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.

A combination of experimental analysis and mathematical modelling shows how the genetic control of tissue polarity plays a fundamental role in the development and evolution of form.

Rapid advances in microscopy and genetic labeling strategies have created new opportunities for time-lapse imaging of embryonic development. However, methods for immobilizing embryos for long periods while maintaining normal development have changed little. In zebrafish, current immobilization techniques rely on the anesthetic tricaine. Unfortunately, prolonged tricaine treatment at concentrations high enough to immobilize the embryo produces undesirable side effects on development. We evaluate three alternative immobilization strategies: combinatorial soaking in tricaine and isoeugenol, injection of α-bungarotoxin protein, and injection of α-bungarotoxin mRNA. We find evidence for co-operation between tricaine and isoeugenol to give immobility with improved health. However, even in combination these anesthetics negatively affect long-term development. α-bungarotoxin is a small protein from snake venom that irreversibly binds and inactivates acetylcholine receptors. We find that α-bungarotoxin either as purified protein from snakes or endogenously expressed in zebrafish from a codon-optimized synthetic gene can immobilize embryos for extended periods of time with few health effects or developmental delays. Using α-bungarotoxin mRNA injection we obtain complete movies of zebrafish embryogenesis from the 1-cell stage to 3 days post fertilization, with normal health and no twitching. These results demonstrate that endogenously expressed α-bungarotoxin provides unprecedented immobility and health for time-lapse microscopy.

A novel combination of molecular genetics, shape analysis, and computational modelling shows how the complex three-dimensional shape of the Snapdragon flower can arise through local gene activity.