Impact of Negative Feedbacks on De Novo Pyrimidines Biosynthesis in Escherichia coli.

Earlier studies aimed at investigating the metabolism of endogenous nucleoside triphosphates in synchronous cultures of E. coli cells revealed an auto-oscillatory mode of functioning of the pyrimidine and purine nucleotide biosynthesis system, which the authors associated with the dynamics of cell division. Theoretically, this system has an intrinsic oscillatory potential, since the dynamics of its functioning are controlled through feedback mechanisms. The question of whether the nucleotide biosynthesis system has its own oscillatory circuit is still open. To address this issue, an integral mathematical model of pyrimidine biosynthesis was developed, taking into account all experimentally verified negative feedback in the regulation of enzymatic reactions, the data of which were obtained under in vitro conditions. Analysis of the dynamic modes of the model functioning has shown that in the pyrimidine biosynthesis system, both the steady-state and oscillatory functioning modes can be realized under certain sets of kinetic parameters that fit in the physiological boundaries of the investigated metabolic system. It has been demonstrated that the occurrence of the oscillatory nature of metabolite synthesis depended on the ratio of two parameters: the Hill coefficient, hUMP1-the nonlinearity of the UMP effect on the activity of carbamoyl-phosphate synthetase, and the parameter r characterizing the contribution of the noncompetitive mechanism of UTP inhibition to the regulation of the enzymatic reaction of UMP phosphorylation. Thus, it has been theoretically shown that the E. coli pyrimidine biosynthesis system possesses its own oscillatory circuit whose oscillatory potential depends to a significant degree on the mechanism of regulation of UMP kinase activity.

In silico evolution of the Drosophila gap gene regulatory sequence under elevated mutational pressure.

BACKGROUND: Cis-regulatory sequences are often composed of many low-affinity transcription factor binding sites (TFBSs). Determining the evolutionary and functional importance of regulatory sequence composition is impeded without a detailed knowledge of the genotype-phenotype map. RESULTS: We simulate the evolution of regulatory sequences involved in Drosophila melanogaster embryo segmentation during early development. Natural selection evaluates gene expression dynamics produced by a computational model of the developmental network. We observe a dramatic decrease in the total number of transcription factor binding sites through the course of evolution. Despite a decrease in average sequence binding energies through time, the regulatory sequences tend towards organisations containing increased high affinity transcription factor binding sites. Additionally, the binding energies of separate sequence segments demonstrate ubiquitous mutual correlations through time. Fewer than 10% of initial TFBSs are maintained throughout the entire simulation, deemed 'core' sites. These sites have increased functional importance as assessed under wild-type conditions and their binding energy distributions are highly conserved. Furthermore, TFBSs within close proximity of core sites exhibit increased longevity, reflecting functional regulatory interactions with core sites. CONCLUSION: In response to elevated mutational pressure, evolution tends to sample regulatory sequence organisations with fewer, albeit on average, stronger functional transcription factor binding sites. These organisations are also shaped by the regulatory interactions among core binding sites with sites in their local vicinity.

Dynamic control of positional information in the early Drosophila embryo.

Morphogen gradients contribute to pattern formation by determining positional information in morphogenetic fields. Interpretation of positional information is thought to rely on direct, concentration-threshold-dependent mechanisms for establishing multiple differential domains of target gene expression. In Drosophila, maternal gradients establish the initial position of boundaries for zygotic gap gene expression, which in turn convey positional information to pair-rule and segment-polarity genes, the latter forming a segmental pre-pattern by the onset of gastrulation. Here we report, on the basis of quantitative gene expression data, substantial anterior shifts in the position of gap domains after their initial establishment. Using a data-driven mathematical modelling approach, we show that these shifts are based on a regulatory mechanism that relies on asymmetric gap-gap cross-repression and does not require the diffusion of gap proteins. Our analysis implies that the threshold-dependent interpretation of maternal morphogen concentration is not sufficient to determine shifting gap domain boundary positions, and suggests that establishing and interpreting positional information are not independent processes in the Drosophila blastoderm.

Dynamical Modeling of the Core Gene Network Controlling Flowering Suggests Cumulative Activation From the FLOWERING LOCUS T Gene Homologs in Chickpea.

