Scaling properties of centering forces

Motivated by the centering of biological objects in large cells, we study the generic properties of centering forces inside a ball (or a volume of spherical topology) in $n$ dimensions. We consider two scenarios : autonomous centering (in which distance information is integrated from the agent perspective) and non-autonomous centering (in which distance to the surface is integrated over the whole surface). We find relations between the net centering force and the mean distance$^p$ to the surface. This allows us to find simple scaling laws between the centering force and the distance to the center, as a function of the dimensionality $n$. Interestingly, if the interactions between the agent and the surface are hyper-elastic, the net centering force can still be sub-elastic in the case of autonomous centering. These scaling laws are increasingly violated as the space becomes less convex. Generically, neither scenarios exactly converge to the center of mass of the space

Influence of Cell Geometry on Division-Plane Positioning

SummaryThe spatial organization of cells depends on their ability to sense their own shape and size. Here, we investigate how cell shape affects the positioning of the nucleus, spindle and subsequent cell division plane. To manipulate geometrical parameters in a systematic manner, we place individual sea urchin eggs into microfabricated chambers of defined geometry (e.g., triangles, rectangles, and ellipses). In each shape, the nucleus is positioned at the center of mass and is stretched by microtubules along an axis maintained through mitosis and predictive of the future division plane. We develop a simple computational model that posits that microtubules sense cell geometry by probing cellular space and orient the nucleus by exerting pulling forces that scale to microtubule length. This model quantitatively predicts division-axis orientation probability for a wide variety of cell shapes, even in multicellular contexts, and estimates scaling exponents for length-dependent microtubule forces

A Positive Feedback between Growth and Polarity Provides Directional Persistency and Flexibility to the Process of Tip Growth

International audiencePolar cell growth is a conserved morphogenetic process needed for survival, mating, and infection [1, 2]. It typically implicates the assembly and spatial stabilization of a cortical polar domain of the active form of a small GTPase of the Rho family, such as Cdc42, which promotes cytoskeleton assembly and secretion needed for local surface expansion [3, 4, 5, 6]. In multiple physiological instances, polarity domains may switch from being spatially unstable, exhibiting a wandering behavior around the cell surface, to being stable at a fixed cellular location [7, 8, 9, 10, 11]. Here, we show that the rate of surface growth may be a key determinant in controlling the spatial stability of active Cdc42 domains. Reducing the growth rate of single rod-shaped fission yeast cells using chemical, genetic, and mechanical means systematically causes polar domains to detach from cell tips and oscillate around the cell surface within minutes. Conversely, an abrupt increase in growth rate improves domain stabilization. A candidate screen identifies vesicular transport along actin cables as an important module mediating this process. Similar behavior observed in distant filamentous fungi suggests that this positive feedback between growth and polarity could represent a basal property of eukaryotic polarization, promoting persistent polar growth as well as growth redirection with respect to the mechanical environment of cells

Establishing New Sites of Polarization by Microtubules

SummaryBackgroundMicrotubules (MTs) participate in the spatial regulation of actin-based processes such as cytokinesis and cell polarization [1]. The fission yeast Schizosaccharomyces pombe is a rod-shaped cell that exhibits polarized cell growth at cell tips. MT plus ends contact and shrink from the cell tips and contribute to polarity regulation.ResultsHere, we investigate the effects of changing cell shape on MTs and cell-polarization machinery. We physically bend fission yeast cells by forcing them into microfabricated femtoliter chambers. In these bent cells, MTs maintain a straight axis and contact and shrink from cortical sites at the sides of cells. At these ectopic sites, polarity factors such as bud6p, for3p (formin), and cdc42p are recruited and assemble actin cables in a MT-dependent manner. MT contact at the cortex induces the appearance of a bud6p dot within seconds. The accumulation of polarity factors leads to cell growth at these sites, when the MT-associated polarity factor tea1p is absent. This process is dependent on MTs, mal3p (EB1), moe1p (an EB1-binding protein), and for3p but, surprisingly, is independent of the tea1p-tea4p pathway.ConclusionsThese studies provide a direct demonstration for how MTs induce actin assembly at specific locations on the cell cortex and begin to identify a new pathway involved in this process. MT interactions with the cortex may be regulated by cortical-attachment sites. These findings highlight the crosstalk between cell shape, polarity mechanisms, and MTs responsible for cell morphogenesis

Cell Division Geometries as Central Organizers of Early Embryo Development

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QUANTITATIVE APPROACHES FOR THE STUDY OF MICROTUBULE ASTER MOTION IN LARGE EGGS

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Cytoskeleton Force Exertion in Bulk Cytoplasm

International audienceThe microtubule and actin cytoskeletons generate forces essential to position centrosomes, nuclei, and spindles for division plane specification. While the largest body of work has documented force exertion at, or close to the cell surface, mounting evidence suggests that cytoskeletal polymers can also produce significant forces directly from within the cytoplasm. Molecular motors such as kinesin or dynein may for instance displace cargos and endomembranes in the viscous cytoplasm yielding friction forces that pull or push microtubules. Similarly, the dynamics of bulk actin assembly/disassembly or myosin-dependent contractions produce cytoplasmic forces which influence the spatial organization of cells in a variety of processes. We here review the molecular and physical mechanisms supporting bulk cytoplasmic force generation by the cytoskeleton, their limits and relevance to organelle positioning, with a particular focus on cell division

How cells sense their own shape – mechanisms to probe cell geometry and their implications in cellular organization and function

International audienceCells come in a variety of shapes that most often underlie their functions. Regulation of cell morphogenesis implies that there are mechanisms for shape sensing that still remain poorly appreciated. Global and local cell geometry features, such as aspect ratio, size or membrane curvature, may be probed by intracellular modules, such as the cytoskeleton, reaction–diffusion systems or molecular complexes. In multicellular tissues, cell shape emerges as an important means to transduce tissue-inherent chemical and mechanical cues into intracellular organization. One emergent paradigm is that cell-shape sensing is most often based upon mechanisms of self-organization, rather than determinism. Here, we review relevant work that has elucidated some of the core principles of how cellular geometry may be conveyed into spatial information to guide processes, such as polarity, signaling, morphogenesis and division-plane positioning