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Cadherin-dependent cell morphology in an epithelium: constructing a quantitative dynamical model.

Gemp IM, Carthew RW, Hilgenfeldt S - PLoS Comput. Biol. (2011)

Bottom Line: 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.The simulations also indicate that N-cadherin protein is recycled from inactive interfaces to active interfaces, thereby modulating adhesion strengths between cells.

View Article: PubMed Central - PubMed

Affiliation: Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois, United States of America.

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.

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Analysis of P cell misexpression simulations.(A) Total error Fe for different simulations as a function of N+/N0. The red line describes the simulation error when P cells express N-cadherin before cone cells, and P cells do not contact each other until after the onset of N-cadherin expression in cone cells. The purple line describes simulation error when P cells express N-cadherin before cone cells but P cells are always in contact with each other. The black line describes simulation error when P cells and cone cells simultaneously begin N-cadherin expression, and P cells always are in contact with each other. (B) Error contributions to the best-fit model are dominated by the same fe terms as in the other misexpression simulation, except that the symmetric structure of this mutant has no Dx contribution to the error. The minimum is located at N+/N0≈1.2. (C) The effect of N+/N0 on the shape of the ommatidium, with only values near the error function minimum approximating the observed cruciform mutant shape. (D) Binding strengths of N-cadherin on various edges of the structure as N+/N0 varies. Note the absence of binding on PP edges for N+/N0<1.2.
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pcbi-1002115-g009: Analysis of P cell misexpression simulations.(A) Total error Fe for different simulations as a function of N+/N0. The red line describes the simulation error when P cells express N-cadherin before cone cells, and P cells do not contact each other until after the onset of N-cadherin expression in cone cells. The purple line describes simulation error when P cells express N-cadherin before cone cells but P cells are always in contact with each other. The black line describes simulation error when P cells and cone cells simultaneously begin N-cadherin expression, and P cells always are in contact with each other. (B) Error contributions to the best-fit model are dominated by the same fe terms as in the other misexpression simulation, except that the symmetric structure of this mutant has no Dx contribution to the error. The minimum is located at N+/N0≈1.2. (C) The effect of N+/N0 on the shape of the ommatidium, with only values near the error function minimum approximating the observed cruciform mutant shape. (D) Binding strengths of N-cadherin on various edges of the structure as N+/N0 varies. Note the absence of binding on PP edges for N+/N0<1.2.

Mentions: We modeled a mosaic ommatidium in which the N-cadherin transgene is switched on in two neighboring P cells. Although this switching occurs at the same time in the two cells, the N-cadherin is unable to pair because the two P cells are not yet neighbors (cf. Fig. 8A). By the time they do become neighbors, the endogenous N-cadherin gene has been expressed in the cone cells for about 10 hours. Therefore, transgenic N-cadherin first pairs on the C1P and C2P edges (Fig. 8A), increasing adhesion and elongating these edges. The binding strength is γNP = βN+/(2LC2P+LC1P), assuming that the P cells are limiting, which leaves N0−N+ LC1P/(2LC2P+LC1P) and N0−N+ LC2P/(2LC2P+LC1P) molecules in the C1 and C2 cells, respectively. The active interface lengths for the two different cone cell species are different (the C2 cells have to cover the center edge as well), but so are the numbers of cadherins to be distributed. The most important feature of the simulation is that, up to N+/N0≈1.2, the PP edges do not have paired N-cadherin at all, and therefore have a relatively high tension, leading to a characteristic acute P/C2/P angle seen in the simulation (Fig. 8B). Strikingly, an experimental mosaic ommatidium with misexpression in two P neighbors shows a similar morphology (Fig. 8D). A penalty function of the simulation compared to experimental showed a well-defined minimum at N+/N0≈1.2 (Fig. 9A–C). While the best-fit simulation yielded the cruciform shape with the acute P/C2/P angles seen in experiment, any significant deviation from this optimal N+/N0 led to large shape changes. Note that this optimal ratio is nearly the same as that obtained from the simulation for the misexpression mutant in Fig. 7. The N-cadherin coverages of the various interfaces are plotted in Fig. 9D; note that any abrupt change in slope of the curves indicates a change in the sequence of limiting cells described above.


