PATTERNING BY EGF RECEPTOR: MODELS FROM DROSOPHILA DEVELOPMENT

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1 PATTERNING BY EGF RECEPTOR: MODELS FROM DROSOPHILA DEVELOPMENT Lea A. Goentoro and Stanislav Y. Shvartsman Department of Chemical Engineering and Lewis-Sigler Institute for Integrative Genomics, Princeton University Corresponding Author: Stanislav Y. Shvartsman Department of Chemical Engineering and Lewis-Sigler Institute for Integrative Genomics, Princeton University Tel: ; Fax: Princeton, NJ 08544, 1

2 1. INTRODUCTION The epidermal growth factor receptor (EGFR) is an evolutionary conserved regulator of epithelial tissues. The first identified receptor tyrosine kinase and a founding member of the ErbB receptor family, EGFR has been implicated in countless physiological and pathological contexts [3, 4]. Most commonly, EGFR is activated by extracellular ligands. Ligand binding induces dimerization of the receptor and activates the kinase in its cytoplasmic domain. By recruiting and phosphorylating the cytoplasmic targets, the activated receptor couples to signal transduction pathways and controls cellular responses. While experiments in cell culture keep providing invaluable insights into the structure and function of the EGFR network, more complex experimental systems are required to study EGFR signaling in tissues. Co-culture models and cultured tissues can be used to probe EGFR signaling in multicellular systems [5, 6]. Finally, analysis of the organism-level effects of EGFR signaling requires studies in vivo. EGFR activation in vivo is mediated by autocrine and paracrine signals. Secreted ligands usually bind to receptors on the ligand-producing cells or their neighbors. Receptor activation depends on the rates of ligand release, receptors levels, and tissue architecture. Typically, ligand/receptor levels and activation of downstream pathways are assessed using in situ hybridization or immunohistochemistry. Since these techniques are nontrivial to quantitate, even the simplest parameters of autocrine and paracrine networks, such as ligand concentrations, cannot be measured directly. In contrast, in the studies conducted in vitro, one can both control the exogenous ligand concentration and measure receptor levels using a number of quantitative assays. In theory, modeling and computations can bridge the apparent gap between the in vitro and in vivo studies of EGFR biology [7]. Again in theory, the biochemical parameters measured in vitro can provide inputs to the tissue-level models. These models can estimate the parameters that are either impossible or difficult to measure directly. For example, the information about receptor dynamics generated in cell culture can be combined with the microscopically derived information about the tissue architecture in order to compute the spatial distribution of autocrine and paracrine signals [8]. In this way, cellular and biochemical studies can drive the development of mechanistic models of cell communication in tissues. The experimental validation of tissue-level models requires a flexible experimental system. The great experimental advantages of Drosophila genetics make fruit fly an excellent testing ground for the validation of models of EGFR signaling in tissues [9]. In this chapter, we describe two examples of EGFR-mediated patterning in fruit fly development and our initial steps towards the mechanistic modeling of this system. Our emphasis is on the spatial range of autocrine and paracrine signals and the dynamics of feedback loops in the Drosophila EGFR (DER) network. The high evolutionary conservation makes the DER network an excellent model for the more complex mammalian EGFR systems [10]. 2

3 2. TWO EXAMPLES FROM EGFR SIGNALING IN FRUIT FLY DEVELOPMENT EGFR is recurrently used in fruit fly development, see [9] for a recent review. The pleiotropic nature of EGFR signaling was realized when mutations affecting different stages of development were mapped to the same location, the Egfr gene. 1 Subsequently, its ligands, all secreted molecules, were identified: Gurken, Spitz, and Keren are homologs of the human Transforming Growth Factor alpha; Vein is a neuregulin homolog, and Argos is an inhibitory ligand with no homologs in higher organisms. Gurken, Spitz, and Keren are expressed as inactive, transmembrane precursors and activated through a proteolytic cleavage; Argos and Vein are expressed in their active, secreted forms. We review two well-studied examples of EGFR-mediated tissue patterning in egg and embryo development. In patterning of the ventral ectoderm, a secreted inhibitor refines the initial gradient of receptor signaling created by a localized secretion of an activator. The activator is Spitz and the inhibitor is Argos. Together they define a spatially distributed network controlling the EGFR activation. In egg development, the initial domain of receptor activity is first expanded by a secreted activator and then split by a secreted inhibitor. Gurken induces the initial pattern; the secreted activator and inhibitor are again Spitz and Argos. These examples illustrate the patterning versatility of autocrine and paracrine EGFR networks EGFR signaling in embryogenesis: ventral ectodermal patterning A fly embryo halfway through embryogenesis are shown in Figure 1A,B. Three layers of cells are present: the ectoderm, which will form the larval epidermis; the neuroblasts, which will give rise to the nervous system; and the mesoderm, which will develop into muscle and connective tissues. The midline cells, which divide the ectoderm along the dorsoventral axis, are distinct from their neighbouring cells. These cells will later delaminate from the ectoderm and give rise to specific neurons and midline glial cells. EGFR induces two different fates in the ventral ectoderm. The ventralmost and ventrolateral fates are identifiable by the expression of different marker genes, Figure 1C. The following paragraph describes the currently accepted mechanism proposed by Golembo et al. in order to explain the EGFR-mediated fate induction, Figure 2 [11]. The patterning process starts when the sim gene, expressed exclusively in the midline, induces the expression of rhomboid in the midline cells. As a result, the midline acts as a localized source of secreted Spitz that establishes a gradient of EGFR activation in the neighbouring ectodermal cells [12]. Following that, the cells nearest to the midline, and hence the ones exposed to the highest level of Spitz, start secreting Argos [13]. This establishes a negative feedback that is thought to refine the initial gradient of Spitz and regulate the number of cells adopting each of the ventral fates. As a result of the interplay between Spitz and Argos, five rows of cells on each side of the midline adopt the ventral 1 The names of genes are conventionally italicized, i.e., gene, while the names of proteins are written with the first letters capitalized, i.e., Protein. 3

