Modeling Tip Growth: Pushing Ahead

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Abstract

Tip growth, the localized extension of a cell at one of its ends, is a beautiful example of morphogenesis. Because of the highly localized nature of the growth process, it is relatively amenable to analysis. Hence, it has attracted the attention of experimentalists and theorists alike, who over the years, have sought to elucidate the mechanisms underlying this form of development, the latter through explicit mathematical models. This review provides an overview of the modeling of tip-growing cells in general, and that of plant root hairs in particular, as it has developed during the last decades. Two main lines of modeling can be distinguished. In geometrical models, the focus is on the shape of the cells alone, while the aim of biomechanical models is to clarify the underlying physical mechanisms. So far, only a few attempts have been made to combine these two approaches. Yet, the incorporation of the mechanical properties of the nascent cell wall and the forces exerted on it is very likely needed to fully understand and ultimately control tip growth. This synthesis would pave the way to fully predictive models and hence could also guide new experiments to verify them. We provide an outlook on possible routes towards this goal.