Limbs Made to Measure

This year marks the 150th anniversary of the birth of D’Arcy Thompson, the British biologist, classicist, and all round polymath (For more information on D’Arcy Thompson see www. darcythompson.org). Like many, he was fascinated by the appearance and structure of living matter, and in his influential book, On Growth and Form [1], he set out to describe and explain the principles of morphogenesis—the way living things grow and acquire their forms. Using a vast range of examples, from the honeycomb in beehives to the spirals in a snail’s shell, he emphasized that form should be studied in the context of growth and that to explain shape it was essential to understand the underlying mechanisms. This led to the central thesis of the book: biological forms are the result of mechanical and physical processes that should be described with mathematical precision. Yet, while the molecular basis of pattern formation and cellular differentiation during development has received much attention, our knowledge of the regulation of growth and organ shape lags behind. Partly, this is because acquiring accurate high-resolution 3-D measurements of organ shape and cellular behaviour and the quantitative analysis of these data has been technically challenging. Thus, 3-D organs are often studied using simpler 2-D representations. However, in recent years new imaging technology and the increase in computational power has begun to overcome these limitations, revealing previously unseen detail and allowing long-standing hypotheses to be tested. In broad terms, the morphogenesis of a developing tissue is achieved by anisotropic growth. That is, the tissue expands in unequal amounts in different directions, so that the final organ shape gradually materializes. Two fundamentally different ways to achieve anisotropic growth can be envisioned (Figure 1). In one case, external mechanical forces mould the final organ form. As a result, cells are reshaped or rearranged by forces imposed from outside. For example, growth substrates exert surface tension on cultured cells, while blood flow exerts shear on endothelial cells (see [2]). Alternatively, shape formation can be inherent to the organ and result from the collective behaviour of the individual cells comprising the organ. Importantly, two distinct classes of cellular behaviour can contribute to this active tissue modelling (Figure 1). In the first class, anisotropy results from cellular processes that occur non-directionally, but at different frequency across the tissue (e.g., proliferation, apoptosis, change of cell shape). For example, differences in proliferation rate across an organ could cause some parts to expand faster than others. For this to happen, cells must ‘‘know’’ only their position in a tissue, but not their spatial orientation. By contrast, the second class of mechanisms relies on directional—anisotropic—cellular activity. These could be, for instance, oriented division or migration of cells in a specified direction. Such mechanisms require a cue that provides cells with a bearing—a vector. Although fundamentally different, experimentally it has often proved difficult to distinguish between these classes of cell behaviour, since each can result in a cell changing its relative position within an organ. Moreover, these mechanisms are not mutually exclusive and a combination of passive, active, directional and non-directional cellular behaviours could play a role in defining organ shape. Thus, determining the contribution of different behaviour types is necessary for understanding the molecular mechanisms of organ morphogenesis. One tissue that exemplifies the problem of distinguishing the mechanism of morphogenesis is the developing limb. From amphibians to mammals, the limbs of tetrapods start growing from small bulges called limb buds. Initially, these buds are composed of loose mesenchymal cells, ensheathed by a layer of ectodermal cells (Figure 2). At the distal rim of the limb bud, the ectoderm is thickened into the ‘‘apical ectodermal ridge’’ (AER), which secretes extracellular signals, notably members of the Fibroblast Growth Factor (FGF) family, that are important for limb outgrowth and patterning (see [3]). Following limb bud initiation, but prior to the laying down of the skeletal elements, limb tissue extends mainly in a distal direction, away from the body, such that the length along the proximal–distal axis increases much faster than the anterior–posterior or dorsal–ventral axes. Thus, the developing limb serves as a good example of anisotropic growth and raises the question of what mechanisms contribute to the distal outgrowth. The realization that the AER is the source of a proliferative signal has provided the inspiration for a ‘‘growth-based morphogenesis’’ model of limb development [4,5]. According to this view, proximal–distal elongation of the limb bud results from a gradient of proliferation rates along this axis, which represents a nondirectional mechanism. Indeed, measurements of cell cycle duration confirmed that distally located cells proliferate faster [6]. Moreover, computational models, some dating back more than 40 years, have been used to check if these differences in proliferation rate could explain limb morphogenesis. These models were restricted to oneor two-dimensional representations of the limb and suggested that ‘‘growth-based morphogenesis’’ could be responsible for shaping the limb. But, other mechanisms were not ruled out, and it is notable that in some models directional