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AMER. ZOOL., 22:91-104 (1982) The Relation Between Scale and the Completeness of Pattern in Vertebrate Embryogenesis: Models and Experiments 1 JONATHAN COOKE The National Institute for Medical Research, Mill Hill, London, NW7 1AA, United Kingdom SYNOPSIS. The distinctive features of the theory of positional information for pattern formation are described, as applied to early vertebrate development. The results that follow two experimental challenges to the pattern control mechanism in the amphibian gastrula and neurula are presented, together with a discussion of the problems they present for most models that have been proposed for the generation of positional signal gradients. An alternative model which is related to the positional information idea, but which departs significantly from it in explaining the proportioning of patterns, is given in outline. Finally, differences between the behaviour of the antero-posterior patterning system of the chick limb-bud and that of the gastrular axial pattern are described and the concept is introduced that features of the limb pattern, namely its repetitive elements, may require the introduction of a growth control system to regulate tissue size in the rudiment in relation to the forming pattern. INTRODUCTION This chapter is concerned with the control mechanism whereby a complete set of developmental tendencies, or determinations, becomes distributed in characteristically proportioned zones across the available space within a sheet of tissue in the early embryo. The particular tissue sheet in question is the roughly cylindrical, essentially monolayered amphibian mesodermal mantle at gastrula and neurula stages, and the pattern is the medial-to-lateral (dorsal-to-ventral) sequence of axial structures in the body pattern. By early tailbud stages this has achieved division into four discrete and recognisable parts, due to patterning processes that are probably completed during gastrulation and neurulation (Holtfreter and Hamburger, 1955; Forman and Slack, 1980). Axial pattern in the remaining, ectodermal and endodermal cell layers is basically coordinated with that of the mesoderm during organogenesis because information is transferred from the latter in processes coming under the heading of "induction." The true pattern formation that occurs within the plane of the mesoderm at early stages is thus, in vertebrates, the ultimate site for control of the whole body plan. 1 From the Symposium on Principles and Problems of Pattern Formation in Animals presented at the An- nual Meeting of the American Society of Zoologists, 27-30 December 1980, at Seattle, Washington. 91 In many types of embryo, development of a qualitatively complete pattern of morphogenesis can occur across whatever material remains, following much removal, addition or rearrangement of material within the early uncommited cell population. Since individual cell migration, leading to change of neighbour relationships, occurs very little during the crucial period of spatial organisation, the developmental tendencies of cells or their descendants must be modifiable according to the relative positions which they sense themselves to occupy within the whole, in order that normal pattern be achieved despite such disturbances. This requires us to postulate a signalling system, operating to coordinate on a wide scale the determinations achieved by cells. In each embryonic system studied there is characteristically an "organiser" region or group of cells (Spemann and Mangold, 1924) whose own fate as part of the pattern is pre-determined from earlier stages, but which acts as a boundary or reference region when grafted elsewhere, so that the fates of surrounding tissue become organised into a typical edition of the pattern of the embryo concerned, but centred upon the organiser. Observations of this type have received renewed interest in the last fifteen years because of a few theoretical contributions, that have re-formulated the basic problem 92 JONATHAN COOKE of pattern in terms which make contemporary biologists in reasonable numbers able to focus on it after a considerable eclipse period. Pre-eminent among these is Lewis Wolpert's concept of positional information (1969, 1971) which builds a precise theory of how pattern might be achieved, growing out of much older but vaguer ideas concerning "physiological gradients" or dominance hierarchies in developing systems (Child, 1941). A decade ago, the otherwise complete surveys of organismic and molecular biology that constituted zoology courses at several major British universities failed completely to confront the problem of the harmony of form that is reliably achieved during early development in each species, and there is no doubt that we owe the recent improvement in this situation largely to the energy and clarity of the positional information formulation. It remains, nevertheless, a stimulating conjecture rather than an established mechanism, as applied to the initial generation of pattern. I shall outline what I