Master equation simulation analysis of immunostained Bicoid morphogen gradient

Background  

The concentration gradient of Bicoid protein which determines the developmental pathways in early Drosophila embryo is the best characterized morphogen gradient at the molecular level. Because different developmental fates can be elicited by different concentrations of Bicoid, it is important to probe the limits of this specification by analyzing intrinsic fluctuations of the Bicoid gradient arising from small molecular number. Stochastic simulations can be applied to further the understanding of the dynamics of Bicoid morphogen gradient formation at the molecular number level, and determine the source of the nucleus-to-nucleus expression variation (noise) observed in the Bicoid gradient.     

Pre-steady-state decoding of the Bicoid morphogen gradient

Morphogen gradients are established by the localized production and subsequent diffusion of signaling molecules. It is generally assumed that cell fates are induced only after morphogen profiles have reached their steady state. Yet, patterning processes during early development occur rapidly, and tissue patterning may precede the convergence of the gradient to its steady state. Here we consider the implications of pre-steady-state decoding of the Bicoid morphogen gradient for patterning of the anterior–posterior axis of the Drosophila embryo. Quantitative analysis of the shift in the expression domains of several Bicoid targets (gap genes) upon alteration of bcd dosage, as well as a temporal analysis of a reporter for Bicoid activity, suggest that a transient decoding mechanism is employed in this setting. We show that decoding the pre-steady-state morphogen profile can reduce patterning errors caused by fluctuations in the rate of morphogen production. This can explain the surprisingly small shifts in gap and pair-rule gene expression domains observed in response to alterations in bcd dosage.     

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.     

Bicoid gradient formation mechanism and dynamics revealed by protein lifetime analysis

Embryogenesis relies on instructions provided by spatially organized signaling molecules known as morphogens. Understanding the principles behind morphogen distribution and how cells interpret locally this information remains a major challenge in developmental biology. Here, we introduce morphogen‐age measurements as a novel approach to test models of morphogen gradient formation. Using a tandem fluorescent timer as a protein age sensor, we find a gradient of increasing age of Bicoid along the anterior–posterior axis in the early Drosophila embryo. Quantitative analysis of the protein age distribution across the embryo reveals that the synthesis–diffusion–degradation model is the most likely model underlying Bicoid gradient formation, and rules out other hypotheses for gradient formation. Moreover, we show that the timer can detect transitions in the dynamics associated with syncytial cellularization. Our results provide new insight into Bicoid gradient formation and demonstrate how morphogen‐age information can complement knowledge about movement, abundance, and distribution, which should be widely applicable to other systems.     

Modeling the bicoid gradient: diffusion and reversible nuclear trapping of a stable protein

The Bicoid gradient in the Drosophila embryo provided the first example of a morphogen gradient studied at the molecular level. The exponential shape of the Bicoid gradient had always been interpreted within the framework of the localized production, diffusion, and degradation model. We propose an alternative mechanism, which assumes no Bicoid degradation. The medium where the Bicoid gradient is formed and interpreted is very dynamic. Most notably, the number of nuclei changes over three orders of magnitude from fertilization, when Bicoid synthesis is initiated, to nuclear cycle 14 when most of the measurements were taken. We demonstrate that a model based on Bicoid diffusion and nucleocytoplasmic shuttling in the presence of the growing number of nuclei can account for most of the properties of the Bicoid concentration profile. Consistent with experimental observations, the Bicoid gradient in our model is established before nuclei migrate to the periphery of the embryo and remains stable during subsequent nuclear divisions.     

A precise Bicoid gradient is nonessential during cycles 11-13 for precise patterning in the Drosophila blastoderm

Background

During development, embryos decode maternal morphogen inputs into highly precise zygotic gene expression. The discovery of the morphogen Bicoid and its profound effect on developmental programming in the Drosophila embryo has been a cornerstone in understanding the decoding of maternal inputs. Bicoid has been described as a classical morphogen that forms a concentration gradient along the antero-posterior axis of the embryo by diffusion and initiates expression of target genes in a concentration-dependent manner in the syncytial blastoderm. Recent work has emphasized the stability of the Bicoid gradient as a function of egg length and the role of nuclear dynamics in maintaining the Bicoid gradient. Bicoid and nuclear dynamics were observed but not modulated under the ideal conditions used previously. Therefore, it has not been tested explicitly whether a temporally stable Bicoid gradient prior to cellularization is required for precise patterning.

