Origin and function of fluctuations in cell behaviour and the emergence of patterns

Seminars in Cell & Developmental Biology 20 (2009) 877–884

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Review

Origin and function of fluctuations in cell behaviour and the emergence of patterns Ana M. Mateus a,b , Nicole Gorfinkiel a , Alfonso Martinez Arias a,∗ a b

Department of Genetics, University of Cambridge, Downing Street, Cambridge CB2 3EH, UK Gulbenkian PhD Programme in Biomedicine, Rua da Quinta Grande, 6, 2780-156 Oeiras, Portugal

a r t i c l e

i n f o

Article history: Available online 7 August 2009 Keywords: Morphogenesis Cytoskeleton Adhesion Planar cell polarity Fluctuations

a b s t r a c t Morphogenesis is the process whereby cells assemble into tissues and organs. Recent studies of this process have revealed heterogeneity of individual cell behaviours that contrasts with the deterministic activity of tissues as a whole. Here we review these observations and suggest that fluctuations and heterogeneities are a central substrate for morphogenesis and that there might exist mechanisms dedicated to the averaging of these fluctuations to ensure robust and reproducible behaviours at the tissue level. © 2009 Published by Elsevier Ltd.

Contents 1. 2. 3. 4. 5. 6.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . From self-organization to self-assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . From cells to tissues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coordinating cells: pattern formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wnt/PCP and the denoising of morphogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . In summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction The observation that cells organize themselves into spatial arrangements to generate tissues, organs and, through combinations of these, the variety of organisms that populate the planet, remains a wondrous phenomenon. Examples include the way in which, upon starvation, seemingly identical Dyctiostelium cells aggregate and differentiate in a position dependent manner to generate spores with defined structures and functions; and the generation of germ layers from an equivalent group of cells, which develop different spatial patterns of organization during metazoan development [1]. The intrinsic ability of cells to form patterns can be demonstrated when embryonic cells are disaggregated and mixed, as they will sort themselves into specific spatial patterns accord-

∗ Corresponding author. Tel.: +44 1223 766742; fax: +44 1223 333992. E-mail address: [email protected] (A.M. Arias). 1084-9521/$ – see front matter © 2009 Published by Elsevier Ltd. doi:10.1016/j.semcdb.2009.07.009

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ing to their germ layer [2]. An extreme example of this behaviour can be observed in the cells that will give rise to the limbs of vertebrates: when mesenchymal cells from the limb bud of a chicken are jumbled up and wrapped inside an epidermal bag, they manage to form digits and muscles with a degree of discernible organization [3]. These examples reveal the tendency of cells to organize themselves in space which, in the context of an embryo, is orchestrated to generate familiar patterns like muscles, limbs, kidneys or the heart. The constrained spatiotemporal organization of cells is referred to as “morphogenesis”. Our perception of the mechanisms (understood as a causal explanation for an observation) underlying biological processes is always determined by the level at which we can describe them. In the case of morphogenesis this is generally done at the level of fields of cells, without much regard for the individual components that configure the fields. As a consequence, the processes are depicted as deterministic, resulting from programmes of gene expression that are transmitted to the cytoskeleton and the adhesion system.

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Fig. 1. Biological phenomena spans different time and spatial scales. Biological processes are multiscale, operating at different time and length scales, ranging from molecules, cells, tissues, organs to organisms. At the lower level scale, the dynamics are fast and noisy but are somehow averaged at a higher scale. Integrated higher scale phenomena appear slower and deterministic (diagram adapted from [7]).

In this vein, at one point the term “topobiology” (“the study of the place dependent regulation of cells resulting from interactions of molecules at cell surfaces with other cells substrates” [4]) was tried as a way of directing the mind to the notion that there are molecular components specifically dedicated to the organization of cells in space. However, as we learn about the molecular fabric of living systems we can see that there are no such dedicated components. On the other hand, developments in our ability to peer into the activity of cells and, most significantly, to follow single cells within large populations are revealing a degree of heterogeneity of behaviour which is not easy to reconcile with the deterministic behaviour of the groups as observed in developing embryos [5,6]. These observations reflect two important general properties of biological systems. The first one is that they are multiscale, i.e. they have events operating at different time and length scales which are integrated at the highest level (Fig. 1); there is something obvious about this, but its implications are only beginning to become clear. The second one, which is also apparent, is that when relating two levels/scales, heterogeneities at one level are averaged and integrated at a higher level. This second property is the subject of this essay in which we shall present evidence that heterogeneities have a basis in molecular fluctuations and are a feature of the cellular systems undergoing morphogenesis. Here we begin to discuss the second in the context of recent molecular and genetic analysis of morphogenesis.

