Cell lineage transport: a mechanism for molecular gradient formation.

Gradient formation is a fundamental patterning mechanism during embryo development, commonly related to secreted proteins that move along an existing field of cells. Here, we mathematically address the feasibility of gradients of mRNAs and non-secreted proteins. We show that these gradients can arise in growing tissues whereby cells dilute and transport their molecular content as they divide and grow, a mechanism we termed 'cell lineage transport.' We provide an experimental test by unveiling a distal-to-proximal gradient of Hoxd13 in the vertebrate developing limb bud driven by cell lineage transport, corroborating our model. Our study indicates that gradients of non-secreted molecules exhibit a power-law profile and can arise for a wide range of biologically relevant parameter values. Dilution and nonlinear growth confer robustness to the spatial gradient under changes in the cell cycle period, but at the expense of sensitivity in the timing of gradient formation. We expect that gradient formation driven by cell lineage transport will provide future insights into understanding the coordination between growth and patterning during embryonic development.