Methods of Computational Analysis in Kidney Development

  • Pauli TikkaEmail author
  • Franz Schaefer
Part of the Methods in Molecular Biology book series (MIMB, volume 1926)


This chapter reviews some currently available methodologies for constructing mathematical models in kidney development. Mammalian nephrogenesis is a complex biological process, which in its earliest stages involves migration, condensation, proliferation, and differentiation of metanephric mesenchymal (MM) cells interacting with the uroepithelial cells of the ureteric bud (UB). First, the mathematical modelling in biology is generally described. Secondly, some accounts to biological pattern formation in modelling are given in general, including models that transcend the Turing model. This is followed by a short assessment on the main branch of models in the kidney development, the evaluation of the branching morphogenesis of the kidney. Finally, two alternative models in the early kidney development processes are given as an example. They also elucidate the difficulties in the model building process. Firstly, a computational model building with the CompuCell3D program for the early nephron progenitor cell movements with the key extracellular signaling effectors is depicted. This collective migration leads to the first pretubular aggregate (PTA). The simulation parameters of the program imitate the program’s cell sorting example with different adhesions and chemoattractants. The program utilizes Cellular Potts Model (CPM) to describe the development. Secondly, an example of PTA to renal vesicle (RV) transition modelling is described. In that case, the model is unique, where the model process is based on the chemoattractants from UB.

