Cell deformability drives fluid-to-fluid phase transition in active cell monolayers.

Cell deformability is an essential determinant for tissue-scale mechanical nature, such as fluidity and rigidity, and is thus crucial for tissue homeostasis and stable developmental processes. However, large-scale simulations of deformable cells have been restricted to those of polygonal-shaped cells, limiting our understanding of populations of arbitrarily deformable cells, such as mesenchymal, amoeboid cells, and nonconfluent epithelial cells. Here, we present an efficient approach for simulating large populations of nonpolygonally deformable cells with considerably higher computational efficiency than existing methods. Using the method, we demonstrate that the densely packed active cell population interacting via excluded volume interactions exhibits a fluid-to-fluid transition. An experimentally measurable index of topological defects, defined using the number of neighboring cells, is also proposed to characterize this transition. This study provides a flexible approach to tissue-scale cell population and a broader perspective on the biological fluid phases.

Mechanical convergence in mixed populations of mammalian epithelial cells.

Tissues consist of cells with different molecular and/or mechanical properties. Measuring the forces and stresses in mixed-cell populations is essential for understanding the mechanisms by which tissue development, homeostasis, and disease emerge from the cooperation of distinct cell types. However, many previous studies have primarily focused their mechanical measurements on dissociated cells or aggregates of a single-cell type, leaving the mechanics of mixed-cell populations largely unexplored. In the present study, we aimed to elucidate the influence of interactions between different cell types on cell mechanics by conducting in situ mechanical measurements on a monolayer of mammalian epithelial cells. Our findings revealed that while individual cell types displayed varying magnitudes of traction and intercellular stress before mixing, these mechanical values shifted in the mixed monolayer, becoming nearly indistinguishable between the cell types. Moreover, by analyzing a mixed-phase model of active tissues, we identified physical conditions under which such mechanical convergence is induced. Overall, the present study underscores the importance of in situ mechanical measurements in mixed-cell populations to deepen our understanding of the mechanics of multicellular systems.

Attachment and detachment of cortical myosin regulates cell junction exchange during cell rearrangement in the Drosophila wing epithelium.

Epithelial cells remodel cell adhesion and change their neighbors to shape a tissue. This cellular rearrangement proceeds in three steps: the shrinkage of a junction, exchange of junctions, and elongation of the newly generated junction. Herein, by combining live imaging and physical modeling, we showed that the formation of myosin-II (myo-II) cables around the cell vertices underlies the exchange of junctions in the Drosophila wing epithelium. The local and transient detachment of myo-II from the cell cortex is regulated by the LIM domain-containing protein Jub and the tricellular septate junction protein M6. Moreover, we found that M6 shifts to the adherens junction plane on jub RNAi and that Jub is persistently retained at reconnecting junctions in m6 RNAi cells. This interplay between Jub and M6 can depend on the junction length and thereby couples the detachment of cortical myo-II cables and the shrinkage/elongation of the junction during cell rearrangement. Furthermore, we developed a mechanical model based on the wetting theory and clarified how the physical properties of myo-II cables are integrated with the junction geometry to induce the transition between the attached and detached states and support the unidirectionality of cell rearrangement. Collectively, this study elucidates the orchestration of geometry, mechanics, and signaling for exchanging junctions.

Image-based parameter inference for epithelial mechanics.

Measuring mechanical parameters in tissues, such as the elastic modulus of cell-cell junctions, is essential to decipher the mechanical control of morphogenesis. However, their in vivo measurement is technically challenging. Here, we formulated an image-based statistical approach to estimate the mechanical parameters of epithelial cells. Candidate mechanical models are constructed based on force-cell shape correlations obtained from image data. Substitution of the model functions into force-balance equations at the cell vertex leads to an equation with respect to the parameters of the model, by which one can estimate the parameter values using a least-squares method. A test using synthetic data confirmed the accuracy of parameter estimation and model selection. By applying this method to Drosophila epithelial tissues, we found that the magnitude and orientation of feedback between the junction tension and shrinkage, which are determined by the spring constant of the junction, were correlated with the elevation of tension and myosin-II on shrinking junctions during cell rearrangement. Further, this method clarified how alterations in tissue polarity and stretching affect the anisotropy in tension parameters. Thus, our method provides a novel approach to uncovering the mechanisms governing epithelial morphogenesis.

