Roie Shlomovitz

Physical model of the dynamic instability in an expanding cell culture.

Collective cell migration is of great significance in many biological processes. The goal of this work is to give a physical model for the dynamics of cell migration during the wound healing response. Experiments demonstrate that an initially uniform cell-culture monolayer expands in a nonuniform manner, developing fingerlike shapes. These fingerlike shapes of the cell culture front are composed of columns of cells that move collectively. We propose a physical model to explain this phenomenon, based on the notion of dynamic instability. In this model, we treat the first layers of cells at the front of the moving cell culture as a continuous one-dimensional membrane (contour), with the usual elasticity of a membrane: curvature and surface-tension. This membrane is active, due to the forces of cellular motility of the cells, and we propose that this motility is related to the local curvature of the culture interface; larger convex curvature correlates with a stronger cellular motility force. This shape-force relation gives rise to a dynamic instability, which we then compare to the patterns observed in the wound healing experiments.

Membrane-mediated interactions drive the condensation and coalescence of FtsZ rings

The role of the coupling between the shape of membrane-bound filaments and the membrane is demonstrated for the dynamics of FtsZ rings on cylindrical membranes. Filaments with an arc-like spontaneous curvature, and a possible added active contractile force, are shown to spontaneously condense into tight rings, associated with a local inward deformation of the membrane. The long-range membrane-mediated interactions are attractive at short ring-ring separations, inducing further coarsening dynamics, whereby smaller rings merge to form larger and fewer rings that deform the membrane more strongly. At the same time, these interactions induce a potential barrier that can suppress further ring coalescence at a separation of about seven times the cylinder radius. These results of the model are in very good agreement with recent in-vitro experiments on the dynamics of FtsZ filaments in cylindrical liposomes. These results emphasize the important role of long-range membrane-mediated interactions in the organization of cytoskeletal elements at the membrane.

Curling and Local Shape Changes of Red Blood Cell Membranes Driven by Cytoskeletal Reorganization

Human red blood cells (RBCs) lack the actin-myosin-microtubule cytoskeleton that is responsible for shape changes in other cells. Nevertheless, they can display highly dynamic local deformations in response to external perturbations, such as those that occur during the process of apical alignment preceding merozoite invasion in malaria. Moreover, after lysis in divalent cation-free media, the isolated membranes of ruptured ghosts show spontaneous inside-out curling motions at the free edges of the lytic hole, leading to inside-out vesiculation. The molecular mechanisms that drive these rapid shape changes are unknown. Here, we propose a molecular model in which the spectrin filaments of the RBC cortical cytoskeleton control the sign and dynamics of membrane curvature depending on whether the ends of the filaments are free or anchored to the bilayer. Computer simulations of the model reveal that curling, as experimentally observed, can be obtained either by an overall excess of weakly-bound filaments throughout the cell, or by the flux of such filaments toward the curling edges. Divalent cations have been shown to arrest the curling process, and Ca2+ ions have also been implicated in local membrane deformations during merozoite invasion. These effects can be replicated in our model by attributing the divalent cation effects to increased filament-membrane binding. This process converts the curl-inducing loose filaments into fully bound filaments that arrest curling. The same basic mechanism can be shown to account for Ca2+-induced local and dynamic membrane deformations in intact RBCs. The implications of these results in terms of RBC membrane dynamics under physiological, pathological, and experimental conditions is discussed.

Theoretical model for cellular shapes driven by protrusive and adhesive forces.

The forces that arise from the actin cytoskeleton play a crucial role in determining the cell shape. These include protrusive forces due to actin polymerization and adhesion to the external matrix. We present here a theoretical model for the cellular shapes resulting from the feedback between the membrane shape and the forces acting on the membrane, mediated by curvature-sensitive membrane complexes of a convex shape. In previous theoretical studies we have investigated the regimes of linear instability where spontaneous formation of cellular protrusions is initiated. Here we calculate the evolution of a two dimensional cell contour beyond the linear regime and determine the final steady-state shapes arising within the model. We find that shapes driven by adhesion or by actin polymerization (lamellipodia) have very different morphologies, as observed in cells. Furthermore, we find that as the strength of the protrusive forces diminish, the system approaches a stabilization of a periodic pattern of protrusions. This result can provide an explanation for a number of puzzling experimental observations regarding cellular shape dependence on the properties of the extra-cellular matrix.

