Mechanics and Regulation of Cell Shape During the Cell Cycle

Chapter
Part of the Results and Problems in Cell Differentiation book series (RESULTS)

Abstract

Many cell types undergo dramatic changes in shape throughout the cell cycle. For individual cells, a tight control of cell shape is crucial during cell division, but also in interphase, for example during cell migration. Moreover, cell cycle-related cell shape changes have been shown to be important for tissue morphogenesis in a number of developmental contexts. Cell shape is the physical result of cellular mechanical properties and of the forces exerted on the cell. An understanding of the causes and repercussions of cell shape changes thus requires knowledge of both the molecular regulation of cellular mechanics and how specific changes in cell mechanics in turn effect global shape changes. In this chapter, we provide an overview of the current knowledge on the control of cell morphology, both in terms of general cell mechanics and specifically during the cell cycle.

3.1 Introduction

The shape of a cell is defined by its mechanical properties and its interactions with the environment (Thompson 1917), and thus the study of cellular mechanics is a prerequisite for the understanding of cell shape control. Cell mechanics can be approached at two levels: (1) by development of physical descriptions of the cell and (2) by experimental studies that combine biological and biophysical methods. While the first approach is critical for understanding which mechanical properties are important for the control of cell shape and how these properties interact to give rise to global cell morphology (Ingber 1993; Bereiter-Hahn 2005; Hoffman and Crocker 2009), the second is essential for understanding how molecular pathways control cellular mechanical properties and, as a result, govern cell shape (Janmey and McCulloch 2007; Lecuit and Lenne 2007; Montell 2008; Paluch and Heisenberg 2009). Such experimental studies rely heavily on the development of tools and methods for measuring cellular mechanical properties and the physical forces generated by living cells.

In this chapter, we discuss cell shape changes that occur throughout the cell cycle. We focus on the mechanical properties that have been shown to be involved in cell shape control and discuss how these properties are regulated, particularly by key biochemical pathways that drive the cell cycle. We first introduce several basic mechanical concepts that are useful for the study of cell shape. The subsequent section describes the geometrical changes in cell volume and surface area that occur during the cell cycle. Sections 3.4 and 3.5 focus on the mechanical control of shape changes during mitosis and interphase, respectively. Section 3.6 discusses specific aspects of cell mechanics within tissues. Finally, the last section summarizes the current knowledge on how cellular mechanics are controlled by cell cycle-related biochemical pathways.

3.2 Physical Descriptions of the Cell

This section briefly introduces the most common physical descriptions of the cell, as well as the basic mechanical concepts that will be used throughout this chapter. Mechanics is the branch of physics that deals with the movements and deformations of physical bodies. Classical mechanics is often subdivided into two branches: kinematics and dynamics. While kinematics describes the motion of objects without considering the causes of this motion, in dynamics, laws of mechanics (e.g., Newton’s laws) are used to predict the motions and deformations caused by the forces exerted on a system. To use a dynamics approach to study the deformation or movement of a cell, one must know not only the forces exerted on the cell, but also the physical properties of the cell (such as its elasticity and viscosity), which determine how it will respond to such forces. A major focus of biomechanics is to design experiments to determine these forces and properties (Bereiter-Hahn et al. 1987). However, it is not always possible to directly measure the mechanical properties of a cell and the forces to which it is subjected, particularly for cells in tissues (Davidson et al. 2009). In the absence of such direct measurements, kinematic approaches, which focus on analyzing the motion and geometrical changes of cells, can provide important insights into cell mechanics (see Sects. 3.2.5 and 3.3, Blanchard et al. 2009).

Mechanical models for cell shape changes, particularly during cell division, and also in the larger context of embryonic development, have been a focus of interest since the late nineteenth century (Roux 1894; Thompson 1917; Rappaport 1996). In the simplest models, the cell is considered as a liquid bag surrounded by a homogenous shell under tension (see Sect. 3.2.2). Successive levels of complexity can then be added by taking into account the physical properties of cytoplasmic structures and spatial variations in the physical parameters describing the cell. The addition of substrate adhesions and interactions with neighboring cells is essential for understanding cell shape in the context of a tissue (Box 3.1).

Notably, even the most complex physical models of cellular objects are only valid within a set of predefined initial conditions and constraints, and these models only account for observations in a given framework. A model that accurately accounts for a set of observations using a certain experimental setup may have no value in another experimental situation. Given the complexity of the cell, it is not clear that physical modeling will ever provide a complete mechanical description of the cell, or even if such a complete description is possible. The primary goal of physical models is not necessarily to completely describe cellular mechanics, but also to provide tools for experiments. A physical description is necessary to interpret any quantitative mechanical experiment. For example, in measurements of cellular tension that rely on cell deformations induced by pipette aspiration or by laser ablation, a physical model is necessary to deduce the tension from the observed deformation (Evans and Yeung 1989; Hochmuth 2000; Rauzi et al. 2008). Models also help to determine which physical properties are likely to affect a given cell shape change and aid in designing experiments to test the effect of these properties on cell morphology. Multidisciplinary approaches that couple experimental manipulation and modeling are currently attracting a growing interest in the field of cell morphogenesis (Farhadifar et al. 2007; Lecuit and Lenne 2007; Solon et al. 2009). These include studies of cell mechanics and shape changes during mitosis (Théry et al. 2007; Stewart et al. 2011).

3.2.1 Box 3.1 Major Physical Properties of the Cell

One of the first attempts to experimentally determine cell surface mechanical properties was with a device called the “Cell Elastimeter,” which uses a pressure differential to aspirate single cells inside of a glass capillary (Mitchison and Swann 1954). This technique, along with other cell aspiration and deformation methods, has been used to measure a number of cell surface properties important for the study of cell mechanics (Hochmuth 2000; Lomakina et al. 2004; Krieg et al. 2008b).

3.2.1.1 Cortical Tension

The most basic cortical structure is present under the membrane of red blood cells. In these cells, a very thin (5–10 nm) network of spectrin and short actin filaments is tightly attached under the plasma membrane. Interfacial tension of red blood cells was one the first experimentally measured and is approximately 15 pN/μm (Rand and Burton 1964). In contrast to red blood cells, most cell types have a tensile actomyosin cortex under the plasma membrane with a thickness ranging between several hundred nanometers and several microns depending on cell type (Hiramoto 1957; Hanakam et al. 1996). The magnitude of the resulting cortical tension also varies between cell types. For example, neutrophils have a relatively low tension of approximately 35 pN/μm (Evans and Yeung 1989), which is comparable to the cortical tension of early embryonic cells isolated from zebrafish embryos (Krieg et al. 2008a). In contrast, fibroblasts typically display tensions of 500–1,000 pN/μm (Thoumine et al. 1999; Tinevez et al. 2009), while in Dictyostelium discoideum cells, cortical tension can reach several thousand pN/μm (Pasternak et al. 1989; Dai et al. 1999; Schwarz et al. 2000).

3.2.1.2 Relationships Between Tension and Other Physical Properties of the Cortex

In the literature, tension is sometimes confused with elasticity (also often called stiffness or rigidity). However, tension and elasticity are two distinct physical properties. Whereas elasticity is a measure of deformability for a solid-like material, tension is related to the sum of all forces within a material. In the context of the cortex, tension is the local stress in the cortical network (i.e., the forces per unit area in the network) integrated over the thickness of the cortex. In cells, surface tension is the combined result of the physical properties of the membrane and of the underlying cortical network. Provided that the cortex is tightly coupled to the membrane, the total surface tension is the sum of the in-plane tension of the plasma membrane, γ, and of cortical tension, Tcortex:
$$ {T_{\rm{total}}} = \gamma + {T_{\rm{cortex}}}. $$
In most cells with an actomyosin cortex, plasma membrane tension is negligible and surface tension is dominated by cortical tension (Krieg et al. 2008a; Tinevez et al. 2009). For a steady-state cortex in the absence of elastic deformations or flows, cortical tension is primarily determined by the active tension (Tactive), which is the result of active processes such as myosin motors pulling on the actin network. Active tension is equal to ζΔμh, where h is the thickness of the cortex and ζΔμ is the active stress exerted in the cortical network (ζ is a coefficient relating the energy provided by ATP hydrolysis, Δμ, to the active stress; ζ depends both on the activity and on the concentration of myosin motors; Kruse et al. 2004). In the presence of deformations or flows, additional terms that depend on viscoelastic properties of the cortex must be taken into account. For example, for purely elastic deformations:
$$ {T_{\rm{cortex}}} = {T_{\rm{active}}} + {T_{\rm{elastic}}} = \zeta \Delta \mu \cdot h + Eh\frac{{{{(A - {A_0})}}}}{{A_0}} $$
where E is the elastic modulus, A is the surface area, and A0 is the equilibrium surface area of the cortex (Tinevez et al. 2009). In this particular case, cortical tension depends on cortex elasticity, though this is not true for all deformations.

3.2.1.3 Membrane-to-Cortex Attachment

In order to translate cortical movements into movements of the plasma membrane, the cortex and the membrane must be attached. Membrane-to-cortex attachment is achieved by specific proteins that bind both to actin filaments and to transmembrane proteins or lipids. The best-studied examples are the ezrin/radixin/moesin (ERM) family proteins, though other molecules such as myosins-1 and filamin are also involved in membrane-to-cortex attachment (Popowicz et al. 2006; Fehon et al. 2010). Membrane-to-cortex attachment can be measured in isolated cells by pulling membrane tubes from the cell: the force necessary to pull and maintain a membrane tether directly depends on the energy of membrane-to-cortex attachment (Sheetz 2001; Brochard-Wyart et al. 2006; Nambiar et al. 2009; Diz-Muñoz et al. 2010).

