This article explores the close relationships between growth rate and allometries of molluscan shells. After reviewing the previous theoretical approaches devoted to the understanding of shell form and its morphogenesis, we present a free-form vector model which can simulate apertural shape changes and nonlinear allometries. Shell morphology is generated by iteratively adding a growth increment onto the last computed aperture. The first growth increment defines so-called growth vectors which are assumed to be constant in direction (relative to the last computed aperture position) during a simulation of a shell (ontogeny). These growth vectors are uniformly scaled at each time step according to various growth rate curves that are used to simulate the mantle growth over time. From the model, we derive morphometric variables that illustrate the ontogenetic trajectories in time-size-shape space. We investigate the effects of changing the growth curves types, growth rate parameters and growth vector maps on the direction, speed and patterns of ontogenetic allometries. Because this model focuses the issue on time, it highlights a plausible effect of growth rate on shell shape and illustrates some fundamental geometrical properties of the logarithmic spiral, in particular the close relationship between the size and the geometry of growth increments. This model could be used to develop a mathematically data-driven approach where experimentally obtained growth curves could be used as inputs in the model. More generally, our study recalls the role of growth rates in the generation of allometries.

The origin of jaws remains largely an enigma that is best addressed by studying fossil and living jawless vertebrates. Conodonts were eel-shaped jawless animals, whose vertebrate affinity is still disputed. The geometrical analysis of exceptional three-dimensionally preserved clusters of oro-pharyngeal elements of the Early Triassic Novispathodus, imaged using propagation phase-contrast X-ray synchrotron microtomography, suggests the presence of a pulley-shaped lingual cartilage similar to that of extant cyclostomes within the feeding apparatus of euconodonts ("true" conodonts). This would lend strong support to their interpretation as vertebrates and demonstrates that the presence of such cartilage is a plesiomorphic condition of crown vertebrates.apical cartilage | conodont oral skeleton | early vertebrates | homology H ow the transition from "agnathans" to gnathostomes ("jawed" vertebrates) occurred is one of the most intriguing problems of evolutionary biology (1). Little is known about the endoskeleton of fossil jawless vertebrates [e.g., fossil cyclostomes (hagfishes and lampreys) and "ostracoderms"]. Although the view is still debated (2), euconodonts would have possessed the very first vertebrate mineralized skeleton in the form of their oral denticles (3, 4).The general architecture of the conodont oral skeleton is a bilaterally symmetrical array of usually 15 phosphatic elements, which generally becomes disarticulated after the decay of the supporting tissues. Hence most conodonts are known only as isolated elements. From the detailed study of hundreds of articulated "natural assemblages" and photographic simulation of their collapse, Purnell and Donoghue (5) constructed a 3D model of the Idiognathodus apparatus [presumably a template for all ozarkodinid apparatuses (6)] in which one pair of obliquely pointed M elements are located rostrally and, behind them, one unpaired S 0 (subscript number indicates distance ordering from the symmetry axis) element lying on the axis of bilateral symmetry and four pairs of elements (S 1-4 ) located on both sides of the S 0 would have grasped food and, more caudally, two pairs of pectiniform elements (P 1 , P 2 ) would have processed this food by crushing and/or slicing (5, 7, 8) ( Fig. 1 A-B) (for "standard" orientation of single elements, see Fig. S1). Purnell and Donoghue's reconstruction of a generalized resting (dead) position is very well supported and in most aspects very convincing. It is therefore adopted here as a basis upon which we build our dynamic reconstruction of the feeding apparatus at work.How could these elements actually grasp or cut prey tissues? Purnell and Donoghue's functional model (section 6 of ref. 5) was based chiefly on analogies with extant agnathans. Indeed, the "quite simple" geometry of the Idiognathodus elements does not provide much indication of what motions are possible or not [except for uncommon natural assemblages (see below)]. Thus, hypotheses were inferred from extant putative closest relatives. In our view, the more "compli...

In recent years, developmental plasticity has received increasing attention. Specifically, some studies highlighted a possible association between shell shape and growth rates in intertidal gastropods. We use a growth vector model to study how hypothetical growth processes could underlie developmental plasticity in molluscs. It illustrates that variation in instantaneous shell growth rate can induce variability in allometric curves. Consequently, morphological variation is time-dependent. Basing our model parameters on a study documenting the results of transplants experiments of three gastropods ecomorphs, we reproduce the main aspects of the variation in size, shape, and growth rates among populations when bred in their own habitat or transplanted to another ecotype habitat. In agreement with empirical results, our simulation shows that a flatter growth profile corresponds to conditions of rapid growth. The model also allows the comparison of allometric slopes using different subdata sets that correspond to static and ontogenetic allometry. Our model highlights that depending on subdata sets, the "main effects" could be attributed to source population or environment. In addition, convergence or divergence of allometric slopes is observed depending on the subdata sets. Although there is evidence that shell shape in gastropods is to some extent growth rate dependent, gaining a general overview of the issue is challenging, in particular because of the scarcity of studies referring to allometry. We argue that the dynamics of development at the "phenotypic level" constitute a non-reducible level of investigation if one seeks to relate the observed amount of phenotypic variation to variability in the underlying factors.

