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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. 

Abstract Background Physical seed dormancy is an important trait in legume domestication. Although seed dormancy is beneficial in wild ecosystems, it is generally considered to be an undesirable trait in crops due to reduction in yield and / or quality. The physiological mechanism and underlying genetic factor(s) of seed dormancy is largely unknown in several legume species. Here we employed an integrative approach to understand the mechanisms controlling physical seed dormancy in common bean ( Phaseolus vulgaris L.). Results Using an innovative CT scan imaging system, we were able to track water movements inside the seed coat. We found that water uptake initiates from the bean seed lens. Using a scanning electron microscopy (SEM) we further identified several micro-cracks on the lens surface of non-dormant bean genotypes. Bulked segregant analysis (BSA) was conducted on a bi-parental RIL (recombinant inbred line) population, segregating for seed dormancy. This analysis revealed that the seed water uptake is associated with a single major QTL on Pv03. The QTL region was fine-mapped to a 118 Kb interval possessing 11 genes. Coding sequence analysis of candidate genes revealed a 5-bp insertion in an ortholog of pectin acetylesterase 8 that causes a frame shift, loss-of-function mutation in non-dormant genotype. Gene expression analysis of the candidate genes in the seed coat of contrasting genotypes indicated 21-fold lower expression of pectin acetylesterase 8 in non-dormant genotype. An analysis of mutational polymorphism was conducted among wild and domesticated beans. Although all the wild beans possessed the functional allele of pectin acetylesterase 8 , the majority (77%) of domesticated beans had the non-functional allele suggesting that this variant was under strong selection pressure through domestication. Conclusions In this study, we identified the physiological mechanism of physical seed dormancy and have identified a candidate allele causing variation in this trait. Our findings suggest that a 5-bp insertion in an ortholog of pectin acetylesterase 8 is likely a major causative mutation underlying the loss of seed dormancy during domestication. Although the results of current study provide strong evidences for the role of pectin acetylesterase 8 in seed dormancy, further confirmations seem necessary by employing transgenic approaches.