3.2.1.4 Cell–Substrate and Cell–Cell Adhesion

Physical descriptions of isolated cells in suspension have provided important insights into cellular mechanics. However, cells both in tissue and in culture physically interact with their environment, be it a culture dish, a matrix or neighboring cells in a tissue. Including the effect of substrate adhesion into mechanical models of cells is not trivial and is still being actively investigated. In most models, a continuum adhesion term is added to liquid core/viscoelastic contractile shell-type descriptions of the cell (Chu et al. 2005; Krieg et al. 2008b; Borghi and Nelson 2009). Such purely physical descriptions, which do not include complex biochemical regulation of cell–substrate adhesion, successfully account for the dynamics of early spreading of a variety of cell types over solid substrates (Cuvelier et al. 2007).

While cortical tension favors a spherical cellular shape, cell–substrate and cell–cell adhesions provide counteracting forces that tend to favor a more flattened, spread shape. The balance between these opposing forces determines the areas of cell–cell or cell–substrate interfaces and defines the overall shape of an adherent cell (Cuvelier et al. 2007; Montell 2008). Predicting the shape of a single cell on a flat substrate or of a doublet of adhering cells is already a theoretical challenge, and modeling the shape of cells within tissues or interacting with three-dimensional substrates is considerably more complex and has only been approached in a few specific situations (Lecuit and Lenne 2007).

3.2.2 Physical Descriptions of the Cell: A Multicomponent Complex Object

Cells are made of “soft” structural components. As such, their behavior can differ considerably from that of rigid, engineered structures typically modeled in the framework of conventional mechanics. Physical properties of cells are usually approached in the context of soft matter physics, which deals with materials such as liquids, colloids, and polymer gels (Boal 2002). A typical soft-matter-type behavior of biological materials is viscoelasticity. When subjected to a force, a viscoelastic material displays liquid-like (viscous) or solid-like (elastic) behaviors, depending on the timescale of the perturbation. Although the time dependency of the response to stress differs among various types of viscoelastic materials, many biological materials respond to an applied force in a solid-like, elastic manner on short timescales and in a liquid-like, viscous manner on long timescales.

In the past few decades, soft-matter physicists have developed theoretical tools for the study of many biological materials, including viscoelastic cytoskeletal networks and fluid lipid bilayers (reviewed in Lipowsky and Sackmann 1995; Boal 2002; Janmey and McCulloch 2007). However, the cell is a complex object, composed of many constituents with very different physical properties that vary in space and time, and thus it cannot be fully described by a simple viscoelastic or fluid model (Bereiter-Hahn et al. 1987; Hochmuth 2000). Moreover, cytoskeletal networks can display active behaviors, such as treadmilling or contraction, where ATP consumption is converted into mechanical work. The presence of active processes makes passive mechanical models incomplete. Recently developed “active gel” models, which integrate such active behaviors with more classical viscoelastic descriptions of cytoskeletal meshworks, provide a more accurate description of cellular networks (Kruse et al. 2004, 2005).

One challenge in modeling cell mechanics resides in choosing the level of detail for a given model. Cellular mechanical properties are the consequence of interactions at the molecular level. However, an accurate model of how molecular interactions give rise to global mechanical properties would require detailed knowledge of all the molecular players involved and the characteristics (e.g., time constants) of their interactions. Thus, only the behavior of relatively simple cytoskeletal structures can be predicted from molecular data using simulations. Such molecular approaches have proven successful in modeling in vitro actin networks (Carlsson 2003; Dayel et al. 2009; Rafelski et al. 2009) and microtubule bundles and spindles (Janson et al. 2007; Dinarina et al. 2009). However, in most cellular processes, the data necessary to develop microscopic models are simply not available. Moreover, molecular models cannot always account for mesoscopic properties like pressure and friction. In contrast to molecular descriptions, coarse-grained models use phenomenological parameters that integrate the influence of microscopic processes without requiring a detailed knowledge of how they occur. For example, in coarse-grained models of cytoskeletal networks, viscosity is described by a generic parameter that globally accounts for all sources of viscosity in the network (turnover of cross-linkers, filament turnover, etc.) without requiring molecular details of the viscosity-generating mechanisms (Kruse et al. 2005; Mayer et al. 2010). Coarse-grained models are frequently used to describe mechanical properties at cellular length scales. They are able to describe processes that are too complex to model at the microscopic level or where emergent mesoscopic properties, rather than molecular details, are central. However, they do not necessarily provide a physical understanding of how molecules influence a given physical property. Therefore, coupling coarse-grained and molecular approaches is necessary to achieve a thorough understanding of cell shape changes.

From experimental and theoretical studies, a number of core mechanical properties have emerged as major determinants of cell shape. These properties, which include cortical tension, membrane-to-cortex attachment and cell–substrate/cell–cell adhesion, are discussed in detail in Box 3.1.

3.2.3 Simplest Models: A Liquid in a Shell

Because most cells assume a spherical shape when put in suspension, a behavior characteristic of liquids, early models describe suspended cells as “liquid drops.” In liquids, surface tension, which determines the energy cost of an interface between the liquid and the surrounding medium, favors the shape with the minimal surface for a given volume (i.e., a sphere). Though very simplistic, liquid drop models have, for example, proven successful in predicting the shape of suspended cells aspirated into a pipette (Evans and Yeung 1989; Yeung and Evans 1989; Dai et al. 1999; Hochmuth 2000).

Cellular surface tension results from a combination of the tensions of the plasma membrane and the cytoskeletal structure present immediately under the membrane, the cell cortex (Box 3.1, Fig. 3.1a). In most cells, a cortical network of cross-linked actin filaments supports the plasma membrane (Bray and White 1988), and this meshwork is under tension as a result of myosin motor activity. Actomyosin tension is different from the passive plasma membrane tension in that it is actively generated by myosins pulling on actin filaments. Its mechanical effects are nevertheless similar to that of a passive surface tension (Dai et al. 1999; Hochmuth 2000; Bereiter-Hahn 2005; Tinevez et al. 2009). Provided that the cortex is tightly attached to the membrane, the total cellular surface tension is the sum of the tensions of the plasma membrane and of the cortex. However, if the coupling of the membrane to the cortex is loose, such that membrane and cortex can move separately from one another, membrane and cortex tensions are not simply additive. Regardless, the tension of the plasma membrane itself is usually negligible compared to the tension of the underlying cortex (Dai et al. 1999; Tinevez et al. 2009).
Fig. 3.1

Surface tension, intracellular pressure and implications for the regulation of the cell volume. (a) In most cells, a cortical network of cross-linked actin filaments lies under the plasma membrane. The surface tension of the cell is a combination of the tension of the plasma membrane, γ, and the cortical tension, T. If the cortex is tightly attached to the membrane, the total surface tension is simply γ + T. In most cells, γ is orders of magnitude smaller than T, and γ can thus be neglected. (b) Cortical tension generates a hydrostatic pressure in the cytoplasm. The law of Laplace relates the difference between intracellular pressure, Pin, and external pressure, Pout, to the cell radius, R, and the cell surface tension, T

In liquid drops, surface tension results in a hydrostatic pressure inside of the drop, given by the law of Laplace. Similarly, in cells, the contractile cortex generates pressure in the cytoplasm, which is related to cortical tension by the law of Laplace (Fig. 3.1b). This has implications for the regulation of cell volume as increasing cortical tension could, in principle, cause the cell to contract and drive water out of the cell, thereby reducing cell volume. At steady state, when the cell volume does not vary, the hydrostatic pressure has to be exactly balanced by the osmotic intracellular pressure (Box 3.2; Bereiter-Hahn 2005). However, even the highest measured cortical tensions (several thousand pN/μm for Dictyostelium cells, see Box 3.1) result in a hydrostatic pressure differential across the cell membrane of around 1,000 Pa (given by the law of Laplace applied to a typical Dictyostelium cell with a tension of 2,500 pN/μm and a radius of 5 μm). In contrast, the osmotic pressures of physiological media are typically around 5 × 105 Pa. Therefore, even a complete disassembly of the contractile actin cortex, reducing the hydrostatic pressure differential from 1,000 to 10 Pa, would result in a volume change of only a few percent (Tinevez et al. 2009; Stewart et al. 2011; see Box 3.2 for details). Cell volume is therefore primarily dictated by osmotic pressure, which is regulated by ion fluxes, while the main function of cortical tension is rather to provide physical resistance to external forces exerted on the cell surface and to drive cellular deformations.

