92 research outputs found
Stable, Precise, and Reproducible Patterning of Bicoid and Hunchback Molecules in the Early Drosophila Embryo
Precise patterning of morphogen molecules and their accurate reading out are of key importance in embryonic development. Recent experiments have visualized distributions of proteins in developing embryos and shown that the gradient of concentration of Bicoid morphogen in Drosophila embryos is established rapidly after fertilization and remains stable through syncytial mitoses. This stable Bicoid gradient is read out in a precise way to distribute Hunchback with small fluctuations in each embryo and in a reproducible way, with small embryo-to-embryo fluctuation. The mechanisms of such stable, precise, and reproducible patterning through noisy cellular processes, however, still remain mysterious. To address these issues, here we develop the one- and three-dimensional stochastic models of the early Drosophila embryo. The simulated results show that the fluctuation in expression of the hunchback gene is dominated by the random arrival of Bicoid at the hunchback enhancer. Slow diffusion of Hunchback protein, however, averages out this intense fluctuation, leading to the precise patterning of distribution of Hunchback without loss of sharpness of the boundary of its distribution. The coordinated rates of diffusion and transport of input Bicoid and output Hunchback play decisive roles in suppressing fluctuations arising from the dynamical structure change in embryos and those arising from the random diffusion of molecules, and give rise to the stable, precise, and reproducible patterning of Bicoid and Hunchback distributions
The Role of Regulated mRNA Stability in Establishing Bicoid Morphogen Gradient in Drosophila Embryonic Development
The Bicoid morphogen is amongst the earliest triggers of differential spatial pattern of gene expression and subsequent cell fate determination in the embryonic development of Drosophila. This maternally deposited morphogen is thought to diffuse in the embryo, establishing a concentration gradient which is sensed by downstream genes. In most model based analyses of this process, the translation of the bicoid mRNA is thought to take place at a fixed rate from the anterior pole of the embryo and a supply of the resulting protein at a constant rate is assumed. Is this process of morphogen generation a passive one as assumed in the modelling literature so far, or would available data support an alternate hypothesis that the stability of the mRNA is regulated by active processes? We introduce a model in which the stability of the maternal mRNA is regulated by being held constant for a length of time, followed by rapid degradation. With this more realistic model of the source, we have analysed three computational models of spatial morphogen propagation along the anterior-posterior axis: (a) passive diffusion modelled as a deterministic differential equation, (b) diffusion enhanced by a cytoplasmic flow term; and (c) diffusion modelled by stochastic simulation of the corresponding chemical reactions. Parameter estimation on these models by matching to publicly available data on spatio-temporal Bicoid profiles suggests strong support for regulated stability over either a constant supply rate or one where the maternal mRNA is permitted to degrade in a passive manner
Drosophila blastoderm patterning
The Drosophila blastoderm embryo is a classic model for the study of the genetics of pattern formation. In recent years, quantitative empirical approaches have been employed extensively in the study of blastoderm pattern formation. This quantitative work has enabled the development of a number of data-driven computational models. More than in other systems, these models have been experimentally validated, and have informed new empirical work. They have led to insights into the establishment of morphogen gradients, the interpretation and transduction of positional information by downstream transcriptional networks, and the mechanisms by which spatial scaling and robustness of gene expression are achieved. Here we review the latest developments in the field
A Multiscale Investigation of Bicoid-Dependent Transcriptional Events in Drosophila Embryos
Background: Morphogen molecules form concentration gradients to provide spatial information to cells in a developing embryo. Precisely how cells decode such information to form patterns with sharp boundaries remains an open question. For example, it remains controversial whether the Drosophila morphogenetic protein Bicoid (Bcd) plays a transient or sustained role in activating its target genes to establish sharp expression boundaries during development. Methodology/Principal Findings: In this study, we describe a method to simultaneously detect Bcd and the nascent transcripts of its target genes in developing embryos. This method allows us to investigate the relationship between Bcd and the transcriptional status of individual copies of its target genes on distinct scales. We show that, on three scales analyzed concurrentlyβembryonic, nuclear and local, the actively-transcribing gene copies are associated with high Bcd concentrations. These results underscore the importance of Bcd as a sustained input for transcriptional decisions of individual copies of its target genes during development. We also show that the Bcd-dependent transcriptional decisions have a significantly higher noise than Bcd-dependent gene products, suggesting that, consistent with theoretical studies, time and/or space averaging reduces the noise of Bcd-activated transcriptional output. Finally, our analysis of an X-linked Bcd target gene reveals that Bcd-dependent transcription bursts at twice the frequency in males as in females, providing a mechanism for dosage compensation in early Drosophila embryos
Positional information, positional error, and read-out precision in morphogenesis: a mathematical framework
The concept of positional information is central to our understanding of how
cells in a multicellular structure determine their developmental fates.
