By the beginning of the 1970s it was becoming evident that genetic approaches were the key to understanding how whole organisms are built. Although the first links between genetics and development were discovered early during the 20th century (reviewed in Gilbert,1991) it was only during the second half of the last century that the idea that mutations were going to open the way to understand the role of genes in the formation of an animal consolidated in a community of developmental geneticists. The rationale behind this idea was that if a mutation involved a developmental defect, such as a malformed embryo or larva, it was because the corresponding gene played a specific role at some stage of development, directing an event essential to complete that stage (Jacob,1998). The understanding of the molecular basis of heredity and the enormous technical progress provided by molecular biology to isolate, purify and sequence genes paved the way for the systematic analysis of embryonic development at the genetic level.
This kind of analysis produced several important ideas that form the current framework for the understanding of embryonic development. The first one is that development proceeds through the hierarchical control of gene expression, in which genes at the top of the hierarchy select specific programs of differentiation (so called “selector genes”) and control the expression of downstream genes, which encode proteins directly required in cell differentiation processes (Garcia-Bellido,1975). The second important idea arising from this approach is that genetic function is conserved across species in such a way that genes can be exchanged between organisms without altering their function.
However, at the dawn of the 21st century, there is an increasing realization that although the identification of all the genes involved in a specific process is important, as well as knowing what they are required for, this will not lead us to a comprehensive understanding of how organisms are built. Although the genetic approach has been fundamental in identifying the main transcription factors and signaling molecules important during embryonic development, new approaches are needed to understand such complex processes. The main reason why the genetic approach is not enough is the realization that biological function does not express itself at the level of individual genes nor individual proteins, but at intermediate levels of organization, involving the interaction among many components (Noble,2006). The formation of a whole organism from a single cell spans different scales of organization, from molecules, sub-cellular modules, cells, groups of cells and tissues. We know very little about how supra-cellular organization and function arises from the interaction of components at a lower level of organization and how different levels of organization impinge on others. To be able to understand the importance of tissue level properties such as stiffness and stresses during morphogenesis and how they emerge from the interaction of cells and their cytoskeletal and adhesive components, it is necessary to focus at intermediate levels of organization, from which it will eventually be possible to develop direct causal relationships. Because any interesting biological process involves dozens of molecular components, interacting in complex ways, it is almost inevitable that computer-assisted models will become fundamental tools with which to represent and understand dynamic processes.
In this review, we will focus on recent progress on Dorsal Closure (DC), a morphogenetic process during Drosophila embryogenesis, which has strong similarities with other processes occurring in vertebrates, such as neural tube closure and wound healing (Wood et al.,2002). At the onset of DC, the dorsal side of the embryo is covered by an extraembryonic tissue, the amnioserosa (AS). During this process, the lateral epidermis of the embryo converges towards the dorsal midline while the AS reduces its surface area until it disappears inside the embryo (Jacinto et al.,2002; Martinez Arias,1993). DC relies on the coordinated cell shape changes of these two tissues: AS cells undergo apical constriction and epidermal cells elongate in the dorso-ventral direction. At the interface between the two tissues, both types of cells contribute to the formation of a supra-cellular actin-myosin cable. Dorsal most epidermal cells also project filopodia and lamellipodia that are important for the matching of opposing epidermal sheets and generate a zipper-like closure once the first epidermal cells meet at the anterior and posterior ends. Here, we will review how different approaches spanning the genetic, cellular, and tissue levels, along with different modeling approaches have contributed to a better understanding of DC and provide a paradigm for the analysis and understanding of more complex morphogenetic processes in higher organisms.
The study of DC benefits from an existing macroscopic framework, in which the main forces contributing to the process have been identified. Laser ablation experiments have determined the main force-generating tissues contributing to DC (Hutson et al.,2003; Kiehart et al.,2000). While tension in both the AS and at the supra-cellular actin cable contributes positively to DC, the lateral epidermis resists the net dorsal ward movement. These forces are transmitted and integrated at the leading edge through the modulation of E-cadherin and integrin mediated adhesion (García Fernández,2007; Gorfinkiel and Martínez Arias,2007; Narasimha and Brown,2004). A fourth contribution to closure is provided by filopodia-mediated zippering of the leading edge once the two lateral epidermal flanks have met at the anterior and posterior canthi (Hutson et al.,2003). This macroscopic description of the main forces involved in DC along with extensive genetic studies (reviewed in Harden, 2002) provides a unique opportunity to integrate events occurring at different spatial and temporal scales. The main questions that arise from these studies are how these tissue-level forces are generated from the activity of constituent cells, how the force generating cellular mechanisms are coordinated across the tissue and how this impinges on the mechanical properties of the tissue that are important for its biological function. Imaging of live embryos using fluorescent proteins coupled to powerful image analysis tools in wild type as well as genetically and mechanically perturbed embryos, along with theoretical frameworks to integrate these data are beginning to provide answers to these questions.