Cylindrical cellular geometry ensures fidelity of division site placement in fission yeast

Summary Successful cytokinesis requires proper assembly of the contractile actomyosin ring, its stable positioning on the cell surface and proper constriction. Over the years, many of the key molecular components and regulators of the assembly and positioning of the actomyosin ring have been elucidated. Here we show that cell geometry and mechanics play a crucial role in the stable positioning and uniform constriction of the contractile ring. Contractile rings that assemble in locally spherical regions of cells are unstable and slip towards the poles. By contrast, actomyosin rings that assemble on locally cylindrical portions of the cell under the same conditions do not slip, but uniformly constrict the cell surface. The stability of the rings and the dynamics of ring slippage can be described by a simple mechanical model. Using fluorescence imaging, we verify some of the quantitative predictions of the model. Our study reveals an intimate interplay between geometry and actomyosin dynamics, which are likely to apply in a variety of cellular contexts.

Membrane-mediated interactions and the dynamics of dynamin oligomers on membrane tubes

Dynamin is a protein that plays a key role in the transport and recycling of membrane tubes and vesicles within a living cell. This protein adsorbs from solution to PIP2-containing membranes, and on these tubes it forms curved oligomers that condense into tight helical domains of uniform radius. The dynamics of this process is treated here in terms of the linear stability of a continuum model, whereby membrane-mediated interactions are shown to drive the spontaneous nucleation of condensed dynamin domains. We furthermore show that the deformation of the membrane outside the dynamin domains induces an energy barrier that can hinder the full coalescence of neighboring growing domains. We compare these calculations to experimental observations on dynamin dynamics in vitro.

Patterning of polar active filaments on a tense cylindrical membrane.

We study the dynamics and patterning of polar contractile filaments on the surface of a cylindrical cell using active hydrodynamic equations that incorporate couplings between curvature and filament orientation. Cables and rings spontaneously emerge as steady state configurations on the cylinder, and can be stationary or moving, helical or tilted segments moving along helical trajectories. We observe phase transitions in the steady state patterns upon changing cell diameter or motor-driven activity and make several testable predictions. Our results are relevant to the dynamics and patterning of a variety of active biopolymers in cylindrical cells.

Cytoskeletal Reorganization of Red Blood Cell Shape: Curling of Free Edges and Malaria Merozoites

Abstract Human red blood cells (RBCs) lack the actin–myosin–microtubule cytoskeleton that is responsible for shape changes in other cells. Nevertheless, they can display highly dynamic local deformations in response to external perturbations, such as those that occur during the process of apical alignment preceding merozoite invasion in malaria. Moreover, after lysis in divalent cation-free media, the isolated membranes of ruptured ghosts show spontaneous inside-out curling motions at the free edges of the lytic hole, leading to inside-out vesiculation. The molecular mechanisms that drive these rapid shape changes are unknown. Here, we propose a molecular model in which the spectrin filaments of the RBC cortical cytoskeleton control the sign and dynamics of membrane curvature depending on two types of spectrin filaments. Type I spectrin filaments that are grafted at one end, or at both ends but not connected to the rest of the cytoskeleton, induce a concave spontaneous curvature. Type II spectrin filaments that are grafted at both ends to the cytoskeleton induce a local convex spontaneous curvature. Computer simulations of the model reveal that curling, as experimentally observed, can be obtained either by an overall excess of type I filaments throughout the cell, or by the flux of such filaments toward the curling edges. Divalent cations have been shown to arrest the curling process and Ca 2+ ions have also been implicated in local membrane deformations during merozoite invasion. These effects can be replicated in our model by attributing the divalent cation effects to increased filament membrane binding. This process converts the curl-inducing loose filaments into fully bound filaments that arrest curling. The same basic mechanism can be shown to account for Ca 2+ -induced local and dynamic membrane deformations in intact RBCs. The implications of these results in terms of RBC membrane dynamics under physiological, pathological, and experimental conditions are discussed.