Expansion of ring-shaped supracellular contractile cables induces epithelial sheet folding.

The folding of epithelial cell sheets is a fundamental process that sculpts developing tissues and organs into their proper shapes required for normal physiological functions. In the absence of detailed biochemical regulations, the epithelial sheet folding may simply proceed through buckling due to mechanical compression arising extrinsically from the surroundings or intrinsically within the sheets. Previous studies hypothesized that the formation of an expanding supracellular actomyosin ring within epithelial sheets could result in compression that ultimately leads to epithelial folding during tracheal development in the Drosophila (fruit fly) embryo. However, the exact mechanism by which the formation of epithelial folds is coordinated by the ring expansion remains unclear. Using a vertex-based mechanical model, here I systematically study the dependence of epithelial fold formation on the physical properties of expanding supracellular contractile rings. The simulations show that depending on the contractile strength, epithelial cell sheets can undergo distinct patterns of folding during ring expansion. The formation of folds in particular is robust against fluctuations in the ring properties such as ring numbers and tensions. These findings provide a systematic view to understand how the expansion of supracellular contractile rings in epithelial sheets mediates epithelial folding morphogenesis.

Autonomous epithelial folding induced by an intracellular mechano-polarity feedback loop.

Epithelial tissues form folded structures during embryonic development and organogenesis. Whereas substantial efforts have been devoted to identifying mechanical and biochemical mechanisms that induce folding, whether and how their interplay synergistically shapes epithelial folds remains poorly understood. Here we propose a mechano-biochemical model for dorsal fold formation in the early Drosophila embryo, an epithelial folding event induced by shifts of cell polarity. Based on experimentally observed apical domain homeostasis, we couple cell mechanics to polarity and find that mechanical changes following the initial polarity shifts alter cell geometry, which in turn influences the reaction-diffusion of polarity proteins, thus forming a feedback loop between cell mechanics and polarity. This model can induce spontaneous fold formation in silico, recapitulate polarity and shape changes observed in vivo, and confer robustness to tissue shape change against small fluctuations in mechanics and polarity. These findings reveal emergent properties of a developing epithelium under control of intracellular mechano-polarity coupling.

A balance between antagonizing PAR proteins specifies the pattern of asymmetric and symmetric divisions in C. elegans embryogenesis.

Coordination between cell differentiation and proliferation during development requires the balance between asymmetric and symmetric modes of cell division. However, the cellular intrinsic cue underlying the choice between these two division modes remains elusive. Here, we show evidence in Caenorhabditis elegans that the invariable lineage of the division modes is specified by the balance between antagonizing complexes of partitioning-defective (PAR) proteins. By uncoupling unequal inheritance of PAR proteins from that of fate determinants during cell division, we demonstrate that changes in the balance between PAR-2 and PAR-6 can be sufficient to re-program the division modes from symmetric to asymmetric and vice versa in two daughter cells. The division mode adopted occurs independently of asymmetry in cytoplasmic fate determinants, cell-size asymmetry, and cell-cycle asynchrony between sister cells. We propose that the balance between PAR proteins represents an intrinsic self-organizing cue for the specification of the two division modes during development.

Tissue-Scale Mechanical Coupling Reduces Morphogenetic Noise to Ensure Precision during Epithelial Folding.

Morphological constancy is universal in developing systems. It is unclear whether precise morphogenesis stems from faithful mechanical interpretation of gene expression patterns. We investigate the formation of the cephalic furrow, an epithelial fold that is precisely positioned with a linear morphology. Fold initiation is specified by a precise genetic code with single-cell row resolution. This positional code activates and spatially confines lateral myosin contractility to induce folding. However, 20% of initiating cells are mis-specified because of fluctuating myosin intensities at the cellular level. Nevertheless, the furrow remains linearly aligned. We find that lateral myosin is planar polarized, integrating contractile membrane interfaces into supracellular "ribbons." Local reduction of mechanical coupling at the "ribbons" using optogenetics decreases furrow linearity. Furthermore, 3D vertex modeling indicates that polarized, interconnected contractility confers morphological robustness against noise. Thus, tissue-scale mechanical coupling functions as a denoising mechanism to ensure morphogenetic precision despite noisy decoding of positional information.

A Switch-like Activation Relay of EGFR-ERK Signaling Regulates a Wave of Cellular Contractility for Epithelial Invagination.

The dynamics of extracellular signal-regulated kinase (ERK) signaling underlies its versatile functions in cell differentiation, cell proliferation, and cell motility. Classical studies in Drosophila established that a gradient of epidermal growth factor receptor (EGFR)-ERK signaling is essential for these cellular responses. However, we challenge this view by the real-time monitoring of ERK activation; we show that a switch-like ERK activation is essential for the invagination movement of the Drosophila tracheal placode. This switch-like ERK activation stems from the positive feedback regulation of the EGFR-ERK signaling and a resultant relay of EGFR-ERK signaling among tracheal cells. A key transcription factor Trachealess (Trh) permissively regulates the iteration of the relay, and the ERK activation becomes graded in trh mutant. A mathematical model based on these observations and a molecular link between ERK activation dynamics and myosin shows that the relay mechanism efficiently promotes epithelial invagination while the gradient mechanism does not.