tures depending on the concentration of associated proteins, e.g. motors and bundling proteins. Their interactions define a phase space, where the relative concentrations determine energetically favourable points of attraction that correspond to dynamic steady states. These sinks or attractors reveal themselves in the form of structures: asters, vortices or spindle networks that emerge from the interactions of microtubules and different concentrations of motor proteins [11–13] or different actin architectures and networks derived from cocktails of actin, myosin and bundling proteins [14,15]. These behaviours can be observed in vitro where, for a defined and very minimal set of parameters (concentrations of monomers and motors), the system self-organizes into a pattern. But in vivo, this pattern is not random, as the organization of the cell selects specific regions of the polymer phase space and endows them with stability. There is evidence that the dynamics of actin and tubulin is constrained into particular configurations as a result of two different levels of regulation: spatial confinement and interaction with other proteins and membranes. For example, confining microtubules and motors inside droplets of Xenopus egg extracts

2. From self-organization to self-assembly There are three functional modules that determine the activity of a cell in the context of morphogenetic processes: the cytoskeleton, the adhesion system and the trafficking machinery. The cytoskeleton, a system of dynamic polymers, provides the structural fabric of a cell. Adhesion is mediated of a system of transmembrane proteins which link cells to each other and to the extracellular matrix. In doing so, they provide links and anchors for their cytoskeletons, allowing for coordination and modulation of behaviour. Finally, trafficking is classically seen as a way to keep molecules in the steady state and is emerging as a central modulatory element of the other two (Fig. 2). Here we shall focus on the first two. The structure and dynamics of the cell relies on the cytoskeleton, a very flexible network of polymers with three components: microtubules (monomer: tubulin), microfilaments (monomer: actin) and intermediate filaments (various monomers). The three are in a constant state of flux and while this can be related to the proteins that are associated with each of the polymers, it is clear that structural instabilities are intrinsic properties of the molecules [8–10]. Actin and tubulin can self-organize into different struc-

Fig. 2. Cellular processes underlying cell behaviour. Three functional modules determine the activity of a cell in the context of morphogenesis: the cytoskeleton activity, the adhesion system and the trafficking machinery. The cytoskeleton provides the structure of the cell. Its main components: actin, microtubules and motors assemble into different structures and networks that render the cell very dynamic. The adhesive system is composed by transmembrane proteins which connect the cells to each other (e.g. Cadherins) or to the extracellular matrix (e.g. Integrins). Adhesion molecules also link the cell membrane to their cytoskeletons, coupling cytoskeleton dynamics to cell shape dynamics. Finally, trafficking is emerging as the central modulatory element because it regulates the other two. Chemical and mechanical signal impinge on these modules to achieve different outputs of cell behaviour differently required during morphogenesis.

