Eya-controlled affinity between cell lineages drives tissue self-organization during Drosophila oogenesis.

Cooperative morphogenesis of cell lineages underlies the development of functional units and organs. To study mechanisms driving the coordination of lineages, we investigated soma-germline interactions during oogenesis. From invertebrates to vertebrates, oocytes develop as part of a germline cyst that consists of the oocyte itself and so-called nurse cells, which feed the oocyte and are eventually removed. The enveloping somatic cells specialize to facilitate either oocyte maturation or nurse cell removal, which makes it essential to establish the right match between germline and somatic cells. We uncover that the transcriptional regulator Eya, expressed in the somatic lineage, controls bilateral cell-cell affinity between germline and somatic cells in Drosophila oogenesis. Employing functional studies and mathematical modelling, we show that differential affinity and the resulting forces drive somatic cell redistribution over the germline surface and control oocyte growth to match oocyte and nurse cells with their respective somatic cells. Thus, our data demonstrate that differential affinity between cell lineages is sufficient to drive the complex assembly of inter-lineage functional units and underlies tissue self-organization during Drosophila oogenesis.

Uniform convergence guarantees for the deep Ritz method for nonlinear problems.

We provide convergence guarantees for the Deep Ritz Method for abstract variational energies. Our results cover nonlinear variational problems such as the p-Laplace equation or the Modica-Mortola energy with essential or natural boundary conditions. Under additional assumptions, we show that the convergence is uniform across bounded families of right-hand sides.

Charting the twist-to-bend ratio of plant axes.

During the evolution of land plants many body plans have been developed. Differences in the cross-sectional geometry and tissue pattern of plant axes influence their flexural rigidity, torsional rigidity and the ratio of both of these rigidities, the so-called twist-to-bend ratio. For comparison, we have designed artificial cross-sections with various cross-sectional geometries and patterns of vascular bundles, collenchyma or sclerenchyma strands, but fixed percentages for these tissues. Our mathematical model allows the calculation of the twist-to-bend ratio by taking both cross-sectional geometry and tissue pattern into account. Each artificial cross-section was placed into a rigidity chart to provide information about its twist-to-bend ratio. In these charts, artificial cross-sections with the same geometry did not form clusters, whereas those with similar tissue patterns formed clusters characterized by vascular bundles, collenchyma or sclerenchyma arranged as one central strand, as a peripheral closed ring or as distributed individual strands. Generally, flexural rigidity increased the more the bundles or fibre strands were placed at the periphery. Torsional rigidity decreased the more the bundles or strands were separated and the less that they were arranged along a peripheral ring. The calculated twist-to-bend ratios ranged between 0.85 (ellipse with central vascular bundles) and 196 (triangle with individual peripheral sclerenchyma strands).

Enabling technologies towards personalization of scaffolds for large bone defect regeneration.

Additive manufacturing (AM) can deliver personalized scaffolds to support large volume defect tissue regeneration - a major clinical challenge in many medical disciplines. The freedom in scaffold design and composition (biomaterials and biologics) offered by AM yields a plethora of possibilities but is confronted with a heterogenous biological regeneration potential across individuals. A key challenge is to make the right choice for individualized scaffolds that match biology, anatomy, and mechanics of patients. This review provides an overview of state-of-the-art technologies, that is, in silico modelling for scaffold design, omics and bioinformatics to capture patient biology and information technology for data management, that, when combined in a synergistic way with AM, have great potential to make personalized tissue regeneration strategies available to all patients, empowering precision medicine.

Influence of structural reinforcements on the twist-to-bend ratio of plant axes: a case study on Carex pendula.

During biological evolution, plants have developed a wide variety of body plans and concepts that enable them to adapt to changing environmental conditions. The trade-off between flexural and torsional rigidity is an important example of sometimes conflicting mechanical requirements, the adaptation to which can be quantified by the dimensionless twist-to-bend ratio. Our study considers the triangular flower stalk of Carex pendula, which shows the highest twist-to-bend ratios ever measured for herbaceous plant axes. For an in-depth understanding of this peak value, we have developed geometric models reflecting the 2D setting of triangular cross-sections comprised of a parenchymatous matrix with vascular bundles surrounded by an epidermis. We analysed the mathematical models (using finite elements) to measure the effect of either reinforcements of the epidermal tissue or fibre reinforcements such as collenchyma and sclerenchyma on the twist-to-bend ratio. The change from an epidermis to a covering tissue of corky periderm increases both the flexural and the torsional rigidity and decreases the twist-to-bend ratio. Furthermore, additional individual fibre reinforcement strands located in the periphery of the cross-section and embedded in a parenchymatous ground tissue lead to a strong increase of the flexural and a weaker increase of the torsional rigidity and thus resulted in a marked increase of the twist-to-bend ratio. Within the developed model, a reinforcement by 49 sclerenchyma fibre strands or 24 collenchyma fibre strands is optimal in order to achieve high twist-to-bend ratios. Dependent on the mechanical quality of the fibres, the twist-to-bend ratio of collenchyma-reinforced axes is noticeably smaller, with collenchyma having an elastic modulus that is approximately 20 times smaller than that of sclerenchyma. Based on our mathematical models, we can thus draw conclusions regarding the influence of mechanical requirements on the development of plant axis geometry, in particular the placement of reinforcements.

