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A Geometrically-Constrained Mathematical Model of Mammary Gland Ductal Elongation Reveals Novel Cellular Dynamics within the Terminal End Bud

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  • Ingrid Paine
  • Arnaud Chauviere
  • John Landua
  • Amulya Sreekumar
  • Vittorio Cristini
  • Jeffrey Rosen
  • Michael T Lewis

Abstract

Mathematics is often used to model biological systems. In mammary gland development, mathematical modeling has been limited to acinar and branching morphogenesis and breast cancer, without reference to normal duct formation. We present a model of ductal elongation that exploits the geometrically-constrained shape of the terminal end bud (TEB), the growing tip of the duct, and incorporates morphometrics, region-specific proliferation and apoptosis rates. Iterative model refinement and behavior analysis, compared with biological data, indicated that the traditional metric of nipple to the ductal front distance, or percent fat pad filled to evaluate ductal elongation rate can be misleading, as it disregards branching events that can reduce its magnitude. Further, model driven investigations of the fates of specific TEB cell types confirmed migration of cap cells into the body cell layer, but showed their subsequent preferential elimination by apoptosis, thus minimizing their contribution to the luminal lineage and the mature duct.Author Summary: Our paper describes a mathematical model of mammary ductal elongation during pubertal development. We make several conclusions that will be of interest to scientists studying mammary gland biology, epithelial tube formation, and branching morphogenesis. First, our model indicates that a common measurement of developmental outgrowth (‘percent fat pad filled’) underestimates the total growth and leads to mischaracterization of mutant phenotypes. Second, we show that cap cells, a population enriched with putative mammary stem cells, do not contribute to the luminal lineage as previously hypothesized. Further, we find that a high percentage of proliferation in these cells is not used productively to actually form the mammary duct. We believe our model has future application to other branching organs and also for the modeling of disease states in the breast.

Suggested Citation

  • Ingrid Paine & Arnaud Chauviere & John Landua & Amulya Sreekumar & Vittorio Cristini & Jeffrey Rosen & Michael T Lewis, 2016. "A Geometrically-Constrained Mathematical Model of Mammary Gland Ductal Elongation Reveals Novel Cellular Dynamics within the Terminal End Bud," PLOS Computational Biology, Public Library of Science, vol. 12(4), pages 1-23, April.
    • Handle: RePEc:plo:pcbi00:1004839
    DOI: 10.1371/journal.pcbi.1004839
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    References listed on IDEAS

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    1. Anne C. Rios & Nai Yang Fu & Geoffrey J. Lindeman & Jane E. Visvader, 2014. "In situ identification of bipotent stem cells in the mammary gland," Nature, Nature, vol. 506(7488), pages 322-327, February.
    2. Alexandra Van Keymeulen & Ana Sofia Rocha & Marielle Ousset & Benjamin Beck & Gaëlle Bouvencourt & Jason Rock & Neha Sharma & Sophie Dekoninck & Cédric Blanpain, 2011. "Distinct stem cells contribute to mammary gland development and maintenance," Nature, Nature, vol. 479(7372), pages 189-193, November.
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    Cited by:

    1. Bryant, Adam S. & Lavrentovich, Maxim O., 2022. "Survival in branching cellular populations," Theoretical Population Biology, Elsevier, vol. 144(C), pages 13-23.
    2. Solís-Pérez, J.E. & Gómez-Aguilar, J.F. & Atangana, A., 2019. "A fractional mathematical model of breast cancer competition model," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 38-54.

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