Computational approaches for simulating luminogenesis.

Lumens, liquid-filled cavities surrounded by polarized tissue cells, are elementary units involved in the morphogenesis of organs. Theoretical modeling and computations, which can integrate various factors involved in biophysics of morphogenesis of cell assembly and lumens, may play significant roles to elucidate the mechanisms in formation of such complex tissue with lumens. However, up to present, it has not been documented well what computational approaches or frameworks can be applied for this purpose and how we can choose the appropriate approach for each problem. In this review, we report some typical lumen morphologies and basic mechanisms for the development of lumens, focusing on three keywords - mechanics, hydraulics and geometry - while outlining pros and cons of the current main computational strategies. We also describe brief guidance of readouts, i.e., what we should measure in experiments to make the comparison with the model's assumptions and predictions.

Interplay between cell height variations and planar pulsations in epithelial monolayers.

Biological tissues change their shapes through collective interactions of cells. This coordination sets length and time scales for dynamics where precision is essential, in particular during morphogenetic events. However, how these scales emerge remains unclear. Here, we address this question using the pulsatile domains observed in confluent epithelial MDCK monolayers where cells exhibit synchronous contraction and extension cycles of [Formula: see text] h duration and [Formula: see text] length scale. We report that the monolayer thickness changes gradually in space and time by more than twofold in order to counterbalance the contraction and extension of the incompressible cytoplasm. We recapitulate these pulsatile dynamics using a continuum model and show that incorporation of cell stiffness dependent height variations is critical both for generating temporal pulsations and establishing the domain size. We propose that this feedback between height and mechanics could be important in coordinating the length scales of tissue dynamics.

Ratchetaxis in Channels: Entry Point and Local Asymmetry Set Cell Directions in Confinement.

Cell motility is essential in a variety of biological phenomena ranging from early development to organ homeostasis and diseases. This phenomenon has mainly been studied and characterized on flat surfaces in vitro, whereas such conditions are rarely observed in vivo. Recently, cell motion in three-dimensional microfabricated channels was reported to be possible, and it was shown that confined cells push on walls. However, rules setting cell directions in this context have not yet been characterized. Here, we show by using assays that ratchetaxis operates in three-dimensional ratchets in fibroblasts and epithelial cancerous cells. Open ratchets rectify cell motion, whereas closed ratchets impose direct cell migration along channels set by the cell orientation at the channel entry point. We also show that nuclei are pressed in constriction zones through mechanisms involving dynamic asymmetries of focal contacts, stress fibers, and intermediate filaments. Interestingly, cells do not pass these constricting zones when they contain a defective keratin fusion protein implicated in squamous cancer. By combining ratchetaxis with chemical gradients, we finally report that cells are sensitive to local asymmetries in confinement and that topological and chemical cues may be encoded differently by cells. Overall, our ratchet channels could mimic small blood vessels in which cells such as circulating tumor cells are confined; cells can probe local asymmetries that determine their entry into tissues and their subsequent direction. Our results shed light on invasion mechanisms in cancer.

'The Forms of Tissues, or Cell-aggregates': D'Arcy Thompson's influence and its limits.

In two chapters of his book On Growth and Form, D'Arcy Thompson used numerous biological and physical observations to show how principles from mathematics and physics - such as pressure differences, surface tension and viscosity - could explain cell shapes and packing within tissues. In this Review, we depict influences that enabled the genesis of his ideas, report examples of his visionary observations and trace his impact over the past 100 years. Recently, his ideas have been revisited as a new field of research emerged, linking cell-level physics with epithelial tissue structure and development. We critically discuss the potential and the limitations of both Thompson's and the modern approaches.

Ends and middle: Global force balance and septum location in fission yeast.

The fission yeast cell is shaped as a very regular cylinder ending by hemi-spheres at both cell ends. Its conserved phenotypes are often used as read-outs for classifying interacting genes and protein networks. Using Pascal and Young-Laplace laws, we proposed a framework where scaling arguments predicted shapes. Here we probed quantitatively one of these relations which predicts that the division site would be located closer to the cell end with the larger radius of curvature. By combining genetics and quantitative imaging, we tested experimentally whether altered shapes of cell end correlate with a displaced division site, leading to asymmetric cell division. Our results show that the division site position depends on the radii of curvatures of both ends. This new geometrical mechanism for the proper division plane positioning could be essential to achieve even partitioning of cellular material at each cell division.

Spatial Fluctuations at Vertices of Epithelial Layers: Quantification of Regulation by Rho Pathway.