Twist-to-bend ratio: an important selective factor for many rod-shaped biological structures.

Mechanical optimisation plays a key role in living beings either as an immediate response of individuals or as an evolutionary adaptation of populations to changing environmental conditions. Since biological structures are the result of multifunctional evolutionary constraints, the dimensionless twist-to-bend ratio is particularly meaningful because it provides information about the ratio of flexural rigidity to torsional rigidity determined by both material properties (bending and shear modulus) and morphometric parameters (axial and polar second moment of area). The determination of the mutual contributions of material properties and structural arrangements (geometry) or their ontogenetic alteration to the overall mechanical functionality of biological structures is difficult. Numerical methods in the form of gradient flows of phase field functionals offer a means of addressing this question and of analysing the influence of the cross-sectional shape of the main load-bearing structures on the mechanical functionality. Three phase field simulations were carried out showing good agreement with the cross-sections found in selected plants: (i) U-shaped cross-sections comparable with those of Musa sp. petioles, (ii) star-shaped cross-sections with deep grooves as can be found in the lianoid wood of Condylocarpon guianense stems, and (iii) flat elliptic cross-sections with one deep groove comparable with the cross-sections of the climbing ribbon-shaped stems of Bauhinia guianensis.

Integrated additive design and manufacturing approach for the bioengineering of bone scaffolds for favorable mechanical and biological properties.

Additive manufacturing (AM) presents the possibility of personalized bone scaffolds with unprecedented structural and functional designs. In contrast to earlier conventional design concepts, e.g. raster-angle, a workflow was established to produce scaffolds with triply periodic minimal surface (TPMS) architecture. A core challenge is the realization of such structures using melt-extrusion based 3D printing. This study presents methods for generation of scaffold design files, finite element (FE) analysis of scaffold Young's moduli, AM of scaffolds with polycaprolactone (PCL), and a customized in vitro assay to evaluate cell migration. The reliability of FE analysis when using computer-aided designed models as input may be impeded by anomalies introduced during 3D printing. Using micro-computed tomography reconstructions of printed scaffolds as an input for numerical simulation in comparison to experimentally obtained scaffold Young's moduli showed a moderate trend (R 2 = 0.62). Interestingly, in a preliminary cell migration assay, adipose-derived mesenchymal stromal cells (AdMSC) migrated furthest on PCL scaffolds with Diamond, followed by Gyroid and Schwarz P architectures. A similar trend, but with an accelerated AdMSC migration rate, was observed for PCL scaffolds surface coated with calcium-phosphate-based apatite. We elaborate on the importance of start-to-finish integration of all steps of AM, i.e. design, engineering and manufacturing. Using such a workflow, specific biological and mechanical functionality, e.g. improved regeneration via enhanced cell migration and higher structural integrity, may be realized for scaffolds intended as temporary guiding structures for endogenous tissue regeneration.

Optimization of Bone Scaffold Porosity Distributions.

Additive manufacturing (AM) is a rapidly emerging technology that has the potential to produce personalized scaffolds for tissue engineering applications with unprecedented control of structural and functional design. Particularly for bone defect regeneration, the complex coupling of biological mechanisms to the scaffolds' properties has led to a predominantly trial-and-error approach. To mitigate this, shape or topology optimization can be a useful tool to design a scaffold architecture that matches the desired design targets, albeit at high computational cost. Here, we consider an efficient macroscopic optimization routine based on a simple one-dimensional time-dependent model for bone regeneration in the presence of a bioresorbable polymer scaffold. The result of the optimization procedure is a scaffold porosity distribution which maximizes the stiffness of the scaffold and regenerated bone system over the entire regeneration time, so that the propensity for mechanical failure is minimized.

Relaxation of the single-slip condition in strain-gradient plasticity.

We consider the variational formulation of both geometrically linear and geometrically nonlinear elasto-plasticity subject to a class of hard single-slip conditions. Such side conditions typically render the associated boundary-value problems non-convex. We show that, for a large class of non-smooth plastic distortions, a given single-slip condition (specification of Burgers vectors) can be relaxed by introducing a microstructure through a two-stage process of mollification and lamination. The relaxed model can be thought of as an aid to simulating macroscopic plastic behaviour without the need to resolve arbitrarily fine spatial scales.