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.     

Shaping a Morphogen Gradient for Positional Precision

Morphogen gradients, which provide positional information to cells in a developing tissue, could in principle adopt any nonuniform profile. To our knowledge, how the profile of a morphogen gradient affects positional precision has not been well studied experimentally. Here, we compare the positional precision provided by the Drosophila morphogenetic protein Bicoid (Bcd) in wild-type (wt) embryos with embryos lacking an interacting cofactor. The Bcd gradient in the latter case exhibits decreased positional precision around mid-embryo compared with its wt counterpart. The domain boundary of Hunchback (Hb), a target activated by Bcd, becomes more variable in mutant embryos. By considering embryo-to-embryo, internal, and measurement fluctuations, we dissect mathematically the relevant sources of fluctuations that contribute to the error in positional information. Using this approach, we show that the defect in Hb boundary positioning in mutant embryos is directly reflective of an altered Bcd gradient profile with increasing flatness toward mid-embryo. Furthermore, we find that noise in the Bcd input signal is dominated by internal fluctuations but, due to time and spatial averaging, the spatial precision of the Hb boundary is primarily affected by embryo-to-embryo variations. Our results demonstrate that the positional information provided by the wt Bcd gradient profile is highly precise and necessary for patterning precision.     

Distance measurements via the morphogen gradient of Bicoid in <Emphasis Type="Italic">Drosophila</Emphasis> embryos

Background  

Patterning along the anterior-posterior (A-P) axis in Drosophila embryos is instructed by the morphogen gradient of Bicoid (Bcd). Despite extensive studies of this morphogen, how embryo geometry may affect gradient formation and target responses has not been investigated experimentally.     

Morphogen gradient formation and action: insights from studying Bicoid protein degradation

In a recent publication, we identified a novel F-box protein, encoded by fates-shifted (fsd), that plays a role in targeting Bcd for ubiquitination and degradation. Our analysis of mutant Drosophila embryos suggests that Bcd protein degradation is important for proper gradient formation and developmental fate specification. Here we describe further experiments that lead to an estimate of Bcd half-life, < 15 min, in embryos during the time of gradient formation. We use our findings to evaluate different models of Bcd gradient formation. With this new estimate, we simulate the Bcd gradient formation process in our own biologically realistic 2-D model. Finally, we discuss the role of Bcd-encoded positional information in controlling the positioning and precision of developmental decisions.     

Modeling the precision and robustness of Hunchback border during Drosophila embryonic development

During anterior-posterior axis specification in the Drosophila embryo, the Hunchback (Hb) protein forms a sharp boundary at the mid-point of the embryo with great positional precision. While Bicoid (Bcd) is a known upstream regulator for hb expression, there is evidence to suggest that Hb effectively filters out “noisy” data received from varied Bcd gradients. We use mathematical models to explore simple regulatory networks which filter out such noise to produce a precise Hb boundary. We find that in addition to Bcd and Hb, at least one freely evolving protein is necessary. An automated search yields a number of examples of three-protein networks exhibiting the desired precision. In all such networks, Hb diffuses much slower than the third protein. In addition, the action of Hb on the third protein is the opposite of the action of the third protein on hb (i.e. if Hb activates the third protein, then the third protein inhibits hb expression, and vice versa). Most of the discovered systems satisfy the known biological properties, that Bcd activates hb, and that Hb activates its own expression. We find that all network topologies satisfying these constraints arise among the networks exhibiting the desired precision. Investigating the dynamics of these networks, we find that under a general class of non-uniform initial conditions, Bcd can be eliminated from the system and the spatiotemporal evolution of these two proteins alone is sufficient to recapture the dynamics. We hypothesize that Bcd is needed only to spatially disturb the gradient of the third protein, and then becomes unnecessary in the further evolution of the Hb border. This provides a possible explanation as to why the Hb dynamics are robust under perturbations of the Bcd gradient. Under this hypothesis, other proteins would be able to assume the role of Bcd in our simulations (possibly in the case of evolutionary divergences or a redundancy in the process), with the only constraint that they act to positively regulate hb.     