4 fate. The two rows nearest to the midline receive a high level of EGFR activation and adopt the ventral-most fate. The next three rows of cells receive a moderate level of EGFR activation and adopt the ventrolateral fates. In summary, the initial gradient of EGFR activity induced by a localized secretion of an activator is refined by the activity of a secreted inhibitor, creating two distinct fates. The network formed by the EGFR, Argos, and Spitz is robust: variations in the dose of secreted Spitz do not change the pattern of genes specifying the fates in the ventral ectoderm [11, 13]. 2.2 EGFR signaling in oogenesis: eggshell patterning A fly egg is composed of three types of cells: the oocyte with its large nucleus; the nurse cells, which supply nutrients to the oocyte; and the follicle cells, which form an epithelium enveloping the oocyte and the nurse cells, Figure 3A. Patterning of the follicle cells is highly regulated in space and time [14]. The net result of this patterning is the subdivision of the layer of the initially equivalent follicle cells into distinct subpopulations. Each subpopulation of follicle cells gives rise to a specialized structure (or a part of it) of the eggshell, Figure 3B, [15]. This section focuses on the pair of respiratory appendages extending from the dorsal-anterior side of the egg, whose positioning along the dorsoventral axis requires EGFR signaling [16]. Gurken is localized around the nucleus throughout the egg development [16]. The relevant patterning process starts during mid-oogenesis, at a time when the oocyte nucleus has just migrated from its previous posterior position to a random point along the anterior circumference. Gurken released from the oocyte induces high level of EGFR signaling in the follicle cells nearest to the nucleus. A dorsal-anterior domain in the follicular epithelium is defined by the overlap between the gradients of the oocytederived Gurken and the transverse gradient of the TGFβ like ligand, Figure 4A [17]. Over time, this domain is subdivided into distinct groups of cells. The dorsal midline cells contribute to the production of operculum 2 ; the dorsolateral cells specify the position of the dorsal appendages; and the dorsal appendage anlagen, Figure 4B. The following mechanism was proposed by Wasserman and Freeman in order to explain how these subsequent refinements in the dorsal cells occur, Figure 5 [18]. Expression of rhomboid is induced by both EGFR and TGFβ signaling in the dorsalanterior domain, leading to a localized secretion of Spitz from that region. This positive feedback amplifies the initial EGFR activity. As a result the dorsal cells with the highest EGFR activity start secreting Argos. The negative feedback splits the initial single domain of high EGFR activity into two and at the same time restricts further expansion of signaling activation into the lateral side. As a consequence, the domain of high EGFR activity is gradually reduced into two L-shaped stripes positioned symmetrically around the midline, Figure 4B. The cells in which the EGFR activity is initially very high and then abruptly extinguished by Argos adopt the dorsal midline fate; the cells in which the EGFR activity is maintained high adopt the dorsolateral fate; the cells in which the EGFR activity is moderate and then quenched by Argos become the dorsal appendage anlagen. 2 An oval-shaped region of the eggshell from which the larva hatches 4