Cadherin-dependent cell morphology in an epithelium: constructing a quantitative dynamical model.

Gemp IM, Carthew RW, Hilgenfeldt S - PLoS Comput. Biol. (2011)

Analysis of P cell misexpression simulations.(A) Total error Fe for different simulations as a function of N+/N0. The red line describes the simulation error when P cells express N-cadherin before cone cells, and P cells do not contact each other until after the onset of N-cadherin expression in cone cells. The purple line describes simulation error when P cells express N-cadherin before cone cells but P cells are always in contact with each other. The black line describes simulation error when P cells and cone cells simultaneously begin N-cadherin expression, and P cells always are in contact with each other. (B) Error contributions to the best-fit model are dominated by the same fe terms as in the other misexpression simulation, except that the symmetric structure of this mutant has no Dx contribution to the error. The minimum is located at N+/N0≈1.2. (C) The effect of N+/N0 on the shape of the ommatidium, with only values near the error function minimum approximating the observed cruciform mutant shape. (D) Binding strengths of N-cadherin on various edges of the structure as N+/N0 varies. Note the absence of binding on PP edges for N+/N0<1.2.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3140965&req=5

pcbi-1002115-g009: Analysis of P cell misexpression simulations.(A) Total error Fe for different simulations as a function of N+/N0. The red line describes the simulation error when P cells express N-cadherin before cone cells, and P cells do not contact each other until after the onset of N-cadherin expression in cone cells. The purple line describes simulation error when P cells express N-cadherin before cone cells but P cells are always in contact with each other. The black line describes simulation error when P cells and cone cells simultaneously begin N-cadherin expression, and P cells always are in contact with each other. (B) Error contributions to the best-fit model are dominated by the same fe terms as in the other misexpression simulation, except that the symmetric structure of this mutant has no Dx contribution to the error. The minimum is located at N+/N0≈1.2. (C) The effect of N+/N0 on the shape of the ommatidium, with only values near the error function minimum approximating the observed cruciform mutant shape. (D) Binding strengths of N-cadherin on various edges of the structure as N+/N0 varies. Note the absence of binding on PP edges for N+/N0<1.2.
Mentions: We modeled a mosaic ommatidium in which the N-cadherin transgene is switched on in two neighboring P cells. Although this switching occurs at the same time in the two cells, the N-cadherin is unable to pair because the two P cells are not yet neighbors (cf. Fig. 8A). By the time they do become neighbors, the endogenous N-cadherin gene has been expressed in the cone cells for about 10 hours. Therefore, transgenic N-cadherin first pairs on the C1P and C2P edges (Fig. 8A), increasing adhesion and elongating these edges. The binding strength is γNP = βN+/(2LC2P+LC1P), assuming that the P cells are limiting, which leaves N0−N+ LC1P/(2LC2P+LC1P) and N0−N+ LC2P/(2LC2P+LC1P) molecules in the C1 and C2 cells, respectively. The active interface lengths for the two different cone cell species are different (the C2 cells have to cover the center edge as well), but so are the numbers of cadherins to be distributed. The most important feature of the simulation is that, up to N+/N0≈1.2, the PP edges do not have paired N-cadherin at all, and therefore have a relatively high tension, leading to a characteristic acute P/C2/P angle seen in the simulation (Fig. 8B). Strikingly, an experimental mosaic ommatidium with misexpression in two P neighbors shows a similar morphology (Fig. 8D). A penalty function of the simulation compared to experimental showed a well-defined minimum at N+/N0≈1.2 (Fig. 9A–C). While the best-fit simulation yielded the cruciform shape with the acute P/C2/P angles seen in experiment, any significant deviation from this optimal N+/N0 led to large shape changes. Note that this optimal ratio is nearly the same as that obtained from the simulation for the misexpression mutant in Fig. 7. The N-cadherin coverages of the various interfaces are plotted in Fig. 9D; note that any abrupt change in slope of the curves indicates a change in the sequence of limiting cells described above.

Bottom Line: 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.The simulations also indicate that N-cadherin protein is recycled from inactive interfaces to active interfaces, thereby modulating adhesion strengths between cells.

View Article: PubMed Central - PubMed

Affiliation: Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois, United States of America.

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.

Show MeSH
Related in: MedlinePlus