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Title: Cadherin-Dependent Cell Morphology in an Epithelium: Constructing a Quantitative Dynamical Model}
Article:
Abstract:
Cells in the Drosophila retina have well-defined morphologies that are attained during tissue morphogenesis. We present a computer simulation of the epithelial tissue in which the global interfacial energy between cells is minimized. Experimental data for both normal cells and mutant cells either lacking or misexpressing the adhesion protein N-cadherin can be explained by a simple model incorporating salient features of morphogenesis that include the timing of N-cadherin expression in cells and its temporal relationship to the remodeling of cell-cell contacts. The simulations reproduce the geometries of wild-type and mutant cells, distinguish features of cadherin dynamics, and emphasize the importance of adhesion protein biogenesis and its timing with respect to cell remodeling. The simulations also indicate that N-cadherin protein is recycled from inactive interfaces to active interfaces, thereby modulating adhesion strengths between cells.
Introduction:
Tissues in multicellular organisms consist of a variety of cells with specialized functions. The differences between cell types are often manifest in the individual cells' shapes, their relative positions, and their neighbor relations[1]. It has become recognized that mechanical forces within cells control cell shapes and their larger-scale organization within tissues[2],[3],[4]. These forces are generated by specific molecules present within and upon the surfaces of cells, including the actin-myosin cytoskeleton and cell-cell adhesion molecules. A fundamental issue is whether tissue morphology can be described as the sum of cell morphologies, which are individually determined by autonomous force generators. An alternative description of tissue morphology assumes that morphology is passively determined by equilibrium mechanics once a small number of force parameters is established by force-generating molecules within cells. This alternative is rationalized by experimental observations finding that cell packing in the Drosophila retina is a consequence of mechanical equilibrium[5]. Moreover, retinal tissue morphology can be quantitatively modeled by assuming global minimization of interfacial energies that are established by cellular force-generating molecules[6]. Models of other epithelial tissues using similar methods have also successfully reproduced morphological properties[7],[8],[9], giving credence to the approach. The Drosophila retina is a pseudostratified epithelium containing over 800 repeating units called ommatidia( Fig. 1). Each ommatidium is on average D≈9·m across its widest axis, and consists of twenty cells, including eight photoreceptor neurons and twelve accessory cells[10]. Four of these accessory cells( called cone cells) adhere together to form a transparent plate that acts as both the floor of the simple lens and the roof of the underlying pool of photoreceptors. Two primary pigment cells optically insulate each cone-cell group; together with the cone cells, they form the “core” structure of the ommatidium. Secondary and tertiary pigment cells form the ommatidium “frame”. Functionally, the cone cells form an “aperture” for focused light to be transmitted from the lens to the photoreceptors, while the opaque primary pigment cells delineate the aperture stop. Cells in the retina express two kinds of cell-cell adhesion molecules: E-cadherin and N-cadherin[5],[11]. All cells contain E-cadherin; however, only the four cone cells contain N-cadherin. The cadherin protein molecules become localized in a thin band of lateral cell membrane( b≈50 nm wide) corresponding to the adherens junction( AJ), which is the major site of adhesion between cells( Fig. 1B). Cadherins in one membrane bind to cadherins located in the membrane of a neighboring cell across the intercellular gap, affecting the adherence of one cell with its neighbor[5]. The binding interactions appear to be homotypic; E- and N-cadherin molecules do not bind to each other[5], even though heterotypic binding has been found for Xenopus cadherins[12]. Intermolecular binding collectively generates adhesion between facing membranes, thereby decreasing the interfacial energy per AJ area and making expansion of the interfacial AJ domain energetically favorable. Membrane that has established such bonds is considered “active”. However, the expansion of one interfacial domain affects other cell-cell interfaces due to constraints on the overall sizes of the AJ membrane domain and cell volume,. Shape changes in one cell induce shape changes in others, and alteration of the elastic energy of the membranes around all cells. Ultimately, the mechanical energy of the entire ommatidium needs to be minimized globally in order to find an equilibrium configuration for the ommatidium[13],[14]. This configuration describes the entire retinal tissue since ommatidia are arranged in the epithelium as identical tiles with six-fold axes of symmetry. It is well known that cell-cell adhesion can play an important role in cell sorting and morphogenesis of tissues[15],[16], as theoretically described and experimentally demonstrated[17],[18]. More elaborate formalisms have been successfully used to simulate a variety of tissues[19],[20]. Our work indicates that in tissues like the Drosophila retina, the role of cadherins goes beyond cell sorting and in fact determines the details of their geometric shapes[6]. In order to understand how cadherin molecules control cell geometry,, one must consider the distribution and dynamic properties of cadherins. In the present work, we apply these considerations to our mechanical model. We then test the fit of various distribution and dynamic models with experimental data for mutants in which certain cells produce altered levels of N-cadherin. We demonstrate( i) that the model describes characteristic shape changes in such mutants,( ii) that the simulations distinguish between different mechanisms of how cadherin levels are attained and controlled, and( iii) that the model, although conceived as an equilibrium tool, incorporates important dynamical features in morphogenesis, such as the temporal sequence of cadherin expression and cell-cell contact remodeling.