5 To summarize, the initial gradient of EGFR activity induced by a localized input (Gurken) is first amplified by a positive feedback (Spitz) and afterward refined by a negative feedback (Argos), thereby creating three distinct fates. In the ovary, Argos inhibits EGFR signaling in the Argos-producing cells and their neighbors. In the embryo, on the other hand, the Argos-producing cells appear to be refractory to its inhibitory action. The origins of this difference in Argos inhibition are not understood at this time. Another difference between the two systems is the absence of the positive feedback in the ventral ectoderm. 3 The ventral ectodermal patterning has been shown to be highly robust. Halving or doubling the level of input from the midline does not alter the pattern [11]. In contrast, varying the level of input from the oocyte generates diverse eggshell morphology phenotypes [16]. In particular, defects in the positive feedback lead to eggshells with fused dorsal appendages [18]. Hence, it appears that the positive feedback is necessary to transform a simple inductive signal (Gurken) into a more complex spatial pattern. 3. MODELING AND COMPUTATIONAL ANALYSIS OF AUTOCRINE AND PARACRINE NETWORKS Here we describe our initial steps towards the mechanistic models of autocrine and paracrine EGFR signaling in epithelial layers. In each case we briefly describe the model and illustrate the representative questions that the model can help to address. The details of the derivations and computational analysis can be found elsewhere [7, 19-24] Models of ligand transport and binding Both of the described mechanisms rely on the quantitative differences between the spatial ranges of Spitz and Argos. In multiple stages of fruit fly development, Spitz was identified as a short-range signal, acting over 3-4 cell diameters [25-27]. Argos, on the other hand, emerged as a long-range inhibitor that can act 8-10 cell lengths from the point of its secretion [13, 27]. In both cases, the spatial ranges of Argos and Spitz were derived from observing their effects on the expression of EGFR-target genes. At this time, the mechanisms governing the differences in the apparent ranges of action are not understood. Since both ligands are secreted, their spatial range can be tuned by the rates of extracellular ligand transport and ligand-receptor interaction. Given a large and rapidly growing amount of information about each of these processes in the EGFR system, it is reasonable to ask, if the experimentally derived estimates of ligand range can be interpreted in terms of the elementary processes, such as binding and receptor-mediated endocytosis. The ability to predict and manipulate the spatial ranges of secreted growth factors can be used to develop computational models of patterning networks and to design new experiments for the evaluation of proposed mechanisms. Below, we use the simplified geometry of cell-cell communication to illustrate the mechanistic models of ligand transport, Figure 6A. 3 Vein has been shown to form a positive feedback loop during the patterning of ventral ectoderm [9]. However, its contribution is redundant and is only important when the level of Spitz is reduced. 5

6 In the model, the ligand diffuses between the receptor-covered and reflecting surfaces. This geometry approximates the one in egg development where EGFR ligands diffuse in the thin gap between the oocyte and follicular epithelium. The motion of secreted ligand is modeled by free diffusion with the effective diffusivity D. Diffusion coefficient can vary in the range set by low values of growth factor diffusion in extracellular matrices 10 2 ( 10 cm / s ) and typical values for protein diffusion in an aqueous solution 6 2 ( 10 cm / s ) [28, 29]. We assume that the number receptor per cell, R tot, is constant. Ligand-receptor interactions are characterized by kinetic rate constants k on and k off ; the endocytosis of receptor-bound ligands is modeled as a first-order process with rate constant k e ; we assume that internalized ligand is not recycled. In the absence of measurements of ligand-receptor interactions in Drosophila EGFR system, the rate constants are approximated by their counterparts measured in mammalian systems [30]. Below, we show how this model can be used to quantify the distances traveled by secreted ligand Analysis of the distance traveled by ligands between the subsequent binding events requires solving the problem of ligand transport in the gap above the receptor-covered plane. The statistical properties of the times and distances to the first binding event depend on the forward binding rate constant, k on, the number of cell surface density of receptors, R cell (moles/area), the extracellular ligand diffusivity, D, and the height of the extracellular medium, h. For the relevant ranges of these parameters, the distribution of times to capture is given by the exponentially distributed random variable: The konrcell t e h probability that a ligand is bound for the first time after time t is given by. This expression leads to the probability density function for the lateral distances traveled until the first binding event: The probability that a ligand is bound in the ring between radii r and r+ dris given by g() r dr = ( konrcell / Dh) K0( r konrcell Dh) rdr, where K0 is the modified Bessel function [31], Figure 6C. We see that for the reasonable ranges for receptor densities and binding rate constants, a majority of secreted ligands is bound for the first time after traveling a very short distance. As an immediate consequence, the ligand-producing cell can recapture a significant fraction of secreted ligand, Figure 6D. Once secreted, the ligand will undergo several cycles of binding and extracellular diffusion before it is removed from the extracellular medium by receptor-mediated endocytosis, Figure 6B. The rate constants for the dissociation and endocytosis of ligandreceptor complexes, k off and k e, determine the number of binding events until the first endocytosis event. In the simplest model, the number of binding events is a geometrically distributed random variable, with the mean equal to 1 + koff / ke [22]. Based on the 1 numbers for human EGFR/TGFα pair ( k off k e 0.1min ) [32], the ligand will be internalized after ~ 2 binding events. Thus, inhibition of receptor-mediated endocytosis can extend the range of secreted ligands. In vivo, this can be realized in mutants with defects in the genes mediating receptor-mediated endocytosis [33, 34]. (In other systems, 6

