An Analysis of One- and Two-Dimensional Patterns in a Mechanical Model for Morphogenesis

In early embryonic development, fibroblast cells move through an extracellular matrix (ECM) exerting large traction forces which deform the ECM. We model these mechanical interactions mathematically and show that the various effects involved can combine to produce pattern in cell density. A linear analysis exhibits a wide selection of dispersion relations, suggesting a richness in pattern forming capability of the model. A nonlinear bifurcation analysis is presented for a simple version of the governing field equations. The one-dimensional analysis requires a non-standard element. The two-dimensional analysis shows the possibility of roll and hexagon pattern formation. A realistic biological application to the formation of feather germ primordia is briefly discussed.