3.2.3.1 Box 3.2 Osmotic Pressure, Cortical Tension and Cell Volume Control

For a spherical cell at steady state, cell volume is fixed, and no net flow of water through the cell membrane occurs. While the difference in hydrostatic pressure across the membrane is given by the law of Laplace, the osmotic pressure difference is the difference between intracellular osmotic pressure, which depends on the number of moles of intracellular osmolites, nosm, and the extracellular osmotic pressure, which is approximately 105 Pa for physiological media [see (Eq. 3), where T is the cortex tension, RC is the cell radius, R is the gas constant, θ is the temperature, and VC is the cell volume]. At steady state, intracellular hydrostatic pressure is exactly balanced by osmotic pressure [(Eq. 1); Bereiter-Hahn 2005; Salbreux 2008; Tinevez et al. 2009]. This means that the hydrostatic pressure differential across the cell membrane is equal to the differential in osmotic pressure (Eq. 2) and (Eq. 3). For cells in culture and in vivo, the absolute value of the extracellular osmotic pressure is much higher than the typical pressure difference across the plasma membrane (Eq. 4). As a consequence, even a dramatic change in cortical tension will be balanced by a change in osmotic pressure resulting from a very small change in cell volume; the contribution of cortical tension can therefore be neglected, and cell volume can be reasonably approximated using osmotic pressure alone ((Eq. 5); see also Salbreux 2008). For example, if cortical tension is reduced from 2,500 to 10 pN/μm (corresponding to the change in tension resulting from cortex disassembly in cells with high surface tension), the hydrostatic pressure difference between the inside and the outside of the cell drops by about 1,000 Pa. This drop represents only 1% of the exterior osmotic pressure. Such a change in pressure would thus be mechanically balanced by an expansion of the cell volume by ~1%. This calculation implies that the cortex is not primarily responsible for preventing cell expansion due to the osmotic pressure difference (Tinevez et al. 2009). This is likely the reason why cells treated with the actin depolymerizing drug Cytochalasin D, for example, which reduces cortical tension by 90%, only display a small increase in volume and do not immediately explode (Stewart et al. 2011).

3.2.4 The Structure of the Cytoplasm

Describing the cytoplasm as a viscous fluid can be sufficient for slow deformations. However, in the case of fast shape changes, elastic, solid-like properties of cytoplasmic structures may play an important role in resisting deformations. Indeed, the nucleus, intracellular cytoskeletal networks (including intermediate filaments) and membrane organelles display elastic properties, at least on short timescales (Brown et al. 2001; Caille et al. 2002; Ingber 2003; Liu and Wang 2004; Mitchison et al. 2008).

A more realistic model of the cell body treats the cytoplasm as a sponge-like poro-elastic material, where fluid cytosol fills an intracellular viscoelastic network (Mitchison et al. 2008). Such poro-elastic models have been successfully used to quantitatively describe cellular deformations driven by flows of cytosol and changes in intracellular pressure (Charras et al. 2008; Tinevez et al. 2009). The presence of a cytoplasmic network has important implications for intracellular hydrostatic pressure. Indeed, a porous cytoplasm hinders the motion of the fluid cytosol, and thus slows down the equilibration of hydrostatic pressure throughout the cell (Charras et al. 2005). The timescale of pressure equilibration is directly related to the effective meshsize of the cytoplasmic network; if the meshsize is small (in the 30 nm range), pressure gradients across the cell could persist on timescales of seconds, and may thus influence cell motility (Mitchison et al. 2008). Experiments in cultured filamin-deficient M2 cells suggest the presence of such gradients (Charras et al. 2005), while experiments in other cell types argue for a faster equilibration of cytoplasmic pressure (Tinevez et al. 2009; Maugis et al. 2010). It is possible that cytoplasmic mesh sizes are within a range where small changes could drastically affect the timescale of pressure equilibration, and thus the structure of the cytoplasm must be tightly regulated. Interestingly, a massive disassembly of intermediate filament networks is observed in mitosis, controlled by p34Cdc2 (Chou et al. 1990), suggesting that the meshsize of the cytoplasmic network increases and that intracellular pressure equilibration may occur faster in this phase of the cell cycle.

3.2.5 Spatial Variations: Cells Are Not Spheres

The models described above mostly consider the cell as a spherical object. To account for cell polarization and local cell deformations, one must take into account spatial inhomogeneities. There are a number of examples where local variations in cellular physical parameters lead to cell deformations:
  • Local changes in dynamics or spatial polarity of cytoskeletal networks underlying the membrane can be sufficient to explain a variety of complex cell shapes. For example, the shapes of keratocytes gliding over flat surfaces can be successfully described by a two-component model where a treadmilling actin network pushes against an inextensible membrane bag (Keren et al. 2008).

  • Local changes in the physical properties of the cortex itself can account for shape changes. For example, physical models of cytokinesis can account for the formation of the cleavage furrow by introducing a gradient in contractility between the poles and the equator (White and Borisy 1983).

  • Local shape changes can result from inhomogeneities in membrane-to-cortex attachment. For example, at places where the cortex is locally decoupled from the membrane, intracellular pressure can drive the formation of membrane protrusions called blebs, which are involved in cell migration, cytokinesis, cell spreading, and apoptosis (Sheetz et al. 2006; Charras and Paluch 2008; Fackler and Grosse 2008).

3.2.6 Mechanics of Cells in Tissues

Beyond the level of the individual cell, tissue morphogenesis also relies on mechanical processes (Thompson 1917). Tissue mechanics arises from the physical properties of the cells that compose the tissue. Deformations of individual cells are coupled by cell–cell or cell–matrix interactions and therefore give rise to global tissue movements. Although there is no general understanding of how these individual properties impact tissue morphogenesis, studies in developing embryos point to cell–cell and cell–substrate adhesion and actomyosin contractility as core physical properties for many of the shape changes observed during embryonic development (Lecuit and Lenne 2007; Montell 2008). For example, the vertex model, which only considers cell elasticity, cell–cell adhesion and actomyosin contractility at apical junctions, can account for various packing geometries observed in the Drosophila wing epithelium as stable and stationary network configurations (Farhadifar et al. 2007; Staple et al. 2010). Moreover, if perturbations in the network due to cell proliferation are introduced in the model, the resulting cell rearrangements are similar to those observed during Drosophila development. Thus, using the vertex model, the epithelial packing geometries observed during development can be successfully accounted for by the combined action of cell mechanics and cell proliferation in the tissue. Further refinements of the vertex model, coupling cell polarity to mechanical properties, account for global tissue polarity during morphogenesis (Aigouy et al. 2010). A similar approach has been used to investigate the mechanics of germ-band elongation during Drosophila development (Rauzi et al. 2008). Coupling a vertex-type model to quantification of cell deformations and laser ablation-based force distribution mapping within cells has identified the tensile properties of individual cells, as opposed to external forces, as the major contributor to the remodeling of the elongating germ-band. Similar models that couple contractility to cell–cell adhesions have been used to describe cell patterning in the Drosophila retina (Käfer et al. 2007; Hilgenfeldt et al. 2008) and to account for size determination during the growth of the Drosophila wing disk (Hufnagel et al. 2007).

There are a number of challenges associated with experimental studies of cell mechanics in tissues. One major problem in investigating which mechanical properties are important during tissue morphogenesis is that it is difficult to specifically modulate a single physical property without affecting others (Lecuit and Lenne 2007). Indeed, many molecular pathways are likely to affect several mechanical properties simultaneously. For example, proteins controlling actin turnover may influence the viscosity of the cortex as well as cortical thickness and tension (Tinevez et al. 2009; Mayer et al. 2010). Moreover, feedback loops between mechanical properties and molecular pathways provide an additional level of coupling between specific mechanical properties. For example, physical stress enhances the recruitment of adhesion proteins to focal adhesions and thus enhances adhesion strength (Riveline et al. 2001). This suggests that a feedback loop between cortical tension, which tends to reduce the area of cell–cell contact, and cell–cell adhesion, which tends to increase this area, could contribute to the regulation of cell shape in tissues (Rauzi et al. 2008; Paluch and Heisenberg 2009). A second problem is the lack of tools to directly measure the mechanical properties of individual cells in a tissue. While many methods exist to quantify properties of isolated cells, such as cell–cell or cell–substrate adhesion, cell elasticity, and cortical tension (reviewed in Paluch and Heisenberg 2009), most of these methods rely on direct manipulation of cells, which is difficult in tissues. The method most commonly used at present to assess mechanical properties of cells within tissues is laser ablation, where the relaxation of a cell–cell boundary upon disruption with a laser gives an indirect measurement of cortical tension or cellular elasticity (Hutson et al. 2003; Landsberg et al. 2009; Rauzi et al. 2008).

Ideally, biomechanics provides an understanding of cellular shape from “first principles,” which means that cellular movements and deformations are analytically derived from the forces causing these movements. Such an approach can, however, be experimentally challenging, given the difficulties associated with directly measuring the physical properties of cells and the forces they generate. When methods to directly measure cellular mechanical properties are not available, quantification of cell movements and deformations can itself provide information about the forces generated in single cells as well as in tissues. Quantitative data on the shapes and positions of cells can be used to solve the so-called inverse problem, where mechanical parameters and force distributions are extracted from the observed cellular deformations. Such kinematic approaches, which focus on describing the motion of objects, have been used to map strain rates during dorsal closure (Blanchard et al. 2009; Gorfinkiel et al. 2009) and germ-band extension (Butler et al. 2009) in Drosophila. The distribution of forces within the tissue can be extrapolated from strain rate maps and these deformation maps can then be quantitatively compared for different experimental conditions, providing insight into the molecular pathways involved in force generation (Butler et al. 2009; Brodland et al. 2010). In such kinematic approaches, changes in cell geometry must be precisely quantified in order to extract information about the physical properties of cells and the forces acting upon them. The following section provides an overview of the changes in cell shape occurring during the cell cycle.