The Power of the Amnioserosa
The AS progressively reduces its surface area in an active process that provides one of the major forces driving DC. This is achieved through the apical constriction of its individual cells and through the basal extrusion of cells in a seemingly random spatial pattern through programmed cell death (García Fernández,2007; Gorfinkiel and Martínez Arias,2007; Kiehart et al.,2000; Toyama et al.,2008). Lack of Myosin II in single AS cells slows down their apical surface area reduction showing that apical constriction is an active process driven by Myo II (Franke et al.,2005). Recent work has provided an in-depth understanding of the mechanism underlying AS cell apical constriction. When imaged with enough time resolution, it is evident that AS cells do not decrease their apical surface area continuously but they undergo regular fluctuations in their shape, with periodic cycles of contraction and expansion (see Fig. 1) (Blanchard et al.,2010; David et al.,2010; Solon et al.,2009). Live-imaging using cytoskeletal reporters shows the presence of transient foci of actin and myosin that flow across the apical surface of the cells (Blanchard et al.,2010; David et al.,2010). These actin-myosin accumulations can be detected in scattered AS cells as early as germ-band retraction. Progressively, more cells develop this activity and by the end of germ-band retraction all the cells show transient actin-myosin foci that flow across the apical surface (David et al.,2010).
Correlation analysis between fluorescence intensity and shape fluctuations (see Box 1) strongly suggests that actin-myosin foci induce shape contraction (Blanchard et al.,2010; David et al.,2010). Similar observations have been made in the presumptive mesoderm of Drosophila, with cells undergoing cycles of rapid contraction, which correspond to bursts of Myosin II coalescence, followed by periods of no contraction corresponding to Myosin II stabilization (Martin et al.,2009). These observations have lead to a new model for the mechanism of actin-myosin activity in pulsed apical constriction. Instead of the classical purse-string model for apical constriction, these new data favor a model in which myosin motors bind and slide along an actin network spanning the medial apical cortex and connected to the cell membrane through discrete adherens junctions (Martin et al.,2010; Martin et al.,2009).
Although the above model provides a suitable framework to understand apical constriction several questions remain. One important question is how the observed actin-myosin foci assemble and disassemble. One hypothesis is that they are the result of the self-organizing properties of myosin motors onto cross-linked actin polymers. In vitro experiments using reconstituted systems of actin, myosin II and cross-linker proteins spontaneously induce the organization of actin into active networks, rings and asters, depending on the relative concentration of these components (Backouche et al.,2006), suggesting that actin-myosin foci may develop spontaneously in the AS. However, in vitro, these patterns are reached at the steady-state, while actin-myosin foci in the AS are transient and disassemble, showing that there is no such steady-state in vivo. Oscillatory behaviors have been described in different muscular systems such as the flight muscles of certain insects and the cardiac muscle as well as in non-muscular systems like the cilia and flagella of some protozoa. These mechanical oscillations are evident in the periodic contractions or movements of sarcomeres and cilia and rely on the activity of molecular motors converting chemical energy to mechanical work (reviewed in Kruse and Julicher,2005). Oscillatory behavior of cytoskeletal systems subject to an elastic load has been predicted on a theoretical basis (Julicher and Prost,1997) and has recently been observed in an in vitro system consisting of an optically trapped single actin filament interacting with several myosin motors (Placais et al.,2009). It is tempting to speculate that the cell shape fluctuations observed in the AS as well as in other tissues undergoing morphogenesis are examples of mechanical oscillators emerging as a consequence of the auto-oscillatory properties of contractile proteins.
