Robustness of Embryonic Spatial Patterning in Drosophila melanogaster

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Publisher Summary

Mathematical models of embryonic development can provide insights into the complex interactions between spatial variations in morphogens, signal transduction, and intracellular response in patterning processes. Mechanistic models of specific processes based on our current understanding of them provide an additional tool to help in understanding the complex regulation of development. The chapter discusses a number of different aspects of robustness in Drosophila embryonic patterning, and have shown how the models lead to new insights concerning scale-invariance in AP patterning, the role of network topology and signature in the switching network used for control of the segment polarity genes, and the role of signaling via heterodimers in dorsal–ventral (DV) patterning. The modular decomposition of DV patterning described in the chapter is based on the current understanding of the kinetic interactions between morphogens and inhibitors in the perivitelline (PV) space, and incorporates the various dimeric forms of inhibitors and signaling the bone morphogenetic proteins (BMPs). Scale-invariance is a basic feature of a number of developmental processes. A rather surprising result is that the robustness of DV spatial patterning can essentially be predicted from an analysis of the local dynamics. The analysis of the spatially distributed system corroborates the earlier results and provides further evidence for the selective advantage of using heterodimers for signal transduction and morphogenesis.

Introduction

Much is known about the molecular components involved in signal transduction and gene expression in a number of model systems in developmental biology, and the focus is now shifting to understanding how these components are integrated into networks, and how these networks transduce the inputs they receive and produce the desired pattern of gene expression. The major question is how the correct genes are turned on at the correct point in space at the correct time in development to produce the numerous cell types present in an adult. Gene expression during embryonic development is not a cell-autonomous process, because cell fate in a multicellular embryo usually depends on the cell's location in the embryo. A spatially-graded distribution of factors that influence development can be used to induce spatially-varying differentiation, and this idea played a central role throughout the early history of theoretical work in the field and was later developed into the theory of positional information by Wolpert (1969). Formally the theory posits that a cell must ‘know’ its position relative to other cells in order to adopt the correct developmental pathway, but of course what a cell ‘knows’ is determined by the information it extracts from the past and current signals received. Pattern formation in development refers to the spatially- and temporally-organized expression of genes in a multicellular array, and positional information is viewed as a necessary part of this process. Frequently pattern formation results from the response of individual cells to a spatial pattern of chemicals called morphogens, a term coined by the British logician Alan Turing in a fundamental paper on pattern formation (Turing, 1952) (cf. Fig. 1). Currently morphogens are defined as secreted signaling molecules that (i) are produced in a restricted portion of a tissue, (ii) are transported by diffusion, active transport, relay mechanisms, or other means to the remainder of the tissue, (iii) are detected by specific receptors or bind to specific sites on DNA, and (iv) initiate an intracellular signal transduction cascade that initiates or terminates the expression of target genes in a concentration-dependent manner. Perhaps the earliest example of a morphogen was the Bicoid protein that is involved in anterior–posterior (AP) patterning in Drosophila (Frohnhöfer and Nüsslein-Volhard, 1986), but many more examples are now known, including Activin, Hedgehog, Wingless, and various members of the transforming growth factor family. Theoretical studies of how different modes of transport and transduction affect patterning are reported in Kerszberg and Wolpert (1998); Kerszberg (1999); Lander et al. (2002); Strigini (2005); Umulis et al. (2006) and many others.

Thus the problem of pattern formation in a given system becomes that of discovering the mechanisms of localized production and transport that generate positional information. The classic paradigm for this is the model shown in Fig. 1A, wherein a source at one boundary of a one-dimensional domain produces the morphogen, which diffuses throughout the domain and initiates gene transcription and cell differentiation in a threshold-dependent manner. This is a static viewpoint, in that cells simply sense the local concentration and respond to it, and neither the transient dynamics of the signal nor the history of exposure to it play any role in patterning. As we show in Sections II Robustness in the Developmental Context, III Scaling of AP Patterning in, patterning by this mechanism is sensitive to changes in length unless some special mechanisms are used to compensate for such changes, and we show in Section V that the history of exposure is important in some contexts.

In many developing systems the outcome is buffered to numerous perturbations, ranging from major ones such as separation of the cells at the 2-cell stage in Xenopus (which can lead to one smaller, but normal adult, and an amorphous mass of tissue), to less severe ones such as changes in the ambient temperature or the loss of one copy of a gene. Indeed, many loss-of function mutations of important developmental genes in higher organisms show weak or no phenotypic effects, as will be discussed later in the context of Drosophila. There are many other instances in which the developmental outcome is buffered to changes in environmental variables that affect reaction rates, transport rates, and other factors that control the morphogen distribution, and the general question is how systems are buffered against variations in such factors. Said otherwise, how robust are developmental processes, and what does robustness even mean in this context? Other mathematical questions regarding morphogen patterning that arise are illustrated in Fig. 1. For instance, how do different organisms within a species preserve proportion even though they vary substantially in body size? How do cells respond to a ‘noisy’ morphogen signal caused by low levels of the morphogen, as in some of the patterning events discussed later? How do cells respond to a morphogen that is evolving in time during the course of development? Mathematical models and analysis can shed light on these issues and suggest mechanisms for mitigating the deleterious effects of some of these factors.

