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.     

<Emphasis Type="Italic">ASYMMETRIC LEAVES1</Emphasis>, an <Emphasis Type="Italic">Arabidopsis</Emphasis> gene that is involved in the control of cell differentiation in leaves

During leaf development, the formation of dorsal-ventral and proximal-distal axes is central to leaf morphogenesis. To investigate the genetic basis of dorsoventrality and proximodistality in the leaf, we screened for mutants of Arabidopsis thaliana (L.) Heynh. with defects in leaf morphogenesis. We describe here the phenotypic analysis of three mutant alleles that we have isolated. These mutants show varying degrees of abnormality including dwarfism, broad leaf lamina, and aberrant floral organs and fruits. Genetic analysis revealed that these mutations are alleles of the previously isolated mutant asymmetric leaves1 ( as1). In addition to the leaf phenotypes described previously, these alleles display other phenotypes that were not observed. These include: (i) some rosette leaves with petiole growth underneath the leaf lamina; (ii) leaf vein branching in the petiole; and (iii) a leaf lamina with an epidermis similar to that on the petiole. The mutant phenotypes suggest that the ASYMMETRIC LEAVES1 ( AS1) gene is involved in the control of cell differentiation in leaves. As the first step in determining a molecular function for AS1, we have identified the AS1 gene using map-based cloning. The AS1 gene encodes a MYB-domain protein that is homologous to the Antirrhinum PHANTASTICA ( PHAN) and maize ROUGH SHEATH2 ( RS2) genes. AS1 is expressed nearly ubiquitously, consistent with the pleiotropic mutant phenotypes. High levels of AS1 expression were found in tissues with highly proliferative cells, which further suggests a role in cell division and early cell differentiation.     

Floral morphogenesis: stochastic explorations of a gene network epigenetic landscape

In contrast to the classical view of development as a preprogrammed and deterministic process, recent studies have demonstrated that stochastic perturbations of highly non-linear systems may underlie the emergence and stability of biological patterns. Herein, we address the question of whether noise contributes to the generation of the stereotypical temporal pattern in gene expression during flower development. We modeled the regulatory network of organ identity genes in the Arabidopsis thaliana flower as a stochastic system. This network has previously been shown to converge to ten fixed-point attractors, each with gene expression arrays that characterize inflorescence cells and primordial cells of sepals, petals, stamens, and carpels. The network used is binary, and the logical rules that govern its dynamics are grounded in experimental evidence. We introduced different levels of uncertainty in the updating rules of the network. Interestingly, for a level of noise of around 0.5-10%, the system exhibited a sequence of transitions among attractors that mimics the sequence of gene activation configurations observed in real flowers. We also implemented the gene regulatory network as a continuous system using the Glass model of differential equations, that can be considered as a first approximation of kinetic-reaction equations, but which are not necessarily equivalent to the Boolean model. Interestingly, the Glass dynamics recover a temporal sequence of attractors, that is qualitatively similar, although not identical, to that obtained using the Boolean model. Thus, time ordering in the emergence of cell-fate patterns is not an artifact of synchronous updating in the Boolean model. Therefore, our model provides a novel explanation for the emergence and robustness of the ubiquitous temporal pattern of floral organ specification. It also constitutes a new approach to understanding morphogenesis, providing predictions on the population dynamics of cells with different genetic configurations during development.     

Molecular genetic approaches to plant development.

Higher plant morphogenesis has received renewed interest over the past few years. The improvement of molecular genetic approaches to generate tagged developmental mutants, for instance by T-DNA insertion, facilitated the isolation and characterization of the altered genes. Here we present recent progress on flower and root morphogenesis in the small crucifer Arabidopsis thaliana. The current model of Arabidopsis flower development is presented. We report on FLOWER1 (Fl1), which is a T-DNA-tagged ap2 allele. Our observations indicate that this Fl1 mutant has, besides the homeotic Ap2 phenotype, an aberrant seed coat, suggesting that this gene has also a function late in flower development. Furthermore, we present a brief summary about root development and focus on the super root (Sur) mutant, which is an ethyl methanesulfonate-induced mutant that produces excess lateral roots. Root explants of the Sur mutant, that do not develop further than the 4-leaf stage, can be induced to produce normal-looking shoots and flowers by addition of only cytokinin to the medium. The phenotype of Sur and its relation to the action of phytohormones is discussed.     

Severe developmental defects,hypersensitivity to DNA-damaging agents,and lengthened telomeres in Arabidopsis MRE11 mutants

The Mre11 protein is essential for the long-term genetic stability of the cell and acts to ensure the efficient repair of DNA damage. Vertebrate cells lacking Mre11 function are not viable. However, we report here that this is not the case in the model plant Arabidopsis. We have isolated two different Arabidopsis lines containing a T-DNA copy integrated at a different point in the MRE11 gene (AtMRE11). Both mutant plant lines were hypersensitive to DNA-damaging treatments but exhibited strikingly different developmental phenotypes. Furthermore, we also observed lengthened telomeres in these plant lines, showing that AtMre11 is involved in telomere maintenance. Thus, the lines we have isolated are unique tools with which to study in detail the role of AtMre11 in the mature plant.     