In living matter, shape fluctuations induced by acto-myosin are usually studied in vitro via reconstituted gels, whose properties are controlled by changing the concentrations of actin, myosin, and cross-linkers. Such an approach deliberately avoids consideration of the complexity of biochemical signaling inherent to living systems. Acto-myosin activity inside living cells is mainly regulated by the Rho signaling pathway, which is composed of multiple layers of coupled activators and inhibitors. Here, we investigate how such a pathway controls the dynamics of confluent epithelial tissues by tracking the displacements of the junction points between cells. Using a phenomenological model to analyze the vertex fluctuations, we rationalize the effects of different Rho signaling targets on the emergent tissue activity by quantifying the effective diffusion coefficient, and the persistence time and length of the fluctuations. Our results reveal an unanticipated correlation between layers of activation/inhibition and spatial fluctuations within tissues. Overall, this work connects regulation via biochemical signaling with mesoscopic spatial fluctuations, with potential application to the study of structural rearrangements in epithelial tissues.

Theoretical study of actin layers attachment and separation.

We use the theory of active gels to study theoretically the merging and separation of two actin dense layers akin to cortical layers of animal cells. The layers bind at a distance equal to twice the thickness of a free layer, thus forming a single dense layer, similar in this sense to a lamellipodium. When that unique layer is stretched apart, it is resilient to break apart up to a critical length larger than twice the thickness of a free layer. We show that this behavior can result from the high contractile properties of the actomyosin gel due to the activity of myosin molecular motors. Furthermore, we establish that the stability of the stretched single layer is highly dependent on the properties of the gel. Indeed, the nematic order of the actin filaments along the polymerizing membranes is a destabilizing factor.

Protrusion fluctuations direct cell motion.

Many physiological phenomena involve directional cell migration. It is usually attributed to chemical gradients in vivo. Recently, other cues have been shown to guide cells in vitro, including stiffness/adhesion gradients or micropatterned adhesive motifs. However, the cellular mechanism leading to these biased migrations remains unknown, and, often, even the direction of motion is unpredictable. In this study, we show the key role of fluctuating protrusions on ratchet-like structures in driving NIH3T3 cell migration. We identified the concept of efficient protrusion and an associated direction index. Our analysis of the protrusion statistics facilitated the quantitative prediction of cell trajectories in all investigated conditions. We varied the external cues by changing the adhesive patterns. We also modified the internal cues using drug treatments, which modified the protrusion activity. Stochasticity affects the short- and long-term steps. We developed a theoretical model showing that an asymmetry in the protrusion fluctuations is sufficient for predicting all measures associated with the long-term motion, which can be described as a biased persistent random walk.

Cells as active particles in asymmetric potentials: motility under external gradients.

Cell migration is a crucial event during development and in disease. Mechanical constraints and chemical gradients can contribute to the establishment of cell direction, but their respective roles remain poorly understood. Using a microfabricated topographical ratchet, we show that the nucleus dictates the direction of cell movement through mechanical guidance by its environment. We demonstrate that this direction can be tuned by combining the topographical ratchet with a biochemical gradient of fibronectin adhesion. We report competition and cooperation between the two external cues. We also quantitatively compare the measurements associated with the trajectory of a model that treats cells as fluctuating particles trapped in a periodic asymmetric potential. We show that the cell nucleus contributes to the strength of the trap, whereas cell protrusions guided by the adhesive gradients add a constant tunable bias to the direction of cell motion.

UBAP2L ensures homeostasis of nuclear pore complexes at the intact nuclear envelope.

Assembly of macromolecular complexes at correct cellular sites is crucial for cell function. Nuclear pore complexes (NPCs) are large cylindrical assemblies with eightfold rotational symmetry, built through hierarchical binding of nucleoporins (Nups) forming distinct subcomplexes. Here, we uncover a role of ubiquitin-associated protein 2-like (UBAP2L) in the assembly and stability of properly organized and functional NPCs at the intact nuclear envelope (NE) in human cells. UBAP2L localizes to the nuclear pores and facilitates the formation of the Y-complex, an essential scaffold component of the NPC, and its localization to the NE. UBAP2L promotes the interaction of the Y-complex with POM121 and Nup153, the critical upstream factors in a well-defined sequential order of Nups assembly onto NE during interphase. Timely localization of the cytoplasmic Nup transport factor fragile X-related protein 1 (FXR1) to the NE and its interaction with the Y-complex are likewise dependent on UBAP2L. Thus, this NPC biogenesis mechanism integrates the cytoplasmic and the nuclear NPC assembly signals and ensures efficient nuclear transport, adaptation to nutrient stress, and cellular proliferative capacity, highlighting the importance of NPC homeostasis at the intact NE.