3.3 Regulation of Cell Volume and Surface Area During the Cell Cycle

Cells undergo considerable geometrical changes during each division cycle, particularly during mitosis. At the onset of M-phase, cells both in vivo and in vitro transform from various adhesive shapes to being nearly spherical and virtually detached from the substrate in the process commonly known as “cell rounding,” or “rounding up” (Strangeways 1922; Sanger and Sanger 1980; Cramer and Mitchison 1997). Concomitant with this drastic shape change, cells undergo significant changes in surface area and volume during the course of M-phase as well as in the final stage of M-phase, cytokinesis, before re-spreading as two daughter cells. Precisely monitoring these geometrical changes can provide information about the underlying forces that drive cell deformations.

3.3.1 The Geometry of Cell Rounding

The surface area of a sphere is the minimal area possible for a given volume. Therefore, when a cell transforms from a flat shape to a sphere during rounding, it must undergo either a reduction in surface area (assuming volume is constant) or an increase in volume (assuming surface area is constant) (Fig. 3.2a; Théry and Bornens 2008). In other words, the surface area-to-volume ratio must decrease as a cell rounds up, and this can be achieved by changing either one or both of these geometrical parameters. In reality, both surface area and volume appear to decrease during cell rounding, but because the reduction in surface area is greater, the surface area-to-volume ratio decreases (Fig. 3.2b; Erickson and Trinkaus 1976; Boucrot and Kirchhausen 2008).
Fig. 3.2

Cell volume and surface changes during the cell cycle. (a) Cell rounding requires a decrease in the cell surface area-to-volume ratio. This can be achieved by decreasing the cell surface area (SA) and/or by increasing cell volume (V). (b) Evolution of cell volume and surface area (upper panel) and surface-to-volume ratio (lower panel) during the cell cycle. Note: after cytokinesis, the volume and surface area of one of the daughter cells are plotted, which explains the jump in volume and surface values in the upper panel at cytokinesis

3.3.2 Changes in Cell Volume

Cell volume gradually increases during interphase to between two and three times the volume observed in early interphase (Graham et al. 1973; Knutton et al. 1975; Habela and Sontheimer 2007). During M-phase, it has been observed that cell volume is reduced by approximately 30% from prophase to metaphase, and subsequently returns to the prophase volume just prior to cytokinesis. Following cytokinesis, each daughter cell then has a volume that is equal to half of the mother’s at the beginning of cytokinesis (Fig. 3.2b; Boucrot and Kirchhausen 2008). Notably, as volume measurements generally rely on three-dimensional reconstructions of cell shape, they are subject to significant errors in accuracy (Tzur et al. 2009), and the extent of mitosis-related volume changes is still a matter of debate. Changes in cell volume could in principle be caused by changes in cortical tension, and the resulting hydrostatic pressure, or in osmotic pressure. However, given the respective magnitudes of extracellular osmotic pressure and of the pressure differential across the plasma membrane, such significant volume changes are more likely controlled by pathways that modify the cell’s osmotic potential rather than by the cytoskeleton (see Sect. 3.2.2 and Box 3.2; Salbreux 2008; Tinevez et al. 2009; Stewart et al. 2011).

3.3.3 Changes in Surface Area

Scanning electron micrographs of cultured mammalian fibroblasts show that the plasma membrane is not a blanket of lipids pulled tightly over the cell, but rather forms a continuous series of folds and ridges overlying the cell (Fig. 3.3a; Knutton et al. 1975; Erickson and Trinkaus 1976). Therefore, one must distinguish between the surface area that includes these folds, the plasma membrane surface area (PMSA), and the apparent cell surface area (CSA), which excludes these folds (Fig. 3.3b). Unlike PMSA, CSA can be measured with a light microscope, which does not resolve membrane folds or very small protrusions. PMSA is controlled by the balance of exocytosis and endocytosis (Steinman et al. 1983), wherein lipids are removed from the PM by endocytosis, sorted in endosomes and re-inserted into the PM by exocytosis. Additionally, new lipids can be synthesized de novo in the Golgi apparatus and then trafficked to the PM (Fig. 3.3c). Electron micrographs indicate that the PMSA-to-CSA ratio, which describes the excess of plasma membrane, increases from approximately 1.5 to 3 between G1 and G2 phases (Erickson and Trinkaus 1976). This suggests that CSA and PMSA are regulated independently of one another. Indeed, while PMSA is necessarily regulated by membrane trafficking, CSA modification does not require changes in membrane trafficking, but rather results from cytoskeleton-driven shape changes (Fig. 3.3b, c).
Fig. 3.3

Cell surface versus plasma membrane area. (a) Electron micrograph of a BHK21 cell detached from the substrate by trypsinization. The plasma membrane displays numerous folds and ridges, which indicates that PMSA is higher than CSA. Picture adapted from (Erickson and Trinkaus 1976). (b) Plasma membrane surface area (PMSA) and cell surface area (CSA) can vary independently from one another. (c) PMSA is controlled by membrane trafficking. Blocking exocytosis decreases PMSA, whereas blocking endocytosis increases PMSA

3.3.3.1 Changes in Cell Surface Area

Cell surface area (CSA) doubles from early interphase to early M-phase, which is accompanied by a comparable increase in cell volume. The subsequent cell rounding upon M-phase entry results in a twofold decrease in surface area (Erickson and Trinkaus 1976). Because cell shape is consistently spherical throughout the first half of M-phase, and volume has been shown to decrease (Boucrot and Kirchhausen 2008), surface area also decreases during this period. Assuming that cell volume does not change during late anaphase, CSA increases as cytokinesis progresses because the cell becomes less spherical. Following cytokinesis, the two new daughter cells re-spread and surface area increases to the original interphase value (Fig. 3.2b).

3.3.3.2 Changes in Plasma Membrane Surface Area

Plasma membrane surface area (PMSA), which is controlled by membrane recycling, varies throughout the cell cycle, though the magnitude of this change is unclear. Estimations of PMSA based on scanning electron micrographs of detached cells indicate that PMSA increases 1.5-fold from early to late interphase (Knutton et al. 1975). During the transition from interphase to metaphase, measurements based on fluorescence intensity of membrane markers indicate a significant decrease in PMSA, though the observed change ranges from two- to sixfold depending on the cell type (Boucrot and Kirchhausen 2007). This loss of PM occurs simultaneously with a decrease in endosomal trafficking and/or exocytosis, which, consistently, would result in a net loss of plasma membrane lipids as endosomes accumulate in the cytoplasm (Berlin et al. 1978; Berlin and Oliver 1980; Warren et al. 1984; Schweitzer et al. 2005; Boucrot and Kirchhausen 2007). Just prior to cytokinesis, PMSA suddenly returns to its interphase value (Boucrot and Kirchhausen 2007). The increase in PMSA during late M-phase is likely the result of exocytosis of endosomes accumulated earlier in M-phase, as exocytosis has been observed to resume during this period, and Golgi-derived vesicles (which contain newly synthesized lipids) are not required for the PMSA increase (Warren et al. 1984; Schweitzer et al. 2005; Boucrot and Kirchhausen 2007). Following cytokinesis, the PM is split between the two daughter cells, which then re-spread as they enter the next round of interphase.

Cyclin Dependent Kinase (Cdk)-Cyclin complexes, the master regulators of cell cycle progression, have been implicated in the regulation of membrane trafficking throughout the cell cycle, though their exact role is still unclear. Cdk1 (the homolog of yeast cdc2, also known as p34cdc2 in other systems), the mitotic Cdk that controls M-phase entry, blocks membrane fusion in vitro (Tuomikoski et al. 1989). This suggests that Cdk1 could be responsible for the observed decrease in exocytosis rates in early M-phase, when Cdk1 activity is highest. However, Cdk1 has also been shown to reduce endocytosis rates, as treatment with mitotic cell extract or purified cyclinB-p34cdc2 decreases invagination of endocytic pits (Pypaert et al. 1991). Such a decrease in endocytosis rates would, in principle, counteract the effects of the observed decrease in exocytosis. These apparently conflicting data indicate that regulation of membrane trafficking by Cdk1 must be precisely tuned.

In addition to global PMSA regulation, local deposition of new membrane at the cleavage furrow is required in many systems for proper cytokinesis. This coincides temporally with the observed increase in PMSA just prior to cytokinesis (Boucrot and Kirchhausen 2007). In the final stages of cytokinesis, membrane vesicles endocytosed from the poles and Golgi-derived vesicles are inserted into the PM at the midbody and contribute to final abscission (Schweitzer et al. 2005; Goss and Toomre 2008). In early divisions of Xenopus embryos, new membrane is inserted specifically in the cleavage furrow throughout cytokinesis, and likely fulfills a requirement for a local increase in PMSA in these very large cells (Bluemink and de Laat 1973). Membrane insertion has also been implicated in cytokinesis and cellularization in Drosophila, Caenorhabditis elegans, and echinoderms (Burgess et al. 1997; Skop et al. 2001; Shuster and Burgess 2002). Following cytokinesis in some cultured cells, PMSA continues to increase during re-spreading. This continued growth in PMSA may directly result from increased membrane tension during spreading, which can both block endocytosis and stimulate exocytosis (Raucher and Sheetz 1999; Gauthier et al. 2009).