Initiation of flowering moves plants from vegetative to reproductive development. The time when this transition happens (flowering time), an important indicator of productivity, depends on both endogenous and environmental factors. The core genetic regulatory network canalizing the flowering signals to the decision to flower has been studied extensively in the model plant Arabidopsis thaliana and has been shown to preserve its main regulatory blocks in other species. It integrates activation from the FLOWERING LOCUS T (FT) gene or its homologs to the flowering decision expressed as high expression of the meristem identity genes, including AP1. We elaborated a dynamical model of this flowering gene regulatory network and applied it to the previously published expression data from two cultivars of domesticated chickpea (Cicer arietinum), obtained for two photoperiod durations. Due to a large number of free parameters in the model, we used an ensemble approach analyzing the model solutions at many parameter sets that provide equally good fit to data. Testing several alternative hypotheses about regulatory roles of the five FT homologs present in chickpea revealed no preference in segregating individual FT copies as singled-out activators with their own regulatory parameters, thus favoring the hypothesis that the five genes possess similar regulatory properties and provide cumulative activation in the network. The analysis reveals that different levels of activation from AP1 can explain a small difference observed in the expression of the two homologs of the repressor gene TFL1. Finally, the model predicts highly reduced activation between LFY and AP1, thus suggesting that this regulatory block is not conserved in chickpea and needs other mechanisms. Overall, this study provides the first attempt to quantitatively test the flowering time gene network in chickpea based on data-driven modeling.

Translating natural genetic variation to gene expression in a computational model of the Drosophila gap gene regulatory network.

Annotating the genotype-phenotype relationship, and developing a proper quantitative description of the relationship, requires understanding the impact of natural genomic variation on gene expression. We apply a sequence-level model of gap gene expression in the early development of Drosophila to analyze single nucleotide polymorphisms (SNPs) in a panel of natural sequenced D. melanogaster lines. Using a thermodynamic modeling framework, we provide both analytical and computational descriptions of how single-nucleotide variants affect gene expression. The analysis reveals that the sequence variants increase (decrease) gene expression if located within binding sites of repressors (activators). We show that the sign of SNP influence (activation or repression) may change in time and space and elucidate the origin of this change in specific examples. The thermodynamic modeling approach predicts non-local and non-linear effects arising from SNPs, and combinations of SNPs, in individual fly genotypes. Simulation of individual fly genotypes using our model reveals that this non-linearity reduces to almost additive inputs from multiple SNPs. Further, we see signatures of the action of purifying selection in the gap gene regulatory regions. To infer the specific targets of purifying selection, we analyze the patterns of polymorphism in the data at two phenotypic levels: the strengths of binding and expression. We find that combinations of SNPs show evidence of being under selective pressure, while individual SNPs do not. The model predicts that SNPs appear to accumulate in the genotypes of the natural population in a way biased towards small increases in activating action on the expression pattern. Taken together, these results provide a systems-level view of how genetic variation translates to the level of gene regulatory networks via combinatorial SNP effects.

Dynamical analysis of regulatory interactions in the gap gene system of Drosophila melanogaster.

Genetic studies have revealed that segment determination in Drosophila melanogaster is based on hierarchical regulatory interactions among maternal coordinate and zygotic segmentation genes. The gap gene system constitutes the most upstream zygotic layer of this regulatory hierarchy, responsible for the initial interpretation of positional information encoded by maternal gradients. We present a detailed analysis of regulatory interactions involved in gap gene regulation based on gap gene circuits, which are mathematical gene network models used to infer regulatory interactions from quantitative gene expression data. Our models reproduce gap gene expression at high accuracy and temporal resolution. Regulatory interactions found in gap gene circuits provide consistent and sufficient mechanisms for gap gene expression, which largely agree with mechanisms previously inferred from qualitative studies of mutant gene expression patterns. Our models predict activation of Kr by Cad and clarify several other regulatory interactions. Our analysis suggests a central role for repressive feedback loops between complementary gap genes. We observe that repressive interactions among overlapping gap genes show anteroposterior asymmetry with posterior dominance. Finally, our models suggest a correlation between timing of gap domain boundary formation and regulatory contributions from the terminal maternal system.

Statistical method for estimation of the predictive power of a gene circuit model.

In this paper, a specific aspect of the prediction problem is considered: high predictive power is understood as a possibility to reproduce correct behavior of model solutions at predefined values of a subset of parameters. The problem is discussed in the context of a specific mathematical model, the gene circuit model for segmentation gap gene system in early Drosophila development. A shortcoming of the model is that it cannot be used for predicting the system behavior in mutants when fitted to wild type (WT) data. In order to answer a question whether experimental data contain enough information for the correct prediction we introduce two measures of predictive power. The first measure reveals the biologically substantiated low sensitivity of the model to parameters that are responsible for correct reconstruction of expression patterns in mutants, while the second one takes into account their correlation with the other parameters. It is demonstrated that the model solution, obtained by fitting to gene expression data in WT and Kr⁻ mutants simultaneously, and exhibiting the high predictive power, is characterized by much higher values of both measures than those fitted to WT data alone. This result leads us to the conclusion that information contained in WT data is insufficient to reliably estimate the large number of model parameters and provide predictions of mutants.

