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Modeling and computational analysis of EGF receptor-mediated cell communication in Drosophila oogenesis

¹ Department of Chemical Engineering and Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ 08544, USA
² Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA
³ Biological Engineering Division and Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

View larger version (29K): [in a new window]   Fig. 1. (A) A schematic representation of the egg at stage 9-10 of Drosophila oogenesis. The oocyte at the posterior part of the egg chamber is covered by a layer of follicle cells. The nucleus of the oocyte is located at its dorsoanterior cortex. D, V, A and P denote the dorsal, ventral, anterior and posterior sides of the egg chamber, respectively. (B) Cell communication between the oocyte and the follicle cells is initiated by the Gurken signal. The spatial distribution of the oocyte-derived Gurken is determined by a combination of localized release, diffusion and binding of Gurken to the EGF receptors uniformly distributed in the follicular epithelium. (C) Positive feedback loop in the follicle cells. Gurken stimulates the EGF receptors in the follicle cells, which activate the MAPK in the follicle cells; MAPK contributes to the cytoplasmic degradation of CF2, a transcription factor that negatively regulates the expression of rhomboid. Rhomboid, an intracellular protease, participates in processing and activation of Spitz, another EGFR ligand. The secreted Spitz further stimulates EGFR in the follicle cells. (D) Negative feedback loop in the follicle cells: high levels of EGF receptor and MAPK activation, via transcription factor Pointed, induce the expression of argos. Argos is a secreted inhibitor of EGFR. Extracellular concentrations of Argos, Gurken and Spitz jointly regulate the level of EGFR activation in the follicle cells.

View larger version (12K): [in a new window]   Fig. 2. (A) Positive- and negative-feedback loops in the EGFR/MAPK/Rhomboid/Spitz/Argos network. The level of MAPK activity regulates the expression of Rhomboid and Argos. The level of MAPK activity is determined by the extracellular concentration of EGFR ligands; EGFR is stimulated by Gurken and Spitz, and is repressed by Argos. Our model neglects additional positive- and negative-feedback loops identified in the interaction between the oocyte and the follicular epithelium. (B) The spatially distributed network of autocrine loops that mediates the oocyte/follicle cells interaction. The spatially distributed Gurken input leads to Argos and Spitz production; both of these signals are diffusing in a narrow gap between the oocyte and the follicular epithelium.

View larger version (28K): [in a new window]   Fig. 3. (A) The spatiotemporal dynamics induced by a monotonically increasing and saturating input. (Left) Time-dependent and spatially nonuniform distribution of Gurken. Center: the colormap of the spatiotemporal dynamics of Rhomboid. Space is along the horizontal axis, time is along the vertical axis. The value of r(x,t) changes continuously from 0 to 1 upon going from blue to red regions. (Right) The snapshots showing the profiles of Spitz and Argos at different points of the transient (t=30, 110 and 150) corresponding to the formation of a narrow single-peaked domain, initiation of the splitting event and an equilibrated two-peaked pattern. (B) The parametric diagram that shows the dependence of the dimensionless Spitz concentration in the center of the domain s(x=0,t) on the amplitude of the Gurken input g(x=0,t). Notice the relatively sharp transitions between qualitatively different patterns during the transient. The model parameters used in computing this transient are: x0=3, g=40, g0=1, ca=0.5, cr=0.4, br=0.2, ba=0.05, =1.6, s=0.1, a=1 and =0.1. See Materials and Methods for the discussion of the selection of the parameter values.

View larger version (27K): [in a new window]   Fig. 4. Four major classes of stationary patterns in the model. The patterns are characterized by the presence of zero (A), one narrow (B), two (C) and one broad (D) peaks in the distribution of Rhomboid (and Spitz, not shown). In the text, we use these patterns to account for several of the eggshell morphology phenotypes schematically shown in the insets. The phenotypes corresponding to patterns A-D are denoted 0, 1, 2 and 1', respectively. The patterns A-D were computed for g0=0.4, 0.6, 1.0 and 1.3, respectively, with all other parameters as in Fig. 3.

View larger version (26K): [in a new window]   Fig. 5. Transitions between the four major classes of stationary patterns in Fig. 4 observed upon variations of model parameters. The patterns are classified according to the number of peaks in the spatial distribution of signaling components. (A-D) The concentration of Spitz in the center of the domain, s(x=0), is plotted as a function of a single model parameter, with all the other parameters fixed at the values corresponding to the transient in Fig. 3. The point corresponding to the ‘wild type’ steady pattern is denoted by ‘’. (A) An increase in the input amplitude, g0, produces the 0121' sequence of transitions. Each transition is accompanied by a hysteresis: there is a region of inputs where qualitatively different patterns co-exist. This sequence of transitions is used to account for different phenotypes observed upon the variation in the level of Gurken, see Discussion. (B) A qualitatively similar sequence of hysteretic transitions is observed upon a variation of the strength of the positive feedback in the model. Experimentally, this sequence of transitions can be realized by uniform changes in the level of Spitz or Rhomboid. (C) A uniform decrease in the strength of the negative feedback by Argos is predicted to generate a hysteretic transition between the phenotypes with two and one broad appendages. (D) The existence of the two-peaked pattern is conditional on the separation of the length scales of Spitz and Argos. Decreasing the length scale of the diffusing inhibitor, corresponding to increasing in the model, leads to disappearance of the two-peaked patterns; this transition is also accompanied by a hysteresis.

View larger version (43K): [in a new window]   Fig. 6. The classification of the stable patterns in the model as a function of input amplitude and width, g0 and x0, respectively. Only the patterns with zero peaks are found in the purple area; single-peaked patterns exist in the blue area, while two-peaked patterns do not; both patterns with one and two peaks co-exist in the green area; two-peaked patterns exist in the red area, while one-peaked patterns do not; and neither one- nor two-peaked patterns exist in the orange area. The eggshell phenotypes corresponding to each of these areas are also shown.