Epithelial Folding Driven by Apical or Basal-Lateral Modulation: Geometric Features, Mechanical Inference, and Boundary Effects.

During embryonic development, epithelial sheets fold into complex structures required for tissue and organ functions. Although substantial efforts have been devoted to identifying molecular mechanisms underlying epithelial folding, far less is understood about how forces deform individual cells to sculpt the overall sheet morphology. Here we describe a simple and general theoretical model for the autonomous folding of monolayered epithelial sheets. We show that active modulation of intracellular mechanics along the basal-lateral as well as the apical surfaces is capable of inducing fold formation in the absence of buckling instability. Apical modulation sculpts epithelia into shallow and V-shaped folds, whereas basal-lateral modulation generates deep and U-shaped folds. These characteristic tissue shapes remain unchanged when subject to mechanical perturbations from the surroundings, illustrating that the autonomous folding is robust against environmental variabilities. At the cellular scale, how cells change shape depends on their initial aspect ratios and the modulation mechanisms. Such cell deformation characteristics are verified via experimental measurements for a canonical folding process driven by apical modulation, indicating that our theory could be used to infer the underlying folding mechanisms based on experimental data. The mechanical principles revealed in our model could potentially guide future studies on epithelial folding in diverse systems.

Spontaneous symmetry breaking for geometrical trajectories of actin-based motility in three dimensions.

Actin-based motility is important for many cellular processes. In this article we extend our previous studies of an actin-propelled circular disk in two dimensions to an actin-propelled spherical bead in three dimensions. We find that for an achiral load the couplings between the motion of the load and the actin network induce a series of bifurcations, starting with a transition from rest to moving state, followed by a transition from straight to planar curves, and finally a further transition from motion in a plane to one with torsion. To address the intriguing, experimentally observed chiral motility of the bacterium Listeria monocytogenes, we also study the motility of a spherical load with a built-in chirality. For such a chiral load, stable circular trajectories are no longer found in numerical simulations. Instead, helical trajectories with handedness that depends on the chirality of the load are found. Our results reveal the relation between the symmetry of actin network and the trajectories of actin-propelled loads.

Statistics of actin-propelled trajectories in noisy environments.

Actin polymerization is ubiquitously utilized to power the locomotion of eukaryotic cells and pathogenic bacteria in living systems. Inevitably, actin polymerization and depolymerization proceed in a fluctuating environment that renders the locomotion stochastic. Previously, we have introduced a deterministic model that manages to reproduce actin-propelled trajectories in experiments, but not to address fluctuations around them. To remedy this, here we supplement the deterministic model with noise terms. It enables us to compute the effects of fluctuating actin density and forces on the trajectories. Specifically, the mean-squared displacement (MSD) of the trajectories is computed and found to show a super-ballistic scaling with an exponent 3 in the early stage, followed by a crossover to a normal, diffusive scaling of exponent 1 in the late stage. For open-end trajectories such as straights and S-shaped curves, the time of crossover matches the decay time of orientational order of the velocities along trajectories, suggesting that it is the spreading of velocities that leads to the crossover. We show that the super-ballistic scaling of MSD arises from the initial, linearly increasing correlation of velocities, before time translational symmetry is established. When the spreading of velocities reaches a steady state in the long-time limit, short-range correlation then yields a diffusive scaling in MSD. In contrast, close-loop trajectories like circles exhibit localized periodic motion, which inhibits spreading. The initial super-ballistic scaling of MSD arises from velocity correlation that both linearly increases and oscillates in time. Finally, we find that the above statistical features of the trajectories transcend the nature of noises, be it additive or multiplicative, and generalize to other self-propelled systems that are not necessarily actin based.

Trajectories of Listeria-type motility in two dimensions.

Force generated by actin polymerization is essential in cell motility and the locomotion of organelles or bacteria such as Listeria monocytogenes. Both in vivo and in vitro experiments on actin-based motility have observed geometrical trajectories including straight lines, circles, S-shaped curves, and translating figure eights. This paper reports a phenomenological model of an actin-propelled disk in two dimensions that generates geometrical trajectories. Our model shows that when the evolutions of actin density and force per filament on the disk are strongly coupled to the disk self-rotation, it is possible for a straight trajectory to lose its stability. When the instability is due to a pitchfork bifurcation, the resulting trajectory is a circle; a straight trajectory can also lose stability through a Hopf bifurcation, and the resulting trajectory is an S-shaped curve. We also show that a half-coated disk, which mimics the distribution of functionalized proteins in Listeria, also undergoes similar symmetry-breaking bifurcations when the straight trajectory loses stability. For both a fully coated disk and a half-coated disk, when the trajectory is an S-shaped curve, the angular frequency of the disk self-rotation is different from that of the disk trajectory. However, for circular trajectories, these angular frequencies are different for a fully coated disk but the same for a half-coated disk.