Structure–property relation and relevance of beam theories for microtubules: a coupled molecular and continuum mechanics study

Quasi-one-dimensional microtubules (MTs) in cells enjoy high axial rigidity but large transverse flexibility due to the inter-protofilament (PF) sliding. This study aims to explore the structure–property relation for MTs and examine the relevance of the beam theories to their unique features. A molecular structural mechanics (MSM) model was used to identify the origin of the inter-PF sliding and its role in bending and vibration of MTs. The beam models were then fitted to the MSM to reveal how they cope with the distinct mechanical responses induced by the inter-PF sliding. Clear evidence showed that the inter-PF sliding is due to the soft inter-PF bonds and leads to the length-dependent bending stiffness. The Euler beam theory is found to adequately describe MT deformation when the inter-PF sliding is largely prohibited. Nevertheless, neither shear deformation nor the nonlocal effect considered in the ‘more accurate’ beam theories can fully capture the effect of the inter-PF sliding. This reflects the distinct deformation mechanisms between an MT and its equivalent continuous body

Regulation of pH During Amelogenesis

During amelogenesis, extracellular matrix proteins interact with growing hydroxyapatite crystals to create one of the most architecturally complex biological tissues. The process of enamel formation is a unique biomineralizing system characterized first by an increase in crystallite length during the secretory phase of amelogenesis, followed by a vast increase in crystallite width and thickness in the later maturation phase when organic complexes are enzymatically removed. Crystal growth is modulated by changes in the pH of the enamel microenvironment that is critical for proper enamel biomineralization. Whereas the genetic bases for most abnormal enamel phenotypes (amelogenesis imperfecta) are generally associated with mutations to enamel matrix specific genes, mutations to genes involved in pH regulation may result in severely affected enamel structure, highlighting the importance of pH regulation for normal enamel development. This review summarizes the intra- and extracellular mechanisms employed by the enamel-forming cells, ameloblasts, to maintain pH homeostasis and, also, discusses the enamel phenotypes associated with disruptions to genes involved in pH regulation

Controller design for a two tank system using structured singular value and direct search methods

The aim of this paper is to show an algebraic approach to controller design using the structured singular value (denoted μ) as a robust stability and performance indicator. The algebraic μ-synthesis is applied to a two-tank system, which is a well known benchmark problem. The design is performed using decoupling of the nominal plant into two identical SISO (single-input single-output) systems. Global optimization methods are used due to multimodality of the cost function. The overall performance is verified by simulations for the nominal and perturbed system and compared with the D-K iteration. © 2011 IFAC