Dynamics of membranes driven by actin polymerization

A motile cell, when stimulated, shows a dramatic increase in the activity of its membrane, manifested by the appearance of dynamic membrane structures such as lamellipodia, filopodia and membrane ruffles. The external stimulus turns on membrane bound activators, like Cdc42 and PIP2, which cause increased branching and polymerization of the actin cytoskeleton in their vicinity leading to a local protrusive force on the membrane. The emergence of the complex membrane structures is a result of the coupling between the dynamics of the membrane, the activators and the protrusive forces. We present a simple model that treats the dynamics of a membrane under the action of actin polymerization forces that depend on the local density of freely diffusing activators on the membrane. We show that, depending on the spontaneous membrane curvature associated with the activators, the resulting membrane motion can be wave-like, corresponding to membrane ruffling and actin-waves, or unstable, indicating the tendency of filopodia to form. Our model also quantitatively explains a variety of related experimental observations and makes several testable predictions.Comment: 37 pages, 8 figures, revte

The patterning and functioning of protrusive activity during convergence and extension of the Xenopus organiser

We discuss the cellular basis and tissue interactions regulating convergence and extension of the vertebrate body axis in early embryogenesls of Xenopus. Convergence and extension occur in the dorsal mesoderm (prospective notochord and somite) and in the posterior nervous system (prospective hindbrain and spinal cord) by sequential cell intercalations. Several layers of cells intercalate to form a thinner, longer array (radial intercalation) and then cells intercalate in the mediolateral orientation to form a longer, narrower array (mediolateral intercalation). Fluorescence microscopy of labeled mesodermal cells in explants shows that protrusive activity is rapid and randomly directed until the midgastrula stage, when it slows and is restricted to the medial and lateral ends of the cells. This bipolar protrusive activity results in elongation, alignment and mediolateral intercalation of the cells. Mediolateral intercalation behavior (MIB) is expressed in an anterior- posterior and lateral-medial progression in the mesoderm. MIB is first expressed laterally in both somitic and notochordal mesoderm. From its lateral origins in each tissue, MIB progresses medially. If convergence does not bring the lateral boundaries of the tissues closer to the medial cells in the notochordal and somitic territories, these cells do not express MIB. Expression of tissue-specific markers follows and parallels the expression of MIB. These facts argue that MIB and some aspects of tissue differentiation are induced by signals emanating from the lateral boundaries of the tissue territories and that convergence must bring medial cells and boundaries closer together for these signals to be effective. Grafts of dorsal marginal zone epithelium to the ventral sides of other embryos, to ventral explants and to UV-ventralized embryos show that it has a role in organising convergence and extension, and dorsal tissue differentiation among deep mesodermal cells. Grafts of involuting marginal zone to animal cap tissue of the early gastrula shows that convergence and extension of the hindbrain-spinal cord are induced by planar signals from the involuting marginal zone

Border forces and friction control epithelial closure dynamics

Epithelization, the process whereby an epithelium covers a cell-free surface, is not only central to wound healing but also pivotal in embryonic morphogenesis, regeneration, and cancer. In the context of wound healing, the epithelization mechanisms differ depending on the sizes and geometries of the wounds as well as on the cell type while a unified theoretical decription is still lacking. Here, we used a barrier-based protocol that allows for making large arrays of well-controlled circular model wounds within an epithelium at confluence, without injuring any cells. We propose a physical model that takes into account border forces, friction with the substrate, and tissue rheology. Despite the presence of a contractile actomyosin cable at the periphery of the wound, epithelization was mostly driven by border protrusive activity. Closure dynamics was quantified by an epithelization coefficient $D = \sigma_p/\xi$ defined as the ratio of the border protrusive stress $\sigma_p$ to the friction coefficient $\xi$ between epithelium and substrate. The same assay and model showed a high sensitivity to the RasV12 mutation on human epithelial cells, demonstrating the general applicability of the approach and its potential to quantitatively characterize metastatic transformations.Comment: 44 pages, 17 figure

A stochastic model for protrusion activity

In this work we approach cell migration under a large-scale assumption, so that the system reduces to a particle in motion. Unlike classical particle models, the cell displacement results from its internal activity: the cell velocity is a function of the (discrete) protrusive forces exerted by filopodia on the substrate. Cell polarisation ability is modeled in the feedback that the cell motion exerts on the protrusion rates: faster cells form preferentially protrusions in the direction of motion. By using the mathematical framework of structured population processes previously developed to study population dynamics [Fournier and M{\'e}l{\'e}ard, 2004], we introduce rigorously the mathematical model and we derive some of its fundamental properties. We perform numerical simulations on this model showing that different types of trajectories may be obtained: Brownian-like, persistent, or intermittent when the cell switches between both previous regimes. We find back the trajectories usually described in the literature for cell migration

