A mathematical model for the induction of the mammalian ureteric bud

JOURNAL OF THEORETICAL BIOLOGY

卷:394

Article

Lawson, Brodie A. J.¹  Flegg, Mark B.² 

[1] Univ Queensland, Sch Math & Phys, St Lucia, Qld 4072, Australia

[2] Monash Univ, Sch Math Sci, Monash Acad Cross & Interdisciplinary Math Applic, Wellington Rd, Clayton, Vic 3800, Australia

关键词: Turing patterning;    Kidney morphogenesis;    Partial differential equations;    Developmental biology;    Mathematical biology;   

DOI  :  10.1016/j.jtbi.2015.12.025

来源: Elsevier

【 摘 要 】

Congenital abnormalities of the kidney and urinary tract collectively form the most common type of prenatally diagnosed malformations. Whilst many of the crucial genes that direct the kidney developmental program are known, the mechanisms by which kidney organogenesis is achieved is still largely unclear. In this paper, we propose a mathematical model for the localisation of the ureteric bud, the precursor to the ureter and collecting duct system of the kidney. The mathematical model presented fundamentally implicates Schnakenberg-like ligand-receptor Turing patterning as the mechanism by which the ureteric bud is localised on the Wolfian duct as proposed by Menshykaul and Iber (2013). This model explores the specific roles of regulatory proteins GREM1 and BMP as well as the domain properties of GDNF production. Our model demonstrates that this proposed pattern formation mechanism is capable of naturally predicting the phenotypical outcomes of many genetic experiments from the literature. Furthermore, we conclude that whilst BMP inhibits GDNF away from the budding site and GREM1 permits GDNF to signal, GREM1 also stabilises the effect of BMP on GDNF signalling from fluctuations in BMP sensitivity but not signal strength. (C) 2016 Elsevier Ltd. All rights reserved.

【 授权许可】

Free