A Geometrically-Constrained Mathematical Model of Mammary Gland Ductal Elongation Reveals Novel Cellular Dynamics within the Terminal End Bud.
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.
Lester and Sue Smith Breast Center, Baylor College of Medicine, Houston, Texas, United States of America.|Department of Molecular and Cellular Biology, Baylor College of Medicine, Houston, Texas, United States of America.
Ingrid
http://orcid.org/0000-0001-6603-8448
I
Paine
University Grenoble Alpes, TIMC-IMAG (DyCTiM), Grenoble, France.
Arnaud
A
Chauviere
Lester and Sue Smith Breast Center, Baylor College of Medicine, Houston, Texas, United States of America.
John
J
Landua
Department of Molecular and Cellular Biology, Baylor College of Medicine, Houston, Texas, United States of America.
Amulya
A
Sreekumar
Department of NanoMedicine and Biomedical Engineering, University of Texas Medical School at Houston, Houston, Texas, United States of America.|Brown Foundation Institute of Molecular Medicine, University of Texas Medical School at Houston, Houston, Texas, United States of America.|Department of Imaging Physics, University of Texas MD Anderson Cancer Center, Houston, Texas, United States of America.|Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia.
Vittorio
V
Cristini
Department of Molecular and Cellular Biology, Baylor College of Medicine, Houston, Texas, United States of America.
Jeffrey
J
Rosen
Lester and Sue Smith Breast Center, Baylor College of Medicine, Houston, Texas, United States of America.|Department of Molecular and Cellular Biology, Baylor College of Medicine, Houston, Texas, United States of America.|Department of Molecular and Cellular Biology and Radiology, Baylor College of Medicine, Houston, Texas, United States of America.
Michael T
MT
Lewis
D000818:Animals; D017209:Apoptosis; D019521:Body Patterning; D002453:Cell Cycle; D049109:Cell Proliferation; D048429:Cell Size; D019295:Computational Biology; D005260:Female; D007700:Kinetics; D008321:Mammary Glands, Animal / Q000166:cytology* / Q000254:growth & development*; D051379:Mice; D008807:Mice, Inbred BALB C; D008822:Mice, Transgenic; D008953:Models, Anatomic; D008954:Models, Biological; D012741:Sexual Maturation