How then is progressive contraction achieved? During DC, there is a temporal evolution of the frequency and amplitude of shape fluctuations. As DC progresses, cells decrease the amplitude and the cycle length of their fluctuations, as they increase their rate of contraction (see Fig. 1) (Blanchard et al.,2010; David et al.,2010). There is a positive correlation between the frequency of fluctuations and the rate of contraction of AS cells (Blanchard et al.,2010). In fact, a decrease in the cycle length of fluctuations precedes the increase in the rate of contraction, which suggests that cells initiate contraction by increasing the frequency of fluctuations and thus of foci formation. Interestingly, in non-adherent oscillating fibroblasts cells, it has been shown that activating myosin increases the frequency of shape fluctuations while blocking myosin activity abolishes them (Salbreux et al.,2007). In agreement with these observations, during DC there is a progressive enrichment of myosin at the apical surface of AS cells, which forms a more continuous although still dynamic network (Blanchard et al.,2010). It has also been proposed that the progressive enrichment of myosin at the apical surface acts as a ratchet to prevent relaxation during shape fluctuations (Martin et al.,2009). One important difference between apical contraction in presumptive mesodermal cells undergoing invagination and AS cells is the time scale of their fluctuations and of the morphogenetic process. While ventral furrow invagination takes about 15 min and the cycle length of ventral cell shape fluctuations is in the range of 1–2 min, AS contraction takes a couple of hours and the cycle length of early AS cell shape fluctuations ranges up to 4 min. It will be interesting to understand how and why these different temporal scales are achieved.
It is not known how myosin is gradually enriched and stabilized onto a more stable actin meshwork but one possibility is that this is achieved through changes in the activity of myosin and the nature of the actin network. This could be achieved through changes in the concentration of myosin, myosin phosphorylation rates, nature, and concentration of cross-linkers and other actin regulating factors. Interestingly, experiments using in vitro reconstituted systems have shown that contractility results from the ATP-dependent motor activity of myosin II onto a cross-linked actin network. These experiments show that contractile behavior develops above a myosin II concentration threshold and below a certain range of cross-linker concentrations (Bendix et al.,2008; Koenderink et al.,2009). This suggests that tuning these parameters may change the ability of the cells to actually contract. Recent observations have shown that increasing levels of Bazooka, a member of the PAR complex involved in regulating apico-basal polarity, increases the persistence of apical actin-myosin networks, presumably making them more stable (David et al.,2010). Whether Bazooka is regulating myosin activity or actin dynamics remains to be elucidated.
One important question during morphogenesis is how individual cell behaviors are coordinated to give rise to the stereotyped patterns of tissue movements and deformations. It is evident that intercellular junctions, in particular adherens junctions, are pivotal for the supra-cellular organization of the tissues. In presimptive mesodermal cells, compromising adherens junction integrity leads to the uncoupling of the actin-myosin apical network from the cell membrane. This results in the contraction of the actin-myosin apical network without reducing the apical surface area of the cells (Dawes-Hoang et al.,2005). Moreover, adherens junction-mediated adhesion between cells allow for the building up of tissue tension, as revealed by tissue-wide tears upon reducing the levels of adherens junction components (Martin et al.,2010). During DC, the generation of tissue-wide tears through laser-ablation has been used to infer the relative magnitude of forces generated by the AS and the other tissues involved (Hutson et al.,2003).
The pulsatile behavior of AS cells raise the question of how fluctuations are coordinated between cells in order to generate tissue-level forces (see Box 1). Initial observations suggested that AS cells mostly oscillate in antiphase (Solon et al.,2009). A closer look reveals a more subtle picture, with cells oscillating mostly in antiphase in one orientation and in-phase in the perpendicular orientation. This leads to strings of cells contracting and expanding together, which are dynamic in space and time (see Fig. 1) (Blanchard et al.,2010). The emergence of these supra-cellular patterns of contraction and expansion evokes the idea of a very dynamic tissue where forces are generated locally and intermittently in groups of cells. We do not know how this local coordination is achieved but laser ablation experiments in which an incision in one cell–cell interface perturbs not only the fluctuations of adjacent cells but also cells further away suggest that a tension-based mechanism maintains cell fluctuations, with cells contracting as a consequence of the stretching of their neighbors (Solon et al.,2009). Moreover, the assembly and disassembly of an actin-myosin focus is often followed by the assembly of a focus in a neighboring cell, next to where the previous focus terminated, suggesting that actin-myosin activity may propagate between cells (David et al.,2010).
As DC advances, fluctuations become undetectable and there is a progressive coordination of AS cell contraction across all the tissue (see Fig. 1). Thus, the evolution of AS cell behavior from a fluctuating behavior which is locally organized to a contractile behavior that spans the whole tissue suggests the existence of an increasing coordination between cells across the AS. It is likely that such long-range coordination develops as a result of the increase in the total tension stored in the tissue, which in turn impinges on the contractile properties of individual cells.