Pattern Propagation Driven by Surface Curvature.

Pattern dynamics on curved surfaces are found everywhere in nature. The geometry of surfaces has been shown to influence dynamics and play a functional role, yet a comprehensive understanding is still elusive. Here, we report for the first time that a static Turing pattern on a flat surface can propagate on a curved surface, as opposed to previous studies, where the pattern is presupposed to be static irrespective of the surface geometry. To understand such significant changes on curved surfaces, we investigate reaction-diffusion systems on axisymmetric curved surfaces. Numerical and theoretical analyses reveal that both the symmetries of the surface and pattern participate in the initiation of pattern propagation. This study provides a novel and generic mechanism of pattern propagation that is caused by surface curvature, as well as insights into the general role of surface geometry.

Planar cell polarity induces local microtubule bundling for coordinated ciliary beating.

Multiciliated cells (MCCs) in tracheas generate mucociliary clearance through coordinated ciliary beating. Apical microtubules (MTs) play a crucial role in this process by organizing the planar cell polarity (PCP)-dependent orientation of ciliary basal bodies (BBs), for which the underlying molecular basis remains elusive. Herein, we found that the deficiency of Daple, a dishevelled-associating protein, in tracheal MCCs impaired the planar polarized apical MTs without affecting the core PCP proteins, causing significant defects in the BB orientation at the cell level but not the tissue level. Using live-cell imaging and ultra-high voltage electron microscope tomography, we found that the apical MTs accumulated and were stabilized by side-by-side association with one side of the apical junctional complex, to which Daple was localized. In vitro binding and single-molecule imaging revealed that Daple directly bound to, bundled, and stabilized MTs through its dimerization. These features convey a PCP-related molecular basis for the polarization of apical MTs, which coordinate ciliary beating in tracheal MCCs.

Cytoskeleton polarity is essential in determining orientational order in basal bodies of multi-ciliated cells.

In multi-ciliated cells, directed and synchronous ciliary beating in the apical membrane occurs through appropriate configuration of basal bodies (BBs, roots of cilia). Although it has been experimentally shown that the position and orientation of BBs are coordinated by apical cytoskeletons (CSKs), such as microtubules (MTs), and planar cell polarity (PCP), the underlying mechanism for achieving the patterning of BBs is not yet understood. In this study, we propose that polarity in bundles of apical MTs play a crucial role in the patterning of BBs. First, the necessity of the polarity was discussed by theoretical consideration on the symmetry of the system. The existence of the polarity was investigated by measuring relative angles between the MTs and BBs using published experimental data. Next, a mathematical model for BB patterning was derived by combining the polarity and self-organizational ability of CSKs. In the model, BBs were treated as finite-size particles in the medium of CSKs and excluded volume effects between BBs and CSKs were taken into account. The model reproduces the various experimental observations, including normal and drug-treated phenotypes. Our model with polarity provides a coherent and testable mechanism for apical BB pattern formation. We have also discussed the implication of our study on cell chirality.

Kalman Inversion Stress Microscopy.

Although mechanical cues are crucial to tissue morphogenesis and development, the tissue mechanical stress field remains poorly characterized. Given traction force time-lapse movies, as obtained by traction force microscopy of in vitro cellular sheets, we show that the tissue stress field can be estimated by Kalman filtering. After validation using numerical data, we apply Kalman inversion stress microscopy to experimental data. We combine the inferred stress field with velocity and cell-shape measurements to quantify the rheology of epithelial cell monolayers in physiological conditions, found to be close to that of an elastic and active material.