'Single molecule': theory and experiments, an introduction.

At scales below micrometers, Brownian motion dictates most of the behaviors. The simple observation of a colloid is striking: a permanent and random motion is seen, whereas inertial forces play a negligible role. This Physics, where velocity is proportional to force, has opened new horizons in biology. The random feature is challenged in living systems where some proteins--molecular motors--have a directed motion whereas their passive behaviors of colloid should lead to a Brownian motion. Individual proteins, polymers of living matter such as DNA, RNA, actin or microtubules, molecular motors, all these objects can be viewed as chains of colloids. They are submitted to shocks from molecules of the solvent. Shapes taken by these biopolymers or dynamics imposed by motors can be measured and modeled from single molecules to their collective effects. Thanks to the development of experimental methods such as optical tweezers, Atomic Force Microscope (AFM), micropipettes, and quantitative fluorescence (such as Förster Resonance Energy Transfer, FRET), it is possible to manipulate these individual biomolecules in an unprecedented manner: experiments allow to probe the validity of models; and a new Physics has thereby emerged with original biological insights. Theories based on statistical mechanics are needed to explain behaviors of these systems. When force-extension curves of these molecules are extracted, the curves need to be fitted with models that predict the deformation of free objects or submitted to a force. When velocity of motors is altered, a quantitative analysis is required to explain the motions of individual molecules under external forces. This lecture will give some elements of introduction to the lectures of the session 'Nanophysics for Molecular Biology'.

'Injecting' yeast.

Yeast is a powerful genetic model system, but its rigid cell wall has prohibited microinjection. Using microfabricated channels to constrain the fission yeast Schizosaccharomyces pombe, we sheared local regions of individual cells with a piezoelectric unit. The cells remained viable, we detected actin patches in the cell after introduction of fluorescent phalloidin into the medium, and the cytokinetic ring was disrupted after injection of the myosin II inhibitor blebbistatin.

Pulsations and flows in tissues as two collective dynamics with simple cellular rules.

Collective motions of epithelial cells are essential for morphogenesis. Tissues elongate, contract, flow, and oscillate, thus sculpting embryos. These tissue level dynamics are known, but the physical mechanisms at the cellular level are unclear. Here, we demonstrate that a single epithelial monolayer of MDCK cells can exhibit two types of local tissue kinematics, pulsations and long range coherent flows, characterized by using quantitative live imaging. We report that these motions can be controlled with internal and external cues such as specific inhibitors and substrate friction modulation. We demonstrate the associated mechanisms with a unified vertex model. When cell velocity alignment and random diffusion of cell polarization are comparable, a pulsatile flow emerges whereas tissue undergoes long-range flows when velocity alignment dominates which is consistent with cytoskeletal dynamics measurements. We propose that environmental friction, acto-myosin distributions, and cell polarization kinetics are important in regulating dynamics of tissue morphogenesis.

3D single cell migration driven by temporal correlation between oscillating force dipoles.

Directional cell locomotion requires symmetry breaking between the front and rear of the cell. In some cells, symmetry breaking manifests itself in a directional flow of actin from the front to the rear of the cell. Many cells, especially in physiological 3D matrices, do not show such coherent actin dynamics and present seemingly competing protrusion/retraction dynamics at their front and back. How symmetry breaking manifests itself for such cells is therefore elusive. We take inspiration from the scallop theorem proposed by Purcell for micro-swimmers in Newtonian fluids: self-propelled objects undergoing persistent motion at low Reynolds number must follow a cycle of shape changes that breaks temporal symmetry. We report similar observations for cells crawling in 3D. We quantified cell motion using a combination of 3D live cell imaging, visualization of the matrix displacement, and a minimal model with multipolar expansion. We show that our cells embedded in a 3D matrix form myosin-driven force dipoles at both sides of the nucleus, that locally and periodically pinch the matrix. The existence of a phase shift between the two dipoles is required for directed cell motion which manifests itself as cycles with finite area in the dipole-quadrupole diagram, a formal equivalence to the Purcell cycle. We confirm this mechanism by triggering local dipolar contractions with a laser. This leads to directed motion. Our study reveals that these cells control their motility by synchronizing dipolar forces distributed at front and back. This result opens new strategies to externally control cell motion as well as for the design of micro-crawlers.