The deformation of tissues in response to forces depends on their mechanical properties. In particular, stiffness measures the resistance of an object to deformation by an applied force, and depends both on the material of the object as well as its geometry and boundary conditions. The stiffness of some tissue explants has been calculated by measuring the deformation (strain) of the tissue when a compressive stress is applied (Davidson et al.,1999; Zhou et al.,2010). Interestingly, it has been found that the main contributor to the stiffness of Xenopus explants is the state of the acto-myosin cortex (Zhou et al.,2009,2010). The relationship between strain and stress determines the type of material, elastic, viscous, or visco-elastic. Such measurements have been performed in cells and have revealed very rich and complex mechanical properties with both elastic and viscous characteristics (reviewed in Kasza et al.,2007). This kind of approach has not yet been tried in developing embryos, but in the AS, laser-ablation has been used to infer relative values for these properties. Thus, laser-ablation of cell interfaces and at cell centers of AS cells has shown that as a general rule during DC the AS evolves from a fluid-like tissue, which is easily deformable under an applied stress, to a solid-like tissue, which is rigid and less deformable (Ma et al.,2009). Interestingly, in vitro experiments using reconstituted systems show that stiffening arises as a consequence of myosin motors pulling on cross-linked actin filaments (Koenderink et al.,2009). Thus, changes in myosin motor concentration or cross-linkers can increase both contractility and stiffness and this may be what happens as DC progresses. However, during early phases, the emergent patterns of locally synchronized contracting and expanding cells suggest that the mechanical properties of the tissue are dynamic parameters that change across space and over time.
Also, the existence of spatial patterns in the rate of contraction of AS cells suggests that the contractility and the mechanical properties of the AS can be fine-tuned in a context-dependent manner. We have previously suggested that these local differences could arise from different mechanical constraints experienced by the cells. Other morphogenetic movements occurring concomitantly with DC, and interactions with other tissues could generate differential tensions across the AS (Gorfinkiel et al., 2009; Peralta et al., 2007). Similarly, the anisotropies in apical constriction observed during DC and also during mesoderm invagination suggest that whole tissue tension provides mechanical constraints that feedback to control cell shape (Gorfinkiel et al.,2009; Martin et al.,2010).
Thus, it seems that the force generated by the AS during DC is a myosin-dependent process regulated at the level of single cells but with clear inputs from neighboring cells as well as other tissues. This generates local and dynamic patterns of contraction that feed back on the mechanical properties of the tissue. As DC progresses, the AS develops a more coordinated behavior that results in fast contraction and a more rigid tissue (see Fig. 2). Thus, the AS reveals that biological tissues are materials with very dynamic mechanical properties that can be changed through both intrinsic and extrinsic influences.
What Is the Actin Cable For?
At the interface between the AS and the epidermis, called the leading edge, the actin-myosin cable has been shown through laser-ablation experiments to contribute to closure (Hutson et al.,2003; Peralta et al.,2007). These experiments have also shown that this cable generates a contractile force oriented along the length of the cable and thus perpendicular to the direction of closure, suggesting that most of this force is lost for closure (Hutson et al.,2003; Peralta et al.,2007). Although the actin-myosin cable is under tension, it effectively contracts only at the canthi as part of the zipping process (Peralta et al.,2008). The bulk of the cable does not change its length but interestingly, small segments of the cable (spanning 5–20 cells) fluctuate in length (Franke et al.,2005; Peralta et al.,2008). Myosin II localizes in puncta along the cable, alternating with a-actinin, an actin cross-linker. Actin itself shows a dynamic distribution at the leading edge and also tends to accumulate in puncta at the level of adherens junctions between neighboring cells (Kaltschmidt et al.,2002). The fluctuating behavior of small segments of the cable suggests that there are mechanical interactions between epidermal cells and that fluctuations could be a common feature of acto-myosin contractile systems under certain regimes. How this fluctuating behavior is turned to an effectively contractile cable at the canthi is not known.
