model within the multilevel random-effects model framework using the expectation-maximization (EM) algorithm. The network of regulatory interactions is then determined by searching for regulatory control elements (activators and inhibitors) shared by the clusters of co-expressed genes, based on a time-lagged correlation coefficients measurement. The method is applied to two real time-course datasets from the budding yeast (Saccharomyces cerevisiae) genome. It is shown that the proposed method provides clusters of cell-cycle regulated genes that are supported by existing gene function annotations, and hence enables inference on regulatory interactions for the genetic network.