Perspectives on polarity - exploring biological asymmetry across scales.

In this Perspective, Journal of Cell Science invited researchers working on cell and tissue polarity to share their thoughts on unique, emerging or open questions relating to their field. The goal of this article is to feature 'voices' from scientists around the world and at various career stages, to bring attention to innovative and thought-provoking topics of interest to the cell biology community. These voices discuss intriguing questions that consider polarity across scales, evolution, development and disease. What can yeast and protists tell us about the evolution of cell and tissue polarity in animals? How are cell fate and development influenced by emerging dynamics in cell polarity? What can we learn from atypical and extreme polarity systems? How can we arrive at a more unified biophysical understanding of polarity? Taken together, these pieces demonstrate the broad relevance of the fascinating phenomenon of cell polarization to diverse fundamental biological questions.

Effect of detachment of motor protein from track on its transport.

The transportation of the cargoes in biological cells is primarily driven by the motor proteins on filamentous protein tracks. The stochastic nature of the motion of motor protein often leads to its spontaneous detachment from the track. We formulate a mathematical model to study the effect of the detachment of motor protein on its track bound transport. We calculate two quantities: the distance traveled by the motor protein in given time, and the average time taken by a single motor protein to reach a target distance. Expectedly, both of these quantities decrease with the increasing detachment rate if the motor velocity is kept fixed. However, the existing experimental data suggest that a change in the detachment rate also affects the velocity of the motor protein. This relation between motor protein speed and its detachment rate results in a non-monotonic dependence on the distance traveled in fixed time and transport rate to a fixed distance. Therefore, we demonstrate that optimal motor speeds can be identified for the time and distance controlled conditions.

Flow driven vesicle unbinding under mechanosensitive adhesion.

Ligand receptor based adhesion is the primary mode of interaction of cellular blood constituents with the endothelium. These adhered entities also experience shear flow imposed by the blood which may lead to their detachment due to the viscous lift forces. Here, we have studied the role of the ligand-receptor bond kinetics in the detachment of an adhered vesicle (a simplified cell model) under shear flow. Using boundary integral formulation we performed numerical simulation of a two dimensional vesicle under shear flow for different values of applied shear rates and time scale of bond kinetics. We observe that the vesicle demonstrates three steady state configurations - adhered, pinned and detached for fast enough ligand-receptor kinetics (akin to Lennard-Jones adhesion). However, for slow bond kinetics the pinned state is not observed. We present scaling laws for the critical shear rates corresponding to the transitions among these three states. These results can help with identifying the processes of cell adhesion/detachment in the blood stream, prevalent features during the immune response and cancer metastasis.

Amoeboid Swimming Is Propelled by Molecular Paddling in Lymphocytes.

Mammalian cells developed two main migration modes. The slow mesenchymatous mode, like crawling of fibroblasts, relies on maturation of adhesion complexes and actin fiber traction, whereas the fast amoeboid mode, observed exclusively for leukocytes and cancer cells, is characterized by weak adhesion, highly dynamic cell shapes, and ubiquitous motility on two-dimensional and in three-dimensional solid matrix. In both cases, interactions with the substrate by adhesion or friction are widely accepted as a prerequisite for mammalian cell motility, which precludes swimming. We show here experimental and computational evidence that leukocytes do swim, and that efficient propulsion is not fueled by waves of cell deformation but by a rearward and inhomogeneous treadmilling of the cell external membrane. Our model consists of a molecular paddling by transmembrane proteins linked to and advected by the actin cortex, whereas freely diffusing transmembrane proteins hinder swimming. Furthermore, continuous paddling is enabled by a combination of external treadmilling and selective recycling by internal vesicular transport of cortex-bound transmembrane proteins. This mechanism explains observations that swimming is five times slower than the retrograde flow of cortex and also that lymphocytes are motile in nonadherent confined environments. Resultantly, the ubiquitous ability of mammalian amoeboid cells to migrate in two dimensions or three dimensions and with or without adhesion can be explained for lymphocytes by a single machinery of heterogeneous membrane treadmilling.