In the following section we discuss robustness in the developmental context in a general framework, and thereafter we discuss specific examples in the context of anterior–posterior patterning (Section III), parasegment patterning (Section IV), and of dorsal–ventral patterning (Section V), all in Drosophila.

Drosophila melanogaster, which is the common fruit fly, has served as a model system to study many aspects of development for the past 100 years. Drosophila has a short life cycle, it is easily grown, the genome is sequenced, and many of the components of the signal transduction and gene control networks involved in patterning are known. However, less is known about how these networks produce the desired spatiotemporal pattern of gene expression. Development is a sequential process in which later stages build on earlier stages, but within stages there are often multiple feedback loops in signaling and gene control networks that may serve to buffer against perturbations caused by fluctuations in morphogen concentration and other components. Understanding the structural features in a network that ensure reliable patterning in the face of various perturbations is a major unresolved problem.

The Drosophila oocyte, or egg, is an approximately prolate ellipsoid that forms from a germline cell in the ovary (cf. Fig. 2). The egg is surrounded by a thin fluid-filled shell, the perivitelline (PV) space, that is bounded on the outside by the vitelline membrane. A coordinate system in the egg is first established by gradients of maternally-inherited cytoplasmic factors in the AP direction and by gradients of factors in the PV space in the dorsal–ventral (DV) direction. About fifty maternal genes set up the AP and DV axes, which provide the early positional information in the zygote. Zygotic gene expression is initiated by transcription factors produced from maternal RNA. Spatial patterning proceeds in stages: first the AP and DV axes are set up, then the whole domains are divided into broad regions, and finally smaller domains are established in which a unique set of zygotic genes is transcribed. The successive stages of patterning are initiated by a strictly-controlled hierarchy of gene expression in both the AP and DV directions. The former is shown in Fig. 3, which shows some of the interactions within and between levels. Both AP and DV patterning will be discussed in detail later, but first we discuss robustness in general terms.

Section snippets

Robustness in the Developmental Context

We define robustness as follows: a component, system or process is robust with respect to a given class of perturbations if its output or response is unchanged to within some tolerance by these perturbations, i.e., if the system is unlikely to ‘fail’ in the face of these perturbations. The perturbations can be in the inputs to the component, system or process, or they can be perturbations or alterations in the internal structure of the component or system. Explicit in this definition is that

Anterior–Posterior Patterning

Here and in later sections we describe only the primary genes and the effects of their products; a more complete description of the patterning process can be found in Gilbert (2006). When referring to genes and their products we italicize the former and capitalize the latter.

Three groups of maternal gene products, anterior, posterior and terminal, are involved in the first stage of AP patterning, in which anterior is distinguished from posterior. Four messenger RNAs (bicoid, hunchback, nanos,

Models of the Segment Polarity Network

As described earlier, the genes involved in spatial patterning are expressed in a temporal sequence that leads to successively more refined spatial patterns of expression. The gap and pair-rule genes are only expressed transiently, but the segment polarity genes, which pattern the parasegments, are expressed throughout the life of the fly. A parasegment comprises four cells, and the gene expression pattern is repeated in each of the fourteen parasegments. The network of gene and protein

Dorsal–Ventral Patterning in Drosophila

Establishment of a coordinate frame for DV patterning in the oocyte begins when the nucleus migrates from a central posterior position to a dorsal, anterior position. The nucleus expresses gurken, which establishes a cortical region of high gurken mRNA and protein levels. Gurken is a secreted growth factor that binds to receptors on the follicle cells surrounding the egg and results in a DV gradient of EGF receptor (Egfr) activation and up- or downregulation of target genes in the EGF pathway (

Conclusions

Mathematical models of embryonic development can provide insights into the complex interactions between spatial variations in morphogens, signal transduction, and intracellular response in patterning processes. Mechanistic models of specific processes based on our current understanding of them provide an additional tool to help in understanding the complex regulation of development. In addition to the fundamental biological questions concerning the structure of components and pathways,

Note added in proof

Since acceptance of this paper, two papers have appeared that deal with the issues discussed herein (Gregor, Gregor). Gregor et al. developed a Bicoid–GFP fusion protein to study the dynamics, reproducibility, and other aspects of morphogen patterning in the Drosophila syncytium, and they discuss theoretical approaches to the reliability of threshold determination.

Acknowledgements

This research was funded in part by NIH Grant GM29123 and NSF Grants DMS-0317372 and DMS-0517884 to HGO, and by a Biotechnology Training Grant (DMU). MBO is an Investigator with the Howard Hughes Medical Institute.

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