Can a continuous mineral foam explain the stiffening of aged bone tissue? A micromechanical approach to mineral fusion in musculoskeletal tissues

Recent experimental data revealed a stiffening of aged cortical bone tissue, which could not be explained by common multiscale elastic material models. We explain this data by incorporating the role of mineral fusion via a new hierarchical modeling approach exploiting the asymptotic (periodic) homogenization (AH) technique for three-dimensional linear elastic composites. We quantify for the first time the stiffening that is obtained by considering a fused mineral structure in a softer matrix in comparison with a composite having non-fused cubic mineral inclusions. We integrate the AH approach in the Eshelby-based hierarchical mineralized turkey leg tendon model (Tiburtius et al 2014 Biomech. Model. Mechanobiol. 13 1003–23), which can be considered as a base for musculoskeletal mineralized tissue modeling. We model the finest scale compartments, i.e. the extrafibrillar space and the mineralized collagen fibril, by replacing the self-consistent scheme with our AH approach. This way, we perform a parametric analysis at increasing mineral volume fraction, by varying the amount of mineral that is fusing in the axial and transverse tissue directions in both compartments. Our effective stiffness results are in good agreement with those reported for aged human radius and support the argument that the axial stiffening in aged bone tissue is caused by the formation of a continuous mineral foam. Moreover, the proposed theoretical and computational approach supports the design of biomimetic materials which require an overall composite stiffening without increasing the amount of the reinforcing material

Operator splitting and approximate factorization for taxis-diffusion-reaction models

In this paper we consider the numerical solution of 2D systems of certain types of taxis-diffusion-reaction equations from mathematical biology. By spatial discretization these PDE systems are approximated by systems of positive, nonlinear ODEs (Method of Lines). The aim of this paper is to examine the numerical integration of these ODE systems for low to moderate accuracy by means of splitting techniques. An important consideration is maintenance of positivity. We apply operator splitting and approximate matrix factorization using low order explicit Runge-Kutta methods and linearly implicit Runge-Kutta-Rosenbrock methods. As a reference method the general purpose solver VODPK is applied

A space-jump derivation for non-local models of cell–cell adhesion and non-local chemotaxis

Cellular adhesion provides one of the fundamental forms of biological interaction between cells and their surroundings, yet the continuum modelling of cellular adhesion has remained mathematically challenging. In 2006, Armstrong et al. proposed a mathematical model in the form of an integro-partial differential equation. Although successful in applications, a derivation from an underlying stochastic random walk has remained elusive. In this work we develop a framework by which non-local models can be derived from a space-jump process. We show how the notions of motility and a cell polarization vector can be naturally included. With this derivation we are able to include microscopic biological properties into the model. We show that particular choices yield the original Armstrong model, while others lead to more general models, including a doubly non-local adhesion model and non-local chemotaxis models. Finally, we use random walk simulations to confirm that the corresponding continuum model represents the mean field behaviour of the stochastic random walk

Self-organizing actin waves that simulate phagocytic cup structures

This report deals with actin waves that are spontaneously generated on the planar, substrate-attached surface of Dictyostelium cells. These waves have the following characteristics. (1) They are circular structures of varying shape, capable of changing the direction of propagation. (2) The waves propagate by treadmilling with a recovery of actin incorporation after photobleaching of less than 10 seconds. (3) The waves are associated with actin-binding proteins in an ordered 3-dimensional organization: with myosin-IB at the front and close to the membrane, the Arp2/3 complex throughout the wave, and coronin at the cytoplasmic face and back of the wave. Coronin is a marker of disassembling actin structures. (4) The waves separate two areas of the cell cortex that differ in actin structure and phosphoinositide composition of the membrane. The waves arise at the border of membrane areas rich in phosphatidylinositol (3,4,5) trisphosphate (PIP3). The inhibition of PIP3 synthesis reversibly inhibits wave formation. (5) The actin wave and PIP3 patterns resemble 2-dimensional projections of phagocytic cups, suggesting that they are involved in the scanning of surfaces for particles to be taken up

Unilateral Cleavage Furrows in Multinucleate Cells

Multinucleate cells can be produced inDictyosteliumby electric pulse-induced fusion. In these cells, unilateral cleavage furrows are formed at spaces between areas that are controlled by aster microtubules. A peculiarity of unilateral cleavage furrows is their propensity to join laterally with other furrows into rings to form constrictions. This means cytokinesis is biphasic in multinucleate cells, the final abscission of daughter cells being independent of the initial direction of furrow progression. Myosin-II and the actin filament cross-linking protein cortexillin accumulate in unilateral furrows, as they do in the normal cleavage furrows of mononucleate cells. In a myosin-II-null background, multinucleate or mononucleate cells were produced by cultivation either in suspension or on an adhesive substrate. Myosin-II is not essential for cytokinesis either in mononucleate or in multinucleate cells but stabilizes and confines the position of the cleavage furrows. In fused wild-type cells, unilateral furrows ingress with an average velocity of 1.7 mu m x min(-1), with no appreciable decrease of velocity in the course of ingression. In multinucleate myosin-II-null cells, some of the furrows stop growing, thus leaving space for the extensive broadening of the few remaining furrows

