A spatially-averaged mathematical model of kidney branching morphogenesis

Handle URI:
http://hdl.handle.net/10754/597410
Title:
A spatially-averaged mathematical model of kidney branching morphogenesis
Authors:
Zubkov, V.S.; Combes, A.N.; Short, K.M.; Lefevre, J.; Hamilton, N.A.; Smyth, I.M.; Little, M.H.; Byrne, H.M.
Abstract:
© 2015 Published by Elsevier Ltd. Kidney development is initiated by the outgrowth of an epithelial ureteric bud into a population of mesenchymal cells. Reciprocal morphogenetic responses between these two populations generate a highly branched epithelial ureteric tree with the mesenchyme differentiating into nephrons, the functional units of the kidney. While we understand some of the mechanisms involved, current knowledge fails to explain the variability of organ sizes and nephron endowment in mice and humans. Here we present a spatially-averaged mathematical model of kidney morphogenesis in which the growth of the two key populations is described by a system of time-dependant ordinary differential equations. We assume that branching is symmetric and is invoked when the number of epithelial cells per tip reaches a threshold value. This process continues until the number of mesenchymal cells falls below a critical value that triggers cessation of branching. The mathematical model and its predictions are validated against experimentally quantified C57Bl6 mouse embryonic kidneys. Numerical simulations are performed to determine how the final number of branches changes as key system parameters are varied (such as the growth rate of tip cells, mesenchyme cells, or component cell population exit rate). Our results predict that the developing kidney responds differently to loss of cap and tip cells. They also indicate that the final number of kidney branches is less sensitive to changes in the growth rate of the ureteric tip cells than to changes in the growth rate of the mesenchymal cells. By inference, increasing the growth rate of mesenchymal cells should maximise branch number. Our model also provides a framework for predicting the branching outcome when ureteric tip or mesenchyme cells change behaviour in response to different genetic or environmental developmental stresses.
Citation:
Zubkov VS, Combes AN, Short KM, Lefevre J, Hamilton NA, et al. (2015) A spatially-averaged mathematical model of kidney branching morphogenesis. Journal of Theoretical Biology 379: 24–37. Available: http://dx.doi.org/10.1016/j.jtbi.2015.04.015.
Publisher:
Elsevier BV
Journal:
Journal of Theoretical Biology
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Aug-2015
DOI:
10.1016/j.jtbi.2015.04.015
PubMed ID:
25913880
Type:
Article
ISSN:
0022-5193
Sponsors:
This work was supported by Human Frontiers Scientific Program (HFSP RGP0039/2011), the National Health and Medical Research Council, Australia (NHMMRC APP1002478; to ML), an Australian Research Council (ARC) Discovery Project Grant (DP130100886; to IS) and in part by Award No. KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST). ML is a Senior Principal Research Fellow of the NHMRC. IS holds an ARC Future Fellowship. We are grateful to Professor Andrew McMahon and Dr Lori O׳Brien for helpful discussions and to Adler Ju for technical support.
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DC FieldValue Language
dc.contributor.authorZubkov, V.S.en
dc.contributor.authorCombes, A.N.en
dc.contributor.authorShort, K.M.en
dc.contributor.authorLefevre, J.en
dc.contributor.authorHamilton, N.A.en
dc.contributor.authorSmyth, I.M.en
dc.contributor.authorLittle, M.H.en
dc.contributor.authorByrne, H.M.en
dc.date.accessioned2016-02-25T12:32:40Zen
dc.date.available2016-02-25T12:32:40Zen
dc.date.issued2015-08en
dc.identifier.citationZubkov VS, Combes AN, Short KM, Lefevre J, Hamilton NA, et al. (2015) A spatially-averaged mathematical model of kidney branching morphogenesis. Journal of Theoretical Biology 379: 24–37. Available: http://dx.doi.org/10.1016/j.jtbi.2015.04.015.en
dc.identifier.issn0022-5193en
dc.identifier.pmid25913880en
dc.identifier.doi10.1016/j.jtbi.2015.04.015en
dc.identifier.urihttp://hdl.handle.net/10754/597410en
dc.description.abstract© 2015 Published by Elsevier Ltd. Kidney development is initiated by the outgrowth of an epithelial ureteric bud into a population of mesenchymal cells. Reciprocal morphogenetic responses between these two populations generate a highly branched epithelial ureteric tree with the mesenchyme differentiating into nephrons, the functional units of the kidney. While we understand some of the mechanisms involved, current knowledge fails to explain the variability of organ sizes and nephron endowment in mice and humans. Here we present a spatially-averaged mathematical model of kidney morphogenesis in which the growth of the two key populations is described by a system of time-dependant ordinary differential equations. We assume that branching is symmetric and is invoked when the number of epithelial cells per tip reaches a threshold value. This process continues until the number of mesenchymal cells falls below a critical value that triggers cessation of branching. The mathematical model and its predictions are validated against experimentally quantified C57Bl6 mouse embryonic kidneys. Numerical simulations are performed to determine how the final number of branches changes as key system parameters are varied (such as the growth rate of tip cells, mesenchyme cells, or component cell population exit rate). Our results predict that the developing kidney responds differently to loss of cap and tip cells. They also indicate that the final number of kidney branches is less sensitive to changes in the growth rate of the ureteric tip cells than to changes in the growth rate of the mesenchymal cells. By inference, increasing the growth rate of mesenchymal cells should maximise branch number. Our model also provides a framework for predicting the branching outcome when ureteric tip or mesenchyme cells change behaviour in response to different genetic or environmental developmental stresses.en
dc.description.sponsorshipThis work was supported by Human Frontiers Scientific Program (HFSP RGP0039/2011), the National Health and Medical Research Council, Australia (NHMMRC APP1002478; to ML), an Australian Research Council (ARC) Discovery Project Grant (DP130100886; to IS) and in part by Award No. KUK-C1-013-04 made by King Abdullah University of Science and Technology (KAUST). ML is a Senior Principal Research Fellow of the NHMRC. IS holds an ARC Future Fellowship. We are grateful to Professor Andrew McMahon and Dr Lori O׳Brien for helpful discussions and to Adler Ju for technical support.en
dc.publisherElsevier BVen
dc.subjectBranching morphogenesisen
dc.subjectCap mesenchymeen
dc.subjectKidney developmenten
dc.subjectMathematical modelingen
dc.subjectNephrogenesisen
dc.subjectOrganogenesisen
dc.subjectUreteric treeen
dc.titleA spatially-averaged mathematical model of kidney branching morphogenesisen
dc.typeArticleen
dc.identifier.journalJournal of Theoretical Biologyen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionUniversity of Queensland, Brisbane, Australiaen
dc.contributor.institutionMonash University, Melbourne, Australiaen
kaust.grant.numberKUK-C1-013-04en

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