perceive as the salient or diagnostic features of the theory as applied to early embryos, since it is through these that one would hope to approach an experimental test of its adequacy by manipulations and observations on actual systems. I thus draw up a list of critical experimental questions we should like to ask embryos in the light of the theory. I shall then describe some quantitative observations on regulation of the amphibian medio-lateral axial pattern, and explain the difficulties they offer to strictly positional information-based models for the control mechanism. An alternative model, sharing features with positional information theory but also departing crucially from some of its tenets, is then outlined. Finally I shall compare the behaviour of this primary vertebrate pattern with that observed in the antero-posterior dimension of pattern formation for a vertebrate limb-bud, a secondary and later-developing field within the body plan as a whole (see also Summerbell and Honig, 1982). In some ways, the chick limb pattern seems to fit the needs of positional information theory more closely than does the primary axial pattern, leading to the speculation that the need to specify two basic aspects of biological patterns independently might underlie variations in the control system. The demands on a positional information system Before the complexity of morphogenetic movements obscures them, two features are exhibited in the large-scale patterns determined under natural and experimental conditions in the tissue-sheets of embryos. They show overall polarity, in that the pattern parts or zones of the various differentiations always occur in a particular sequence centred around or proceeding from the element deriving from the organiser region. They also follow the rule of continuity, in that pattern parts are never missed out from within the normal sequence, although they may be omitted from one end if regulation does not occur or if two incomplete sequences of opposite polarity are joined due to the presence of two organisers in one experimental embryo. These features are illustrated for formation of the medio-lateral pattern of the amphibian in Figure la. The application of the idea of positional information to this is shown in Figure lb. Normal pattern, and its regulation despite early disturbances, is achieved because a signalling system operates through the entire field to ensure that some cellular variable, whose local value sets the cells' state to determine which particular pattern part shall develop, becomes distributed in a gradient profile with absolute "boundary" levels at the extremes of pattern and a particular, monotonically graded distribution (i.e., a single slope) in between. Boundary characteristics are pre-set by localisation in the egg structure, or are achieved early on in development due to symmetry-breaking processes (e.g., Gierer and Meinhardt, 1972) to give regions having organiser status. These then behave autonomously if grafted, as they set up gradients in surrounding tissues to re-organise their development. This accounts nicely for the properties of polarity and continuity in the final patterns, but note that the achievement of normal pattern is crucially dependent on SCALE AND VERTEBRATE PATTERN FORMATION 93 (a) chemical and physical limits upon the ability to obtain a normal-shaped and complete gradient occupying the whole system regardless of the extent of tissue available, and (b) the "interpretation" machinery of the cells whereby they utilise particular bands or zones of signal level in order reliably to choose between however many alternative pathways of development are available to them. It is important to distinguish between, on the one hand, the abstract idea or formalism of the positional information gradient which seems to flow naturally from the empirical observations of pattern polarity and continuity and the organiser phenomenon, and on the other hand particular mechanistic hypotheses (models) as to what the positional signal and the intercommunication system really are. Such models may or may not postulate a literal FIG. 1. a. Schematic transverse sections of a midgradient in concentration of a signal mol- gastrula and a tailbud stage amphibian embryo, midecule (morphogen), organised by diffu- way along the antero-posterior axis. Density of stipsion. Any cell state variable which obeys pling, graded in the gastrular mesodermal cylinder which is essentially one cell thick, represents the laws of continuous, monotonic varia- (M) graded development tendences which ultimately betion between "boundary" value settings come fixed as differentiating pattern parts, notocould fit the bill (e.g., Goodwin and Cohen, chord (N), somite (S), pro-nephros (PN) and lateral 1969). In practice, however, the diffusion plate (LP). These have undergone their initial differand concentration gradient has been most entiations, including a dorsal convergence or piling of cells, by the time of the second diagram when used in detailed models applied to partic- up pattern is assayed by cell