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Abstract Highly polarized cotton fibre cells that develop from the seed coat surface are the foundation of a multi-billion-dollar international textile industry. The unicellular trichoblast emerges as a hemispherical bulge that is efficiently converted to a narrower and elongated shape that extends for about 2 weeks before transitioning into a cellulose-generating machine. The polarized elongation phase employs an evolutionarily conserved microtubule-cellulose synthase control module that patterns the cell wall and enables highly anisotropic diffuse growth. As the multi-scale interactions and feedback controls among cytoskeletal systems, morphologically potent cell wall properties, and a changing cell geometry are uncovered, opportunities emerge to engineer architectural traits. However, in cotton, such efforts are hampered by insufficient knowledge about the underlying control mechanisms. For example, fibre diameter is an important trait that is determined during the earliest stages of development, but the basic growth mode and the mechanisms by which cytoskeletal and cell wall systems mediate fibre tapering are not known. This paper combines multiparametric and multiscale fibre phenotyping and finite element computational modelling of a growing cell to discover an evolutionarily conserved tapering mechanism. The actin network interconverts between two distinct longitudinal organizations that broadly distributes organelles and likely enables matrix secretion patterns that maintain cell wall thickness during growth. Based on plausible finite element models and quantitative analyses of the microtubule cytoskeleton, tapering and anisotropic growth is programmed by a constricting apical microtubule depletion zone and highly aligned microtubules along the fibre shaft. The finite element model points to a central role for tensile forces in the cell wall to dictate the densities and orientations of morphologically potent microtubules that pattern the cell wall. 

Abstract Shape plays a fundamental role in biology. Traditional phenotypic analysis methods measure some features but fail to measure the information embedded in shape comprehensively. To extract, compare and analyse this information embedded in a robust and concise way, we turn to topological data analysis (TDA), specifically the Euler characteristic transform. TDA measures shape comprehensively using mathematical representations based on algebraic topology features. To study its use, we compute both traditional and topological shape descriptors to quantify the morphology of 3121 barley seeds scanned with X-ray computed tomography (CT) technology at 127 μm resolution. The Euler characteristic transform measures shape by analysing topological features of an object at thresholds across a number of directional axes. A Kruskal–Wallis analysis of the information encoded by the topological signature reveals that the Euler characteristic transform picks up successfully the shape of the crease and bottom of the seeds. Moreover, while traditional shape descriptors can cluster the seeds based on their accession, topological shape descriptors can cluster them further based on their panicle. We then successfully train a support vector machine to classify 28 different accessions of barley based exclusively on the shape of their grains. We observe that combining both traditional and topological descriptors classifies barley seeds better than using just traditional descriptors alone. This improvement suggests that TDA is thus a powerful complement to traditional morphometrics to comprehensively describe a multitude of ‘hidden’ shape nuances which are otherwise not detected.