7 where ligand is efficiently recycled to the cell surface, the opposite can be true. In fact, endocytosis might actually be the main mechanism for the spatial propagation of secreted signals [35]). According to this simple model, reducing the rate of receptor-mediated endocytosis can extend the spatial range of secreted ligands. This might explain the long-range inhibitory action of Argos. Argos inhibits receptor phosphorylation [36]. Since receptor phosphorylation is required for ligand-induced receptor endocytosis [37, 38], this suggests that Argos will be internalized at a lower rate when compared to Spitz that readily induces receptor phosphorylation. An experimental test of this mechanism requires the measurement of internalization rate constants of Argos and Spitz Positive feedback by Rhomboid and Spitz The Rhomboid/Spitz module amplifies the oocyte-derived Gurken signal in eggshell patterning [18, 39, 40]. In the emerging picture, EGFR-activated the Ras/MAPK pathway relieves the transcriptional repression of rhomboid [41, 42]. Rhomboid then stimulates the secretion of Spitz that binds to EGFR on the ligand-producing cells and their neighbors [26], Figure 7A. This information about signaling in a single cell can be combined with the transport model from the previous section to analyze the operation of the Rhomboid/Spitz feedback in a multicellular system such as an epithelial layer. The resulting description is useful in analyzing the effects of exogenous signals presented to the epithelial layer. For example, in the case of oogenesis, it is important to characterize the domain affected by Gurken and Gurken-induced EGFR ligands [18, 39, 40]. To understand the operation of the Rhomboid/Spitz circuit we started to develop models of autocrine signaling in epithelial layers [19]. In addition to ligand transport, binding, and internalization, these models account for Rhomboid induction and Rhomboidmediated Spitz release. Rhomboid induction was modeled as a threshold-like function of the total number of ligand-receptors in the cell. The balance for the level of Rhomboid in the cell ( i, j), P i, j, takes the following form: dpi, j Pi, j tot = + σ ( C C ) i, j T dt τ tot where C is the total number of occupied EGF receptors in the cell ( i, j ), C i, j T is the threshold-value for Rhomboid induction. The time-scale for rhomboid degradation, τ ~20 minutes, can be estimated from the experiments in the embryo [43]. Receptor occupancy on any given cell within the epithelial layer depends on the pattern of ligand release, and hence the pattern of Rhomboid expression in the entire layer. Our analysis suggests that ligand binding and transport rapidly adjust to the much slower dynamics of Rhomboid expression [19]. In other words, the equations for ligand binding and transport reach the steady state dictated by the pattern of Rhomboid across the epithelial layer. In the ligand-limited regime, receptor occupancy for a given cell is computed from the linear superposition of ligand fields due to individual cells, Figure 7B. 7

