Mathematical study on robust tissue pattern formation in growing epididymal tubule

Tissue pattern formation during development is a reproducible morphogenetic process organized by a series of kinetic cellular activities, leading to the building of functional and stable organs. Recent studies focusing on mechanical aspects have revealed physical mechanisms on how the cellular activities contribute to the formation of reproducible tissue patterns; however, the understanding for what factors achieve the reproducibility of such patterning and how it occurs is far from complete. Here, I focus on a tube pattern formation during murine epididymal development, and show that two factors influencing physical design for the patterning, the proliferative zone within the tubule and the viscosity of tissues surrounding to the tubule, control the reproducibility of epididymal tubule pattern, using a mathematical model based on experimental data. Extensive numerical simulation of the simple mathematical model revealed that a spatially localized proliferative zone within the tubule, observed in experiments, results in more reproducible tubule pattern. Moreover, I found that the viscosity of tissues surrounding to the tubule imposes a trade-off regarding pattern reproducibility and spatial accuracy relating to the region where the tubule pattern is formed. This indicates an existence of optimality in material properties of tissues for the robust patterning of epididymal tubule. The results obtained by numerical analysis based on experimental observations provide a general insight on how physical design realizes robust tissue pattern formation.