Key words

Modelling in biology Computational modelling CompuCell3D Early nephrogenesis 


  1. 1.
    Cartwright N (1983) How the laws of physics lie. Oxford University Press, OxfordCrossRefGoogle Scholar
  2. 2.
    Berg VD (2011) Mathematical models of biological systems, Oxford University Press, OxfordGoogle Scholar
  3. 3.
    Lawson B, Flegg M (2016) A mathematical model for the induction of the mammalian ureteric bud. J Theor Biol 394:43–56PubMedCrossRefGoogle Scholar
  4. 4.
    Short KM, Combes AN, Lefevre J et al (2014) Global quantification of tissue dynamics in the developing mouse kidney. Dev Cell 29:188–202PubMedPubMedCentralCrossRefGoogle Scholar
  5. 5.
    Junttila S, Saarela U, Halt K et al (2014) Functional genetic targeting of embryonic kidney progenitor cells ex vivo. J Am Soc Nephrol 26:1126–1137PubMedPubMedCentralCrossRefGoogle Scholar
  6. 6.
    Takasato M, Little MH (2015) The origin of the mammalian kidney: implications for recreating the kidney in vitro. Development 142:1937–1947PubMedCrossRefGoogle Scholar
  7. 7.
    Krause M, Rak–Raszewska A, Pietilä I et al (2015) Signaling during kidney development. Cells 4:112–132PubMedPubMedCentralCrossRefGoogle Scholar
  8. 8.
    Zubkov VS, Combes AN, Short KM et al (2015) A spatially-averaged mathematical model of kidney branching morphogenesis. J Theor Biol 379:24–37PubMedCrossRefGoogle Scholar
  9. 9.
    McMahon AP (2016) Development of the mammalian kidney. Curr Top Dev Biol 117:31–64PubMedPubMedCentralCrossRefGoogle Scholar
  10. 10.
    Little M et al (2015) Kidney development, disease, repair and regeneration, 1st edn. Academic Press, LondonGoogle Scholar
  11. 11.
    Karner C et al (2011) Canonical Wnt9b signaling balances progenitor cell expansion and differentiation during kidney development. Development 138:1247–1257PubMedPubMedCentralCrossRefGoogle Scholar
  12. 12.
    Graner F, Glazier JA (1992) Simulation of biological cell sorting using a two-dimensional extended Potts model. Phys Rev Lett 69:2013–2017PubMedCrossRefGoogle Scholar
  13. 13.
    Hirashima T, Elisabeth R, Roeland M (2017) Cellular Potts modeling of complex multicellular behaviors in tissue morphogenesis. Dev Growth Amp Differ 59:329–339CrossRefGoogle Scholar
  14. 14.
    Turing AM (1952) The chemical basis of morphogenesis. Philos Trans Roy Soc London 237(641):37–72Google Scholar
  15. 15.
    Gierer A, Meinhardt H (1972) A theory of biological pattern formation. Kybernetic 12:10–39CrossRefGoogle Scholar
  16. 16.
    Schnakenberg J (1979) Simple chemical reaction systems with limit cycle behaviour. J Theor Biol 81:389–400PubMedCrossRefGoogle Scholar
  17. 17.
    Combes A, Lefevre J, Wilson S, Hamilton N et al (2016) Cap mesenchyme cell swarming during kidney development is influenced by attraction, repulsion, and adhesion to the ureteric tip. Dev Biol 418:297–306CrossRefGoogle Scholar
  18. 18.
    Meinhardt H, Gierer A (1980) Generation and regeneration of sequence of structures during morphogenesis. J Theor Biol 85:429–450PubMedCrossRefGoogle Scholar
  19. 19.
    Kohonen T (1982) Self-organized formation of topologically correct feature maps. Biol Cybern 43:59–69CrossRefGoogle Scholar
  20. 20.
    Murray JD, Oster GF, Harris AG et al (1983) A mechanical model for mesenchymal morphogenesis. J Math Biol 17:125–129PubMedCrossRefGoogle Scholar
  21. 21.
    Murray JD, Maini PK (1988) Mechanochemical models for generating biological pattern and form in development. Phys Rep 2:171Google Scholar
  22. 22.
    Koch AJ, Meinhardt H (1994) Biological pattern formation: from basic mechanisms to complex structures. Rev Mod Phys 4:66Google Scholar
  23. 23.
    Plaza RG, Sánchez–Garduño F, Padilla P et al (2004) The effect of growth and curvature on pattern formation. J Dyn Diff Equat 4:16Google Scholar
  24. 24.
    Mercker M, Hartmann D, Marciniak–Czochra A (2013) A mechanochemical model for embryonic pattern formation: coupling tissue mechanics and morphogen expression. PLoS One 8:12CrossRefGoogle Scholar
  25. 25.
    Mercker M, Köthe A, Marciniak-Czochra A (2015) Mechanochemical symmetry breaking in hydra aggregates. Biophys J 108:2396–2407PubMedPubMedCentralCrossRefGoogle Scholar
  26. 26.
    Mercker M, Brinkmann F, Marciniak–Czochra A et al (2016) Beyond Turing: mechanochemical pattern formation in biological tissues. Biol Direct 22:11Google Scholar
  27. 27.
    Adivarahan S, Menshykau D, Michos O et al (2013) Dynamic image-based modelling of kidney branching morphogenesis. Swiss Inst Bioinform 1:30100305Google Scholar
  28. 28.
    Menshykau D, Dagmar D (2013) Kidney branching morphogenesis under the control of a ligand-receptor-based Turing mechanism. Phys Biol 10:046003PubMedCrossRefGoogle Scholar
  29. 29.
    Menshykau D, Iber D (2013) The control of branching morphogenesis. Open Biol 3:130088PubMedPubMedCentralCrossRefGoogle Scholar
  30. 30.
    Inc, Mathworks (2018) Matlab program.
  31. 31.
    Inc, Comsol. (2018) Comsol program.
  32. 32.
    Hao W, Rovin BH, Friedman A (2014) Mathematical model of renal interstitial fibrosis. PNAS 39:111Google Scholar
  33. 33.
    Lefevre JG et al (2017) Self-organisation after embryonic kidney dissociation is driven via selective adhesion of ureteric epithelial cells. Development 144(6):1087–1096CrossRefGoogle Scholar
  34. 34.
    Saxén L (1987) Organogenesis of the kidney. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  35. 35.
    Carter (2009) Visual group theory. Mathematical Association of America, Washington, DCGoogle Scholar
  36. 36.
    Andasari V, Roper RT, Swat MH et al (2012) Integrating intracellular dynamics using CompuCell3D and Bionetsolver: applications to multiscale modelling of cancer cell growth and invasion. PLoS One 7(3):e33726PubMedPubMedCentralCrossRefGoogle Scholar
  37. 37.
    Little MH (2015) The life cycle of the nephron progenitor. Dev Cell 35:5–6PubMedCrossRefGoogle Scholar
  38. 38.
    Belmonte JM, Clendenon SG, Oliveira GM et al (2016) Virtual-tissue computer simulations define the roles of cell adhesion and proliferation in the onset of kidney cystic disease. Mol Biol Cell 27:3673–3685PubMedPubMedCentralCrossRefGoogle Scholar
  39. 39.
    Swat MH et al (2009) Multicell simulations of development and disease using the CompuCell3D simulation environment, vol 500, pp 361–428Google Scholar
  40. 40.
    Lorenzi T, Lorz A, Perthame B (2017) On interfaces between cell populations with different mobilities. Kine Relat Models 10:299–311CrossRefGoogle Scholar
  41. 41.
    Tweedy L, Knecht D, Mackay G (2016) Self-generated chemoattractant gradients: attractant depletion extends the range and robustness of chemotaxis. PLoS Biol 14:e1002404PubMedPubMedCentralCrossRefGoogle Scholar
  42. 42.
    Magno R, Grieneisen VA, Athanasius FMM (2015) The biophysical nature of cells: potential cell behaviours revealed by analytical and computational studies of cell surface mechanics. BMC Biophys 8:2046–1682CrossRefGoogle Scholar
  43. 43.
    Kofahl B, Wolf J (2010) Mathematical modelling of Wnt/ β–catenin signalling. Biochem Soc Trans 38:1281PubMedCrossRefGoogle Scholar
  44. 44.
    Blessing OE et al (2015) A mathematical model of quorum sensing induced biofilm detachment. PLoS One 10:e0132385CrossRefGoogle Scholar
  45. 45.
    David E et al (2016) Physical forces shape group identity of swimming pseudomonas putida cells. Front Microbiol 7:1437Google Scholar
  46. 46.
    Albert PJ, Schwarz US (2016) Dynamics of cell ensembles on adhesive micropatterns: bridging the gap between single cell spreading and collective cell migration. PLoS Comput Biol 12:e1004863PubMedPubMedCentralCrossRefGoogle Scholar
  47. 47.
    Murphy PM (2010) Double duty for CCL21 in dendritic cell trafficking. Immunity 32:590–592PubMedPubMedCentralCrossRefGoogle Scholar
  48. 48.
    Marciano DK (2016) A holey pursuit: lumen formation in the developing kidney. Pediatr Nephrol 32:7–20PubMedPubMedCentralCrossRefGoogle Scholar
  49. 49.

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MedicineUniversity of HeidelbergHeidelbergGermany

Personalised recommendations