8 As a result, the dynamics of cells coupled by secreted signals can be described entirely in terms of the intracellular variables: dpi, j Pi, j = + σ ( I i m, j n Pm, n CT ) dt τ m, n where I i m, j n are the cell-cell coupling coefficients that quantify the strength and the spatial range of autocrine and paracrine signals. Importantly, these coefficients were derived as a function of the biophysical parameters of the problem, such as the diffusion and transport rates, as well as the rates and the levels of ligand release by single cells within the layer. We found that the coupling coefficients decay rapidly as a function of cell-cell distance. This suggests that only a small number of cell-cell interactions must be taken into account in calculating receptor occupancy on any given cell, a fact that is very useful in solving the problem numerically [19]. This biophysical framework can be used to predict the possible effects of localized perturbations of epithelial layers. For example, Peri et al have constitutively activated Rhomboid in a small group of cells within the follicular epithelium in order to elucidate the spatial range of secreted Spitz [44]. The effect of this perturbation was localized to a small its neighborhood: the EGFR-target genes were affected a few cell diameters from the cluster with the constitutively active ligand release. What is the outcome of such perturbations in general? Under what conditions will they remain localized or, alternatively, generate a propagating wave where secreted Spitz will be inducing Rhomboid expression and further Spitz release from the neighboring cells? This question can be easily addressed with the described model. For example, Figure 7C shows how the transition between the stationary and propagating patterns is affected by the size of the perturbation and the rate of ligand release. Clearly, high rates of ligand release and large size of the perturbation promote the generation of traveling waves. Because of its potential for a runaway behavior, this positive feedback is tightly regulated. Genetic studies in the ovary indicate that the domain that can be affected by this feedback loop is restricted in space, presumably to prevent the propagation of the traveling waves [17]. In the ventral ectoderm patterning, this autocrine feedback seems to be altogether removed [13] Pattern formation by interacting feedback loops Dorsal appendage morphogenesis provides a genetically tractable system for studying the mechanisms by which simple inductive cues are converted into more elaborate spatial patterns [18]. The components of the mechanism proposed by Wasserman and Freeman are well established [16]. But, is the proposed mechanism actually correct? Specifically, does it account for the phenotypes that are induced by various genetic manipulations of the DER network and can it make testable predictions? These questions led us to develop our initial phenomenological model of EGFR-mediated patterning in Drosophila oogenesis [20, 24]. The model accounts for the interaction of the spatially nonuniform input by Gurken and the feedback loops by Spitz and Argos, Figure 8A. We formulated the model in one spatial dimension and assumed that the characteristic size of the pattern greatly exceeds the size of a single cell. This led to a system of nonlinear reactiondiffusion equations that was analyzed by simulations and numerical bifurcation analysis. 8

9 Our main goal is to test whether the mechanism can account for the various eggshell morphology phenotypes. We are particularly interested in the phenotypes generated by the manipulations in the dose and the spatial distribution of the oocyte-derived signal [16]. It is known that systematic decrease in the level of Gurken signal can generate eggshells with one or zero dorsal appendages. At the same time, increase in the dose leads to eggs with widely spaced appendages or one broad dorsal appendage. These observations provide important constraints on the modeling. Analysis of the phenomenological model shows that the peak-splitting mechanism can be realized in one spatial dimension, Figure 8B. This means that a single-peaked input in the model, mimicking the oocyte-derived Gurken, can generate a stable pattern with two large-amplitude peaks in the spatial distribution of Rhomboid. The two-peaked pattern emerges as a result of the instability of the one-peaked solution that is realized at lower inputs. At a critical input level, this single-peaked solution splits, giving rise to the blueprint for the formation of two dorsal appendages. Thus, patterning leading to the formation of dorsal appendages can be viewed as a transition between the two kinds of solutions in the model (i.e. one- and two-peaked). The variations in the level and the spatial distribution of Gurken input can induce transitions between different classes of patterns that are characterized by the different number of large-amplitude peaks in the spatial distribution of Rhomboid. We correlate these patterns with the dorsal appendage phenotypes in mutants with either lower Gurken doses or with defects in DER signal transduction, Figure 8B [16]. Predicted transitions between the zero-, one-, and two-peaked patterns in the model correspond to the experimentally observed transitions between eggshells with zero, one, and two dorsal appendages [20, 24]. Finally, stable patterns with three or four peaks emerge in the model when the two-peaked pattern is destabilized by the same mechanisms that generate the two-peaked pattern itself [20]. Since the number of peaks in the pattern corresponds to the number of dorsal appendages, this finding provides the mechanistic basis for explaining complex morphologies in mutants of Drosophila melanogaster [45, 46]. In addition, this versatility in patterning may account for more complex eggshell morphologies in related fly species [47, 48]. We are currently extending our models to account for the effects of discrete cells and a second spatial dimension. In addition, we are constructing a database of gene expression images of the main components in the patterning network and use it to calibrate our computational models. The eventual success of the future models critically depends on the more detailed understanding of the biochemical mechanism of inhibition by Argos. 9

