Biological remodelling: Stationary energy, configurational change, internal variables and dissipation

Remodelling is defined as an evolution of microstructure or variations in the configuration of the underlying manifold. The manner in which a biological tissue and its subsystems remodel their structure is treated in a continuum mechanical setting. While some examples of remodelling are conveniently modelled as evolution of the reference configuration (Case I), others are more suited to an internal variable description (Case II). In this paper we explore the applicability of stationary energy states to remodelled systems. A variational treatment is introduced by assuming that stationary energy states are attained by changes in microstructure via one of the two mechanisms--Cases I and II. An example is presented to illustrate each case. The example illustrating Case II is further studied in the context of the thermodynamic dissipation inequality.Comment: 24 pages, 4 figures. Replaced version has corrections to typos in equations, and the corresponding correct plot of the solution--all in Section

Simulating the Mammalian Blastocyst - Molecular and Mechanical Interactions Pattern the Embryo

Mammalian embryogenesis is a dynamic process involving gene expression and mechanical forces between proliferating cells. The exact nature of these interactions, which determine the lineage patterning of the trophectoderm and endoderm tissues occurring in a highly regulated manner at precise periods during the embryonic development, is an area of debate. We have developed a computational modeling framework for studying this process, by which the combined effects of mechanical and genetic interactions are analyzed within the context of proliferating cells. At a purely mechanical level, we demonstrate that the perpendicular alignment of the animal-vegetal (a-v) and embryonic-abembryonic (eb-ab) axes is a result of minimizing the total elastic conformational energy of the entire collection of cells, which are constrained by the zona pellucida. The coupling of gene expression with the mechanics of cell movement is important for formation of both the trophectoderm and the endoderm. In studying the formation of the trophectoderm, we contrast and compare quantitatively two hypotheses: (1) The position determines gene expression, and (2) the gene expression determines the position. Our model, which couples gene expression with mechanics, suggests that differential adhesion between different cell types is a critical determinant in the robust endoderm formation. In addition to differential adhesion, two different testable hypotheses emerge when considering endoderm formation: (1) A directional force acts on certain cells and moves them into forming the endoderm layer, which separates the blastocoel and the cells of the inner cell mass (ICM). In this case the blastocoel simply acts as a static boundary. (2) The blastocoel dynamically applies pressure upon the cells in contact with it, such that cell segregation in the presence of differential adhesion leads to the endoderm formation. To our knowledge, this is the first attempt to combine cell-based spatial mechanical simulations with genetic networks to explain mammalian embryogenesis. Such a framework provides the means to test hypotheses in a controlled in silico environment

Chromosome segregation in plant meiosis

Faithful chromosome segregation in meiosis is essential for ploidy stability over sexual life cycles. In plants, defective chromosome segregation caused by gene mutations or other factors leads to the formation of unbalanced or unreduced gametes creating aneuploid or polyploid progeny, respectively. Accurate segregation requires the coordinated execution of conserved processes occurring throughout the two meiotic cell divisions. Synapsis and recombination ensure the establishment of chiasmata that hold homologous chromosomes together allowing their correct segregation in the first meiotic division, which is also tightly regulated by cell-cycle dependent release of cohesin and monopolar attachment of sister kinetochores to microtubules. In meiosis II, bi-orientation of sister kinetochores and proper spindle orientation correctly segregate chromosomes in four haploid cells. Checkpoint mechanisms acting at kinetochores control the accuracy of kinetochore-microtubule attachment, thus ensuring the completion of segregation. Here we review the current knowledge on the processes taking place during chromosome segregation in plant meiosis, focusing on the characterization of the molecular factors involved

A Unified Dissertation on Bearing Rigidity Theory

This work focuses on the bearing rigidity theory, namely the branch of knowledge investigating the structural properties necessary for multi-element systems to preserve the inter-units bearings when exposed to deformations. The original contributions are twofold. The first one consists in the definition of a general framework for the statement of the principal definitions and results that are then particularized by evaluating the most studied metric spaces, providing a complete overview of the existing literature about the bearing rigidity theory. The second one rests on the determination of a necessary and sufficient condition guaranteeing the rigidity properties of a given multi-element system, independently of its metric space

PTEN controls glandular morphogenesis through a juxtamembrane β-Arrestin1/ARHGAP21 scaffolding complex

PTEN controls three-dimensional (3D) glandular morphogenesis by coupling juxtamembrane signalling to mitotic spindle machinery. While molecular mechanisms remain unclear, PTEN interacts through its C2 membrane-binding domain with the scaffold protein β-Arrestin1. Because β-Arrestin1 binds and suppresses the Cdc42 GTPase-activating protein ARHGAP21, we hypothesize that PTEN controls Cdc42-dependent morphogenic processes through a β-Arrestin1-ARHGAP21 complex. Here we show that PTEN knockdown (KD) impairs β-Arrestin1 membrane localization, β-Arrestin1-ARHGAP21 interactions, Cdc42 activation, mitotic spindle orientation and 3D glandular morphogenesis. Effects of PTEN-deficiency were phenocopied by β-Arrestin1 KD or inhibition of β-Arrestin1-ARHGAP21 interactions. Conversely, silencing of ARHGAP21 enhanced Cdc42 activation and rescued aberrant morphogenic processes of PTEN-deficient cultures. Expression of the PTEN C2 domain mimicked effects of full-length PTEN but a membrane-binding defective mutant of the C2 domain abrogated these properties. Our results show that PTEN controls multicellular assembly through a membrane-associated regulatory protein complex composed of β-Arrestin1, ARHGAP21 and Cdc42

Distributed Orientation Localization of Multi-agent Systems in 3-dimensional Space with Direction-only Measurements

When a group of agents such as unmanned aerial vehicles are operating in 3-dimensional space, their coordinated action in pursuit of some group objective generally requires all agents to share a common coordinate frame or orientations of the coordinate axes of agents up to an unknown coordinate rotation common to all agents, which are simply referred to as having common coordinate axis orientations. Given coordinate axes that are initially unaligned, this paper considers the process of using direction measurements between agent pairs (obtained in their own coordinate frames) to achieve orientation localization, i.e. determination of common coordinate axis orientations, the calculations all being distributed. The process builds on the initial determination of relative orientations of agent pairs in a common coordinate basis. Distributed differential equations then allow determination of a common set of coordinate axis orientations, uniquely up to a common rotation transformation, which can itself be determined if and only if one or more agents have access to global coordinates.This work was supported, in part, by the National Research Foundation (NRF) of Korea under the grants NRF2016M1B3A1A01937575 and NRF-2017R1A2B3007034, and in part, by the Australian Research Council under grants DP-130103610 and DP-160104500, and Data61-CSIRO