Dynamic Image-Based Modelling of Kidney Branching Morphogenesis
Kidney branching morphogenesis has been studied extensively, but the mechanism that defines the branch points is still elusive. Here we obtained a 2D movie of kidney branching morphogenesis in culture to test different models of branching morphogenesis with physiological growth dynamics. We carried out image segmentation and calculated the displacement fields between the frames. The models were subsequently solved on the 2D domain, that was extracted from the movie. We find that Turing patterns are sensitive to the initial conditions when solved on the epithelial shapes. A previously proposed diffusion-dependent geometry effect allowed us to reproduce the growth fields reasonably well, both for an inhibitor of branching that was produced in the epithelium, and for an inducer of branching that was produced in the mesenchyme. The latter could be represented by Glial-derived neurotrophic factor (GDNF), which is expressed in the mesenchyme and induces outgrowth of ureteric branches. Considering that the Turing model represents the interaction between the GDNF and its receptor RET very well and that the model reproduces the relevant expression patterns in developing wildtype and mutant kidneys, it is well possible that a combination of the Turing mechanism and the geometry effect control branching morphogenesis.
Keywordsimage-based modelling kidney branching morphogenesis signaling networks in silico organogenesis
Unable to display preview. Download preview PDF.
- 2.Iber, D., Tanaka, S., Fried, P., Germann, P., Menshykau, D.: Simulating Tissue Morphogenesis and Signaling. In: Nelson, C.M. (ed.) Tissue Morphogenesis: Methods and Protocols, Methods in Molecular Biology. Springer (2013)Google Scholar
- 5.Meyer, T.N., Schwesinger, C., Bush, K.T., Stuart, R.O., Rose, D.W., et al.: Spatiotemporal regulation of morphogenetic molecules during in vitro branching of the isolated ureteric bud: toward a model of branching through budding in the developing kidney. Developmental Biology 275, 44–67 (2004)CrossRefGoogle Scholar
- 20.Gleghorn, J.P., Kwak, J., Pavlovich, A.L., Nelson, C.M.: Inhibitory morphogens and monopodial branching of the embryonic chicken lung. Developmental dynamics: An official publication of the American Association of Anatomists (2012)Google Scholar
- 23.D’Errico, R.: Interparc function (2012), http://www.mathworks.in/matlabcentral/fileexchange/34874-interparc
- 24.D’Errico, R.: Normal distance function (2012), http://www.mathworks.com/matlabcentral/fileexchange/34869-distance2curve
- 26.Carin, M.: Numerical Simulation of Moving Boundary Problems with the ALE Method: Validation in the Case of a Free Surface and a Moving Solidification Front. In: Excert from the Proceedings of the COMSOL Conference (2006)Google Scholar
- 27.Thummler, V., Weddemann, A.: Computation of Space-Time Patterns via ALE Methods. In: Excert from the Proceedings of the COMSOL Conference (2007)Google Scholar
- 28.Weddemann, A., Thummler, V.: Stability Analysis of ALE-Methods for Advection-Diffusion Problems. In: Excert from the Proceedings of the COMSOL Conference (2008)Google Scholar
- 29.Menshykau, D., Iber, D.: Simulating Organogenesis with Comsol: Interacting and Deforming Domains. In: Proceedings of COMSOL Conference 2012 (2012)Google Scholar
- 30.Germann, P., Menshykau, D., Tanaka, S., Iber, D.: Simulating Organogensis in COMSOL. In: Proceedings of COMSOL Conference 2011 (2011)Google Scholar
- 31.Pachnis, V., Mankoo, B., Costantini, F.: Expression of the c-ret proto-oncogene during mouse embryogenesis. Development 119, 1005–1017 (1993)Google Scholar
- 32.Bookstein, F.L.: Principal warps: Thin-plate splines and the decomposition of deformations. Pattern Analysis and Machine Intelligence (1989)Google Scholar