10 4. CONCLUSIONS AND OUTLOOK At this time, a few dozens out of ~30000 EGFR-related PubMed entries are dedicated to the modeling and computational analysis of EGFR signaling. Most of the existing models are formulated at the molecular and cellular level [7]. However, to understand how this system operates in vivo we need modeling at the level of tissues. Even the simplest models of EGFR signaling in multicellular systems must simultaneously account for ligand release, transport, binding, intracellular signaling, and gene expression. Given this complexity, the integrated models are nontrivial to test experimentally. We believe that a combined modeling-experimental approach is possible in Drosophila, where a number of genetic tools are available for implementing the model-directed manipulations in vivo. We have described two systems from Drosophila development where modeling seems both feasible and necessary [11, 18]. In both cases, a large amount of data was summarized in the form of a complex patterning mechanism. The feasibility of these mechanisms depends on the quantitative parameters, such as the spatial ranges of secreted signals and the strengths of the feedback loops. Modeling can be used to elucidate the quantitative constraints on the proposed patterning mechanisms and to dissect the relative contributions of multiple cellular processes. We are just beginning to develop and test mechanistic models of EGFR signaling in tissues. Currently, we rely on the large amount of biochemical and cellular experiments in mammalian systems. In the future, direct biophysical characterization of Drosophila EGFR network will be required in order to develop truly mechanistic models of EGFR signaling in fruit fly development. We hope that in addition to being applicable to the mechanisms in Drosophila development, our models will be useful for the quantitative description of EGFR signaling in higher organisms. Indeed, the molecular components and the feedback loops in EGFR signaling are conserved across species. For example, the positive feedback, similar to the one in the Rhomboid/Spitz system, was identified in radiation responses of human autocrine carcinoma cells [23]. There, a pulse of ionizing radiation induces a primary wave of EGFR activation that was then amplified by the positive feedback that is based on the MAPK-mediated TGFα release and recapture by the cell. Central to this feedback is the activation of the ligand-releasing protease (TACE) that serves as the rate limiting component that controls ligand availability and, hence, receptor activation. Negative feedback loop by Argos does not have a direct counterpart in mammalian EGFR systems. The closest mode of regulation, discovered by N. Maihle and colleagues, relies on secreted form of EGFR. Secreted receptors compete with the ones on the cell surface for the extracellular ligands, and in this way control the level of cellular EGFR activation. This mode of regulation has been described for both the ErbB1 and ErbB3 receptors, indicating that it is a general mechanism in the ErbB receptor family [49]. Several lines of evidence support the physiological significance of this negative mode of control. For example, the levels of secreted receptors can be used as diagnostic markers in ovarian epithelial cancer [50]. In the future, it will be important to compare the functional capabilities of EGFR inhibition by secreted receptors and secreted receptor inhibitors, such as Argos. 10

11 Acknowledgements: The authors are indebted to Trudi Schupbach and Lazaros Batsilas for their critical reading of the manuscript. SYS thanks Sasha Berezhkovskii, Doug Lauffenburger, Mark Lemmon, Cyrill Muratov, Michal Pribyl, and Steve Wiley for numerous helpful discussions. This work was supported by the grants from the NSF and the Searle Foundation References 1. Schweitzer, R. and B.Z. Shilo, A thousand and one roles for the Drosophila EGF receptor. Trends Genet, : p Queenan, A.M., A. Ghabrial, and T. Schupbach, Ectopic activation of torpedo/egfr, a Drosophila receptor tyrosine kinase, dorsalizes both the eggshell and the embryo. Development, : p Jorissen, R.N., et al., Epidermal growth factor receptor: mechanisms of activation and signalling. Exp Cell Res, : p Yarden, Y. and M.X. Sliwkowski, Untangling the ErbB signalling network. Nat Rev Mol Cell Biol., : p Pierce, K.L., et al., Epidermal growth factor (EGF) receptor-dependent ERK activation by G protein-coupled receptors: a co-culture system for identifying intermediates upstream and downstream of heparin-binding EGF shedding. J Biol Chem, : p Vermeer, P.D., et al., Segregation of receptor and ligand regulates activation of epithelial growth factor receptor. Nature, : p Wiley, H.S., S.Y. Shvartsman, and D.A. Lauffenburger, Computational modeling of the EGF receptor system: a paradigm for systems biology. Trends Cell Biol, Lander, A.D., W. Nie, and F.Y. Wan, Do morphogen gradients arise by diffusion? Dev Cell, : p Shilo, B.Z., Signaling by the Drosophila epidermal growth factor receptor pathway during development. Exp Cell Res, : p Casci, T. and M. Freeman, Control of EGF receptor signalling: Lessons from fruitflies. Cancer Metastasis Rev, : p Golembo, M., et al., Vein expression is induced by the EGF receptor pathway to provide a positive feedback loop in patterning the Drosophila embryonic ventral ectoderm. Genes Dev, : p Golembo, M., E. Raz, and B.Z. Shilo, The Drosophila embryonic midline is the site of Spitz processing, and induces activation of the EGF receptor in the ventral ectoderm. Development, : p Golembo, M., et al., argos transcription is induced by the Drosophila EGF receptor pathway to form an inhibitory feedback loop. Development, : p Dobens, L.L. and L.A. Raftery, Integration of epithelial patterning and morphogenesis in Drosophila oogenesis. Dev Dyn, : p Spradling, A.C., Developmental Genetics of oogenesis, in The development of Drosophila Melanogaster. 1993, Cold Spring Harbor Laboratory Press: Plainview. p

