Cell Polarity: Tension Quenches the Rear

Orientation of Cell Polarity by Chemical Gradients

Accurate decoding of spatial chemical landscapes is critical for many cell functions. Eukaryotic cells decode local chemical gradients to orient growth or movement in productive directions. Recent work on yeast model systems, whose gradient sensing pathways display much less complexity than those in animal cells, has suggested new paradigms for how these very small cells successfully exploit information in noisy and dynamic pheromone gradients to identify their mates. Pheromone receptors regulate a polarity circuit centered on the conserved Rho-family GTPase, Cdc42. The polarity circuit contains both positive and negative feedback pathways, allowing spontaneous symmetry breaking and also polarity site disassembly and relocation. Cdc42 orients the actin cytoskeleton, leading to focused vesicle traffic that promotes movement of the polarity site and also reshapes the cortical distribution of receptors at the cell surface. In this article, we review the advances from work on yeasts and compare them with the excitable signaling pathways that have been revealed in chemotactic animal cells. Expected final online publication date for the Annual Review of Biophysics, Volume 51 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Coordinating cell polarization and morphogenesis through mechanical feedback

Many cellular processes require cell polarization to be maintained as the cell changes shape, grows or moves. Without feedback mechanisms relaying information about cell shape to the polarity molecular machinery, the coordination between cell polarization and morphogenesis, movement or growth would not be possible. Here we theoretically and computationally study the role of a genetically-encoded mechanical feedback (in the Cell Wall Integrity pathway) as a potential coordination mechanism between cell morphogenesis and polarity during budding yeast mating projection growth. We developed a coarse-grained continuum description of the coupled dynamics of cell polarization and morphogenesis as well as 3D stochastic simulations of the molecular polarization machinery in the evolving cell shape. Both theoretical approaches show that in the absence of mechanical feedback (or in the presence of weak feedback), cell polarity cannot be maintained at the projection tip during growth, with the polarization cap wandering off the projection tip, arresting morphogenesis. In contrast, for mechanical feedback strengths above a threshold, cells can robustly maintain cell polarization at the tip and simultaneously sustain mating projection growth. These results indicate that the mechanical feedback encoded in the Cell Wall Integrity pathway can provide important positional information to the molecular machinery in the cell, thereby enabling the coordination of cell polarization and morphogenesis.

Modeling large-scale dynamic processes in the cell: polarization, waves, and division

The past decade has witnessed significant developments in molecular biology techniques, fluorescent labeling, and super-resolution microscopy, and together these advances have vastly increased our quantitative understanding of the cell. This detailed knowledge has concomitantly opened the door for biophysical modeling on a cellular scale. There have been comprehensive models produced describing many processes such as motility, transport, gene regulation, and chemotaxis. However, in this review we focus on a specific set of phenomena, namely cell polarization, F-actin waves, and cytokinesis. In each case, we compare and contrast various published models, highlight the relevant aspects of the biology, and provide a sense of the direction in which the field is moving.

Feedback mechanisms in a mechanical model of cell polarization

Directed cell migration requires a spatially polarized distribution of polymerized actin. We develop and treat a mechanical model of cell polarization based on polymerization and depolymerization of actin filaments at the two ends of a cell, modulated by forces at either end that are coupled by the cell membrane. We solve this model using both a simulation approach that treats filament nucleation, polymerization, and depolymerization stochastically, and a rate-equation approach based on key properties such as the number of filaments N and the number of polymerized subunits F at either end of the cell. The rate-equation approach agrees closely with the stochastic approach at steady state and, when appropriately generalized, also predicts the dynamic behavior accurately. The calculated transitions from symmetric to polarized states show that polarization is enhanced by a high free-actin concentration, a large pointed-end off-rate, a small barbed-end off-rate, and a small spontaneous nucleation rate. The rate-equation approach allows us to perform a linear-stability analysis to pin down the key interactions that drive the polarization. The polarization is driven by a positive-feedback loop having two interactions. First, an increase in F at one side of the cell lengthens the filaments and thus reduces the decay rate of N (increasing N); second, increasing N enhances F because the force per growing filament tip is reduced. We find that the transitions induced by changing system properties result from supercritical pitchfork bifurcations. The filament lifetime depends strongly on the average filament length, and this effect is crucial for obtaining polarization correctly.

Contact angle at the leading edge controls cell protrusion rate

Plasma membrane tension and the pressure generated by actin polymerization are two antagonistic forces believed to define the protrusion rate at the leading edge of migrating cells [1-5]. Quantitatively, resistance to actin protrusion is a product of membrane tension and mean local curvature (Laplace's law); thus, it depends on the local geometry of the membrane interface. However, the role of the geometry of the leading edge in protrusion control has not been yet investigated. Here, we manipulate both the cell shape and substrate topography in the model system of persistently migrating fish epidermal keratocytes. We find that the protrusion rate does not correlate with membrane tension, but, instead, strongly correlates with cell roundness, and that the leading edge of the cell exhibits pinning on substrate ridges-a phenomenon characteristic of spreading of liquid drops. These results indicate that the leading edge could be considered a triple interface between the substrate, membrane, and extracellular medium and that the contact angle between the membrane and the substrate determines the load on actin polymerization and, therefore, the protrusion rate. Our findings thus illuminate a novel relationship between the 3D shape of the cell and its dynamics, which may have implications for cell migration in 3D environments.