counting. E = ectoderm and ular systems (Wolpert et al., 1974; Sum- induced neural tube. End. = yolky endoderm or gut merbell and Tickle, 1977), while Crick anlage. b. Profile of a graded distribution in a cellular (1970) offered plausibility calculations to variable (e.g., concentration of a morphogen) representing the normal size and proportions of the meshow that diffusion transfer of substances dio-lateral mesodermal pattern. The four thicknesses of reasonable molecular weight is consis- of baseline represent the extents of the pattern zones tent with the timespans (—a few hours) in tissue at their first determination, while arrowand extents (—around 1 mm) across which heads on the ordinate denote threshold signal values significant gradients must be set up and that might determine the boundaries between them. Use for reference when examining the results of exremain in order to encompass the phe- periments as represented in Figure 3. The profile is nomena of biological pattern formation. drawn concavely nonlinear simply because most conModels invoking autocatalytic processes crete models for gradient control (e.g., diffusion from which produce a particular state of cellular a source) produce such a profile, but only a monoactivation locally, but also lead to longer- tonic nature to the gradient is necessary to the posirange diffusive fields of an inhibitor of tional information theory. their own activity (—reaction/diffusion processes), and others postulating pre-dif- struction of morphogen at separate sites ferentiated morphogen sources with uni- are postulated, then two sites having comform destruction elsewhere, have been plementary organiser or "boundary" propused to simulate gradient formation and erties should be expected in each system. match the data from various developing When we remember that on the positional systems (Meinhardt, 1978; Herth and information paradigm the production of Sander, 1973). a complete and proportioned pattern deIf localised synthesis and localised de- pends upon the prior existence (—if only 94 JONATHAN COOKE d 3.5% = N = b.0% 40%= S = 4 ,11%=PN=1 b FIG. 2. a. The removal of blastomeres by pricking with a hot needle at morula/early blastula stages, followed by healing under pressure of the vitelline membrane to give a small, morphologically intact blastula and gastrula. There is a short delay, after which development proceeds at normal speed through the periods of pattern determination and expression without any intervening rise in the rate of cell multiplication, b. Normal and experimentally small embryos at tailbud stages (Fig. la) used to assay pattern proportions by cell counting. Frames mark the anterior and posterior limits between which pattern was assayed, since head and tailbud each represent morphologically complex situations that involve a small percentage of the total cells present. There is independent evidence for size-independence of pattern in the head-to-tail dimension, c. The operation transplanting an early gastrula dorsal lip (organiser) graft to the ventral marginal zone of a late blastula host. The control (sham) operation involves no positional disparity, as one organiser region is replaced with SCALE AND VERTEBRATE PATTERN FORMATION 95 transiently) of a complete and normal gra- plete the process of specification, and in dient profile in the signal, then each set of evolution have acquired mechanisms to asprocesses that has been postulated places sure them of this? its own constraints on the actual performance that would be expected on the part Experiments on the amphibian pattern of the regulatory system as studied experUsing histological techniques, a stanimentally. It is to be hoped that detailed dard estimate can be made of the numbers information on the performance features of cells in the mesodermal pattern parts of of models can be derived from the litera- the amphibian embryo shortly after the ture on them, but at least it is evident that completion of pattern specification at concrete hypotheses, rather than the ab- young tailbud stages. The medio-lateral stract notion of positional information, pattern proportions (i.e., those seen in acgive the whole idea its power as a scientific curate transverse section) have been astheory because they render it most chal- sayed between two set levels in the long lenging to experimentalists. axis (see Fig. 2b) for normal individuals in I would regard the following empirical two species, the anuran Xenopus laevis and questions about actual pattern-forming the urodele Ambystoma mexicanum, and for systems in embryos as of prime importance their sibling embryos where the process of pattern specification had been challenged for assessing adequacy of models. 