Principal Findings

Here, we modulate both nuclear dynamics and the Bicoid gradient using laminar flows of different temperature in a microfluidic device to determine if stability of the Bicoid gradient prior to cellularization is essential for precise patterning. Dramatic motion of both cytoplasm and nuclei was observed prior to cellularization, and the Bicoid gradient was disrupted by nuclear motion and was highly abnormal as a function of egg length. Despite an abnormal Bicoid gradient during cycles 11–13, Even-skipped patterning in these embryos remained precise.

Conclusions

These results indicate that the stability of the Bicoid gradient as a function of egg length is nonessential during syncytial blastoderm stages. Further, presumably no gradient formed by simple diffusion on the scale of egg length could be responsible for the robust antero-posterior patterning observed, as severe cytoplasmic and nuclear motion would disrupt such a gradient. Additional mechanisms for how the embryo could sense its dimensions and interpret the Bicoid gradient are discussed.     

A system of repressor gradients spatially organizes the boundaries of Bicoid-dependent target genes

The homeodomain (HD) protein Bicoid (Bcd) is thought to function as a gradient morphogen that positions boundaries of target genes via threshold-dependent activation mechanisms. Here, we analyze 66 Bcd-dependent regulatory elements and show that their boundaries are positioned primarily by repressive gradients that antagonize Bcd-mediated activation. A major repressor is the pair-rule protein Runt (Run), which is expressed in an opposing gradient and is necessary and sufficient for limiting Bcd-dependent activation. Evidence is presented that Run functions with the maternal repressor Capicua and the gap protein Kruppel as the principal components of a repression system that correctly orders boundaries throughout the anterior half of the embryo. These results put conceptual limits on the Bcd morphogen hypothesis and demonstrate how the Bcd gradient functions within the gene network that patterns the embryo.     

Probing intrinsic properties of a robust morphogen gradient in Drosophila

A remarkable feature of development is its reproducibility, the ability to correct embryo-to-embryo variations and instruct precise patterning. In Drosophila, embryonic patterning along the anterior-posterior axis is controlled by the morphogen gradient Bicoid (Bcd). In this article, we describe quantitative studies of the native Bcd gradient and its target Hunchback (Hb). We show that the native Bcd gradient is highly reproducible and is itself scaled with embryo length. While a precise Bcd gradient is necessary for precise Hb expression, it still has positional errors greater than Hb expression. We describe analyses further probing mechanisms for Bcd gradient scaling and correction of its residual positional errors. Our results suggest a simple model of a robust Bcd gradient sufficient to achieve scaled and precise activation of its targets. The robustness of this gradient is conferred by its intrinsic properties of "self-correcting" the inevitable input variations to achieve a precise and reproducible output.     

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.     

Stability and nuclear dynamics of the bicoid morphogen gradient

Patterning in multicellular organisms results from spatial gradients in morphogen concentration, but the dynamics of these gradients remain largely unexplored. We characterize, through in vivo optical imaging, the development and stability of the Bicoid morphogen gradient in Drosophila embryos that express a Bicoid-eGFP fusion protein. The gradient is established rapidly (approximately 1 hr after fertilization), with nuclear Bicoid concentration rising and falling during mitosis. Interphase levels result from a rapid equilibrium between Bicoid uptake and removal. Initial interphase concentration in nuclei in successive cycles is constant (+/-10%), demonstrating a form of gradient stability, but it subsequently decays by approximately 30%. Both direct photobleaching measurements and indirect estimates of Bicoid-eGFP diffusion constants (D < or = 1 microm(2)/s) provide a consistent picture of Bicoid transport on short ( approximately min) time scales but challenge traditional models of long-range gradient formation. A new model is presented emphasizing the possible role of nuclear dynamics in shaping and scaling the gradient.     