Nevertheless, positional information has neither been defined mathematically
nor quantified in a principled way. Here we provide an information-theoretic
definition in the context of developmental gene expression patterns and examine
which features of expression patterns increase or decrease positional
information. We connect positional information with the concept of positional
error and develop tools to directly measure information and error from
experimental data. We illustrate our framework for the case of gap gene
expression patterns in the early Drosophila embryo and show how information
that is distributed among only four genes is sufficient to determine
developmental fates with single cell resolution. Our approach can be
generalized to a variety of different model systems; procedures and examples
are discussed in detail
A Two-Dimensional Simulation Model of the Bicoid Gradient in Drosophila
BACKGROUND:Bicoid (Bcd) is a Drosophila morphogenetic protein responsible for patterning the anterior structures in embryos. Recent experimental studies have revealed important insights into the behavior of this morphogen gradient, making it necessary to develop a model that can recapitulate the biological features of the system, including its dynamic and scaling properties. METHODOLOGY/PRINCIPAL FINDINGS:We present a biologically realistic 2-D model of the dynamics of the Bcd gradient in Drosophila embryos. This model is based on equilibrium binding of Bcd molecules to non-specific, low affinity DNA sites throughout the Drosophila genome. It considers both the diffusion media within which the Bcd gradient is formed and the dynamic and other relevant properties of bcd mRNA from which Bcd protein is produced. Our model recapitulates key features of the Bcd protein gradient observed experimentally, including its scaling properties and the stability of its nuclear concentrations during development. Our simulation model also allows us to evaluate the effects of other biological activities on Bcd gradient formation, including the dynamic redistribution of bcd mRNA in early embryos. Our simulation results suggest that, in our model, Bcd protein diffusion is important for the formation of an exponential gradient in embryos. CONCLUSIONS/SIGNIFICANCE:The 2-D model described in this report is a simple and versatile simulation procedure, providing a quantitative evaluation of the Bcd gradient system. Our results suggest an important role of Bcd binding to non-specific, low-affinity DNA sites in proper formation of the Bcd gradient in our model. They demonstrate that highly complex biological systems can be effectively modeled with relatively few parameters
Analysis of Gap Gene Regulation in a 3D Organism-Scale Model of the Drosophila melanogaster Embryo
The axial bodyplan of Drosophila melanogaster is determined during a process called morphogenesis. Shortly after fertilization, maternal bicoid mRNA is translated into Bicoid (Bcd). This protein establishes a spatially graded morphogen distribution along the anterior-posterior (AP) axis of the embryo. Bcd initiates AP axis determination by triggering expression of gap genes that subsequently regulate each other's expression to form a precisely controlled spatial distribution of gene products. Reaction-diffusion models of gap gene expression on a 1D domain have previously been used to infer complex genetic regulatory network (GRN) interactions by optimizing model parameters with respect to 1D gap gene expression data. Here we construct a finite element reaction-diffusion model with a realistic 3D geometry fit to full 3D gap gene expression data. Though gap gene products exhibit dorsal-ventral asymmetries, we discover that previously inferred gap GRNs yield qualitatively correct AP distributions on the 3D domain only when DV-symmetric initial conditions are employed. Model patterning loses qualitative agreement with experimental data when we incorporate a realistic DV-asymmetric distribution of Bcd. Further, we find that geometry alone is insufficient to account for DV-asymmetries in the final gap gene distribution. Additional GRN optimization confirms that the 3D model remains sensitive to GRN parameter perturbations. Finally, we find that incorporation of 3D data in simulation and optimization does not constrain the search space or improve optimization results
Mutual Repression enhances the Steepness and Precision of Gene Expression Boundaries
Embryonic development is driven by spatial patterns of gene expression that
determine the fate of each cell in the embryo. While gene expression is often
highly erratic, embryonic development is usually exceedingly precise. In
particular, gene expression boundaries are robust not only against intrinsic
noise from gene expression and protein diffusion, but also against
embryo-to-embryo variations in the morphogen gradients, which provide
positional information to the differentiating cells. How development is robust
against intra- and inter-embryonic variations is not understood. A common motif
in the gene regulation networks that control embryonic development is mutual
repression between pairs of genes. To assess the role of mutual repression in
the robust formation of gene expression patterns, we have performed large-scale
stochastic simulations of a minimal model of two mutually repressing gap genes
in Drosophila, hunchback (hb) and knirps (kni). Our model includes not only
mutual repression between hb and kni, but also the stochastic and cooperative
activation of hb by the anterior morphogen Bicoid (Bcd) and of kni by the
posterior morphogen Caudal (Cad), as well as the diffusion of Hb and Kni. Our
analysis reveals that mutual repression can markedly increase the steepness and
precision of the gap gene expression boundaries. In contrast to spatial
averaging and cooperative gene activation, mutual repression thus allows for
gene-expression boundaries that are both steep and precise. Moreover, mutual
repression dramatically enhances their robustness against embryo-to-embryo
variations in the morphogen levels. Finally, our simulations reveal that gap
protein diffusion plays a critical role not only in reducing the width of gap
gene expression boundaries via spatial averaging, but also in repairing
patterning errors that could arise due to the bistability induced by mutual
repression.Comment: 29 pages, 9 figures, supporting text with 9 supporting figures;
accepted for publication in PLoS Comp. Bio
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