Heterophilic cell-cell adhesion of atypical cadherins Fat and Dachsous regulate epithelial cell size dynamics during Drosophila thorax morphogenesis.

Spatiotemporal changes in epithelial cell sizes-or epithelial cell size dynamics (ECD)-during morphogenesis entail interplay between two opposing forces: cell contraction via actomyosin cytoskeleton and cell expansion via cell-cell adhesion. Cell-cell adhesion-based ECD, however, has not yet been clearly demonstrated. For instance, changing levels of homophilic E-cadherin-based cell-cell adhesion induce cell sorting, but not ECD. Here we show that cell-expansive forces of heterophilic cell-cell adhesion regulate ECD: higher cell-cell adhesion results in cell size enlargement. Thus, ECD during morphogenesis in the heminotal epithelia of Drosophila pupae leading to thorax closure corresponds with spatiotemporal gradients of two heterophilic atypical cadherins-Fat (Ft) and Dachsous (Ds)-and the levels of Ft-Ds heterodimers formed concomitantly. Our mathematical modeling and genetic tests validate this mechanism of dynamic heterophilic cell-cell adhesion-based regulation of ECD. Conservation of these atypical cadherins suggests a wider prevalence of heterophilic cell-cell adhesion-based ECD regulation during animal morphogenesis.

Three-bead steering microswimmers.

The self-propelled microswimmers have recently attracted considerable attention as model systems for biological cell migration as well as artificial micromachines. A simple and well-studied microswimmer model consists of three identical spherical beads joined by two springs in a linear fashion with active oscillatory forces being applied on the beads to generate self-propulsion. We have extended this linear microswimmer configuration to a triangular geometry where the three beads are connected by three identical springs in an equilateral triangular manner. The active forces acting on each spring can lead to autonomous steering motion; i.e., allowing the swimmer to move along arbitrary paths. We explore the microswimmer dynamics analytically and pinpoint its rich character depending on the nature of the active forces. The microswimmers can translate along a straight trajectory, rotate at a fixed location, as well as perform a simultaneous translation and rotation resulting in complex curved trajectories. The sinusoidal active forces on the three springs of the microswimmer contain naturally four operating parameters which are more than required for the steering motion. We identify the minimal operating parameters which are essential for the motion of the microswimmer along any given arbitrary trajectory. Therefore, along with providing insights into the mechanics of the complex motion of the natural and artificial microswimmers, the triangular three-bead microswimmer can be utilized as a model for targeted drug delivery systems and autonomous underwater vehicles where intricate trajectories are involved.

Structure-induced nonlinear viscoelasticity of non-woven fibrous matrices.

Fibrous materials are widely utilized as tissue engineering scaffolds for tissue regeneration and other bioengineering applications. The structural as well as mechanical characteristics of the fibrous matrices under static and dynamic mechanical loading conditions influence the response of the cells. In this paper, we study the mechanical response of the non-woven fibrous matrices under oscillatory loading conditions and its dependence on the structural properties of fibrous matrix. We demonstrate that under oscillatory shear and elongation, the fibrous matrices demonstrate nonlinear viscoelasticity at all strain amplitudes. This is contrary to the behavior of other soft polymeric materials for which nonlinearity in the viscoelastic response vanishes for small strains. These observations suggest that despite their prevalence, the measures of linear viscoelasticity (e.g., storage and loss moduli) are inadequate for the general description of the viscoelastic nature of the fibrous materials. It was, however, found that linear viscoelastic nature of fibrous matrices for small amplitudes is restored when a pre-stretch is applied to the fibrous matrix along with oscillatory strains. Further, we also explored the influence of the structural properties of the fibrous matrices (fiber orientation, alignment and curvature) on their viscoelastic nature.

Statistical model for the mechanical behavior of the tissue engineering non-woven fibrous matrices under large deformation.

