Generation of Diverse Biological Forms through Combinatorial Interactions between Tissue Polarity and Growth

A major problem in biology is to understand how complex tissue shapes may arise through growth. In many cases this process involves preferential growth along particular orientations raising the question of how these orientations are specified. One view is that orientations are specified through stresses in the tissue (axiality-based system). Another possibility is that orientations can be specified independently of stresses through molecular signalling (polarity-based system). The axiality-based system has recently been explored through computational modelling. Here we develop and apply a polarity-based system which we call the Growing Polarised Tissue (GPT) framework. Tissue is treated as a continuous material within which regionally expressed factors under genetic control may interact and propagate. Polarity is established by signals that propagate through the tissue and is anchored in regions termed tissue polarity organisers that are also under genetic control. Rates of growth parallel or perpendicular to the local polarity may then be specified through a regulatory network. The resulting growth depends on how specified growth patterns interact within the constraints of mechanically connected tissue. This constraint leads to the emergence of features such as curvature that were not directly specified by the regulatory networks. Resultant growth feeds back to influence spatial arrangements and local orientations of tissue, allowing complex shapes to emerge from simple rules. Moreover, asymmetries may emerge through interactions between polarity fields. We illustrate the value of the GPT-framework for understanding morphogenesis by applying it to a growing Snapdragon flower and indicate how the underlying hypotheses may be tested by computational simulation. We propose that combinatorial intractions between orientations and rates of growth, which are a key feature of polarity-based systems, have been exploited during evolution to generate a range of observed biological shapes. Author Summary: How do genes control the growth of cells into complex tissue shapes such as flowers, wings or hearts? A key requirement is that genes must be able to modulate growth along particular directions. Two mechanisms have been proposed for how this may work; one based on the directions of mechanical stresses in the tissue and the other on molecular signals that propagate and provide local polarities. Here we show how a polarity-based system has the advantage of being able to act in combination with growth rates to generate a wide range of shapes. By applying this system to the development of the Snapdragon flower, we show, by comparison of computational simulations with actual flower development, how a simple set of polarity controls may underlie the formation of complex biological structures.