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

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.

WNT-Mediated Regulation of FOXO1 Constitutes a Critical Axis Maintaining Pubertal Mammary Stem Cell Homeostasis

“…2D). Indeed, as recently reported (Paine et al, 2016), we confirmed that a vast majority of the cap-in-body cell population (69.1 ± 13.1%) was apoptotic, measured by cleaved caspase 3 (cc3) expression and terminal deoxynucleotidyl transferase dUTP nick end labeling (TUNEL) assays (Fig. 2E, Fig.…”

“…2A). Cap cells display expeditious cell cycling, with durations in the range of 16 h (Paine et al, 2016). To test whether cap-in-body cell clusters are a product of cell division, we assessed p63 CreERT2/+ lineage-traced TEBs at early time points, where GFP + cells are labeled more sparsely to ask if labeled clusters were clonal.…”

“…In addition to dampened WNT signaling, cap-in-body cell apoptosis may also be a consequence of anoikis, as has been proposed (Mailleux et al, 2007). Based on our previous study mathematically modeling ductal elongation (Paine et al, 2016), we speculate that surplus cap cells may slough off from the outer cap cell layer and undergo apoptosis in an attempt to maintain a steady state number of cap cells. This idea is reminiscent of crowding-induced cell extrusion that has been proposed in the intestine as a mechanism to eliminate cells resulting from excessive cell division, thus maintaining a fixed range of intestinal cell numbers (Eisenhoffer et al, 2012).…”

“…Adapted after (Paine et al, 2016). TEBs were identified as the bulbous tips of ducts and demarcated distinct from the duct at the narrowest region of the bulb structure (in the case of sections with trailing ducts).…”

“…TEBs drive ductal extension at an incredible rate of ~0.5mm/day (Hinck and Silberstein, 2005; Paine et al, 2016). While cell division and differentiation in the TEBs result in arborization of the mammary ducts, apoptosis enables lumen formation through cell clearance (Humphreys et al, 1996; Mailleux et al, 2007).…”