Kinematic approaches in cell mechanics, in which cell movements and changes in surface area and volume are precisely quantified, can provide clues about the forces responsible for such changes. For example, during cell rounding, the fact that cells become more spherical (i.e., their surface area-to-volume ratio decreases) suggests that there could be an increase in cortical tension during rounding (see also Sect. 3.2.2). Such changes in cell shape observed throughout the cell cycle can be further studied using a dynamics-style approach, where the forces required to produce certain cell shapes and the proteins responsible for generating these forces are considered.

3.4 Shape Changes During M-Phase: Cell Rounding and Cytokinesis

Cells undergo two major shape changes during M-phase, cell rounding, which occurs at M-phase entry, and cytokinesis, the final step of mitosis. Cortical tension and cell–substrate or cell–cell adhesion both play major roles in determining cell shape during M-phase. In cultured cells, for example, cell rounding involves an increase in tension and a decrease in cell adhesion that causes a transformation from a spread morphology to a sphere (see also Sect. 3.3, Fig. 3.2). In cytokinesis, a spatial gradient of active tension effects a shape change that results in the physical division of one cell into two. These physical properties are controlled directly by the actomyosin cytoskeleton and adhesion proteins.

3.4.1 Cell Rounding

Entry into M-phase is characterized morphologically by cell rounding, which results from major changes in a cell’s physical properties between interphase and M-phase. For example, the elastic modulus of the cell surface increases approximately threefold between interphase and M-phase (Matzke et al. 2001; Maddox and Burridge 2003; Kunda et al. 2008). Rounding is observed both in cultured cells and in vivo. However, most mechanistic studies of cell rounding have been performed using cultured cells. Therefore, this section will deal only with rounding in cultured cells, though most of the described shape changes and underlying mechanics are likely to be similar during mitotic rounding in tissues. For most cultured cell lines, interphase cells have a spread morphology and stable cell surface adhesions. The actin cytoskeleton is organized into flat, ruffled actin-filled protrusions at the periphery and stable, contractile actin bundles, called stress fibers, in the cell body (Cramer and Mitchison 1997). In addition, interphase cells have an actin cortex on their “top” side that supports the plasma membrane (Morone et al. 2006; Estecha et al. 2009), though this structure does not seem to be as well-developed as in M-phase. In sharp contrast, cells in M-phase have a nearly spherical shape with a uniform, well-developed actin cortex at their periphery as well as retraction fibers, thin, actin-filled tethers that connect the cells to the underlying substrate (Bradley et al. 1980; Cramer and Mitchison 1997).

3.4.1.1 Surface Tension and Adhesion: Opposing Forces During Cell Rounding

Cell rounding is thought to result from two simultaneous processes: (1) disassembly of cell surface adhesions and (2) reorganization of the actin cytoskeleton into an active, stress-generating cortex (Bradley et al. 1980; Cramer and Mitchison 1997). While cell surface adhesions cause the cell to increase its contact area with the substrate, and hence promote a flattened morphology, increased surface tension will cause the cell to become more spherical (Lecuit and Lenne 2007). A number of observations suggest that both a reduction in cell–substrate adhesion and an increase in tension contribute to cell rounding.

During rounding in cultured cells, stable focal adhesions are disassembled (Yamakita et al. 1999), which suggests that cell–substrate adhesion is important for retaining a flat morphology. Indeed, cells can be forced to round up by treatments that cause disassembly of focal adhesions. For example, when flattened cells are treated with proteases like trypsin, which disrupts cell–substrate adhesions, they round up (Britch and Allen 1980). Interphase cells can also be forced to round up by treatment with functional antibodies against integrin β1, a protein that links actin filaments to focal adhesion proteins and whose phosphorylation is important for mitotic rounding (Suzuki and Takahashi 2003). In the case of M-phase rounding, not all focal adhesions are disassembled, as evidenced by the presence of retraction fibers, which stay attached to the substrate (Mitchison 1992). Also, the forces generated by cell rounding are higher for M-phase rounding than for trypsin-mediated rounding (Stewart et al. 2011), indicating that focal adhesion disassembly is not the only mechanics change during M-phase rounding.

In addition to disassembly of focal adhesions, the presence of a contractile actin cortex is required for cell rounding in mitosis. Addition of the actin depolymerizing drug Cytochalasin D, which causes disassembly of the cortex, inhibits mitotic cell rounding (Cramer and Mitchison 1997). Myosin-2 activity has been shown to be required for cell rounding during M-phase, both in human and Drosophila cultured cells, and is thought to generate the cortical contractility required for cell rounding (Maddox and Burridge 2003; Kunda et al. 2008). The presence of a well developed, contractile actomyosin cortex is likely the reason for the observed increase in elastic modulus from interphase to mitosis (Matzke et al. 2001), and is directly responsible for higher forces during mitotic rounding compared to trypsin-mediated rounding (Stewart et al. 2011).

3.4.1.2 Moesin in Cell Rounding

In addition to myosins, another family of actin-binding proteins, the Ezrin–Radixin–Moesin (ERM) family, which link the cortex to the plasma membrane (see Box 3.1), has also been implicated in cell rounding. Moesin, the single ERM family member present in Drosophila, is required for cell rounding in Drosophila S2 cells (Carreno et al. 2008; Kunda et al. 2008). Moesin, which is activated by the mitotic kinase Slik, is five times more active in M-phase (Carreno et al. 2008). Strikingly, when myosin-2 is knocked down, overexpression of a phosphomimetic version of moesin is sufficient to induce rounding in S2 cells. In these myosin-2 knockdown cells, the activation of moesin during M-phase may contribute to cell retraction by causing actin filaments to preferentially align parallel to the plasma membrane, which could increase cortex tension (Carreno et al. 2008; Kunda et al. 2008). Moesin may also play a signaling role during this process, as ERM proteins can activate RhoA (Bretscher et al. 2002), an upstream activator of actin polymerization and actomyosin contractility (Kimura et al. 1996; Jaffe and Hall 2005). Indeed, RhoA is required for proper cell rounding (Maddox and Burridge 2003), and moesin knockdown causes mislocalization of RhoA during M-phase in Drosophila cultured cells (Carreno et al. 2008). These data suggest that at least part of moesin’s role in mitotic rounding is mediated by RhoA signaling.

3.4.2 Cytokinesis

As the initially spherical metaphase cell enters anaphase, it elongates and progressively forms a cleavage furrow at the cell equator. The cleavage furrow then ingresses until only a narrow bridge, the midbody, remains between the two daughter cells. Finally, sometimes hours after the completion of cytokinesis, midbody abscission occurs, leading to complete separation of the daughter cells (Rappaport 1996).

The mechanics of cytokinesis have been the subject of investigation for more than 100 years (Flemming 1895), and a multitude of physical models of cytokinesis have been proposed (reviewed in Rappaport 1996). In most metazoan cells, cytokinesis is the result of myosin-driven contraction (Glotzer 2001). In metaphase, the actomyosin cortex is uniformly distributed under the plasma membrane. Upon anaphase entry, actin and myosin progressively accumulate at the cell equator by a combination of local assembly of new filaments and cortical flows of existing filaments from the poles towards the equator (Cao and Wang 1990a, b; Fishkind et al. 1991; DeBiasio et al. 1996). This results in a higher actomyosin tension at the equator, which leads to furrow ingression (White and Borisy 1983; Matzke et al. 2001). Although most cells require myosin-2 for cytokinesis, adherent Dictyostelium cells are able to divide in the absence of myosin-2 (Neujahr et al. 1997). Daughter cell separation in these cells appears to be achieved without the formation of a contractile ring. Instead, the two daughters form lamellapodia and seem to tear themselves apart by crawling away from one another (Nagasaki et al. 2009; King et al. 2010).

The position of the cleavage furrow is crucial for accurate segregation of genetic material between the two daughter cells, and thus, furrow positioning must be precisely coupled to chromosomes separation (Rappaport 1996). The mitotic spindle, which segregates the chromosomes, also directly controls the formation of spatial gradients in cortical contractility and directs furrow formation (Rappaport 1961; Werner and Glotzer 2008). There are two major theories regarding how the spindle achieves this (1) astral spindle microtubules locally reduce contractility at the poles of the cell or (2) the spindle midzone and/or equatorial microtubules increase contractility at the equator (reviewed in Rappaport 1996; Glotzer 2004; Burgess and Chang 2005). These mechanisms are not mutually exclusive, and both appear to be used to various extents in different cell types (Wang 2001; Bringmann and Hyman 2005).

Early studies of force generation during cleavage furrow ingression often modeled the contractile ring as a sarcomere-like structure where parallel bundles of actin filaments are contracted by myosin motors in a muscle-like manner (Rappaport 1996; Pollard 2010). Although in some species, such as fission yeast, the equatorial ring appears to indeed be formed by parallel bundles of filaments (Kamasaki et al. 2007; Pollard and Wu 2010), in animal cells, the ring is rather an accumulation of actomyosin cortex with varying levels of alignment of the actin filaments (Wang and Taylor 1979; Maupin and Pollard 1986; Mabuchi et al. 1988; Schroeder 1990; Fishkind and Wang 1993). Moreover, the cortex itself is far from being a stable structure, as actin filaments in the cortex constantly turn over; it has both been shown experimentally and predicted theoretically that this dynamic behavior is essential for proper ingression of the cleavage furrow (Mukhina et al. 2007; Zumdieck et al. 2007; Salbreux et al. 2009; Pollard 2010).