From cells to tissue: A continuum model of epithelial mechanics.

A two-dimensional continuum model of epithelial tissue mechanics was formulated using cellular-level mechanical ingredients and cell morphogenetic processes, including cellular shape changes and cellular rearrangements. This model incorporates stress and deformation tensors, which can be compared with experimental data. Focusing on the interplay between cell shape changes and cell rearrangements, we elucidated dynamical behavior underlying passive relaxation, active contraction-elongation, and tissue shear flow, including a mechanism for contraction-elongation, whereby tissue flows perpendicularly to the axis of cell elongation. This study provides an integrated scheme for the understanding of the orchestration of morphogenetic processes in individual cells to achieve epithelial tissue morphogenesis.

Multiciliated cell basal bodies align in stereotypical patterns coordinated by the apical cytoskeleton.

Multiciliated cells (MCCs) promote fluid flow through coordinated ciliary beating, which requires properly organized basal bodies (BBs). Airway MCCs have large numbers of BBs, which are uniformly oriented and, as we show here, align linearly. The mechanism for BB alignment is unexplored. To study this mechanism, we developed a long-term and high-resolution live-imaging system and used it to observe green fluorescent protein-centrin2-labeled BBs in cultured mouse tracheal MCCs. During MCC differentiation, the BB array adopted four stereotypical patterns, from a clustering "floret" pattern to the linear "alignment." This alignment process was correlated with BB orientations, revealed by double immunostaining for BBs and their asymmetrically associated basal feet (BF). The BB alignment was disrupted by disturbing apical microtubules with nocodazole and by a BF-depleting Odf2 mutation. We constructed a theoretical model, which indicated that the apical cytoskeleton, acting like a viscoelastic fluid, provides a self-organizing mechanism in tracheal MCCs to align BBs linearly for mucociliary transport.

Spontaneous Formation of a Globally Connected Contractile Network in a Microtubule-Motor System.

Microtubule (MT) networks play key roles in cell division, intracellular transport, and cell motility. These functions of MT networks occur through interactions between MTs and various associated proteins, notably motor proteins that bundle and slide MTs. Our objective in this study was to address the question of how motors determine the nature of MT networks. We conducted in vitro assays using homotetrameric kinesin Eg5, a motor protein involved in the formation and maintenance of the mitotic spindle. The mixing of Eg5 and MTs produced a range of spatiotemporal dynamics depending on the motor/filament ratio. Low motor/filament ratios produced globally connected static MT networks with sparsely distributed contractile active nodes (motor-accumulating points with radially extending MTs). Increasing the motor/filament ratio facilitated the linking of contractile active nodes and led to a global contraction of the network. When the motor/filament ratio was further increased, densely distributed active nodes formed local clusters and segmented the network into pieces with their strong contractile forces. Altering the properties of the motor through the use of chimeric Eg5, which has kinesin-1 heads, resulted in the generation of many isolated asters. These results suggest that the spatial distribution of contractile active nodes determines the dynamics of MT-motor networks. We then developed a coarse-grained model of MT-motor networks and identified two essential features for reproducing the experimentally observed patterns: an accumulation of motors that form the active nodes necessary to generate contractile forces, and a nonlinear dependency of contractile force on motor densities. Our model also enabled us to characterize the mechanical properties of the contractile network. Our study provides insight into how local motor-MT interactions generate the spatiotemporal dynamics of macroscopic network structures.

Collective dynamics of active filament complexes.

Networks of biofilaments are essential for the formation of cellular structures that support various biological functions. For the most part, previous studies have investigated the collective dynamics of rodlike biofilaments; however, the shapes of the actual subcellular components are often more elaborate. In this study, we considered an active object composed of two active filaments, which represents the progression from rodlike biofilaments to complex-shaped biofilaments. Specifically, we numerically assessed the collective behaviors of these active objects in two dimensions and observed several types of dynamics, depending on the density and the angle of the two filaments as shape parameters of the object. Among the observed collective dynamics, a moving density band that we named a "moving smectic" is introduced here for the first time. By analyzing the trajectories of individual objects and the interactions among them, this study demonstrated how interactions among active biofilaments with complex shapes could produce collective dynamics in a nontrivial manner.

