Majority Rules with Random Tie-Breaking in Boolean Gene Regulatory Networks

We consider threshold Boolean gene regulatory networks, where the update function of each gene is described as a majority rule evaluated among the regulators of that gene: it is turned ON when the sum of its regulator contributions is positive (activators contribute positively whereas repressors contribute negatively) and turned OFF when this sum is negative. In case of a tie (when contributions cancel each other out), it is often assumed that the gene keeps it current state. This framework has been successfully used to model cell cycle control in yeast. Moreover, several studies consider stochastic extensions to assess the robustness of such a model.Here, we introduce a novel, natural stochastic extension of the majority rule. It consists in randomly choosing the next value of a gene only in case of a tie. Hence, the resulting model includes deterministic and probabilistic updates. We present variants of the majority rule, including alternate treatments of the tie situation. Impact of these variants on the corresponding dynamical behaviours is discussed. After a thorough study of a class of two-node networks, we illustrate the interest of our stochastic extension using a published cell cycle model. In particular, we demonstrate that steady state analysis can be rigorously performed and can lead to effective predictions; these relate for example to the identification of interactions whose addition would ensure that a specific state is absorbing.     

Investigating autocatalytic gene expression systems through mechanistic modeling.

A structured model of gene expression, which incorporates the stochastic behavior of cellular processes, was developed to examine the "all-or-none" phenomenon observed in autocatalytic systems (e.g. the lac operon). Autocatalytic expression systems typically have the genes encoding the inducer transport proteins controlled by internal inducer levels, so that transport of the inducer increases production of the transport protein. The model was able to predict the unique behaviors of autocatalytic expression systems that have been experimentally observed and provided valuable insight into the role of population heterogeneity in these systems. The simulations substantiate the importance of stochastic processes on induction of gene expression in autocatalytic systems. The simulation results show that the all-or-none phenomenon is governed largely by random cellular events, and that population-averaged variations in gene expression are due to changes in the frequency of full gene induction in individual cells rather than to uniform variations in gene expression across the entire population. In addition, the model shows how concentrations of inducer too low to induce expression in uninduced cells can maintain induction in pre-induced cultures. A comparison of induction behaviors from an autocatalytic system and a system having constitutive synthesis of the transport protein showed that transport protein levels must be decoupled from inducer control to achieve homogeneous expression of a gene of interest in all cells of a culture.     

An analysis of the class of gene regulatory functions implied by a biochemical model

Understanding the integrated behavior of genetic regulatory networks, in which genes regulate one another's activities via RNA and protein products, is emerging as a dominant problem in systems biology. One widely studied class of models of such networks includes genes whose expression values assume Boolean values (i.e., on or off). Design decisions in the development of Boolean network models of gene regulatory systems include the topology of the network (including the distribution of input- and output-connectivity) and the class of Boolean functions used by each gene (e.g., canalizing functions, post functions, etc.). For example, evidence from simulations suggests that biologically realistic dynamics can be produced by scale-free network topologies with canalizing Boolean functions. This work seeks further insights into the design of Boolean network models through the construction and analysis of a class of models that include more concrete biochemical mechanisms than the usual abstract model, including genes and gene products, dimerization, cis-binding sites, promoters and repressors. In this model, it is assumed that the system consists of N genes, with each gene producing one protein product. Proteins may form complexes such as dimers, trimers, etc. The model also includes cis-binding sites to which proteins may bind to form activators or repressors. Binding affinities are based on structural complementarity between proteins and binding sites, with molecular binding sites modeled by bit-strings. Biochemically plausible gene expression rules are used to derive a Boolean regulatory function for each gene in the system. The result is a network model in which both topological features and Boolean functions arise as emergent properties of the interactions of components at the biochemical level. A highly biased set of Boolean functions is observed in simulations of networks of various sizes, suggesting a new characterization of the subset of Boolean functions that are likely to appear in gene regulatory networks.     

Transcript profiling of terpenoid indole alkaloid pathway genes and regulators reveals strong expression of repressors in <Emphasis Type="Italic">Catharanthus roseus</Emphasis> cell cultures

The understanding of the complexities and molecular events regulating genes and the activators involved in terpenoid indole alkaloid (TIA) metabolism is known to a certain extent in cell cultures of an important TIA yielding plant, Catharanthus roseus, though it is not yet complete. Recently, the repressors of early TIA pathway genes have also been identified. However, their roles in the regulation of TIA pathway in C. roseus cell cultures remains yet unknown. We have made a comparative profiling of genes catalyzing the important steps of 2-C methyl-D-erythritol-4-phosphate (MEP), shikimate and TIA biosynthetic pathways, their activator and repressors using macroarray, semiquantitative RT-PCR and northern analyses in a rotation culture system of C. roseus comprising differentiated and proliferated cells. Our results demonstrate that TIA biosynthetic pathway genes and their activators show variable expression pattern, which was correlated with the changes in the cellular conditions in these systems. Under similar conditions, TIA pathway repressors show strong and consistent expression. The role of repressors in the complex regulation of the TIA pathway in C. roseus cell cultures is discussed. The results were supported by HPLC data, which demonstrated that the molecular program of cellular differentiation is intimately linked with TIA pathway gene expression and TIA production in C. roseus cell cultures.     

Dual functions of thyroid hormone receptors during Xenopus development

Thyroid hormone (TH) plays a causative role in anuran metamorphosis. This effect is presumed to be manifested through the regulation of gene expression by TH receptors (TRs). TRs can act as both activators and repressors of a TH-inducible gene depending upon the presence and absence of TH, respectively. We have been investigating the roles of TRs during Xenopus laevis development, including premetamorphic and metamorphosing stages. In this review, we summarize some of the studies on the TRs by others and us. These studies reveal that TRs have dual functions in frog development as reflected in the following two aspects. First, TRs function initially as repressors of TH-inducible genes in premetamorphic tadpoles to prevent precocious metamorphosis, thus ensuring a proper period of tadpole growth, and later as activators of these genes to activate the metamorphic process. Second, TRs can promote both cell proliferation and apoptosis during metamorphosis, depending upon the cell type in which they are expressed.     

Gene networks inference using dynamic Bayesian networks

This article deals with the identification of gene regulatory networks from experimental data using a statistical machine learning approach. A stochastic model of gene interactions capable of handling missing variables is proposed. It can be described as a dynamic Bayesian network particularly well suited to tackle the stochastic nature of gene regulation and gene expression measurement. Parameters of the model are learned through a penalized likelihood maximization implemented through an extended version of EM algorithm. Our approach is tested against experimental data relative to the S.O.S. DNA Repair network of the Escherichia coli bacterium. It appears to be able to extract the main regulations between the genes involved in this network. An added missing variable is found to model the main protein of the network. Good prediction abilities on unlearned data are observed. These first results are very promising: they show the power of the learning algorithm and the ability of the model to capture gene interactions.