Estimating the spatiotemporal pattern of volumetric growth rate from fate maps in chick limb development

Morphogenesis is achieved through volumetric growth of tissue at a rate varying over space and time. The volumetric growth rate of each piece of tissue reflects the behaviors of constituent cells such as cell proliferation and death. Hence, clarifying its spatiotemporal pattern accurately is a key to bridge between cell behaviors and organ morphogenesis. We here propose a new method to estimate the spatiotemporal pattern of volumetric growth rate from fate map data with limited resolution on space and time by using a mathematical model. We apply the method to chick wing data along the proximodistal axis, and find that the volumetric growth pattern is biphasic: it is spatially uniform in earlier stages (until stage 23), but in later stages the volumetric growth occurs approximately 4.5 times as fast as in the distal region (within approximately 100 microm from the limb tip) than in the proximal region.