The fibrous matrices are widely used as scaffolds for the regeneration of load-bearing tissues due to their structural and mechanical similarities with the fibrous components of the extracellular matrix. These scaffolds not only provide the appropriate microenvironment for the residing cells but also act as medium for the transmission of the mechanical stimuli, essential for the tissue regeneration, from macroscopic scale of the scaffolds to the microscopic scale of cells. The requirement of the mechanical loading for the tissue regeneration requires the fibrous scaffolds to be able to sustain the complex three-dimensional mechanical loading conditions. In order to gain insight into the mechanical behavior of the fibrous matrices under large amount of elongation as well as shear, a statistical model has been formulated to study the macroscopic mechanical behavior of the electrospun fibrous matrix and the transmission of the mechanical stimuli from scaffolds to the cells via the constituting fibers. The study establishes the load-deformation relationships for the fibrous matrices for different structural parameters. It also quantifies the changes in the fiber arrangement and tension generated in the fibers with the deformation of the matrix. The model reveals that the tension generated in the fibers on matrix deformation is not homogeneous and hence the cells located in different regions of the fibrous scaffold might experience different mechanical stimuli. The mechanical response of fibrous matrices was also found to be dependent on the aspect ratio of the matrix. Therefore, the model establishes a structure-mechanics interdependence of the fibrous matrices under large deformation, which can be utilized in identifying the appropriate structure and external mechanical loading conditions for the regeneration of load-bearing tissues.

Mathematical modeling of sub-cellular asymmetry of fat-dachsous heterodimer for generation of planar cell polarity.

Planar Cell Polarity (PCP) is an evolutionarily conserved characteristic of animal tissues marked by coordinated polarization of cells or structures in the plane of a tissue. In insect wing epithelium, for instance, PCP is characterized by en masse orientation of hairs orthogonal to its apical-basal axis and pointing along the proximal-distal axis of the organ. Directional cue for PCP has been proposed to be generated by complex sets of interactions amongst three proteins - Fat (Ft), Dachsous (Ds) and Four-jointed (Fj). Ft and Ds are two atypical cadherins, which are phosphorylated by Fj, a Golgi kinase. Ft and Ds from adjacent cells bind heterophilically via their tandem cadherin repeats, and their binding affinities are regulated by Fj. Further, in the wing epithelium, sub-cellular levels of Ft-Ds heterodimers are seen to be elevated at the distal edges of individual cells, prefiguring their PCP. Mechanisms generating this sub-cellular asymmetry of Ft-Ds heterodimer in proximal and distal edges of cells, however, have not been resolved yet. Using a mathematical modeling approach, here we provide a framework for generation of this sub-cellular asymmetry of Ft-Ds heterodimer. First, we explain how the known interactions within Ft-Ds-Fj system translate into sub-cellular asymmetry of Ft-Ds heterodimer. Second, we show that this asymmetric localization of Ft-Ds heterodimer is lost when tissue-level gradient of Fj is flattened, or when phosphorylation of Ft by Fj is abolished, but not when tissue-level gradient of Ds is flattened or when phosphorylation of Ds is abrogated. Finally, we show that distal enrichment of Ds also amplifies Ft-Ds asymmetry. These observations reveal that gradient of Fj expression, phosphorylation of Ft by Fj and sub-cellular distal accumulation of Ds are three critical elements required for generating sub-cellular asymmetry of Ft-Ds heterodimer. Our model integrates the known experimental data and presents testable predictions for future studies.

Role of membrane addition in animal cell cytokinesis.

Addition of membrane in the form of vesicles is essential for the cytokinesis of animal and plant cells. In the animal cell cytokinesis, membrane fusion acts along with the contraction of an actomyosin ring to separate the cytoplasmic contents. In this study, the possible driving mechanisms for the membrane addition to the plasma membrane of the dividing animal cell and their consequences are presented. Taking cues from earlier studies, we propose that the membrane addition to the plasma membrane in the form of vesicles can be governed by the lateral tension present in the plasma membrane or, the concentrations of actin and myosin proteins at the cleavage furrow or, both simultaneously. The study attempts to elucidate the relationship between membrane addition and the force exerted by the contractile ring. The predictions from our study agree qualitatively with the experimental studies in which the vesicle fusion or the acto-myosin assembly were blocked during cytokinesis. However, the precise role of the two above mentioned mechanisms may depend on various parameters including but not limited to the cell type, organism and microenvironment around the dividing cell.