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with different sizes showed that the size of the droplet determines the final steady state of the microtubule network [16]. Droplets encapsulated in a lipid bilayer with different membrane stiffness revealed that the properties of the membrane also influenced the structure formed by the microtubules. For example, vesicles with more rigid membranes acquired a quasi-spherical shape, displaying cortical-like bundles or semi-asters (depending on the vesicle size) but vesicles with lower bending stiffness exhibited single or multiple microtubule-based protrusions [16]. Thus, the physical domains of the system can select domains of the phase space. Another level of regulation and activity constraining the behaviour of cytoskeletal monomers is brought into play by the collection of regulatory proteins that stabilize certain structures, in certain locations, at particular times. For example, interaction of actin nucleators, actin monomers and other cytoskeletal components results in the assembly of structurally and functionally different collections of actin configurations, such as filopodia, lamellipodia and structures involved in the internalization of extracellular materials or in cell contractility [17]. The constraints that proteins impose on the organization and activity of other proteins is also highlighted by the fact that in some cells their shape oscillates due to the actomyosin network, but in others this property is restrained by the microtubule system, possibly by buffering regulatory molecules or by balancing the tension in the cells. Microtubule depolymerization leads to blebbing and oscillatory behaviour in different cell types in culture [18–21]. On the contrary, fibroblasts oscillate spontaneously when not adhering to a substrate, even without microtubule depolymerization [18], suggesting that certain constraining mechanisms are used in some cells but not in others. Moreover, the cell has the ability to spontaneously self-organize different domains in the absence of any cues. Such symmetrybreaking events were first described by Turing [22] and can result from amplification of random fluctuations in protein concentration through local positive feedback loops and global inhibitors [23]. Organization of domains of different structural stability can even result in motility, as illustrated by the locomotion of cellular fragments of fish epidermal keratocytes [24]. This ability of spontaneous generation of cell polarity and even generation of cell moving states suggests that, in vivo, this behaviour might have to be actively repressed. On the other hand, in certain cases, the axis of cell polarization or movement could be stabilized by chemical signals or mechanical constraints that bias this intrinsic property of the system, making it biologically relevant. Hence the components of the cytoskeleton are versatile elements prone to self-organize into different structures, depending on their environment and interactions. In the cell, regulation of the motor concentration, spatial confinement and interactions with other proteins channels into a defined structure. Obviously, regulation at the genetic level can also modulate the levels of motor concentration and regulatory proteins. With these different constraining elements available, cells are still highly dynamic structures, but there is a certain degree of control over its internal structure.

3. From cells to tissues Above the molecular level, cells exhibit dynamic behaviours linked to the natural properties of their components but, within the confines of an organism, cells are linked and sometimes woven into tissues by adhesive molecules. The adhesive contacts between cells are mediated by Cadherins and other cell adhesion molecules; and with the extracellular matrix, through Integrins. Adhesion imposes constraints and also impinges in the cell internal organization and orientation of cell polarity [25]. It is becoming clear

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that adhesion also exhibits a dynamic that has a close interaction with the cytoskeleton and intracellular trafficking [26,27]. Some of these links have been known for a long time as adhesion molecules anchor the cytoskeleton to the cell membrane, coupling changes in the cytoskeleton to changes in cell shape. Apical cell constriction during Drosophila gastrulation provides a seminal example of such requirement. The force generated by actomyosin contraction results in reduction of the apical area of each cell because the cytoskeleton is tethered to the adherens junctions [28]. Because the adherens junctions are connecting several cells, the result is the linkage of several cytoskeleton cellular units into a supracellular cytoskeleton network that spreads across the tissue [29]. This allows, for example, apical constriction of cells to deform the tissue into a tubular structure as in vertebrate neurulation [30]. Cell–cell cohesion and organization of a supracellular cytoskeleton network also underlies collective cell migration such as the migrating mechanosensory primordium in the lateral line of zebrafish that originates the mechanosensory organs called neuromasts [29]. It has been suggested that the combination of different levels of cell–cell adhesion and cell–matrix with different cytoskeletal activities, manifested in protrusive behaviour and contractility, originates diverse collective cell behaviour. Different follicle cell types in the Drosophila ovary are an example of such combinatorial effect of adhesiveness and cytoskeletal activity, exhibiting cuboidal epithelium, border cells, squamous epithelium and columnar epithelium [31]. Thus, adhesion has an important role in constraining, creating and maintaining groups of cells in the organism, thus generating a higher level of organization. There are two characteristics that became evident in of groups of cells: the emergence of new properties at the level of cell populations and the intrinsic activity at the cellular level that is still exhibited at the tissue level and must be coordinated. This coordination requires interactions mediated by signals but adhesive molecules also act as mediators of collective cell interactions. These interactions, together with the dynamics of individual cells, lead to the emergence of new properties at a higher level. Examples of new properties emerging from cell interactions are the assembly of single Dictyostelium cells into a multicellular slug composed of thousands of cells with complex behaviour [32] and the migrating primordium of the mechanosensory lateral line organ in zebrafish composed of more than 100 cells [29] a moving and dividing cohesive group of cells with a complex and dynamic organization [33]. Single cell analysis of tissue dynamics shows that even when constrained in apparently homogeneous tissues, cells exhibit heterogeneities in cell behaviour. This variability is obvious in the asynchrony of cytoskeletal activity of individual cells. Gastrulation in Drosophila provides a well studied example of this. When cells at the ventral midline invaginate to generate the mesoderm, individual cells go through asynchronous rounds of pulsation and contraction that are a consequence of their actin and myosin dynamics [34], revealing the intrinsic dynamic and variable nature of their cytoskeletal activity. Similarly, during Drosophila dorsal closure, an extra-embryonic tissue, the amnioserosa, contracts through the apical constriction of its individual cells and thus generates one of the main driving forces of this morphogenetic process [35,36]. Individual amnioserosa cells also undergo cycles of contraction and expansion, which show a dynamic degree of correlation between neighbouring cells [37], uncovering the intrinsic variability of the amnioserosa cells (Fig. 3). This dynamic behaviour is driven again by the actomyosin cytoskeleton (Gorfinkiel, G. Blanchard et al., in preparation) and results in a net apical contraction whose rate is not homogenous across the tissue [38]. Another indication that even in a tissue, cells remain highly active is the observation of fluctuations in the position of cell vertices and cell boundaries during cell rearrangements that occur