Hormonal Signal Amplification Mediates Environmental Conditions during Development and Controls an Irreversible Commitment to Adulthood

Many animals can choose between different developmental fates to maximize fitness. Despite the complexity of environmental cues and life history, different developmental fates are executed in a robust fashion. The nematode Caenorhabditis elegans serves as a powerful model to examine this phenomenon because it can adopt one of two developmental fates (adulthood or diapause) depending on environmental conditions. The steroid hormone dafachronic acid (DA) directs development to adulthood by regulating the transcriptional activity of the nuclear hormone receptor DAF-12. The known role of DA suggests that it may be the molecular mediator of environmental condition effects on the developmental fate decision, although the mechanism is yet unknown. We used a combination of physiological and molecular biology techniques to demonstrate that commitment to reproductive adult development occurs when DA levels, produced in the neuroendocrine XXX cells, exceed a threshold. Furthermore, imaging and cell ablation experiments demonstrate that the XXX cells act as a source of DA, which, upon commitment to adult development, is amplified and propagated in the epidermis in a DAF-12 dependent manner. This positive feedback loop increases DA levels and drives adult programs in the gonad and epidermis, thus conferring the irreversibility of the decision. We show that the positive feedback loop canalizes development by ensuring that sufficient amounts of DA are dispersed throughout the body and serves as a robust fate-locking mechanism to enforce an organism-wide binary decision, despite noisy and complex environmental cues. These mechanisms are not only relevant to C. elegans but may be extended to other hormonal-based decision-making mechanisms in insects and mammals

Different modes of state transitions determine pattern in the Phosphatidylinositide-Actin system

<p>Abstract</p> <p>Background</p> <p>In a motile polarized cell the actin system is differentiated to allow protrusion at the front and retraction at the tail. This differentiation is linked to the phosphoinositide pattern in the plasma membrane. In the highly motile <it>Dictyostelium </it>cells studied here, the front is dominated by PI3-kinases producing PI(3,4,5)tris-phosphate (PIP3), the tail by the PI3-phosphatase PTEN that hydrolyses PIP3 to PI(4,5)bis-phosphate. To study de-novo cell polarization, we first depolymerized actin and subsequently recorded the spontaneous reorganization of actin patterns in relation to PTEN.</p> <p>Results</p> <p>In a transient stage of recovery from depolymerization, symmetric actin patterns alternate periodically with asymmetric ones. The switches to asymmetry coincide with the unilateral membrane-binding of PTEN. The modes of state transitions in the actin and PTEN systems differ. Transitions in the actin system propagate as waves that are initiated at single sites by the amplification of spontaneous fluctuations. In PTEN-null cells, these waves still propagate with normal speed but loose their regular periodicity. Membrane-binding of PTEN is induced at the border of a coherent PTEN-rich area in the form of expanding and regressing gradients.</p> <p>Conclusions</p> <p>The state transitions in actin organization and the reversible transition from cytoplasmic to membrane-bound PTEN are synchronized but their patterns differ. The transitions in actin organization are independent of PTEN, but when PTEN is present, they are coupled to periodic changes in the membrane-binding of this PIP3-degrading phosphatase. The PTEN oscillations are related to motility patterns of chemotaxing cells.</p

Steroids as Central Regulators of Organismal Development and Lifespan

Larvae of the nematode Caenorhabditis elegans must choose between reproductive development and dauer diapause. This decision is based on sensing of environmental inputs and dauer pheromone, a small molecule signal that serves to monitor population density. These signals are integrated via conserved neuroendocrine pathways that converge on steroidal ligands of the nuclear receptor DAF-12, a homolog of the mammalian vitamin D receptor and liver X receptor. DAF-12 acts as the main switch between gene expression programs that drive either reproductive development or dauer entry. Extensive studies in the past two decades demonstrated that biosynthesis of two bile acid-like DAF-12 ligands, named dafachronic acids (DA), controls developmental fate. In this issue of PLoS Biology, Wollam et al. showed that a conserved steroid-modifying enzyme, DHS-16, introduces a key feature in the structures of the DAF-12 ligands, closing a major gap in the DA biosynthesis pathway. The emerging picture of DA biosynthesis in C. elegans enables us to address a key question in the field: how are complex environmental signals integrated to enforce binary, organism-wide decisions on developmental fate? Schaedel et al. demonstrated that pheromone and DA serve as competing signals, and that a positive feedback loop based on regulation of DA biosynthesis ensures organism-wide commitment to reproductive development. Considering that many components of DA signaling are highly conserved, ongoing studies in C. elegans may reveal new aspects of bile acid function and lifespan regulation in mammals