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13 36. Jin, M.H., et al., The interaction between the Drosophila secreted protein argos and the epidermal growth factor receptor inhibits dimerization of the receptor and binding of secreted protein spitz. Mol Biol Cell, : p Lamaze, C. and S.L. Schmid, Recruitment of epidermal growth factor receptors into coated pits requires their activated tyrosine kinase. J Cell Biol, : p Sorkina, T., et al., Effect of tyrosine kinase inhibitors on clathrin-coated pit recruitment and internalization of epidermal growth factor receptor. J Biol Chem, : p Peri, F., C. Bokel, and S. Roth, Local Gurken signaling and dynamic MAPK activation during Drosophila oogenesis. Mech Dev, : p Sapir, A., R. Schweitzer, and B.Z. Shilo, Sequential activation of the EGF receptor pathway during Drosophila oogenesis establishes the dorsoventral axis. Development, : p Hsu, T., et al., Drosophila Pin1 prolyl isomerase Dodo is a MAP kinase signal responder during oogenesis. Nat Cell Biol, : p Mantrova, E. and T. Hsu, Down-regulation of transcription factor CF2 by Drosophila Ras/MAP kinase signaling in oogenesis: cytoplasmic retention and degradation. Genes Dev, : p Sturtevant, M.A., et al., The Drosophila rhomboid protein is concentrated in patches at the apical cell surface. Dev Biol, : p Peri, F., M. Technau, and S. Roth, Mechanisms of Gurken-dependent pipe regulation and the robustness of dorsoventral patterning in Drosophila. Development, : p Reich, A., A. Sapir, and B.Z. Shilo, Sprouty, a general inhibitor of receptor tyrosine kinase signaling. Development, : p Deng, W.M. and M. Bownes, Two signalling pathways specify localised expression of the Broad-Complex in Drosophila eggshell patterning and morphogenesis. Development, : p Perrimon, N. and J.B. Duffy, Developmental biology. Sending all the right signals. Nature, : p Hinton, H.E., Biology of Insect Eggs. Vol , Oxford; New York: Pergamon Press. 49. Lee, H., et al., A naturally occurring secreted human ErbB3 receptor isoform inhibits heregulin-stimulated activation of ErbB2, ErbB3, and ErbB4. Cancer Res, : p Baron, A.T., et al., Soluble Epidermal Growth Factor Receptor(sEGFR/sErbB1) as a Potential Risk, Screening, and Diagnostic Serum Biomarker of Epithelial Ovarian Cancer. Cancer Epidemiol Biomarkers Prev, : p

14 (A) D (B) D A P V V (C) Ectodermal cell fascicliniii Midline cell orthodenticle argos Neuroblast Mesodermal cell Figure 1. (A) A mid-stage fly embryo (D=dorsal, V=ventral, A=anterior, P=posterior) (B) Cross section of the embryo at the indicated plane in Fig.A. (C) The ventral ectodermal cells are patterned by Egfr into two subgroups. The ventral-most cells (red) express all the genes listed, whereas the ventrolateral cells (yellow) express the fascicliniii gene only [1]. 14

15 0 min 30 min 70 min Spitz Spitz Argos Spitz Figure 2. Ventral ectodermal patterning. In the graphs, the y-axis is the Egfr activity and the x-axis is the distance away from the midline. All cells are initially uniform. Patterning is initiated by the secretion of Spitz from the midline cells (blue). This creates a graded activation of EGFR and induction of the low-threshold ventrolateral fate (yellow) in the nearby ectodermal cells. In time, the signaling activity increases such that the cells nearest to the midline (red) reach the high threshold of the ventral-most fate and start secreting Argos. Inhibition by Argos modifies the gradient of activity, restricting the domain of each ventral fate. This pattern persists for at least 3 more hours. Argos Note: the timeline is an approximation Ventrolateral threshold Ventral-most fate (Argos) threshold Midline cell Ventrolateral cell Ventral-most cell 15