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Fig. 3. Heterogeneity and averaging in cell behaviour during dorsal closure. Graphs showing the rate of contraction per minute of AS cells as a function of their AP location over time of one Drosophila wild-type embryo undergoing dorsal closure [38]. In (A), the data plotted is the average rate of contraction of all individual cells according to their location and time. In the lower panel, a single cell is highlighted in red. In (B), the data plotted is the average rate of contraction of every cell and its immediate neighbours. In the lower panel, a single cell (red) and its immediate neighbours (orange) are highlighted. In (C), the data plotted is the average rate of contraction of every cell and its two immediate rows of neighbours. In the lower panel, a single cell (red) and its two immediate neighbours (orange and yellow) are highlighted. As the rate of contraction is measured from individual cells (A) to small groups of cells (B and C), the variability in this parameter decreases (Gorfinkiel and Blanchard, unpublished).

during germband extension and eye imaginal disc morphogenesis in Drosophila [39–41]. 4. Coordinating cells: pattern formation The intrinsic properties of molecular complexes within cells and of cells in the context of tissues fuel the processes of migration, invagination, rolling, fusion, convergence and extension that are the toolkit of morphogenesis. As we have seen, random fluctuations in molecular activities are an integral element of biological systems and these have to be dampened and coordinated across fields of cells as their variability can introduce severe disruptions in patterning processes. It is easy to find examples of this principle and some have been the subject of detailed study, e.g. body axis extension and gastrulation in several species [42], neurulation in vertebrates [30] and dorsal closure in Drosophila [43]. In all these cases, morphogenesis relies on directed cell movement, adhesion and compliance and, although the behaviour of the group is always deterministic and highly stereotyped, the individual components exhibit a degree of heterogeneity. Gastrulation provides a particularly clear example of the relationship between individual activities and global behaviour. In vertebrates it is associated with large scale concerted tissue movement that Ray Keller has called convergent extension (CE) [44] to depict the observation that the tissues involved in this process extend along a longitudinal axis, that will become the anteroposterior axis, at the same time that they converge towards the midline where cells will ingress to form the three layered embryo. In this manner, a hollow sphere or cylinder is transformed into a multilayered axial structure. Analysis of this process in zebrafish and Xenopus has allowed a combined metric and genetic study of the underlying cellular events and has revealed that although as a whole the tissue moves towards the midline and performs detail intercalations, the trajectories of individual cells are variable and on the whole noisy [6,45]. Similar situations in which a deterministic tissue movement emerges from noisy individual cell behaviours have been described in Drosophila gastrulation [34,46,47], germband extension [48–50] and the process of dorsal closure [38]. In all cases, genetic analysis indicates that heterogeneities result from cytoskeletal activities within individual cells, which are shown to provide a central force for the processes of