Actin dynamics, architecture, and mechanics in cell motility

Tight coupling between biochemical and mechanical properties of the actin cytoskeleton drives a large range of cellular processes including polarity establishment, morphogenesis, and motility. This is possible because actin filaments are semi-flexible polymers that, in conjunction with the molecular motor myosin, can act as biological active springs or "dashpots" (in laymen's terms, shock absorbers or fluidizers) able to exert or resist against force in a cellular environment. To modulate their mechanical properties, actin filaments can organize into a variety of architectures generating a diversity of cellular organizations including branched or crosslinked networks in the lamellipodium, parallel bundles in filopodia, and antiparallel structures in contractile fibers. In this review we describe the feedback loop between biochemical and mechanical properties of actin organization at the molecular level in vitro, then we integrate this knowledge into our current understanding of cellular actin organization and its physiological roles.

Directed actin assembly and motility

The actin cytoskeleton is a key component of the cellular architecture. However, understanding actin organization and dynamics in vivo is a complex challenge. Reconstitution of actin structures in vitro, in simplified media, allows one to pinpoint the cellular biochemical components and their molecular interactions underlying the architecture and dynamics of the actin network. Previously, little was known about the extent to which geometrical constraints influence the dynamic ultrastructure of these networks. Therefore, in order to study the balance between biochemical and geometrical control of complex actin organization, we used the innovative methodologies of UV and laser patterning to design a wide repertoire of nucleation geometries from which we assembled branched actin networks. Using these methods, we were able to reconstitute complex actin network organizations, closely related to cellular architecture, to precisely direct and control their 3D connections. This methodology mimics the actin networks encountered in cells and can serve in the fabrication of innovative bioinspired systems.

Plasma membrane--cortical cytoskeleton interactions: a cell biology approach with biophysical considerations

From a biophysical standpoint, the interface between the cell membrane and the cytoskeleton is an intriguing site where a "two-dimensional fluid" interacts with an exceedingly complex three-dimensional protein meshwork. The membrane is a key regulator of the cytoskeleton, which not only provides docking sites for cytoskeletal elements through transmembrane proteins, lipid binding-based, and electrostatic interactions, but also serves as the source of the signaling events and molecules that control cytoskeletal organization and remolding. Conversely, the cytoskeleton is a key determinant of the biophysical and biochemical properties of the membrane, including its shape, tension, movement, composition, as well as the mobility, partitioning, and recycling of its constituents. From a cell biological standpoint, the membrane-cytoskeleton interplay underlies--as a central executor and/or regulator--a multitude of complex processes including chemical and mechanical signal transduction, motility/migration, endo-/exo-/phagocytosis, and other forms of membrane traffic, cell-cell, and cell-matrix adhesion. The aim of this article is to provide an overview of the tight structural and functional coupling between the membrane and the cytoskeleton. As biophysical approaches, both theoretical and experimental, proved to be instrumental for our understanding of the membrane/cytoskeleton interplay, this review will "oscillate" between the cell biological phenomena and the corresponding biophysical principles and considerations. After describing the types of connections between the membrane and the cytoskeleton, we will focus on a few key physical parameters and processes (force generation, curvature, tension, and surface charge) and will discuss how these contribute to a variety of fundamental cell biological functions.

Divergent lymphocyte signalling revealed by a powerful new tool for analysis of time-lapse microscopy

We describe a new approach for interactive analysis of time-lapse microscopy, and apply this approach to elucidating whether polarity regulation is conserved between epithelial cells and lymphocytes. A key advantage of our analysis platform, 'TACTICS', is the capacity to visualize individual data points in the context of large data sets, similar to standard approaches in flow cytometry. Scatter plots representing microscopic parameters or their derivations such as polarity ratios are linked to the original data such that clicking on each dot enables a link to images and movies of the corresponding cell. Similar to flow cytometric analysis, subsets of the data can be gated and reanalyzed to explore the relationships between different parameters. TACTICS was used to dissect the regulation of polarization of the cell fate determinant, Numb, in migrating lymphocytes. We show here that residues of Numb that are phosphorylated by atypical protein kinase C (aPKC) to mediate apicobasal polarity in epithelial cells are not required for polarization of Numb in T cells, indicating that the role of aPKC is not conserved between lymphocytes and epithelia.

Mechanical feedback between membrane tension and dynamics

The plasma membrane represents a physical inelastic barrier with a given area that adheres to the underlying cytoskeleton. The tension in the membrane physically affects cell functions and recent studies have highlighted that this physical signal orchestrates complex aspects of trafficking and motility. Despite its undeniable importance, little is known about the mechanisms by which membrane tension regulates cell functions or stimulates signals. The maintenance of membrane tension is also a matter of debate, particularly the nature of the membrane reservoir and trafficking pathways that buffer tension. In this review we discuss the importance of membrane area and of tension as a master integrator of cell functions, particularly for membrane traffic.