Morphogen gradient formation and action

In a recent publication, we identified a novel F-box protein, encoded by fates-shifted (fsd), that plays a role in targeting Bcd for ubiquitination and degradation. Our analysis of mutant Drosophila embryos suggests that Bcd protein degradation is important for proper gradient formation and developmental fate specification. Here we describe further experiments that lead to an estimate of Bcd half-life, &lt;15 min, in embryos during the time of gradient formation. We use our findings to evaluate different models of Bcd gradient formation. With this new estimate, we simulate the Bcd gradient formation process in our own biologically realistic 2-D model. Finally, we discuss the role of Bcd-encoded positional information in controlling the positioning and precision of developmental decisions.     

αTubulin 67C and Ncd Are Essential for Establishing a Cortical Microtubular Network and Formation of the Bicoid mRNA Gradient in Drosophila

The Bicoid (Bcd) protein gradient in Drosophila serves as a paradigm for gradient formation in textbooks. To explain the generation of the gradient, the ARTS model, which is based on the observation of a bcd mRNA gradient, proposes that the bcd mRNA, localized at the anterior pole at fertilization, migrates along microtubules (MTs) at the cortex to the posterior to form a bcd mRNA gradient which is translated to form a protein gradient. To fulfil the criteria of the ARTS model, an early cortical MT network is thus a prerequisite. We report hitherto undiscovered MT activities in the early embryo important for bcd mRNA transport: (i) an early and omnidirectional MT network exclusively at the anterior cortex of early nuclear cycle embryos showing activity during metaphase and anaphase only, (ii) long MTs up to 50 µm extending into the yolk at blastoderm stage to enable basal-apical transport. The cortical MT network is not anchored to the actin cytoskeleton. The posterior transport of the mRNA via the cortical MT network critically depends on maternally-expressed αTubulin67C and the minus-end motor Ncd. In either mutant, cortical transport of the bcd mRNA does not take place and the mRNA migrates along another yet undisclosed interior MT network, instead. Our data strongly corroborate the ARTS model and explain the occurrence of the bcd mRNA gradient.     

Fluorescence Correlation Spectroscopy Measurements of the Membrane Protein TetA in Escherichia coli Suggest Rapid Diffusion at Short Length Scales

Structural inhomogeneities in biomembranes can lead to complex diffusive behavior of membrane proteins that depend on the length or time scales that are probed. This effect is well studied in eukaryotic cells, but has been explored only recently in bacteria. Here we used fluorescence recovery after photobleaching (FRAP) and fluorescence correlation spectroscopy (FCS) to study diffusion of the membrane protein TetA-YFP in E. coli. We find that the diffusion constant determined from FRAP is comparable to other reports of inner membrane protein diffusion constants in E. coli. However, FCS, which probes diffusion on shorter length scales, gives a value that is almost two orders of magnitude higher and is comparable to lipid diffusion constants. These results suggest there is a population of TetA-YFP molecules in the membrane that move rapidly over short length scales (∼ 400 nm) but move significantly more slowly over the longer length scales probed by FRAP.     

Fluorescence techniques in developmental biology

Advanced fluorescence techniques, commonly known as the F-techniques, measure the kinetics and the interactions of biomolecules with high sensitivity and spatiotemporal resolution. Applications of the F-techniques, which were initially limited to cells, were further extended to study in vivo protein organization and dynamics in whole organisms. The integration of F-techniques with multi-photon microscopy and light-sheet microscopy widened their applications in the field of developmental biology. It became possible to penetrate the thick tissues of living organisms and obtain good signal-to-noise ratio with reduced photo-induced toxicity. In this review, we discuss the principle and the applications of the three most commonly used F-techniques in developmental biology: Fluorescence Recovery After Photo-bleaching (FRAP), Förster Resonance Energy Transfer (FRET), and Fluorescence Correlation and Cross-Correlation Spectroscopy (FCS and FCCS).     