Several fused clusters of conodont elements of the genera Neospathodus and Novispathodus were recovered from limestone beds at the Dienerian–Smithian and Smithian–Spathian boundaries, respectively, from several localities in Guangxi province, South China. Conodont clusters are otherwise extremely rare in the Triassic, and these are first described for the Early Triassic. The exceptional specimens partially preserve the relative three‐dimensional position and orientation of ramiform elements and are therefore extremely important for testing hypotheses on the architecture of apparatuses. These specimens partly confirm the previous reconstruction of the Novispathodus apparatus by Orchard. Within apparatuses of members of superfamily Gondolelloidea, elements previously identified as occupying the S1 and S2 positions instead occupy the S2 and S1 positions. Similarly, within apparatuses of members of the subfamily Novispathodinae, elements previously referred to S3 and S4 positions are reinterpreted to have occupied S4 and S3 positions, respectively.

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In the 1950s, embryology was conceptualized as four relatively independent problems: cell differentiation, growth, pattern formation and morphogenesis. The mechanisms underlying the first three traditionally have been viewed as being chemical in nature, whereas those underlying morphogenesis have usually been discussed in terms of mechanics. Often, morphogenesis and its mechanical processes have been regarded as subordinate to chemical ones. However, a growing body of evidence indicates that the biomechanics of cells and tissues affect in striking ways those phenomena often thought of as mainly under the control of cell-cell signalling. This accumulation of data has led to a revival of the mechano-transduction concept in particular, and of complexity in general, causing us now to consider whether we should retain the traditional conceptualization of development. The researchers' semantic preferences for the terms 'patterning', 'pattern formation' or 'morphogenesis' can be used to describe three main 'schools of thought' which emerged in the late 1970s. In the 'molecular school', the term patterning is deeply tied to the positional information concept. In the 'chemical school', the term 'pattern formation' regularly implies reaction-diffusion models. In the 'mechanical school', the term 'morphogenesis' is more frequently used in relation to mechanical instabilities. Major differences among these three schools pertain to the concept of self-organization, and models can be classified as morphostatic or morphodynamic. Various examples illustrate the distorted picture that arises from the distinction among differentiation, growth, pattern formation and morphogenesis, based on the idea that the underlying mechanisms are respectively chemical or mechanical. Emerging quantitative approaches integrate the concepts and methods of complex sciences and emphasize the interplay between hierarchical levels of organization via mechano-chemical interactions. They draw upon recent improvements in mathematical and numerical morphogenetic models and upon considerable progress in collecting new quantitative data. This review highlights a variety of such models, which exhibit important advances, such as hybrid, stochastic and multiscale simulations.

Summary Madin-Darby canine kidney II (MDCKII) cells are widely used to study epithelial morphogenesis. To better understand this process, we performed time course RNA-seq analysis of MDCKII 3D cystogenesis, along with polarized 2D cells for comparison. Our study reveals a biphasic change in the transcriptome that occurs after the first cell cycle and coincides with lumen establishment. This change appears to be linked to translocation of β-catenin, supported by analyses with AVL9 - and DENND5A -knockdown clones, and regulation by HNF1B, supported by ATAC-seq study. These findings indicate a qualitative change model for transcriptome remodeling during epithelial morphogenesis, leading to cell proliferation decrease and cell polarity establishment. Furthermore, our study reveals that active mitochondria are retained and chromatin accessibility decreases in 3D cysts but not in 2D polarized cells. This indicates that 3D culture is a better model than 2D culture for studying epithelial morphogenesis.

The molluscan shell can be viewed as a petrified representation of the organism’s ontogeny and thus can be used as a record of changes in form during growth. However, little empirical data is available on the actual growth and form of shells, as these are hard to quantify and examine simultaneously. To address these issues, we studied the growth and form of a land snail that has an irregularly coiled and heavily ornamented shell–Plectostoma concinnum. The growth data were collected in a natural growth experiment and the actual form changes of the aperture during shell ontogeny were quantified. We used an ontogeny axis that allows data of growth and form to be analysed simultaneously. Then, we examined the association between the growth and the form during three different whorl growing phases, namely, the regular coiled spire phase, the transitional constriction phase, and the distortedly-coiled tuba phase. In addition, we also explored the association between growth rate and the switching between whorl growing mode and rib growing mode. As a result, we show how the changes in the aperture ontogeny profiles in terms of aperture shape, size and growth trajectory, and the changes in growth rates, are associated with the different shell forms at different parts of the shell ontogeny. These associations suggest plausible constraints that underlie the three different shell ontogeny phases and the two different growth modes. We found that the mechanism behind the irregularly coiled-shell is the rotational changes of the animal’s body and mantle edge with respect to the previously secreted shell. Overall, we propose that future study should focus on the role of the mantle and the columellar muscular system in the determination of shell form.