Inference of Internal Stress in a Cell Monolayer.

We combine traction force data with Bayesian inversion to obtain an absolute estimate of the internal stress field of a cell monolayer. The method, Bayesian inversion stress microscopy, is validated using numerical simulations performed in a wide range of conditions. It is robust to changes in each ingredient of the underlying statistical model. Importantly, its accuracy does not depend on the rheology of the tissue. We apply Bayesian inversion stress microscopy to experimental traction force data measured in a narrow ring of cohesive epithelial cells, and check that the inferred stress field coincides with that obtained by direct spatial integration of the traction force data in this quasi one-dimensional geometry.

Unified quantitative characterization of epithelial tissue development.

Understanding the mechanisms regulating development requires a quantitative characterization of cell divisions, rearrangements, cell size and shape changes, and apoptoses. We developed a multiscale formalism that relates the characterizations of each cell process to tissue growth and morphogenesis. Having validated the formalism on computer simulations, we quantified separately all morphogenetic events in the Drosophila dorsal thorax and wing pupal epithelia to obtain comprehensive statistical maps linking cell and tissue scale dynamics. While globally cell shape changes, rearrangements and divisions all significantly participate in tissue morphogenesis, locally, their relative participations display major variations in space and time. By blocking division we analyzed the impact of division on rearrangements, cell shape changes and tissue morphogenesis. Finally, by combining the formalism with mechanical stress measurement, we evidenced unexpected interplays between patterns of tissue elongation, cell division and stress. Our formalism provides a novel and rigorous approach to uncover mechanisms governing tissue development.

Rectified directional sensing in long-range cell migration.

How spatial and temporal information are integrated to determine the direction of cell migration remains poorly understood. Here, by precise microfluidics emulation of dynamic chemoattractant waves, we demonstrate that, in Dictyostelium, directional movement as well as activation of small guanosine triphosphatase Ras at the leading edge is suppressed when the chemoattractant concentration is decreasing over time. This 'rectification' of directional sensing occurs only at an intermediate range of wave speed and does not require phosphoinositide-3-kinase or F-actin. From modelling analysis, we show that rectification arises naturally in a single-layered incoherent feedforward circuit with zero-order ultrasensitivity. The required stimulus time-window predicts ~5 s transient for directional sensing response close to Ras activation and inhibitor diffusion typical for protein in the cytosol. We suggest that the ability of Dictyostelium cells to move only in the wavefront is closely associated with rectification of adaptive response combined with local activation and global inhibition.

Robustness of force and stress inference in an epithelial tissue.

During morphogenesis, the shape of a tissue emerges from collective cellular behaviors, which are in part regulated by mechanical and biochemical interactions between cells. Quantification of force and stress is therefore necessary to analyze the mechanisms controlling tissue morphogenesis. Recently, a mechanical measurement method based on force inference from cell shapes and connectivity has been developed. It is non-invasive, and can provide space-time maps of force and stress within an epithelial tissue, up to prefactors. We previously performed a comparative study of three force-inference methods, which differ in their approach of treating indefiniteness in an inverse problem between cell shapes and forces. In the present study, to further validate and compare the three force inference methods, we tested their robustness by measuring temporal fluctuation of estimated forces. Quantitative data of cell-level dynamics in a developing tissue suggests that variation of forces and stress will remain small within a short period of time (~minutes). Here, we showed that cell-junction tensions and global stress inferred by the Bayesian force inference method varied less with time than those inferred by the method that estimates only tension. In contrast, the amplitude of temporal fluctuations of estimated cell pressures differs less between different methods. Altogether, the present study strengthens the validity and robustness of the Bayesian force-inference method.