A new stochastic model for subgenomic hepatitis C virus replication considers drug resistant mutants.

As an RNA virus, hepatitis C virus (HCV) is able to rapidly acquire drug resistance, and for this reason the design of effective anti-HCV drugs is a real challenge. The HCV subgenomic replicon-containing cells are widely used for experimental studies of the HCV genome replication mechanisms, for drug testing in vitro and in studies of HCV drug resistance. The NS3/4A protease is essential for virus replication and, therefore, it is one of the most attractive targets for developing specific antiviral agents against HCV. We have developed a stochastic model of subgenomic HCV replicon replication, in which the emergence and selection of drug resistant mutant viral RNAs in replicon cells is taken into account. Incorporation into the model of key NS3 protease mutations leading to resistance to BILN-2061 (A156T, D168V, R155Q), VX-950 (A156S, A156T, T54A) and SCH 503034 (A156T, A156S, T54A) inhibitors allows us to describe the long term dynamics of the viral RNA suppression for various inhibitor concentrations. We theoretically showed that the observable difference between the viral RNA kinetics for different inhibitor concentrations can be explained by differences in the replication rate and inhibitor sensitivity of the mutant RNAs. The pre-existing mutants of the NS3 protease contribute more significantly to appearance of new resistant mutants during treatment with inhibitors than wild-type replicon. The model can be used to interpret the results of anti-HCV drug testing on replicon systems, as well as to estimate the efficacy of potential drugs and predict optimal schemes of their usage.

Preparation of Drosophila embryos for quantitative imaging of gene expression.

Quantitative measurements derived using sophisticated microscopy techniques are essential for understanding the basic principles that control the behavior of biological systems. We have developed a five-step data pipeline to extract quantitative data on segmentation gene expression from confocal images of gene expression patterns in Drosophila. This protocol describes the preparation of Drosophila embryos for imaging by confocal microscopy. Embryos are collected at the appropriate developmental stage and fixed. They are then stained with both primary antibodies and secondary antibodies conjugated with fluorophores to reveal the segmentation gene expression patterns.

Quantitative imaging of gene expression in Drosophila embryos.

Quantitative measurements derived using sophisticated microscopy techniques are essential for understanding the basic principles that control the behavior of biological systems. Here we describe a data pipeline developed to extract quantitative data on segmentation gene expression from confocal images of gene expression patterns in Drosophila. The pipeline consists of image segmentation, background removal, temporal characterization of an embryo, data registration, and data averaging. This pipeline has been successfully applied to obtain quantitative gene expression data at cellular resolution in space and at 6.5-min resolution in time. It has also enabled the construction of a spatiotemporal atlas of segmentation gene expression. We describe the software used to construct a workflow for extracting quantitative data on segmentation gene expression and the BREReA package, which implements the methods for background removal and registration of segmentation gene expression patterns.

GCPReg package for registration of the segmentation gene expression data in Drosophila.

In modern functional genomics registration techniques areused to construct reference gene expression patterns and createa spatiotemporal atlas of the expression of all the genes in anetwork. In this paper we present a software package calledGCPReg, which can be used to register the expression patterns ofsegmentation genes in the early Drosophila embryo. The key task,which this package performs, is the extraction of spatially localizedcharacteristic features of expression patterns. To facilitatethis task, we have developed an easy-to-use interactive graphicalinterface. We describe GCPReg usage and demonstrate how thispackage can be applied to register gene expression patterns inwild type and mutants. GCPReg has been designed to operate ona UNIX platform and is freely available via the Internet at http://urchin.spbcas.ru/downloads/GCPReg/GCPReg.htm.

Pipeline for acquisition of quantitative data on segmentation gene expression from confocal images.

We describe a data pipeline developed to extract the quantitative data on segmentation gene expression from confocal images of gene expression patterns in Drosophila. The pipeline consists of five steps: image segmentation, background removal, temporal characterization of an embryo, data registration and data averaging. This pipeline was successfully applied to obtain quantitative gene expression data at cellular resolution in space and at the 6.5-minute resolution in time, as well as to construct a spatiotemporal atlas of segmentation gene expression. Each data pipeline step can be easily adapted to process a wide range of images of gene expression patterns.