The effective contraction of the actin-myosin cable at the canthi is strongly linked to the zippering, the interdigitation of epidermal filopodia that brings the two epidermal sheets together. Filopodia are actin-based cellular projections that also contain other cytoskeletal components such as tubulin, unconventional myosins and actin regulators (Gates et al.,2007; Jacinto et al.,2000; Jankovics and Brunner,2006; Liu et al.,2008). Filopodia are important for the cell-cell matching that occurs during epithelial fusion (Jacinto et al.,2000; Millard and Martin,2008) but there are several pieces of evidence showing that filopodia can exert pulling forces and thus contribute to closure. For example, in situations where the number and length of filopodia are compromised through perturbation of actin elongation, the zippering is slower (Gates et al.,2007). More compelling is the observation that filopodia from one cell can recognize filopodia from its partner cells even if this is misaligned, and form tethers, which upon contraction bring opposing matching cells together (Millard and Martin,2008). The nature of this contractile behavior is not known. How both the contractile cable at the canthi and the filopodia-dependent mechanism interact to give rise to the macroscopic “zippering force” is not known.
A different role for the actin cable has been suggested in which it would act as a supra-cellular ratchet progressively preventing the relaxation of AS cells during their periodic cycles of contraction and expansion. In this model, the actin cable would ratchet AS cells that are in contact with the epidermis, which then would ratchet the following row of AS cells, and so on (Solon et al.,2009). In support of this idea, there is a radial gradient of fluctuation damping in AS cells, starting from peripheral cells towards the center of the AS (Solon et al.,2009), as well as a radial gradient of the rate of contraction of these cells (Gorfinkiel et al.,2009). However, in the absence of a fully functional actin-myosin cable the AS can contract, suggesting that AS cells have the intrinsic capability to contract (Gorfinkiel et al.,2009; Laplante and Nilson,2006). In any case, it is clear that in wild type embryos the contraction of the AS, the contractility of the cable and the contraction of filopodia tethers between opposing epidermal cells has to be tightly coordinated for DC to progress at normal rates and to generate the appropriate pattern. In support of this idea, we have found a positive correlation between the rate of zippering and the rate of contraction of AS cells. Interfering with filopodia formation slows down the rate of contraction of AS cells and perturbing the rate of contraction of AS cells affects the rate of zippering (Gorfinkiel et al.,2009), which suggest that both processes combine to contract the AS and are interdependent (Gorfinkiel et al.,2009; Heisenberg,2009).
The lateral epidermis of the embryo resists the dorsal ward movement of DC as shown by early laser ablation experiments in which the epidermis was observed to recoil ventrally upon lateral epidermal incisions. As DC progresses, epidermal cells elongate in the dorso-ventral axis in a process closely connected with the contraction of the AS, and epidermal cells can lose their elongated shape if the epidermis detaches from the AS (NG and GBB, unpublished observations). However, defects in the shape of epidermal cells observed in embryos mutant for the JNK, Dpp or Wg pathways (reviewed in Harden,2002) have raised the question of whether epidermal cell elongation is an active process or whether these cells are passively stretched by the pulling of the AS. Because cell shape changes in the epidermis are closely related to the formation of the actin cable, and because it is not always possible to perturb the epidermis and the AS separately, the contribution of epidermal elongation to closure has been difficult to assess. Recent observations on the contribution of the trafficking machinery in the cell shape changes during DC suggest that epidermal cells elongate through an active process of membrane growth, probably mediated by Rab11 (Mateus et al., submitted). Moreover, the lack of elongation of epidermal cells upon expression of a dominant negative form of Rab11 seems to pull the AS cells in the ventral ward direction thus perturbing their contraction, and can sometimes disrupt the tissues. These observations suggest that epidermal cells can respond to the pulling force of the AS by modulating their trafficking machinery. Interestingly, it has been suggested that mechanical deformation can inhibit endocytosis (Pouille et al.,2009) raising the possibility that mechanical modulation of membrane growth could occur during DC.
We have shown that genetics combined with new approaches like laser ablation, imaging techniques and tools for image analysis (see Box 1) are providing quantitative information on the kinematic properties of tissues, individual cells and sub-cellular components and their temporal evolution. These data are very good at describing the behavior of the system quantitatively. However, to reveal the underlying mechanisms, in the engineering rather than the biological sense, and the links between the different scales that lie at the heart of the process, we need one further tool: mathematical modeling. This approach integrates the different parameters and measurements into a coherent whole that attempts to reproduce the behavior of the system and its response to perturbations. Thereby, modeling can help us highlight basic properties of the system, validate hypotheses as well as determine subsequent experiments. In this section, we discuss four recent approaches to the modeling of DC. We start with two models that focus on the tissue level and then move down the scales by discussing models that consider a cellular and a sub-cellular granularity, respectively.