morphogenesis [51]. Furthermore, these activities are likely to be the target of the coordination that leads to deterministic tissue behaviours. As coordination has to occur over large fields of cells, the best candidates to mediate it are signals of varying range and there is evidence that both chemical and mechanical signals play a role. Chemical signals can trigger and simply modulate the level of activity of cells as well as impose a directional component on the cell activity, but it is still early days to discriminate between the two. It is known, however, that either by impinging upon the activity or directionality, several signalling pathways, such as FGF/PDFG and TGF␤/BMPs, coordinate cell movements in many systems [52]. FGF signalling has been shown to control cell movement during gastrulation in different organisms. For example, in chick embryos, directional patterned cell movements are controlled by FGF signalling which acts as a positive and negative chemoattractant. Blocking the FGF receptor in this system shows that the cells that are able to migrate loose directionality suggesting that in this case the signal is acting on the directionality component [53]. FGF also plays a role in Drosophila gastrulation, especially in the spreading of the mesodermal cells over the ectoderm [54] and directs cell migration during CE in Xenopus and zebrafish [55,56]. PDGF acts during CE and has additional roles in mesendoderm migration in zebrafish and Xenopus [57,58]. The related VEGF in Drosophila instructs border cells to migrate towards the oocyte and control blood cell migration during development [59,60]. Members of the TGF␤/BMP family of signalling molecules are known to target the cytoskeleton and adhesion and have been shown to have an impact in morphogenetic processes [61]. For instance, in zebrafish, BMP determines the direction of lateral mesodermal cell migration during CE by regulating cell–cell adhesion [62]. It has been suggested that TGF␤ family members coordinate cell behaviour in Drosophila during dorsal closure through regulation of the cytoskeleton [63,64]. Acting in concert with chemical signals, there are also mechanical signals sensed by the cells that trigger cell behaviour. For example, during Drosophila gastrulation mechanical signals trigger redistribution of the contractile machinery and mesoderm invagination [65] and have also been suggested to coordinate and pattern cellular behaviour during Drosophila dorsal closure [37,38]. There is little question that members of the FGF/PDGF and TGF␤/BMP families of signalling molecules are instructive, i.e. their

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position and intensity instructs the activity of the cells. However, another group of signalling molecules appears to be more concerned with coordination than with instruction. In many systems, mutations in a group of genes encoding elements of the so called planar cell polarity (PCP) pathway, result in defects in morphogenesis [51]. This group of genes is associated with Wnt signalling and was identified initially in Drosophila where they play a role in determining the global orientation of hairs and bristles [66]. A core and central PCP component is Dishevelled (Dsh), an adaptor protein which links to a large variety of proteins and processes [67]. Genetic studies in other organisms have revealed related functions of PCP proteins in the polarization of cells within tissues or organs [68] through effects on cytoskeletal dynamics and adhesion [51,69,70]. In many instances, rescue experiments suggest that the source of the signal, often a Wnt protein or the levels of the effector protein, e.g. Dsh, do not determine the outcome, i.e. ubiquitous expression of Wnt/PCP ligands can complement the directed activity of the cells. This suggests to us that the role of the PCP module is to buffer cell variability and that heterogeneity alone, without any higher scale coordination, impairs tissue morphogenesis. In Xenopus CE, inhibition of PCP activity by disruption of Dsh triggers more cellular activity: cells form more but less stable and randomly oriented protrusions. On the other hand, overexpression of wild-type Dsh does not affect stability of protrusion but randomizes their orientation. In both cases, cells do not polarize along the mediolateral axis and CE fails [71]. Similarly, impairment of Strabismus (Stbm), another protein involved in promoting PCP, in Xenopus embryo explants leads to unorganized protrusive activity and failure of cells to bipolarize [72]. Studies in zebrafish CE movements also show that Stbm bias cell polarity along mediolateral axis and that this underlies effective intercalation, directionality and speed of dorsal migration [73]. In zebrafish, expression of a mutant form of Dsh that blocks axis elongation revealed that, in fact, the PCP pathway regulates two processes during CE: orientation of cell elongation and cell division. The mutant form of Dsh, randomizes elongation of cells that otherwise would elongate mediolaterally and randomizes the divisions that in control embryos are aligned with the