Maternal Co-ordinate Gene Regulation and Axis Polarity in the Scuttle Fly Megaselia abdita

Axis specification and segment determination in dipteran insects are an excellent model system for comparative analyses of gene network evolution. Antero-posterior polarity of the embryo is established through systems of maternal morphogen gradients. In Drosophila melanogaster, the anterior system acts through opposing gradients of Bicoid (Bcd) and Caudal (Cad), while the posterior system involves Nanos (Nos) and Hunchback (Hb) protein. These systems act redundantly. Both Bcd and Hb need to be eliminated to cause a complete loss of polarity resulting in mirror-duplicated abdomens, so-called bicaudal phenotypes. In contrast, knock-down of bcd alone is sufficient to induce double abdomens in non-drosophilid cyclorrhaphan dipterans such as the hoverfly Episyrphus balteatus or the scuttle fly Megaselia abdita. We investigate conserved and divergent aspects of axis specification in the cyclorrhaphan lineage through a detailed study of the establishment and regulatory effect of maternal gradients in M. abdita. Our results show that the function of the anterior maternal system is highly conserved in this species, despite the loss of maternal cad expression. In contrast, hb does not activate gap genes in this species. The absence of this activatory role provides a precise genetic explanation for the loss of polarity upon bcd knock-down in M. abdita, and suggests a general scenario in which the posterior maternal system is increasingly replaced by the anterior one during the evolution of the cyclorrhaphan dipteran lineage.     

Scaling of the Bicoid morphogen gradient by a volume-dependent production rate

An important feature of development is the formation of patterns that are proportional to the overall size of the embryo. But how such proportionality, or scaling, is achieved mechanistically remains poorly understood. Furthermore, it is currently unclear whether organisms utilize similar or distinct mechanisms to achieve scaling within a species and between species. Here we investigate within-species scaling mechanisms for anterior-posterior (A-P) patterning in Drosophila melanogaster, focusing specifically on the properties of the Bicoid (Bcd) morphogen gradient. Using embryos from lines artificially selected for large and small egg volume, we show that large embryos have higher nuclear Bcd concentrations in the anterior than small embryos. This anterior difference leads to scaling properties of the Bcd gradient profiles: in broad regions of the large and small embryos along the A-P axis, normalizing their positions to embryo length reduces the differences in both the nuclear Bcd concentrations and Bcd-encoded positional information. We further trace the origin of Bcd gradient scaling by showing directly that large embryos have more maternally deposited bcd mRNA than small embryos. Our results suggest a simple model for how within-species Bcd gradient scaling can be achieved. In this model, the Bcd production rate, which is dependent on the total number of bcd mRNA molecules in the anterior, is scaled with embryo volume.     

A Generalization of Theory for Two-Dimensional Fluorescence Recovery after Photobleaching Applicable to Confocal Laser Scanning Microscopes

Fluorescence recovery after photobleaching (FRAP) using confocal laser scanning microscopes (confocal FRAP) has become a valuable technique for studying the diffusion of biomolecules in cells. However, two-dimensional confocal FRAP sometimes yields results that vary with experimental setups, such as different bleaching protocols and bleaching spot sizes. In addition, when confocal FRAP is used to measure diffusion coefficients (D) for fast diffusing molecules, it often yields D-values that are one or two orders-of-magnitude smaller than that predicted theoretically or measured by alternative methods such as fluorescence correlation spectroscopy. Recently, it was demonstrated that this underestimation of D can be corrected by taking diffusion during photobleaching into consideration. However, there is currently no consensus on confocal FRAP theory, and no efforts have been made to unify theories on conventional and confocal FRAP. To this end, we generalized conventional FRAP theory to incorporate diffusion during photobleaching so that analysis by conventional FRAP theory for a circular region of interest is easily applicable to confocal FRAP. Finally, we demonstrate the accuracy of these new (to our knowledge) formulae by measuring D for soluble enhanced green fluorescent protein in aqueous glycerol solution and in the cytoplasm and nucleus of COS7 cells.