One modeling approach (Hutson et al.,2003; Layton et al.,2009) has focused on the tissue level with the aim of reproducing the evolution of the shape of the AS and getting some insight into the interplay between the contractile forces generated by the AS and the actin cable, the resistance of the epidermis, and the contribution of zippering. In this context, the individual cells are negligible and therefore the AS as well as the actin cable are represented as two-dimensional biological force producers (Fig. 3a) with both elastic and active contractile properties, motivated by a model for actin stress fibers (Colombelli et al.,2009). The contractile behavior of myosin and filamentous actin is represented while omitting a detailed force producing mechanism at the molecular level. Since the main focus of the model is on the AS, and the understanding of the mechanical properties of the other two key players—the epidermis and the zippering—is still rather basic, they have been introduced in very simplified manners. The epidermis is represented as a constant pulling force and the zippering is included through an empirically derived law for the time evolution of the distance between the two canthi. These assumptions establish the different parameters of the model, but to conduct computer simulations their values have to be determined as well. Only the initial shape of the actin cable and the initial values of the forces were inferred directly from experimental data. The parameter values determining the zippering rate and the force laws of the epidermis, the amnioserosa and the actin cable were optimized such that the model reproduced native closure, closure after removal of the AS and closure in homozygous myospheroid mutants. The latter embryos lack the βPS integrin subunit, a cellular receptor for intercellular and cell-extracellular matrix interactions, show defects in zippering and fail to close. The completed model proved to be relevant because it was able to reproduce closure influenced by laser-nicking of one canthus or both canthi if the force from the AS was up-regulated. In addition, it provided insight into the mechanical properties of the actin cable. An analysis of the model's two limits, the elastic case in which the contraction of the AS and the actin cable are a purely passive response and the contractile case in which the AS and the actin cable contraction are purely active, revealed that both versions can reproduce wild-type closure, but neither can reproduce the recoil of the leading edge after removal of the AS, indicating a misrepresentation of the actin cable. The elastic version leads to too much recoil while in the contractile case recoil is too small. These results lead to the conclusion that both the active contractile and the passive visco-elastic features of the actin cable were essential to capture its involvement in DC after ablation of the AS.
The second approach (Almeida et al.,2010) for modeling the tissue level dynamics of DC is not based on mechanical considerations but utilizes a method for shape analysis. The interest is in how the shape of the leading edge relates to the relative magnitudes of the contractile force generated by the amnioserosa and the actin cable, the resistive force from the epidermis and the zippering force at the canthi (which occurs in the region where the two leading edges are closer together than twice the length of a filopodium). To address this question, it is sufficient to consider the amnioserosa as a whole tissue omitting the individual cells (Fig. 3b).The tissue forces are represented as coefficients without taking into account their physical nature (i.e., whether they are elastic or visco-elastic) and their values are obtained through optimization with respect to the experimental results. Applying this analysis to wild type embryos and embryos ubiquitously expressing the microtubule severing protein Spastin shows that in the latter the resistance from the epidermis and the zippering force are significantly down regulated compared with the wild type, in agreement with previous experimental results (Gorfinkiel et al.,2009; Jankovics and Brunner,2006). Although conceptually very simple, this model is computationally rather expensive and due to its lack of mechanical detail cannot provide insight into the mechanical properties of the cells and tissues.