16 (A) (B) Nurse cell A Oocyte nucleus P Follicular epithelium Oocyte Dorsal appendages Collar Micropyle Operculum Figure 3. (A) A mid-stage egg chamber. At this stage, the nucleus has just migrated from the posterior to the future dorsal position (A=anterior, P=posterior). (B) Top: a dark micrograph of a mature fly egg chamber with the dorsal appendages extending out from the dorsal-anterior side; bottom: a scanning electron micrograph of the dorsal anterior section [2]. (Reproduced with permission of Development, Company of Biologists.) Specialized regions can be identified: micropyle, the entry point of the sperm; operculum, the larval exit door; and collar region, which delineates the operculum. The broken orange line indicates the midline (i.e., the dorsal-most aspect of the egg). (A) A A A D V P P P (B) A P Figure 4. (A) The overlap between the anterior-posterior gradient of a TGFβ ligand (blue) and the gradient of Gurken originating from the dorsal-anterior corner (green) defines the dorsal-anterior region that will be patterned by Egfr signaling (orange). The broken circle indicates the position of the oocyte nucleus (A=anterior, P=posterior, D=dorsal, V=ventral). (B) The dorsal-anterior is patterned by EGFR signaling into three different fates: the operculumproducing dorsal midline cells (red), the dorsolateral cells that position the future dorsal appendages (blue), and the appendage progenitors (yellow). 16

17 16 hours 12 hours 6 hours 0 hour Gurken Spitz Spitz Argos Spitz Argos Note: the timeline and the number of cells are approximations Figure 5. Eggshell patterning. In the graphs, the y-axis is the EGFR activity and the x-axis is the distance away from the midline. All cells are initially uniform. Patterning is initiated by the secretion of Gurken from the oocyte. This creates a graded activation of EGFR in the cells nearest to the oocyte nucleus (see legend below for color coding). Although omitted from the subsequent figures, Gurken secretion is constant for at least 12 hours. The AP gradient of the TGFβ ligand is not formed until ~6 hours later, upon which the cells start secreting Spitz. Due to the amplification by Spitz, the cells nearest to the midline reach the high threshold and start secreting Argos. Inhibition by Argos splits the domain of EGFR activity into two and restricts expansion to the lateral side. As a consequence of its own inhibitory action, Argos expression also splits into two stripes, coinciding with the high EGFR activity domains. This pattern persists, throughout the morphogenetic movements during the appendage formation, until the end of oogenesis (~6 more hours). Egfr activity threshold Argos threshold Cell exhibiting a high level of EGFR activity Cell exhibiting a moderate level of EGFR activity Cell exhibiting a low level of EGFR activity 17

18 (A) D h (B) k c k deg k rec k e k c k deg k rec (C) (D) Figure 6: (A) Simplified model of ligand transport, binding, and trafficking. Ligand diffuses in the gap between the reflective and receptor-covered surfaces. Receptor density is uniform across the surface of the epithelial layer. (B) Rate constants for binding and trafficking. (C) Probability density function for the lateral distances traveled by secreted ligands in the time between the binding events. grdr ( ) is equal to the probability that a ligand will be bound between r and r+ dr. All computations are based on the hexagonal cell with the area of 25 µm 2. (D) Fraction of the ligands that are recaptured by the ligandreleasing cell plotted as a function of the cell surface receptor number, ligand-receptor 1 1 affinity ( k R [ M min #/ cell] ), and extracellular ligand diffusivity. on tot 18

19 B A DER Spitz Ras MAPK CF 2 C Rhomboid rho Figure 7: (A) A tentative structure of a positive feedback loop in the Rhomboid/Spitz system. Ligand binding stimulates ligand release. Receptor activation leads to the degradation of a factor inhibiting the transcription of the ligand-releasing protease. In the absence of inhibition, the protease is synthesized and generates the secreted ligand. (B) The steady state ligand field due to a single ligand-releasing cell. Parameters: h = 0.5 µm, k e = 0.1 min -1, k off = 0.1 min -1, molecules/cell surface, D = cm 2 s -1, k on = 0.1 nm -1 min -1, maximal rate of ligand release Q s = 100 molecules/cell/min, cell area - 25 µm 2. (C) A small cluster of cells with constitutively active Rhomboid expression can generate an expanding wave of Rhomboid induction. The critical value of ligand release is plotted as a function of the number of cells within the cluster. The generation function for Rhomboid was approximated by a Heaviside function, such that Rhomboid expression can be only in two states, on and off. See Pribyl et al for the detailed definition of model parameters and its computational analysis [19]. 19

20 (A) (A) Gurken input Gurken input Rho mboid Gurken g 0 x 0 oocyte membrane Spitz Argos (B) EGFR follicle cell Figure 8: (A) Input and feedback loops in the model of pattern formation by peak splitting. (B) Summary of the results of the computational analysis of the onedimensional model of pattern formation by DER autocrine feedback loops. The regions of existence of different stationary patterns as a function of the width (x 0 ) and the amplitude (g 0 ) of the input (Gurken) signal. Patterns with the different number of peaks are associated with the eggshells with different number of dorsal appendages (shown by insets). See Shvartsman et al for the detailed definition of model parameters and its computational analysis [24]. 20