RESUMO

Here we discuss the formation of phyllotactic patterns in the shoot apical meristem (SAM) of plants, where the spatial distribution of the phytohormone auxin determines phyllotaxis in a domain that is growing and changing in time. We assume that the concentration of auxin modifies the mechanical properties of the domain and that the mechanical stress field in the SAM orients the flux of auxin. To study this problem we propose a mechanism for pattern formation in growing domains with variable curvature. The dynamics of chemicals is modeled by a reaction-diffusion system that produces a three dimensional pattern of chemical concentrations that changes the stress field in the domain while growing. The growth process is modeled by a phase-field order parameter which determines the location of the boundaries of the domain. This field is coupled to the chemical concentration through a curvature term that affects the local mechanical stress in the domain. The local stress changes in turn modify the chemical patterns. Our model constitutes a useful and novel approach in theoretical biology, as many developmental processes in organisms seem to be affected by the changes of curvature, size, mechanical stress and other physical aspects. Several patterns seen in many plants are reproduced under certain conditions by our model.

Assuntos

Ácidos Indolacéticos/metabolismo , Meristema/crescimento & desenvolvimento , Modelos Biológicos , Desenvolvimento Vegetal , Folhas de Planta/crescimento & desenvolvimento , Brotos de Planta/crescimento & desenvolvimento , Fenômenos Biomecânicos , Quimiotaxia , Simulação por Computador , Difusão , Meristema/metabolismo , Folhas de Planta/anatomia & histologia , Folhas de Planta/metabolismo , Brotos de Planta/anatomia & histologia , Brotos de Planta/metabolismo , Plantas/anatomia & histologia , Plantas/metabolismo , Estresse Mecânico

RESUMO

We developed a measurement framework of spatial organization to categorize 2-dimensional patterns from 2 multiscalar biological architectures. We propose that underlying shapes of biological entities can be approached using the statistical concept of degrees of freedom, defining it through expansion of area variability in a pattern. To help scope this suggestion, we developed a mathematical argument recognizing the deep foundations of area variability in a polygonal pattern (spatial heterogeneity). This measure uses a parameter called eutacticity. Our measuring platform of spatial heterogeneity can assign particular ranges of distribution of spatial areas for 2 biological architectures: ecological patterns of Namibia fairy circles and epithelial sheets. The spatial organizations of our 2 analyzed biological architectures are demarcated by being in a particular position among spatial order and disorder. We suggest that this theoretical platform can give us some insights about the nature of shapes in biological systems to understand organizational constraints.