Fig. 4. PCP as a coordinating molecular device. Cells that perform a coordinated and directed operation, e.g. movement, have an inherent activity determined by the selforganization of their components. This is indicated by the ‘moving arrows’ on the left and is reflected in the background level of the three cells shown. The activity could be the assembly and dynamics of the cytoskeleton. A spatially localized signal introduces a bias in the activity and determines a certain directionality. However, there is still a problem of signal to noise (red in lower graph) and although the individual vectors have an orientation, there is an element of noncoordination. We surmise that the function of the planar cell polarity (PCP) input is to increase the signal to noise and thus achieve a coordinated readout of the signal. Many PCP mutants in zebrafish gastrulation and Drosophila hair polarization show PCP phenotypes which are consistent with this outline.

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animal/vegetal axis [74]. In the above morphogenetic processes the underlying cell behaviour, such as emission of cell protrusions, cell elongation or cell division is still exhibited in the absence of Wnt/PCP but the orientation is randomized. This points towards a role of Wnt/PCP in reducing noise and variability in cell behaviour in large groups of cells through coordination of cell behaviour (Fig. 4). 5. Wnt/PCP and the denoising of morphogenesis The results summarized above indicate that there are two kinds of operations mediated by signals during morphogenesis: the patterning and spatial organization of individual cell behaviour and the coordination of these behaviours. The input for the first operation is provided by the spatiotemporal localization of signals which act directly on the cytoskeleton or on the adhesive system to promote a particular pattern of activity: filopodial extensions, modulations of the adhesion to the basement membrane or to other cells, changes in the compliance of the cell. However, these signals are targeted to individual cells and lead to an asynchronous response, which will vary from cell to cell (Fig. 4). Furthermore, the signal might be weak and this will increase the fluctuations in the response. So, if patterning processes were left to the interpretation of signals by individual cells, they might never occur above a few, perhaps, very few cells. This suggests that there are mechanisms to dampen these fluctuations, increase the signal to noise ratio and coordinate the activity of the group. This is what we see as the main function of Wnt–PCP signalling. In fact, the targets of these processes are both the cytoskeleton and adhesion system and it is likely that Wnt acts on both. Our suggestion for the role of Wnt/PCP signalling contrasts with the widely held view that it is instructive. The difference has been put to test in a series of elegant experiments in Caenorhabditis elegans. Early in development, the EMS blastomere divides to generate two precursor cells, one for the endoderm and one for the mesoderm. The plane of cell division is important in determining

Fig. 5. Requirement for polarization of the PCP input. In many systems, PCP signals are determined by Wnt signalling and in some instances there is a polarized requirement which suggests an instructive input (see text). However, the function of PCP coordinating activities across cells and enhancing signal to noise levels can be maintained by incorporating the strength of the signal. In the two situations shown, the input signal is polarized. If the signal to noise ratio of the input signal is low (left) a polarized PCP signal, in the form of a gradient will have a big impact and will polarize the enhancement of the signal. On the other hand, if the signal to noise ratio of the input is strong (right), a uniform PCP signal will still lead to a polarized output following the lead of the input signal.

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Table 1 Examples of cellular variability in different organisms and biological processes. Organism

Process

Description

Escherichia coli

Swimming behaviour

Chlamydomonas

Flagella beating

Dictyostelium

Aggregation

The swimming behaviour of Escherichia coli cells varies significantly from cell to cell and this might be the result of fluctuations in the concentration of regulatory proteins [82,83]. In the dark C. reinhardtii can vary the intrinsic frequencies of its flagella, alternating between synchronous and asynchronous beating and, ultimately, to the diffusive behaviour of a population [84]. Large variability in the gradient-sensing response of Dictyostelium cells when exposed to the chemoattractant [85].

Drosophila

Gastrulation

Dorsal closure

Apical constriction required for invagination of the ectoderm occurs through pulses of contraction which are disorganized across the tissue [34]. Tracking of ectodermal and internalized mesodermal individual cells shows variation in the migration [47]. During dorsal closure amnioserosa cell shape fluctuates, with a dynamic degree of correlation and this behaviour seems to be key in the early steps of closure [37,38].