Shape and function of the Bicoid morphogen gradient in dipteran species with different sized embryos

The Bicoid morphogen evolved approximately 150 MYA from a Hox3 duplication and is only found in higher dipterans. A major difference between dipteran species, however, is the size of the embryo, which varies up to 5-fold. Although the expression of developmental factors scale with egg length, it remains unknown how this scaling is achieved. To test whether scaling is accounted for by the properties of Bicoid, we expressed eGFP fused to the coding region of bicoid from three dipteran species in transgenic Drosophila embryos using the Drosophila bicoid cis-regulatory and mRNA localization sequences. In such embryos, we find that Lucilia sericata and Calliphora vicina Bicoid produce gradients very similar to the endogenous Drosophila gradient and much shorter than what they would have produced in their own respective species. The common shape of the Drosophila, Lucilia and Calliphora Bicoid gradients appears to be a conserved feature of the Bicoid protein. Surprisingly, despite their similar distributions, we find that Bicoid from Lucilia and Calliphora do not rescue Drosophila bicoid mutants, suggesting that that Bicoid proteins have evolved species-specific functional amino acid differences. We also found that maternal expression and anteriorly localization of proteins other than Bcd does not necessarily give rise to a gradient; eGFP produced a uniform protein distribution. However, a shallow gradient was observed using eGFP-NLS, suggesting nuclear localization may be necessary but not sufficient for gradient formation.     

Robust Generation and Decoding of Morphogen Gradients

Morphogen gradients play a key role in multiple differentiation processes. Both the formation of the gradient and its interpretation by the receiving cells need to occur at high precision to ensure reproducible patterning. This need for quantitative precision is challenged by fluctuations in the environmental conditions and by variations in the genetic makeup of the developing embryos. We discuss mechanisms that buffer morphogen profiles against variations in gene dosage. Self-enhanced morphogen degradation and pre-steady-state decoding provide general means for buffering the morphogen profile against fluctuations in morphogen production rate. A more specific “shuttling” mechanism, which establishes a sharp and robust activation profile of a widely expressed morphogen, and enables the adjustment of morphogen profile with embryo size, is also described. Finally, we consider the transformation of the smooth gradient profile into sharp borders of gene expression in the signal-receiving cells. The integration theory and experiments are increasingly used, providing key insights into the system-level functioning of the developmental system.In order for a uniform field of cells to differentiate into a reproducible pattern of organs and tissues, cells need to receive information about their position within the field. During development, positional information is often conveyed by spatial gradients of morphogens (Wolpert 1989). In the presence of such gradients, cells are subject to different levels of morphogen, depending on their positions within the field, and activate, accordingly, one of several gene expression cassettes. The quantitative shape of the morphogen gradient is critical for patterning, with cell-fate boundaries established at specific concentration thresholds. Although these general features of morphogen-based patterning are universal, the range and form of the morphogen profile, and the pattern of induced target genes, vary significantly depending on the tissue setting and the signaling pathways used.The formation of a morphogen gradient is a dynamic process, influenced by the kinetics of morphogen production, diffusion, and degradation. These processes are tightly controlled through intricate networks of positive and negative feedback loops, which shape the gradient and enhance its reproducibility between individual embryos and developmental contexts. In the past three decades, many of the components comprising the morphogen signaling cascades have been identified and sorted into pathways, enabling one to start addressing seminal questions regarding their functionality: How is it that morphogen signaling is reproducible from one embryo to the next, despite fluctuations in the levels of signaling components, temperature differences, variations in size, or unequal distribution of components between daughter cells? Are there underlying mechanisms that assure a reproducible response? Are these mechanisms conserved across species, similar to the signaling pathways they control?In this review, we outline insights we gained by quantitatively analyzing the process of morphogen gradient formation. We focus on mechanisms that buffer morphogen profiles against fluctuations in gene dosage, and describe general means by which such buffering is enhanced. These mechanisms include self-enhanced morphogen degradation and pre-steady-state decoding. In addition, we describe a more specific “shuttling” mechanism that is used to generate a sharp and robust profile of a morphogen activity from a source that is broadly produced. We discuss the implication of the shuttling mechanism for the ability of embryos to adjust their pattern with size. Finally, we consider the transformation of the smooth gradient profile into sharp borders of gene expression in the signal-receiving cells.     

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.     

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.