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In the past 20-30 years, developmental biologists have made tremendous progress in identifying genes required for the specification of individual cell types of an organ and in describing how they interact in genetic networks. In comparison, very little is known about the mechanisms that regulate tissue polarity and overall organ patterning. Gynoecia and fruits from members of the Brassicaceae family of flowering plants provide excellent model systems to study organ patterning and tissue specification because they become partitioned into distinct domains whose formation is determined by polarity establishment both at a cellular and whole tissue level. Interactions among key regulators of Arabidopsis gynoecium and fruit development have revealed a network of upstream transcription factor activities required for such tissue differentiation. Regulation of the plant hormone auxin is emerging as both an immediate downstream output and input of these activities, and here we aim to provide an overview of the current knowledge regarding the link between auxin and female reproductive development in plants. In this review, we will also demonstrate how available data can be exploited in a mathematical modeling approach to reveal and understand the feedback regulatory circuits that underpin the polarity establishment, necessary to guide auxin flows. [ABSTRACT FROM AUTHOR]

A synthesis is presented of recent work by the authors and others on the formation of localised patterns, isolated spots, or sharp fronts in models of natural processes governed by reaction–diffusion equations. Contrasting with the well-known Turing mechanism of periodic pattern formation, a general picture is presented in one spatial dimension for models on long domains that exhibit sub-critical Turing instabilities. Localised patterns naturally emerge in generalised Schnakenberg models within the pinning region formed by bistability between the patterned state and the background. A further long-wavelength transition creates parameter regimes of isolated spots which can be described by semi-strong asymptotic analysis. In the species-conservation limit, another form of wave pinning leads to sharp fronts. Such fronts can also arise given only one active species and a weak spatial parameter gradient. Several important applications of this theory within natural systems are presented, at different lengthscales: cellular polarity formation in developmental biology, including root-hair formation, leaf pavement cells, keratocyte locomotion; and the transitions between vegetation states on continental scales. Philosophical remarks are offered on the connections between different pattern formation mechanisms and on the benefit of subcritical instabilities in the natural world. • Localised patterns, isolated spots and sharp fronts emerge in biological models. • These naturally occurring patterns can be linked to subcritical Turing instabilities. • Combining theoretical approaches helps elucidating the different mechanisms involved. • It sheds light on disjointed developmental and ecological phenomena in nature. • Biology favours multistability and hysteresis above supercritical instability. [ABSTRACT FROM AUTHOR]