Finally, although mechanical studies of cytokinesis have mostly focused on the cleavage furrow, an actomyosin cortex remains present at the poles of the dividing cell throughout cytokinesis. Passive mechanical resistance of this polar cortex to deformation must be taken into account in mechanical models of cell division (Robinson and Spudich 2004; Reichl et al. 2005). Moreover, active contractile forces exerted by the polar cortex can lead to asymmetric division. During asymmetric division of Drosophila neuroblasts, for example, myosin accumulates at the cortex of the smaller of the two future daughter cells (Barros et al. 2003; Cabernard et al. 2010). A similarly polarized distribution of cortical myosin has been shown to be essential for asymmetric division in some neuroblasts of the C. elegans Q neuroblast lineage, resulting in the generation of two daughter cells of different sizes (Ou et al. 2010). In symmetric divisions, polar cortex contractility can perturb cytokinetic mechanics and lead to cell shape instabilities where unbalanced polar contractions propel cytoplasmic material between the two poles, destabilizing the position of the cleavage furrow (Sedzinski et al. 2011).

3.5 Mechanical Changes During Interphase

Most studies of cell mechanics focus on mitosis, likely because shape changes are most dramatic during this phase of the cell cycle. However, there is evidence that cells have different mechanical properties at different stages of interphase. For example, global cell viscosity has been shown to increase approximately 1.5-fold from G1 to S-phase, and though viscosity is primarily governed by the actin cytoskeleton, microtubules are responsible for this G1 to S-phase viscosity increase (Tsai et al. 1996). There are only few direct mechanical studies of physical changes during interphase. However, several indirect examples indicate that such changes occur. Cell cycle-dependent differences in cell migration and cell cycle-specific morphogenesis in neural stem cells are both indirect indications that cell mechanics differ between the different stages of interphase.

3.5.1 Differences in Cell Migration During Interphase

In a number of different cell lines, cell migration dynamics vary throughout interphase. In general, migration is enhanced during G1 and early S-phase compared to late S-phase and G2 (Ratner et al. 1988; Iwasaki et al. 1995; Walmod et al. 2004). However, the reasons for reduced migration efficiency vary across cell lines; for some cell types, reduced migration is a result of lower migration speed, while in others, it is a result of decreased migratory persistence (Walmod et al. 2004).

Variations in the strength of cell–substrate adhesion could cause cell cycle-dependent differences in cell migration. Indeed, various cultured mammalian cell lines have different optimal cell–substrate adhesiveness that maximizes migration speed (Palecek et al. 1997), and the observed increase in adhesion force as cells progress from G1 to S and then to G2/M-phase coincides with a gradual reduction in migration speed (Giet et al. 2002). These examples imply that cell cycle-mediated changes in adhesion are likely to play an important role in the observed differences in cell migration. In addition to variations in cell–substrate adhesion, it is likely that changes in other mechanical properties, such as contractility, also contribute to differences in cell migration at different stages of interphase. Indeed, a theoretical model combining effects of cell–substrate adhesion and contractility suggests that the interplay of these two properties determine cell migration speed (DiMilla et al. 1991).

3.5.2 Interkinetic Nuclear Migration and Cell Cycle-Specific Morphogenesis in Neural Stem Cells

Another indirect example of changes in mechanical properties of cells during interphase is interkinetic nuclear migration in developing neuroepithelia of vertebrates. In these tissues, neurons have an elongate shape with a single bulge formed by the nucleus and are attached to the basal and apical membranes at the extremities of the tissue. For most neural stem cells, M-phase onset is characterized by a rapid movement of the nucleus toward the apical surface (Gotz and Huttner 2005; Norden et al. 2009). Following division, nuclei migrate away from the apical surface and back toward the basal lamina. Although these movements have been observed in a number of different vertebrate systems, the underlying mechanisms are unclear; actomyosin contractility, microtubule/dynein-based transport, and passive displacement have all been implicated to varying degrees (Schenk et al. 2009; Norden et al. 2009; Tsai et al. 2010). Most neurons within the neuroepithelium indeed undergo mitosis at the apical surface, though a subset of these neurons, the basal progenitors, division occurs more basally, and this eventually gives rise to a subventricular zone rich in basal progenitors (Haubensak et al. 2004). During G1 phase, basal progenitors retract their apical processes and transform from an elongate shape, spanning the entire ventricular zone and neuronal layer, to a short and wide morphology residing in the basal or subventricular zone (Miyata et al. 2004). The nucleus therefore cannot translocate to the apical surface during mitosis, and as a result, these cells divide on the basal side of the tissue. This shape change may be the result of a decrease in adhesion and/or an increase in cortical tension. Notably, in this example, this interphase-specific change may be responsible for part of the overall structure of the vertebrate nervous system.

3.6 Cell Cycle-Related Shape Changes in Tissues

Although much of the work related to cell mechanics during the cell cycle has been done in culture and in embryos up to blastula stage, cell shape changes are also an essential part of tissue morphogenesis. Changes in the mechanical properties of the individual cells that make up a tissue affect the general organization of the tissue, as in the example of interkinetic nuclear migration in brain development (Sect. 3.5.2). Because cells within a tissue are connected by cell–cell adhesions, when a single cell in a tissue rounds up or undergoes cytokinesis, for example, it will push and pull on neighboring cells. This coupling of single cell mechanics and cell–cell adhesion gives rise to tissue-scale morphogenesis and has been directly related to cell cycle progression in the cases of mitotic cell rounding and division plane orientation.

3.6.1 Cell Rounding in Tissues

Cell rounding at mitosis entry has been observed in cultured cells as well as in vivo, both during early embryonic development and in early epithelia. Cells in early amphibian embryos, for example, undergo periodic changes from being disk-shaped to being spherical, and the timing of these periodic changes corresponds with the timing of the cell cycle (Selman and Waddington 1955; Hara et al. 1980). The extent of cell shape change is not as great in vivo as in culture, as cells in tissues are never as flat as cells in culture, which is largely a consequence of extensive cell–cell contacts of cells within tissues. In tissues, cells do not undergo a disassembly of cell–cell contacts at mitosis, at least in the case of confluent epithelial cells. This includes the retention of desmosomes, tight junctions, and intermediate junctions (E-cadherin-mediated junctions; Baker and Garrod 1993). Indeed, maintenance of cell–cell adhesions is vital for preservation of a tissue, as a loss of such adhesions (especially if the cell cycle were synchronized between cells, as in the case of early development) would cause the tissue to simply fall apart. This suggests that rounding in tissues may be more dependent on the contraction of a well-developed actomyosin cortex rather than on disassembly of adhesions. In contrast to cell–cell adhesions, cell–ECM adhesions, specifically those mediated by integrins, may be partially disassembled in a cell cycle-dependent manner (B Baum, personal communication). An additional consequence of extensive cell–cell contacts is that cells in tissues stay much more tightly packed than cells in culture, and as a result, retraction fibers (see Sect. 3.4) are typically not observed.

3.6.2 Division Plane Orientation

Orientation of the division plane can play a significant role in determining the shape of a tissue or epithelium. A coordinated bias of division plane orientation can have substantial effects on the shape of a tissue, regardless of whether or not total cell volume increases (Fig. 3.4). Division axis orientation can be determined by a number of mechanisms, including anisotropies in cell shape or stresses upon cells, or by polarity proteins.
Fig. 3.4

Effect of a coordinated bias in division plane orientation on the shape of a tissue. A coordinated bias towards one axis in division plane orientation leads to tissue elongation both in the presence (panel a) and in the absence (panel b) of tissue growth

3.6.2.1 Effects of Division Plane Orientation on Tissue Organization

Oriented cell divisions are known to play a role in early embryonic development, specifically during gastrulation. Polarized divisions have been implicated as early as during formation of the primitive streak, an elongated group of cells that specifies the site of gastrulation in higher amniotes (Wei and Mikawa 2000). Although treatment with cell division inhibitors does not disrupt initial development of the primitive streak, such treatment does inhibit extension of the streak once it is formed, though it is not entirely clear if oriented divisions or simply cell divisions in general are required for this process (Cui et al. 2005). The preferential orientation of cell divisions during gastrulation has been observed in a number of different organisms (Hertzler and Clark 1992; Concha and Adams 1998; Gong et al. 2004; Wang et al. 2008). In zebrafish gastrulae, for example, oriented cell division has been shown to contribute significantly to the required tissue extension (Gong et al. 2004). Despite this, it has been shown that some organisms, including sea urchins, do not require cell divisions for proper gastrulation (Stephens et al. 1986). The difference in the requirement of oriented cell division in sea urchins and other organisms may be due to the vast difference in the geometries of gastrulation between model systems.

Biased division plane orientation is also important later in development, during tissue morphogenesis. Division plane bias during neural development, for example, has been proposed to contribute to the elongated geometry of the early neural tissue in a number of different model systems (Schoenwolf and Alvarez 1989; Sausedo et al. 1997; Geldmacher-Voss et al. 2003). It has also been proposed that oriented cell divisions promote cell intercalation, which in turn drive further oriented cell divisions based on the resultant cell shapes and pulling forces. This leads to a positive feedback between these two morphogenetic processes that allows for formation of the characteristically long, thin neural tissue (Kimmel et al. 1994). A physical model of this type of positive feedback suggests that coupling of oriented cell divisions and cell intercalation movements is sufficient to drive anisotropic tissue growth in development of the Drosophila imaginal wing disk (Bittig et al. 2009), which agrees with experimental evidence showing that oriented cell divisions are important in determining the final morphologies of organs developing from imaginal disks (Baena-López et al. 2005). Division plane orientation is also important in model tissues in culture. For example, Madin–Darby canine kidney cells are capable of forming lumens in culture, and this process has been shown to depend on oriented cell divisions (Qin et al. 2010; Rodriguez-Fraticelli et al. 2010).