Zebrafish

Gastrulation

Cell movement trajectories in convergence and extension domains are different: some follow zig-zagging paths, others meander considerably and other cells move along relatively straight trajectories [5]. The orientation of cell division in zebrafish gastrula occurs mostly in lines that are AV oriented, but there is some degree of variability [74].

Xenopus

Gastrulation

The local tugging activity of cells seems uncoordinated but CE is relatively constant with minor fluctuations in rate in normal development [6].

the fate of the daughter cells but both processes (fate assignation and mitosis) are linked and genetic analysis has shown that both depend on the coordinated activity of a mom gene, encoding a member of the Wnt family and MES, a Src-like kinase. Using an ingenious experimental design, Goldstein et al. have shown that although both activities are needed for the correct decision, it is the polarity of Wnt that determines the polarity of the decision [75]. While the evidence is suggestive for a positional instructive role for Wnt signalling, there is an alternative explanation for the observation compatible with our suggestion above. The nature of the requirement for Wnt will depend on the signal to noise ratio of the instructive input. If the signal to noise is high, the Wnt input will not need to be polar and it will work even if it is homogeneously distributed. This is often the case in hair polarity in Drosophila [66] or during zebrafish gastrulation [76]. However, with low signal to noise ratios, a polar Wnt signal will have an advantage as it will have the effect of amplifying and coordinating the signal in a spatial manner (Fig. 5). In this instance it might appear that Wnt is being instructive but it is acting in the general way we suggest and the polar requirement might have more to say about the strength and information content of the instructive input, which in the case of C. elegans EMS cells, might be MES. A corollary of this consideration is that time allowed for interpretation might be an issue when there are low signal to noise ratios. The shorter the time allowed for the decision, the more important the requirement for a polar Wnt. Thus, while we cannot rule out that in some instances there is a positional input to Wnt, we believe that the unifying functional property is the coordination (dynamic and spatial) of the response of single cells to inputs.

biological systems but it is also clear that, in these systems, some of the averaging results from regulatory processes. This is probably due to the need of biological systems to have fast, coordinated and reproducible averaging. While in some instances, the averaging results from the nature of the molecules and reactions involved in the processes, e.g. the assembly of actin into particular structures, it is interesting to envision the possibility that specific molecular systems have evolved to perform this averaging. Accepting that fluctuations are an inevitable consequence of the fabric of Biology, the question arises whether they play any role in the functioning of living systems [77,78]. After all, biological systems could have evolved components and interactions that minimize fluctuations by using more rigid building blocks or robust reactions. However, as we begin to be able to measure physicochemical properties of particular systems we begin to see that fluctuations are tightly linked with the regulative behaviour of the system, perhaps for a good reason and play a major role in patterning processes [79,80]. We would like to suggest that fluctuations provide a basis for plasticity and a substrate for pattern formation. By allowing the cells to explore the phase spaces created by their components, biological systems (molecular or cellular) can adapt to changes and even evolve. In some sense it might be that fluctuations have been selected and tuned during evolution. In this case it will not be surprising that specific systems have evolved to promote, integrate and regulate them in space and time and that Wnt signalling, through its PCP branch is dedicated to this task in morphogenesis [81].

6. In summary

This work was funded by the Wellcome Trust (AMA), Fundacao para a Ciencia e Tecnologia (AMM) and the BBSRC (AMA and NG). We want to thank Joaquin de Navascues, Guy Blanchard and Richard Adams for discussions that have helped us shape the ideas that we have tried to articulate here.

Fluctuations, time dependent stochastic variations of a particular behaviour, are a common feature of biological systems (see Table 1 for some examples) and result from the nonequilibrium chemical nature of biological processes. However, they become slower and less obvious as one moves through length scales (Fig. 1). This type of averaging is well known in physical systems and, in some instances, it is understood to result from changes in the timescale of the fluctuations as one moves from individual to a collective behaviour; usually the higher the length scale, the slower the fluctuation (Fig. 3). There is an element of this behaviour in

Acknowledgements

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