Modeling real eukaryotic control gene subnetworks based on generalized threshold models]

Mathematical and computational means are developed that take into consideration the specifics of control processes at the molecular level and allow one to obtain both qualitative and quantitative patterns of gene network dynamics. Using the method of generalized threshold models, models are constructed for the Arabidopsis thaliana flower morphogenesis control subsystem and gene subnetwork controlling the Drosophila melanogaster early ontogeny. The dynamics of these systems are investigated: kinetic curves are computed for molecular components (RNA, proteins), possible modes of functioning and steady states of the nets are revealed and biologically interpreted. The models are shown to be adequate to the real processes. The effectiveness of the generalized threshold model method is evaluated in the analysis of the actual eukaryotic gene networks.     

Tissue-Specific Functional Networks for Prioritizing Phenotype and Disease Genes

Integrated analyses of functional genomics data have enormous potential for identifying phenotype-associated genes. Tissue-specificity is an important aspect of many genetic diseases, reflecting the potentially different roles of proteins and pathways in diverse cell lineages. Accounting for tissue specificity in global integration of functional genomics data is challenging, as “functionality” and “functional relationships” are often not resolved for specific tissue types. We address this challenge by generating tissue-specific functional networks, which can effectively represent the diversity of protein function for more accurate identification of phenotype-associated genes in the laboratory mouse. Specifically, we created 107 tissue-specific functional relationship networks through integration of genomic data utilizing knowledge of tissue-specific gene expression patterns. Cross-network comparison revealed significantly changed genes enriched for functions related to specific tissue development. We then utilized these tissue-specific networks to predict genes associated with different phenotypes. Our results demonstrate that prediction performance is significantly improved through using the tissue-specific networks as compared to the global functional network. We used a testis-specific functional relationship network to predict genes associated with male fertility and spermatogenesis phenotypes, and experimentally confirmed one top prediction, Mbyl1. We then focused on a less-common genetic disease, ataxia, and identified candidates uniquely predicted by the cerebellum network, which are supported by both literature and experimental evidence. Our systems-level, tissue-specific scheme advances over traditional global integration and analyses and establishes a prototype to address the tissue-specific effects of genetic perturbations, diseases and drugs.     

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.     

An integrative approach to the identification of Arabidopsis and rice genes involved in xylan and secondary wall development

Xylans constitute the major non-cellulosic component of plant biomass. Xylan biosynthesis is particularly pronounced in cells with secondary walls, implying that the synthesis network consists of a set of highly expressed genes in such cells. To improve the understanding of xylan biosynthesis, we performed a comparative analysis of co-expression networks between Arabidopsis and rice as reference species with different wall types. Many co-expressed genes were represented by orthologs in both species, which implies common biological features, while some gene families were only found in one of the species, and therefore likely to be related to differences in their cell walls. To predict the subcellular location of the identified proteins, we developed a new method, PFANTOM (plant protein family information-based predictor for endomembrane), which was shown to perform better for proteins in the endomembrane system than other available prediction methods. Based on the combined approach of co-expression and predicted cellular localization, we propose a model for Arabidopsis and rice xylan synthesis in the Golgi apparatus and signaling from plasma membrane to nucleus for secondary cell wall differentiation. As an experimental validation of the model, we show that an Arabidopsis mutant in the PGSIP1 gene encoding one of the Golgi localized candidate proteins has a highly decreased content of glucuronic acid in secondary cell walls and substantially reduced xylan glucuronosyltransferase activity.     

Plant microtubule-associated proteins: the HEAT is off in temperature-sensitive mor1.

Microtubules perform essential functions in plant cells and govern, with other cytoskeletal elements, cell division, formation of cell walls and morphogenesis. For microtubules to perform their roles in the cell their organization and dynamics must be regulated and microtubule-associated proteins bear the main responsibility for these activities. We are just beginning to identify these plant microtubule-regulating proteins. Biochemical, molecular and genetic procedures have identified plant homologues of known microtubule-associated proteins, such as kinesins, katanin and XMAP215, and novel classes of plant microtubule-associated proteins, such as MAP65 and MAP190. Showing how these proteins coordinate the microtubule cytoskeleton in vivo is now the challenge. The recent identification and characterization of the Arabidopsis thaliana microtubule organization mutant, mor1, begins to address this challenge and here we highlight the significance of this work.     

A gene regulatory network model for cell-fate determination during Arabidopsis thaliana flower development that is robust and recovers experimental gene expression profiles

Flowers are icons in developmental studies of complex structures. The vast majority of 250,000 angiosperm plant species have flowers with a conserved organ plan bearing sepals, petals, stamens, and carpels in the center. The combinatorial model for the activity of the so-called ABC homeotic floral genes has guided extensive experimental studies in Arabidopsis thaliana and many other plant species. However, a mechanistic and dynamical explanation for the ABC model and prevalence among flowering plants is lacking. Here, we put forward a simple discrete model that postulates logical rules that formally summarize published ABC and non-ABC gene interaction data for Arabidopsis floral organ cell fate determination and integrates this data into a dynamic network model. This model shows that all possible initial conditions converge to few steady gene activity states that match gene expression profiles observed experimentally in primordial floral organ cells of wild-type and mutant plants. Therefore, the network proposed here provides a dynamical explanation for the ABC model and shows that precise signaling pathways are not required to restrain cell types to those found in Arabidopsis, but these are rather determined by the overall gene network dynamics. Furthermore, we performed robustness analyses that clearly show that the cell types recovered depend on the network architecture rather than on specific values of the model's gene interaction parameters. These results support the hypothesis that such a network constitutes a developmental module, and hence provide a possible explanation for the overall conservation of the ABC model and overall floral plan among angiosperms. In addition, we have been able to predict the effects of differences in network architecture between Arabidopsis and Petunia hybrida.