Modelling cell motility and chemotaxis with evolving surface finite elements

We present a mathematical and a computational framework for the modelling of cell motility. The cell membrane is represented by an evolving surface, with the movement of the cell determined by the interaction of various forces that act normal to the surface. We consider external forces such as those that may arise owing to inhomogeneities in the medium and a pressure that constrains the enclosed volume, as well as internal forces that arise from the reaction of the cells' surface to stretching and bending. We also consider a protrusive force associated with a reaction-diffusion system (RDS) posed on the cell membrane, with cell polarization modelled by this surface RDS. The computational method is based on an evolving surface finite-element method. The general method can account for the large deformations that arise in cell motility and allows the simulation of cell migration in three dimensions. We illustrate applications of the proposed modelling framework and numerical method by reporting on numerical simulations of a model for eukaryotic chemotaxis and a model for the persistent movement of keratocytes in two and three space dimensions. Movies of the simulated cells can be obtained from http://homepages.warwick.ac.uk/maskae/CV_Warwick/Chemotaxis.html

Cell motility driving mediolateral intercalation in explants of Xenopus laevis

In Xenopus, convergence and extension are produced by active intercalation of the deep mesodermal cells between one another along the mediolateral axis (mediolateral cell intercalation), to form a narrower, longer array. The cell motility driving this intercalation is poorly understood. A companion paper shows that the endodermal epithelium organizes the outermost mesodermal cells immediately beneath it to undergo convergence and extension, and other evidence suggests that these deep cells are the most active participants in mediolateral intercalation (Shih, J. and Keller, R. (1992) Development 116, 887–899). In this paper, we shave off the deeper layers of mesodermal cells, which allows us to observe the protrusive activity of the mesodermal cells next to the organizing epithelium with high resolution video microscopy. These mesodermal cells divide in the early gastrula and show rapid, randomly directed protrusive activity. At the early midgastrula stage, they begin to express a characteristic sequence of behaviors, called mediolateral intercalation behavior (MIB): (1) large, stable, filiform and lamelliform protrusions form in the lateral and medial directions, thus making the cells bipolar; (2) these protrusions are applied directly to adjacent cell surfaces and exert traction on them, without contact inhibition; (3) as a result, the cells elongate and align parallel to the mediolateral axis and perpendicular to the axis of extension; (4) the elongate, aligned cells intercalate between one another along the mediolateral axis, thus producing a longer, narrower array. Explants of essentially a single layer of deep mesodermal cells, made at stage 10.5, converge and extend by mediolateral intercalation. Thus by stage 10.5 (early midgastrula), expression of MIB among deep mesodermal cells is physiologically and mechanically independent of the organizing influence of the endodermal epithelium, described previously (Shih, J. and Keller, R. (1992) Development 116 887–899), and is the fundamental cell motility underlying mediolateral intercalation and convergence and extension of the body axis

The distribution of Dishevelled in convergently extending mesoderm

Convergent extension (CE) is a conserved morphogenetic movement that drives axial lengthening of the primary body axis and depends on the planar cell polarity (PCP) pathway. In Drosophila epithelia, a polarised subcellular accumulation of PCP core components, such as Dishevelled (Dvl) protein, is associated with PCP function. Dvl has long been thought to accumulate in the mediolateral protrusions in Xenopus chordamesoderm cells undergoing CE. Here we present a quantitative analysis of Dvl intracellular localisation in Xenopus chordamesoderm cells. We find that, surprisingly, accumulations previously observed at mediolateral protrusions of chordamesodermal cells are not protrusion-specific but reflect yolk-free cytoplasm and are quantitatively matched by the distribution of the cytoplasm-filling lineage marker dextran. However, separating cell cortex-associated from bulk Dvl signal reveals a statistical enrichment of Dvl in notochord–somite boundary-(NSB)-directed protrusions, which is dependent upon NSB proximity. Dvl puncta were also observed, but only upon elevated overexpression. These puncta showed no statistically significant spatial bias, in contrast to the strongly posteriorly-enriched GFP-Dvl puncta previously reported in zebrafish. We propose that Dvl distribution is more subtle and dynamic than previously appreciated and that in vertebrate mesoderm it reflects processes other than protrusion as such