3.6.2.2 Mechanisms of Division Plane Orientation

Division plane orientation can be regulated through a number of physical and molecular mechanisms. From a geometrical standpoint, cells tend to divide in a plane perpendicular to their long axis. This is the result of orientation of the mitotic spindle parallel to the long axis of the cell during metaphase. Such geometry-dependent spindle orientation can occur even when the length of the long and short axes differs only by a few percent and has been observed in a number of systems, including cultured mammalian cells, mouse zygotes, Xenopus embryos, fission yeast, and plant cells (Rappaport 1960; O’Connell and Wang 2000; Smith 2001; Gray et al. 2004; Strauss et al. 2006; Vogel et al. 2007). In addition, it has been shown in several of these systems that if the long axis is changed, the mitotic spindle will reorient such that it aligns parallel to the new long axis, and thus the division plane will be perpendicular to it (O’Connell and Wang 2000; Gray et al. 2004). Despite the prevalence of this phenomenon, the mechanism by which it occurs is poorly understood.

Geometry-dependent division plane orientation has been shown in some cases to be overridden by internal signaling cues, as in the first cleavage of C. elegans embryos. Compression of C. elegans zygotes to change the long axis does not change the position of the division plane. In these cells, spindle plane orientation is rather governed by activity of the Par family proteins, which are important for polarity in a number of biological contexts including asymmetric cell division (Cheng et al. 1995). It should be noted, however, that geometry dependence of spindle plane orientation is “restored” in embryos with compromised Par function (Tsou et al. 2003).

Spindle plane orientation, and therefore division plane orientation, is dependent on an intact actin cortex (Gray et al. 2004; Théry et al. 2007; Carreno et al. 2008; Kaji et al. 2008; Kunda et al. 2008) as well as on astral spindle microtubules and dynein (O’Connell and Wang 2000; Théry et al. 2005). In cultured cells, mitotic spindle orientation can be directed by anisotropic stresses. These stresses can either be caused by pulling from unequally distributed retraction fibers or can be applied externally (Fink et al. 2011). Anisotropic stresses promote polarized reinforcement of the cortex, which is thought to recruit dynein, and this in turn pulls the spindle poles toward this region (Fink et al. 2011; Théry and Bornens 2006). This mechanism ensures that cells preferentially divide in a plane perpendicular to the force field (Fink et al. 2011). In cultured Drosophila cells, spindle orientation also requires moesin activity (Carreno et al. 2008); in these cells, activated Moesin accumulates at the bases of retraction fibers (Kunda et al. 2008), and may play some role in local cortex reinforcement or dynein recruitment. It is possible that such mechanisms may also lead to biased division plane orientation in tissues, though division plane orientation has previously been shown in tissues to be primarily controlled by polarity signaling pathways, namely by the Planar Cell Polarity (PCP) pathway and the Par polarity proteins (Geldmacher-Voss et al. 2003; Gong et al. 2004; Siegrist and Doe 2006). In addition, oriented divisions in tissues are dependent on adherens junctions (Lu et al. 2001; Geldmacher-Voss et al. 2003), though it is not clear whether junctions play a signaling or mechanical role in this process.

Finally, in addition to cortical cues, intracellular actin networks can also contribute to spindle positioning. In mouse oocytes, spindle repositioning to the cortex, which precedes polar body extrusion, depends on a cytoplasmic actin network nucleated by Formin 2 (Azoury et al. 2008; Schuh and Ellenberg 2008). Myosin 2 is enriched at the spindle poles and repositions the spindle to the cortex by physically pulling on the intracellular actin network (Schuh and Ellenberg 2008). Dynamic, Arp2/3 nucleated cytoplasmic actin structures have also been observed during symmetric divisions of cultured cells (Mitsushima et al. 2010) where they may also influence the orientation of the spindle (Fink et al. 2011).

3.7 Linking Cell Cycle Biochemistry and Cell Mechanics

In order to understand how cells control their shape during the cell cycle, one must understand not only which mechanical properties drive specific shape changes, but also how the proteins regulating these properties are controlled. Like other cell cycle-regulated processes, mechanical changes are controlled by Cdk–Cyclin complexes. These complexes, and in particular the mitotic Cdk–Cyclin complex CyclinB-Cdk1, were first postulated to affect cell mechanics based on their influence on cell shape during surface contraction waves in amphibian embryos and during mitotic cell rounding. Although it is not clear exactly how it affects cell mechanics, CyclinB-Cdk1 signals via a number of downstream pathways to eventually affect the actomyosin cytoskeleton and cell adhesions. These signaling pathways, most of which involve other protein kinases, modulate the regulation of actin-binding proteins and adhesion-associated proteins; such proteins can in turn affect properties like actin dynamics, myosin activity or turnover of adhesions, which govern physical properties like tension or cell–substrate or cell–cell adhesion. As it is clear that CyclinB–Cdk1 does not act on the actin cytoskeleton or adhesions via a single pathway, it is likely that the combined effects of many pathways allow Cdk–Cyclin complexes to precisely control cell shape during the cell cycle.

3.7.1 CyclinB–Cdk1 and Surface Contraction Waves

One of the first known examples where Cdk–Cyclin complexes were shown to influence cell mechanics is in surface contraction waves in early amphibian embryos. During early development, amphibian embryos undergo a series of surface contractions that are regulated cyclically by CyclinB-Cdk1. Before each cleavage in early axolotl, newt, and Xenopus embryos, a wave of surface relaxation, followed closely by a wave of surface contraction, moves from the animal pole to the vegetal pole (Hara 1971; Sawai and Yoneda 1974; Hara et al. 1980). Such surface contraction waves can be observed simply by tracking pigment displacements at the surface of these embryos. These waves are driven by transient waves of CyclinB-Cdk1 activity (Rankin and Kirschner 1997; Perez-Mongiovi et al. 1998) and still occur in cells lacking nuclei or that do not actually cleave (Sawai 1979; Hara et al. 1980). Although it is clear that the changes in surface properties associated with Xenopus surface contraction waves are organized by CyclinB-Cdk1 signaling, the mechanism of propagation of these activity waves and how exactly these biochemical signals affect cortical contractility is not understood.

3.7.2 CyclinB-Cdk1 in Cell Rounding

The CyclinB-Cdk1 complex also controls cell rounding in cultured cells. In addition to a high temporal correlation between CyclinB-Cdk1 activation and mitotic rounding (Gavet and Pines 2010), perturbation of CyclinB-Cdk1 activity has been shown to affect rounding. Injection of purified CyclinB-Cdk1 causes disassembly of stress fibers and ectopic cell rounding in interphase mouse fibroblasts, similar to the changes seen during mitotic rounding (Lamb et al. 1990). Consistently, injection of functional antibodies against Cdk1 prevents entry into mitosis and results in a failure to round up, but does not disrupt maintenance of a round morphology in mitosis (Riabowol et al. 1989). Though it is clear from these data that CyclinB-Cdk1 affects cell rounding (and thus the underlying cell mechanics), it is not understood whether these effects are direct, or whether they are mediated by intermediate pathways.

3.7.3 The LIMK1-Cofilin Pathway in Cell Rounding

One biochemical pathway that has been shown to directly affect cell rounding is the LIM Domain Kinase 1 (LIMK1)-Cofilin pathway. Though no direct relationship between CyclinB-Cdk1 and this pathway has yet been documented, LIMK1 is a cell cycle-regulated kinase that affects M-phase cell mechanics by deactivating the actin severing protein cofilin. Cofilin regulates actin dynamics through its ability to sever actin filaments and is inactive when phosphorylated (Moon and Drubin 1995; Bamburg et al. 1999; Pollard and Borisy 2003; Hotulainen et al. 2005; Pfaendtner et al. 2010). As cofilin knockdown is sufficient to cause a twofold increase in surface tension in cultured cells (Tinevez et al. 2009), its inactivation during mitosis is likely to contribute to increasing surface tension. LIMK1 can induce stabilization of actin filaments in a cofilin phosphorylation-dependent manner (Arber et al. 1998; Yang et al. 1998), and this actin stabilizing effect is likely the cause of increased surface tension, presumably through an increase in cortex thickness (see Box 3.1 for the relationship between cortex thickness and tension). Cofilin can also affect cell rounding and morphology. Cells expressing nonphosphorylatable cofilin are still able to round up, but often have morphological irregularities (Kaji et al. 2008). In addition, the actin interacting protein 1 (AIP1), which decreases cofilin’s ability to sever actin filaments, is required for mitotic cell rounding (Fujibuchi et al. 2005).

3.7.4 Other Pathways Involved in Cell Rounding

A number of other biochemical pathways have been implicated in control of cell rounding, though none has been as firmly linked to mitotic rounding as the CyclinB-Cdk1 and LIMK1-Cofilin pathways. Nonetheless, these other pathways display high activity during M-phase and are known to affect properties such as actomyosin contractility and substrate adhesion, both of which are important for cell rounding. In addition, several of these pathways have links to the CyclinB-Cdk1 pathway, which indicate that CyclinB-Cdk1 may regulate a number of separate pathways during M-phase to effect changes in cell mechanics and thereby promote mitotic cell rounding.

