Therefore, the main focus of recent patterning studies has been to clarify the designs of the

interdependent relationships that achieve robust patterning. Over the past few years, as a first step toward addressing this problem, the mechanisms for achieving robust patterning independent of tissue size, ensuring a body plan of reproducible Wnt antagonist proportions, have been studied. The mechanisms are important because the size of the developing organism is highly variable, depending on external nutrient conditions and genetic polymorphisms. In the simplest situation, tissue growth rate is spatially uniform, and the morphogen gradient scales with tissue size without change in its source level (Figure 4b). In this case, the relative position of each cell within a growing tissue and the morphogen concentration

that the cell experiences are time invariant. Thus, a threshold-like response is sufficient to achieve size-independent patterning. Possible mechanisms have been proposed to achieve such a scaled gradient [42 and 43••]. This type of patterning is reported for Dpp in the wing PLX4032 disc [44• and 45] and nuclear Bicoid in the early Drosophila embryo [46 and 47]. In other systems, gradient scaling with time-variant source intensity is observed (Figure 4c). For example, during early development of Drosophila, the Dorsal gradient along the dorso-ventral axis scales with increasing source intensity [48, 49 and 50]. The gradient of Dpp signaling along the AP axis in the wing disc also scales with the increasing source Ponatinib cell line intensity during larval stages [43••] (although this result is inconsistent with the report by [45]). In the latter system, interestingly,

the cell proliferation rate is independent of position (i.e. spatially uniform growth) in the wing disc, even though cell proliferation itself depends on Dpp signaling, whose level is different depending on position. This can be explained by a growth rule by which cells divide when Dpp signaling levels have increased by 50%. Such a rule is considered to be achieved by adaptation or fold change detection (FCD) mechanisms [51• and 52••]. For scaling gradients with time-variant source intensity, this mechanism achieves position-independent growth rates. It is not clear whether gradient scaling with spatially uniform growth is universally observed. Actually, in some systems, the spatial profile of morphogen gradients changes dynamically over time without scaling (Figure 4d); for example, Hh in the wing disc, Broad in eggshell, and Shh in vertebrate neural tube [53, 54• and 55••]. In particular, during neural tube development, the identity of neural precursor subtypes of ventral cells is determined by Shh signals from the notochord. It is reported that Shh expression levels in the notochord increase with time and that cell fate decisions depend on the duration of Shh signaling and the signaling level [55••].