A different kind of approach intends to bridge the gap between the activity of individual cells and the behavior of the tissue and has been used to model the shape fluctuations of AS cells (Solon et al.,2009). In this model, the AS is represented by an ellipse, which is filled with two dimensional visco-elastic polygons—the cells (Fig. 3c). The epidermis is represented by a collection of springs that attach the marginal AS cells to a second outer ellipse. In addition, each AS cell in the model actively contracts depending on its intracellular tension, a force that each cell experiences due to its neighbors and that is assumed to be proportional to its size. If the tension of a given cell is above a critical value, the cell starts contracting until its tension drops below the threshold. While it is contracting it stretches its neighbor, thereby increasing the neighbor's tension. Having passed a critical tension the neighbor will start contracting and will stretch the previous cell. Hence, this mechanism leads to fluctuations of the cell areas. The determination of the values for the parameters defining the viscoelastic properties and the contraction forces for each cell is done through a systematic analysis of a wide range of possible values, a parameter scan. The parameter values that provide the closest fit to the experimental data are chosen. If the critical tension that is incorporated in the contraction force of the cells is close to the tissue tension at mechanical equilibrium, this model generates fluctuations of the apical cell area that are in antiphase with their direct neighbors and in-phase with cells further away, and thus cannot reproduce the observed mesoscopic patterns of cell shape fluctuations (Blanchard et al.,2010). To ensure net contraction of the tissue an actin cable that acts like a ratchet to prevent the AS cells from returning to their initial size after contraction is introduced. This in turn leads to a decrease in tissue tension over time, which stops the oscillations. The introduction of a sequential arrest of pulsations starting from the most ventral cells and moving dorsally, as observed in vivo, maintains the oscillations of the remaining cells. Hence, this model suggests that only the initial oscillatory behavior is intrinsic to the AS cells, while net contraction and continued oscillation upon shrinking of the tissue are achieved via external constraints. However, there is good evidence that the tension of the AS increases over time (Ma et al.,2009) and that AS cells can contract even in the absence of an actin cable (Blanchard et al.,2010; Laplante and Nilson,2006), which disagrees with the predictions of the model that there are external mechanisms imposing conservation of the tissue tension and net contraction.
To gain insight into the mechanical properties of cells, a model focussing at the cellular level has been generated to simulate the behavior of AS cells after ablation (Hutson et al.,2009). In this model, the outer constraints of the tissue including its overall shape and the forces generated by the epidermis, the actin cable and the zippering are of minor interest. These are generalised as constant external forces, while the objects of main focus, the cells in the centre of the AS are represented with a sub-cellular granularity. Each cell is introduced as a polygon that is divided into a cortical and a cytoplasmic region, and together they form a rectangular patch, which maintains its shape due to the constant external forces representing the outer constraints in the embryo (Fig. 3d). Each cell in this model has the same mechanical properties: a uniform tension along cell-cell interfaces to mimic intercellular adhesion, a uniform viscosity to represent deformability of the cytoplasm and the cytoskeleton and an internal cell stress to capture the incompressibility of the cytoplasm and the tension from the cortical cytoskeleton. Values for these parameters are determined by comparing the simulation with the experimental results for single laser holes at cell edges and cell centres of AS cells. Having established the model, the authors addressed two experimental observations. Anisotropies in the recoil velocities after ablation are explained by anisotropies in the far-field stresses in the embryo caused by the developmental events happening prior to DC. This is in agreement with the observed anisotropic contraction of AS cells, which was not attributed to an intrinsic polarity in the mechanism of contraction but to external mechanical constraints (Gorfinkiel et al.,2009). To reproduce the recoil observed in double-wounding experiments with their model, a prestressed intracellular visco-elastic network has to be included into each cell, showing that the internal cell stresses are as essential as the cell edge tensions to reproduce the full mechanical behavior of the AS cells. This is in agreement with experimental findings of both an actin-myosin mesh that spans the apical region of AS cells and an actin-myosin population at the level of cell–cell junctions (Blanchard et al.,2010; David et al.,2010; Ma et al.,2009).
The three mechanically motivated approaches discussed here (Hutson et al.,2009; Layton et al.,2009; Solon et al.,2009) provide a good starting point for understanding how different cellular and subcellular processes are integrated across time and length scales to generate robust morphogenetic processes. Models so far have used a combination of generic visco-elastic and active contractile properties to represent the AS and the actin cable (Layton et al.,2009; Solon et al.,2009). Details of the visco-elastic properties of cells have also been investigated (Hutson et al.,2009), but the source of active contractile forces still has to be specified. Finding a more suitable approach for the active contraction of the cells and the tissue requires a better understanding of how the subcellular, cellular, and tissue levels interact. We know that the behavior at the molecular level determines the mechanical properties and the behavior of a cell and that the cellular behavior impinges on the tissue level. Recent experimental information also proposes a top down effect, suggesting that tissue level forces affect the polarity and the pattern of contraction at the cellular level (Aigouy et al.,2010; Gorfinkiel et al.,2009; Martin et al.,2010). Together with the recent findings on the force-driving mechanisms of individual cells over time these results should provide the raw material that has to be incorporated into future models of DC, which should be able to relate individual cell behavior to the detailed macroscopic visco-elasticity of the AS, via intermediate scales of cellular organization.