3.7.4.1 The PAK Pathway

The p21-activated kinases 1 and 2 (PAK-1, PAK-2) are required for proper mitosis and are regulated in a cell cycle-dependent fashion. These kinases affect cell mechanics via their downstream effects on actin and myosin. PAK-1 autophosphorylation, which has been shown in vitro to indicate PAK-1 activity, is highest during M-phase, and PAK-1 depletion delays mitotic entry (Maroto et al. 2008). In addition, PAKs promote lamellipodia retraction, focal adhesion disassembly and increased contractility, and this suggests that they may be involved in the mechanical changes leading to cell rounding (Kiosses et al. 1999; Zeng et al. 2000; Szczepanowska et al. 2006). More specifically, PAKs-1 and -2 have been shown in a number of cell types to phosphorylate Myosin Regulatory Light Chain (MRLC) on S19, which increases myosin-2 motor activity (Chew et al. 1998; Sells et al. 1999; Zeng et al. 2000; Szczepanowska et al. 2006; Coniglio et al. 2008). PAKs are also involved in myosin-2 regulation through phosphorylation of caldesmon (Foster et al. 2000; Eppinga et al. 2006; Van Eyk et al. 1998). Dephoshporylated caldesmon inhibits myosin-2 activity, and its phosphorylation relieves this inhibition (Yamashiro and Matsumura 1991; Foster et al. 2000). Therefore, mitosis-specific phosphorylation of caldesmon by PAKs is likely to increase cortical tension during rounding by promoting myosin-2 activity. Consistent with this, if caldesmon phosphorylation is blocked by expression of a nonphoshporylatable dominant negative, cell rounding and entry into mitosis are delayed, and cells fail to sufficiently disassemble stress fibers (Yamashiro et al. 2001). High PAK activity during M-phase, therefore, is likely to promote an increase in actomyosin contractility, via its effect on myosin II. In addition to its regulation by PAKs, caldesmon can also be phosphorylated directly by CyclinB-Cdk1 (Yamashiro et al. 1990).

PAK1 also interacts with the actin cross-linking protein filamin (Vadlamudi et al. 2002). Filamin-deficient cells in interphase display lower migration speeds, increased cell blebbing and a twofold increase in global cellular elastic modulus (Cunningham et al. 1992). Filamin and PAK have a coordinated activation, wherein PAK1 phosphorylates filamin, and phosphorylated filamin can in turn bind PAK1, thereby allowing for autophosphorylation and activation of PAK1 (Vadlamudi et al. 2002). The filamin branch of the PAK pathway is thus a secondary mechanism by which high PAK activity during M-phase can affect actomyosin activity and dynamics to control cell rounding.

3.7.4.2 Nonreceptor Tyrosine Kinases

The Src family of nonreceptor tyrosine kinases has been implicated in cell rounding, both by promoting disassembly of adhesions and by modification of the actin cytoskeleton. Injection of mouse fibroblasts with functional antibodies against the three Src kinases, c-Src, Fyn, and Yes, results in arrest prior to mitosis without rounding and without nuclear envelope breakdown (Roche et al. 1995). The Src family member pp60c-Src is highly phosphorylated during M-phase and its activity increases up to sevenfold from interphase to mitosis (Chackalaparampil and Shalloway 1988). pp60c-Src has been implicated in both disassembly of cell adhesions and reorganization of actin (Henderson and Rohrschneider 1987; Warren and Nelson 1987). In mouse oocytes, Fyn kinase is required for maturation and polar body extrusion; in this system, Fyn is enriched at the cortex near the meiotic spindle and is involved in signaling for contractile ring formation (Levi et al. 2010). Additionally, the Transmembrane and Associated with Src kinases (Trask) protein can induce cell rounding when overexpressed (Bhatt et al. 2005). Trask is a cell adhesion protein that, like Src kinases (David-Pfeuty and Nouvian-Dooghe 1990), undergoes a dramatic membrane-to-cytoplasm redistribution upon entry into mitosis (Bhatt et al. 2005), indicating again that Src kinases may also be involved in disassembly of adhesions during cell rounding.

3.7.4.3 pEG3/Kin1/PAR-1/MARK Kinase Family

Another kinase family that is implicated in M-phase specific shape changes is the pEG3/KIN1/PAR-1/MARK family (Xenopus/S. pombe/Drosophila, C. elegans/mammalian homologs, respectively). Members of this family localize to the actomyosin cortex specifically during M-phase in an actin-dependent fashion (Chartrain et al. 2006) and are most highly phosphorylated (and therefore most active) during mitosis (Blot et al. 2002). Disruption of these proteins causes aberrant morphologies in cultured mammalian cells by interfering with microtubule dynamics (Drewes et al. 1997); it is not clear if this change in microtubule dynamics directly affects cell shape or plays a signaling role. This family of proteins is therefore potentially important in regulating M-phase-specific mechanical changes given its high mitotic activity and effects on cell morphology in interphase.

3.7.4.4 Rap1 GTPase

Rap1 is a small GTPase that has been shown in a number of systems to promote integrin- and cadherin-mediated adhesion via a number of downstream effectors (Bos 2005). Rap1 activity is significantly reduced during M-phase, correlating temporally with a loss of cell–substrate adhesion, and expression of constitutively active Rap1 prevents focal adhesion and stress fiber disassembly at mitosis onset, leading to defects in cell rounding. Furthermore, cells expressing dominant negative Rap1 round up ectopically and fail to re-spread following division (Dao et al. 2009). Although the Rap1 inactivating protein Rap1GAP can be phosphorylated by Cdk1, both in vitro and in cultured cells (Rubinfeld et al. 1992; Janoueix-Lerosey et al. 1994), it is not clear whether this phosphorylation contributes to Rap1 inactivation during M-phase.

3.7.4.5 The TCTP Chaperone

In addition to protein kinases, translationally controlled tumor-associated protein (TCTP) has also been implicated in control of cell rounding. Knockdown of TCTP, which is important in calcium regulation (Arcuri et al. 2005) and is a potential chaperone protein (Thaw et al. 2001), causes rounding defects. During M-phase, knockdown cells often retain long protrusions, indicative of a failure to sufficiently de-adhere from the substrate (Bazile et al. 2009). Surprisingly, TCTP knockdown actually decreases cell–substrate adhesion on several different substrates in other cell types (Ma et al. 2009). This well-conserved and highly expressed protein is known to associate with actin and microtubules and could be involved in local folding of proteins important for regulating the cytoskeleton or adhesions during mitosis, given its potential as a chaperone (Bazile et al. 2009).

3.7.5 The Role of Mechanosensing in Cell Cycle Regulation

In addition to modification of cell mechanics by cell cycle-mediated signaling, there are many indications that forces experienced by the cell may in turn affect cell cycle progression. For example, pharmacological treatments leading to increased cell spreading in cultured cells also cause an increase in DNA synthesis and cell proliferation (Folkman and Moscona 1978), and if cultured cells are subjected to physical stresses, their proliferation rate increases (Nelson et al. 2005). Furthermore, the Rho/ROCK/Diaphanous pathway, an upstream signaling pathway for actin assembly and contractility, is necessary for entry into S-phase (Seasholtz et al. 1999; Iwamoto et al. 2000; Zhao and Rivkees 2003), suggesting that contractility itself could potentially affect cell cycle progression.

Beyond its influence on cell cycle progression, mechanotransduction is also used to fine-tune cell shape changes. Dictyostelium cells, for example, demonstrate an M-phase-specific response to mechanical perturbation, wherein an externally induced deformation promotes local recruitment of myosin-2 and the actin-binding protein cortexillin I, which counteracts the deformation and helps to stabilize cell shape (Effler et al. 2006; Ren et al. 2009). Such mechanical feedback systems allow cells to more precisely control their shape and can also contribute to the maintenance of correct cell shape in the presence of external forces.

3.8 Conclusion

Progression through the cell cycle involves a number of shape changes that rely on the precise modification of a cell’s physical properties. As these events are mechanical in nature, a firm theoretical understanding of the cell as a multicomponent complex object is necessary to understand how key parameters such as tension, viscoelasticity, and cell adhesion give rise to the diverse shapes observed in different phases of the cell cycle. Experimentally, understanding cell cycle biomechanics can be approached using kinematics, wherein cell movements and deformations are precisely quantified, providing information on the forces leading to these movements, or using dynamics, where forces and physical properties are measured directly and then used to predict cell behavior. These forces and physical properties are mediated on the molecular level by a number of proteins, including actin, actin-binding proteins, and cell adhesion proteins, whose activity is controlled by Cdk cyclins and other upstream signaling pathways. The study of cell cycle-mediated shape change therefore requires a combination of general cell mechanics and the use of modern biophysical and cell biological methods. Such interdisciplinary approaches have helped cell cycle biomechanics to reemerge as a major field in cell and developmental biology.

Notes

Acknowledgments

We thank B. Baum, J.S. Bois, S.W. Grill, C. Norden, and G. Salbreux for their comments on the manuscript, A. Rudnick for assistance with the illustrations, and The Polish Ministry for Science and Higher Education, the Max Planck Society, and the Human Frontier Science Program for financial support.

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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Max Planck Institute of Molecular Cell Biology and GeneticsDresdenGermany
  2. 2.International Institute of Molecular and Cell BiologyWarsawPoland

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