Epithelial colonies in vitro elongate through collective effects.

Epithelial tissues of the developing embryos elongate by different mechanisms, such as neighbor exchange, cell elongation, and oriented cell division. Since autonomous tissue self-organization is influenced by external cues such as morphogen gradients or neighboring tissues, it is difficult to distinguish intrinsic from directed tissue behavior. The mesoscopic processes leading to the different mechanisms remain elusive. Here, we study the spontaneous elongation behavior of spreading circular epithelial colonies in vitro. By quantifying deformation kinematics at multiple scales, we report that global elongation happens primarily due to cell elongations, and its direction correlates with the anisotropy of the average cell elongation. By imposing an external time-periodic stretch, the axis of this global symmetry breaking can be modified and elongation occurs primarily due to orientated neighbor exchange. These different behaviors are confirmed using a vertex model for collective cell behavior, providing a framework for understanding autonomous tissue elongation and its origins.

Generation of fluorescent cell-derived-matrix to study 3D cell migration.

Cell migration is involved in key phenomena in biology, ranging from development to cancer. Fibroblasts move between organs in 3D polymeric networks. So far, motile cells were mainly tracked in vitro on Petri dishes or on coverslips, i.e., 2D flat surfaces, which made the extrapolation to 3D physiological environments difficult. We therefore prepared 3D Cell Derived Matrices (CDM) with specific characteristics with the goal of extracting the main readouts required to measure and characterize cell motion: cell specific matrix deformation through the tracking of fluorescent fibronectin within CDM, focal contacts as the cell anchor and acto-myosin cytoskeleton which applies cellular forces. We report our method for generating this assay of physiological-like gel with relevant readouts together with its potential impact in explaining cell motility in vivo.

How to orient cells in microcavities for high resolution imaging of cytokinesis and lumen formation.

Imaging dynamics of cellular morphogenesis with high spatial-temporal resolution in 3D is challenging, due to the low spatial resolution along the optical axis and photo-toxicity. However, some cellular structures are planar and hence 2D imaging should be sufficient, provided that the structure of interest can be oriented with respect to the optical axis of the microscope. Here, we report a 3D microfabrication method which positions and orients cell divisions very close to the microscope coverglass. We use this approach to study cytokinesis in fission yeasts and polarization to lumen formation in mammalian epithelial cells. We show that this method improves spatial resolution on range of common microscopies, including super-resolution STED. Altogether, this method could shed new lights on self-organization phenomena in single cells and 3D cell culture systems.

Collective Dynamics of Focal Adhesions Regulate Direction of Cell Motion.

Directed cell motion is essential in physiological and pathological processes such as morphogenesis, wound healing, and cancer spreading. Chemotaxis has often been proposed as the driving mechanism, even though evidence of long-range gradients is often lacking in vivo. By patterning adhesive regions in space, we control cell shape and the potential to move along one direction in another migration mode coined ratchetaxis. We report that focal contact distributions collectively dictate cell directionality, and bias is non-linearly increased by gap distance between adhesive regions. Focal contact dynamics on micro-patterns allow to integrate these phenomena in a model where each focal contact is translated into a force with known amplitude and direction, leading to quantitative predictions for cell motion in new conditions with their successful experimental tests. Altogether, our study shows how local and minute timescale dynamics of focal adhesions and their distribution lead to long-term cellular motion with simple geometric rules. A record of this paper's Transparent Peer Review process is included in the Supplemental Information.

The asymmetric self-assembly mechanism of adherens junctions: a cellular push-pull unit.

To form adherens junctions (AJ), cells first establish contact by sending out lamellipodia onto neighboring cells. We investigated the role of contacting cells in AJ assembly by studying an asymmetric AJ motif: finger-like AJ extending across the cell-cell interface. Using a cytoskeleton replica and immunofluorescence, we observed that actin bundles embedded in the lamellipodia are co-localized with stress fibers in the neighboring cell at the AJ. This suggests that donor lamellipodia present actin fingers, which are stabilized by acceptor lamellae via acto-myosin contractility. Indeed, we show that changes in actin network geometry promoted by Rac overexpression lead to corresponding changes in AJ morphology. Moreover, contractility inhibition and enhancement (via drugs or local traction) lead respectively to the disappearance and further growth of AJ fingers. Thus, we propose that receiving lamellae exert a local pull on AJ, promoting further polymerization of the donor actin bundles. In spite of different compositions, AJ and focal contacts both act as cellular mechanosensors.