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The phytohormone auxin is implied in steering various developmental decisions during plant morphogenesis in a concentration-dependent manner. Auxin maxima have been shown to maintain meristematic activity, for example, of the root apical meristem, and position new sites of outgrowth, such as during lateral root initiation and phyllotaxis. More recently, it has been demonstrated that sites of auxin minima also provide positional information. In the developing Arabidopsis fruit, auxin minima are required for correct differentiation of the valve margin. It remains unclear, however, how this auxin minimum is generated and maintained. Here, we employ a systems biology approach to model auxin transport based on experimental observations. This allows us to determine the minimal requirements for its establishment. Our simulations reveal that two alternative processes—which we coin “flux-barrier” and “flux-passage”—are both able to generate an auxin minimum, but under different parameter settings. Both models are in principle able to yield similar auxin profiles but present qualitatively distinct patterns of auxin flux. The models were tested by tissue-specific inducible ablation, revealing that the auxin minimum in the fruit is most likely generated by a flux-passage process. Model predictions were further supported through 3D PIN localization imaging and implementing experimentally observed transporter localization. Through such an experimental–modeling cycle, we predict how the auxin minimum gradually matures during fruit development to ensure timely fruit opening and seed dispersal.

Background Segmentation, the subdivision of the major body axis into repeated elements, is considered one of the major evolutionary innovations in bilaterian animals. In all three segmented animal clades, the predominant segmentation mechanism is sequential segmentation, where segments are generated one by one in anterior–posterior order from a posterior undifferentiated zone. In vertebrates and arthropods, sequential segmentation is thought to arise from a clock-and-wavefront-type mechanism, where oscillations in the posterior growth zone are transformed into a segmental prepattern in the anterior by a receding wavefront. Previous evo-devo simulation studies have demonstrated that this segmentation type repeatedly arises, supporting the idea of parallel evolutionary origins in these animal clades. Sequential segmentation has been studied most extensively in vertebrates, where travelling waves have been observed that reflect the slowing down of oscillations prior to their cessation and where these oscillations involve a highly complex regulatory network. It is currently unclear under which conditions this oscillator complexity and slowing should be expected to evolve, how they are related and to what extent similar properties should be expected for sequential segmentation in other animal species. Results To investigate these questions, we extend a previously developed computational model for the evolution of segmentation. We vary the slope of the posterior morphogen gradient and the strength of gene expression noise. We find that compared to a shallow gradient, a steep morphogen gradient allows for faster evolution and evolved oscillator networks are simpler. Furthermore, under steep gradients, damped oscillators often evolve, whereas shallow gradients appear to require persistent oscillators which are regularly accompanied by travelling waves, indicative of a frequency gradient. We show that gene expression noise increases the likelihood of evolving persistent oscillators under steep gradients and of evolving frequency gradients under shallow gradients. Surprisingly, we find that the evolutions of oscillator complexity and travelling waves are not correlated, suggesting that these properties may have evolved separately. Conclusions Based on our findings, we suggest that travelling waves may have evolved in response to shallow morphogen gradients and gene expression noise. These two factors may thus also be responsible for the observed differences between different species within both the arthropod and chordate phyla. Electronic supplementary material The online version of this article (10.1186/s13227-018-0113-2) contains supplementary material, which is available to authorized users.

Somitogenesis is one of the major hallmarks of bilateral symmetry in vertebrates. This symmetry is lost when retinoic acid (RA) signalling is inhibited, allowing the left-right determination pathway to influence somitogenesis. In all three studied vertebrate model species, zebrafish, chicken and mouse, the frequency of somite formation becomes asymmetric, with slower gene expression oscillations driving somitogenesis on the right side. Still, intriguingly, the resulting left-right asymmetric phenotypes differ significantly between these model species. While somitogenesis is generally considered as functionally equivalent among different vertebrates, substantial differences exist in the subset of oscillating genes between different vertebrate species. Variation also appears to exist in the way oscillations cease and somite boundaries become patterned. In addition, in absence of RA, the FGF8 gradient thought to constitute the determination wavefront becomes asymmetric in zebrafish and mouse, extending more anteriorly to the right, while remaining symmetric in chicken. Here we use a computational modelling approach to decipher the causes underlying species differences in asymmetric somitogenesis. Specifically, we investigate to what extent differences can be explained from observed differences in FGF asymmetry and whether differences in somite determination dynamics may also be involved. We demonstrate that a simple clock-and-wavefront model incorporating the observed left-right differences in somitogenesis frequency readily reproduces asymmetric somitogenesis in chicken. However, incorporating asymmetry in FGF signalling was insufficient to robustly reproduce mouse or zebrafish asymmetry phenotypes. In order to explain these phenoptypes we needed to extend the basic model, incorporating species-specific details of the somitogenesis determination mechanism. Our results thus demonstrate that a combination of differences in FGF dynamics and somite determination cause species differences in asymmetric somitogenesis. In addition,they highlight the power of using computational models as well as studying left-right asymmetry to obtain more insight in somitogenesis.