The mechanical anisotropy in a tissue promotes ordering in hexagonal cell packing.

Many epithelial tissues pack cells into a honeycomb pattern to support their structural and functional integrity. Developmental changes in cell packing geometry have been shown to be regulated by both mechanical and biochemical interactions between cells; however, it is largely unknown how molecular and cellular dynamics and tissue mechanics are orchestrated to realize the correct and robust development of hexagonal cell packing. Here, by combining mechanical and genetic perturbations along with live imaging and Bayesian force inference, we investigate how mechanical forces regulate cellular dynamics to attain a hexagonal cell configuration in the Drosophila pupal wing. We show that tissue stress is oriented towards the proximal-distal axis by extrinsic forces acting on the wing. Cells respond to tissue stretching and orient cell contact surfaces with the stretching direction of the tissue, thereby stabilizing the balance between the intrinsic cell junction tension and the extrinsic force at the cell-population level. Consequently, under topological constraints of the two-dimensional epithelial sheet, mismatches in the orientation of hexagonal arrays are suppressed, allowing more rapid relaxation to the hexagonal cell pattern. Thus, our results identify the mechanism through which the mechanical anisotropy in a tissue promotes ordering in cell packing geometry.

Baldwin effect under multipeaked fitness landscapes: phenotypic fluctuation accelerates evolutionary rate.

Phenotypic fluctuations and plasticity can generally affect the course of evolution, a process known as the Baldwin effect. Several studies have recast this effect and claimed that phenotypic plasticity accelerates evolutionary rate (the Baldwin expediting effect); however, the validity of this claim is still controversial. In this study, we investigate the evolutionary population dynamics of a quantitative genetic model under a multipeaked fitness landscape, in order to evaluate the validity of the effect. We provide analytical expressions for the evolutionary rate and average population fitness. Our results indicate that under a multipeaked fitness landscape, phenotypic fluctuation always accelerates evolutionary rate, but it decreases the average fitness. As an extreme case of the trade-off between the rate of evolution and average fitness, phenotypic fluctuation is shown to accelerate the error catastrophe, in which a population fails to sustain a high-fitness peak. In the context of our findings, we discuss the role of phenotypic plasticity in adaptive evolution.

Identifying dynamical systems with bifurcations from noisy partial observation.

We propose a statistical machine-learning approach to derive low-dimensional models by integrating noisy time-series data from partial observation of high-dimensional systems, aiming to utilize quantitative data on biological phenomena in the cell. In particular, the method estimates a model from data at different values of a bifurcation parameter in order to characterize biological functions as bifurcation types that are insensitive to system details and experimental errors. The method is tested using artificial data generated from two cell-cycle control system models that exhibit different bifurcations and the learned systems are shown to robustly inherit the bifurcation types.

Phase geometries of two-dimensional excitable waves govern self-organized morphodynamics of amoeboid cells.

In both randomly moving Dictyostelium and mammalian cells, phosphatidylinositol (3,4,5)-trisphosphate and F-actin are known to propagate as waves at the membrane and act to push out the protruding edge. To date, however, the relationship between the wave geometry and the patterns of amoeboid shape change remains elusive. Here, by using phase map analysis, we show that morphology dynamics of randomly moving Dictyostelium discoideum cells can be characterized by the number, topology, and position of spatial phase singularities, i.e., points that represent organizing centers of rotating waves. A single isolated singularity near the cellular edge induced a rotational protrusion, whereas a pair of singularities supported a symmetric extension. These singularities appeared by strong phase resetting due to de novo nucleation at the back of preexisting waves. Analysis of a theoretical model indicated excitability of the system that is governed by positive feedback from phosphatidylinositol (3,4,5)-trisphosphate to PI3-kinase activation, and we showed experimentally that this requires F-actin. Furthermore, by incorporating membrane deformation into the model, we demonstrated that geometries of competing waves explain most of the observed semiperiodic changes in amoeboid morphology.