Defect driven shapes in nematic droplets: analogies with cell division

A theoretical model of anaphase

This paper develops a theory for anaphase in cells. After a brief description of microtubules, the mitotic spindle and the centrosome, a mathematical model for anaphase is introduced and developed in the context of the cell cytoplasm and liquid crystalline structures. Prophase, prometaphase and metaphase are then briefly described in order to focus on anaphase, which is the main study of this paper. The entities involved are modelled in terms of liquid crystal defects and microtubules are represented as defect flux lines. The mathematical techniques employed make extensive use of energy considerations based on the work that was developed by Dafermos (1970) from the classical Frank-Oseen nematic liquid crystal energy (Frank, 1958; Oseen, 1933). With regard to liquid crystal theory we introduce the concept of regions of influence for defects which it is believed have important implications beyond the subject of this paper. The results of this paper align with observed biochemical phenomena and are explored in application to HeLa cells and Caenorhabditis elegans. This unified approach offers the possibility of gaining insight into various consequences of mitotic abnormalities which may result in Down syndrome, Hodgkin lymphoma, breast, prostate and various other types of cancer.

Phase-field model for elastocapillary flows of liquid crystals

We propose a phase-field model to study interfacial flows of nematic liquid crystals that couple the capillary forces on the interface with the elastic stresses in the nematic phase. The theoretical model has two key ingredients: A tensor order parameter that provides a consistent description of the molecular and distortional elasticity, and a phase-field formalism that accurately represents the interfacial tension and the nematic anchoring stress by approximating a sharp-interface limit. Using this model, we carry out finite-element simulations of drop retraction in a surrounding fluid, with either component being nematic. The results are summarized by eight representative steady-state solutions in planar and axisymmetric geometries, each featuring a distinct configuration for the drop and the defects. The dynamics is dominated by the competition between the interfacial tension and the distortional elasticity in the nematic phase, mediated by the anchoring condition on the drop surface. As consequences of this competition, the steady-state drop deformation and the clearance between the defects and the drop surface both depend linearly on the elastocapillary number.

Periodicity in the embryo: Emergence of order in space, diffusion of order in time

Does embryonic development exhibit characteristic temporal features? This is apparent in evolution, where evolutionary change has been shown to occur in bursts of activity. Using two animal models (Nematode, Caenorhabditis elegans and Zebrafish, Danio rerio) and simulated data, we demonstrate that temporal heterogeneity exists in embryogenesis at the cellular level, and may have functional consequences. Cell proliferation and division from cell tracking data is subject to analysis to characterize specific features in each model species. Simulated data is then used to understand what role this variation might play in producing phenotypic variation in the adult phenotype. This goes beyond a molecular characterization of developmental regulation to provide a quantitative result at the phenotypic scale of complexity.

Establishment of hematopoietic tissue primary cell cultures from the giant freshwater prawn Macrobrachium rosenbergii

The giant freshwater prawn Macrobrachium rosenbergii is one of the most important aquaculture species in Southeast Asia. In this study, in vitro culture of its hematopoietic tissue cells was achieved and characterized for use as a tool to study its pathogens that cause major farm losses. By transmission electron microscopy, the ultrastructure of the primary culture cells was similar to that of cells lining intact hematopoietic tissue lobes. Proliferating cell nuclear antigen (PCNA) (a marker for hematopoietic stem cell proliferation) was detected in some of the cultured cells by polymerase chain reaction (PCR) testing and flow cytometry. Using a specific staining method to detect phenoloxidase activity and using PCR to detect expression markers for semigranular and granular hemocytes (e.g., prophenoloxidase activating enzyme and prophenoloxidase) revealed that some of the primary cells were able to differentiate into mature hemocytes within 24 h. These results showed that some cells in the cultures were hematopoietic stem cells that could be used to study other interesting research topics (e.g. host pathogen interactions and development of an immortal hematopoietic stem cell line).

Active microfluidic transport in two-dimensional handlebodies

Unlike traditional nematic liquid crystals, which adopt ordered equilibrium configurations compatible with the topological constraints imposed by the boundaries, active nematics are intrinsically disordered because of their self-sustained internal flows. Controlling the flow patterns of active nematics remains a limiting step towards their use as functional materials. Here we show that confining a tubulin-kinesin active nematic to a network of connected annular microfluidic channels enables controlled directional flows and autonomous transport. In single annular channels, for narrow widths, the typically chaotic streams transform into well-defined circulating flows, whose direction or handedness can be controlled by introducing asymmetric corrugations on the channel walls. The dynamics is altered when two or three annular channels are interconnected. These more complex topologies lead to scenarios of synchronization, anti-correlation, and frustration of the active flows, and to the stabilisation of high topological singularities in both the flow field and the orientational field of the material. Controlling textures and flows in these microfluidic platforms opens unexplored perspectives towards their application in biotechnology and materials science.