Discussion:
We have applied and extended the mechanical energy functional modeling on the morphology of Drosophila eye tissue in several crucial ways. This model relies entirely on passive global minimization of a simple interfacial energy functional. However, we have shown how to incorporate new features that, implicitly, describe observed biological features of the tissue. These features include: recycling and redistribution of unpaired N-cadherin molecules from the surface of cells, the temporal dynamics of N-cadherin gene expression, and the temporal dynamics of cell-cell contacts. Note that we established these model features without any additional free parameters. Because the dynamics of morphogenesis and gene expression are experimentally described phenomena, and because the Surface Evolver simulations are capable of varying these features, we incorporated these phenomena into a model that describes the experimental data with a high degree of accuracy. When we incorporate features into the model that are not observed in the tissue, the model does not simulate the experiments to the same degree. Two points can be made. First, it is essential for any morphogenesis model to be flexible enough that critical biological features can be modified. Second, our morphogenesis model not only simulates normal morphology but also morphologies observed in complex genetic mutants. In fact, it is the asymmetries in ommatidial shape and the cadherin expression dynamics introduced through mutants that allowed us to successfully test these features within the framework of the model. The success of these simulations suggests that models employing energy minimization can go beyond the quantitative computation of local equilibrium morphologies, and become useful tools for simulating morphogenetic changes that are quasistatic with respect to the time scale of mechanical equilibration. In the case of changes in gene expression or cell neighbor relations, this condition is fulfilled, as these changes can take hours[41],[42],[43]. In contrast, mechanical equilibria are established in minutes at most, depending on dissipative effects[44],[45]. In the experiments we have described, there is also sufficient separation between the onset of cadherin expression and the changes in cell-cell contacts. We simulated misexpression of a N-cadherin transgene to test many of the biological features of the model. In all of these simulations, the best-fit solutions predicted a level of transgenic N-cadherin expression level to be 1. 2-fold greater than that of the endogenous N-cadherin gene. One would expect that independent simulations predict the same level of transgene expression because its expression is independent of which cell or combination of cells express it. Also encouraging is that the level of transgene expression is predicted by simulations to be comparable to the level of endogenous N-cadherin gene expression. The transgene uses the transcriptional promoter from the actin5c gene to indirectly drive transcription of the N-cadherin coding region[5]. Actin5c is one of six actin isoforms and represents only 5–10% of the actin in pupal head cells[46]. Thus, we estimate that 50, 000 to 100, 000 actin5c protein molecules would be present in these cells, and presumably a similar number of heterologous proteins produced from an actin5c transgene. About 50, 000 endogenous cadherin protein molecules are present in a typical animal cell[47]. Therefore, it is reasonable to find that transgenic and endogenous production of N-cadherin are not different by orders of magnitude. Most computer models of tissue morphogenesis simulate visual changes in cell shape and neighbor relations that occur over time[48]. However, use of qualitative visual information to compare normal and perturbed morphogenesis limits their abilities to find optimum mechanical parameters. Our model introduces a novel method for exploring morphogenesis: the effect of perturbations during morphogenesis can be simulated by the final cell shapes and neighbor relations that are achieved at the end of morphogenesis. The simplicity of the final cell geometry allows for unambiguous quantitative comparisons between different morphogenetic conditions, particularly for highly ordered tissues like the Drosophila retinal epithelium.
Tissues are intricate , heterogeneous systems , consisting of individual cells whose shapes and relative positions are of great importance to the tissue's function , as well as to its formation during morphogenesis . To make progress in our understanding of the formation of organs , their malfunction , and their therapeutic replacement in regenerative medicine , it is crucial to elucidate the connection between shape and function . We have developed a quantitative mechanical model of an epithelial tissue , the retina of Drosophila , and compare the modeling results with experimental data . The model successfully predicts shape changes induced by different expression levels of cell-cell adhesion molecules . Furthermore , the model gives new insight into the changes a tissue undergoes during morphogenesis . Comparing simulations and experiments , we are able to accept or reject different hypotheses about morphogenetic dynamics . In this way , we can identify the time course of adhesion molecule synthesis and of cell-cell contact , as well as gain new insight into the regulation of adhesion strength . Given the prominent role of adhesion in wound healing , cancer research , and many other fields , our fundamental work introduces a novel modeling tool of universal applicability and importance .