Active forces shape the metaphase spindle through a mechanical instability

The metaphase spindle is a dynamic structure orchestrating chromosome segregation during cell division. Recently, soft matter approaches have shown that the spindle behaves as an active liquid crystal. Still, it remains unclear how active force generation contributes to its characteristic spindle-like shape. Here we combine theory and experiments to show that molecular motor-driven forces shape the structure through a barreling-type instability. We test our physical model by titrating dynein activity in Xenopus egg extract spindles and quantifying the shape and microtubule orientation. We conclude that spindles are shaped by the interplay between surface tension, nematic elasticity, and motor-driven active forces. Our study reveals how motor proteins can mold liquid crystalline droplets and has implications for the design of active soft materials.

Nucleation and shape dynamics of model nematic tactoids around adhesive colloids

Recent experiments have shown how nematically ordered tactoid shaped actin droplets can be reorganized and divided by the action of myosin molecular motors. In this paper, we consider how similar morphological changes can potentially be achieved under equilibrium conditions. Using simulations, both atomistic and continuum, and a simple macroscopic model, we explore how the nucleation dynamics, shape changes, and the final steady state of a nematic tactoid droplet can be modified by interactions with model adhesive colloids that mimic a myosin motor cluster. We show how tactoid reorganization may occur in an equilibrium colloidal-nematic setting. We then suggest based on the simple macroscopic model how the simulation models may be extended to potentially stabilize divided tactoids.

Topology and Morphology of Self-Deforming Active Shells

We present a generic framework for modeling three-dimensional deformable shells of active matter that captures the orientational dynamics of the active particles and hydrodynamic interactions on the shell and with the surrounding environment. We find that the cross talk between the self-induced flows of active particles and dynamic reshaping of the shell can result in conformations that are tunable by varying the form and magnitude of active stresses. We further demonstrate and explain how self-induced topological defects in the active layer can direct the morphodynamics of the shell. These findings are relevant to understanding morphological changes during organ development and the design of bioinspired materials that are capable of self-organization.

Self-organizing motors divide active liquid droplets

The cytoskeleton is a collection of protein assemblies that dynamically impose spatial structure in cells and coordinate processes such as cell division and mechanical regulation. Biopolymer filaments, cross-linking proteins, and enzymatically active motor proteins collectively self-organize into various precise cytoskeletal assemblies critical for specific biological functions. An outstanding question is how the precise spatial organization arises from the component macromolecules. We develop a system to investigate simple physical mechanisms of self-organization in biological assemblies. Using a minimal set of purified proteins, we create droplets of cross-linked biopolymer filaments. Through the addition of enzymatically active motor proteins, we construct composite assemblies, evocative of cellular structures such as spindles, where the inherent anisotropy drives motor self-organization, droplet deformation, and division into two droplets. These results suggest that simple physical principles underlie self-organization in complex biological assemblies and inform bioinspired materials design.

Advances in Biological Liquid Crystals

Biological liquid crystals, a rich set of soft materials with rod-like structures widely existing in nature, possess typical lyotropic liquid crystalline phase properties both in vitro (e.g., cellulose, peptides, and protein assemblies) and in vivo (e.g., cellular lipid membrane, packed DNA in bacteria, and aligned fibroblasts). Given the ability to undergo phase transition in response to various stimuli, numerous practices are exercised to spatially arrange biological liquid crystals. Here, a fundamental understanding of interactions between rod-shaped biological building blocks and their orientational ordering across multiple length scales is addressed. Discussions are made with regard to the dependence of physical properties of nonmotile objects on the first-order phase transition and the coexistence of multi-phases in passive liquid crystalline systems. This work also focuses on how the applied physical stimuli drives the reorganization of constituent passive particles for a new steady-state alignment. A number of recent progresses in the dynamics behaviors of active liquid crystals are presented, and particular attention is given to those self-propelled animate elements, like the formation of motile topological defects, active turbulence, correlation of orientational ordering, and cellular functions. Finally, future implications and potential applications of the biological liquid crystalline materials are discussed.

Curvature-driven stability of defects in nematic textures over spherical disks

Stabilizing defects in liquid-crystal systems is crucial for many physical processes and applications ranging from functionalizing liquid-crystal textures to recently reported command of chaotic behaviors of active matters. In this work, we perform analytical calculations to study the curvature-driven stability mechanism of defects based on the isotropic nematic disk model that is free of any topological constraint. We show that in a growing spherical disk covering a sphere the accumulation of curvature effect can prevent typical +1 and +1/2 defects from forming boojum textures where the defects are repelled to the boundary of the disk. Our calculations reveal that the movement of the equilibrium position of the +1 defect from the boundary to the center of the spherical disk occurs in a very narrow window of the disk area, exhibiting the first-order phase-transition-like behavior. For the pair of +1/2 defects by splitting a +1 defect, we find the curvature-driven alternating repulsive and attractive interactions between the two defects. With the growth of the spherical disk these two defects tend to approach and finally recombine towards a +1 defect texture. The sensitive response of defects to curvature and the curvature-driven stability mechanism demonstrated in this work in nematic disk systems may have implications towards versatile control and engineering of liquid-crystal textures in various applications.