1) How precise is the maintenance of the experimentally by creating two different proportions between pattern parts, in sets of abnormal conditions. terms of the relative space or cell numbers In the first test, so many presumptively devoted to them, under development at ventral cells (—those furthest from the different overall sizes, or when two organ- pre-determined dorsal organiser region) iser regions have been situated in one nor- had been removed at the blastula stage, mal-sized field so as to partition its terri- that the system was faced with specifying tory into two patterns? pattern across an abnormally small though 2) Is there evidence for two active geometrically normal mesoderm cell sheet "boundary regions" or organisers main- in the gastrula and neurula (Fig. 2a, b). taining complementary ends of the pat- Morphologically normal small gastrulae tern, or is one, "the" organiser, sufficient with as little as 20% of the usual mesoto control and proportion each edition of dermal cell population can be produced, provided that the future dorsal lip region the pattern. 3) Does a supernumerary organiser is left in the embryo. In cell lineage terms, when implanted to an abnormal site within only cells whose normal fates would have the embryo, interact with the original one been to contribute their descendents to the to influence the scale of the pattern parts dorsal two of the four pattern parts recontrolled by it, as well as setting up a new main. In the second test, embryos have been provided at late blastula stage with an pattern centred upon itself? 4) Is there a system at early stages which extra organiser by grafting a second dorsal seems to control the schedule of cell divi- blastoporal lip, from a donor early gastrusion in the tissue in relation to require- la, into the ventral marginal zone. Under ments of the pattern-controlling system; these conditions the small donor cell group i.e., do any biological systems behave as if organises some third of the total mesothey require a set amount of tissue to com- derm into a new axis of pattern, having another one, resulting in normal morphogenesis, d. Transverse sectional appearance of tailbud embryos as in Figure la, but after the sham operation and the ventral organiser graft. Again without any measurable increase in the schedule of cell division since operation, the experimental mesoderm has become determined as two small axial patterns, each remarkably complete in its organisation. The total porportion of cells devoted to each pattern part within doubly organised embryos closely approaches that normal for the species, as ventral pattern is only slightly under-represented. Labelling as in Figure la. 96 JONATHAN COOKE full cellular continuity in the mesodermal cylinder with that centred on the original dorsal midline (Fig. 2c, d). Elements of the pattern are notochord (dorsal midline)—some 3.5% of the cells, followed by paired somite-producing zones—40% of cells, paired pronephrosproducing zones—8-12% of cells, and the remaining lateral plate and blood-producing mesoderm containing some 45—50% of the cells laterally and ventrally. The determination of pattern occurs according to a generally medio-lateral time sequence, normally over a period of some 24 hr (very variable according to species and temperature) and across some 1 mm or 70 cell diameters in the dimension we are considering. Earlier cell cycle studies (Cooke, 1979a, b) have indicated that cell numbers increase only modestly by division over this period (undergoing an average of perhaps 1.5 cycles) and have shown no feedback effect upon the schedule of cell divisions from processes that are modifying the fates of cells during regulation after surgical manipulations (see question 4 in previous section). Thus newly determined patterns in initially small embryos have the proportionately reduced cell populations expected in view of the material removed, while patterns with two dorsal midlines in single embryos consist of the same number of cells in toto as the singly organised ones in normal sibling embryos at identical developmental stages. These situations continue across stages when the proportions of patterns are assessed in this work, but whether there is ever compensatory growth to "normalise" the tissue within each body pattern is a quite separate problem in organismic biology. Does the completeness of pattern ultimately control tissue mass in the differentiated, growing body, as opposed to possible effects of cell number upon the completeness of pattern in the embryo? We do not know the answer. ure 3. Proportions in the patterns of normal individuals have appreciable variability—some 20% relative variation in notochord and pronephros, centred on absolute values of 3.5 and 10% of the mesoderm respectively, and some 10% relative variation for the larger elements, somite and lateral plate. Although the Ambystoma mesoderm contains more than five times as many cells as the Xenopus at these stages, their proportions for the four pattern elements are indistinguishable. Small embryos showing down to little more than one third the usual cell number in transverse section also achieve medio-lateral proportions that are comparable with normal siblings. Present observations suggest that pronephros is more variable in proportion than normal, in very small embryos, and that perhaps relatively more tissue than normal is devoted to lateral plate—the reverse of what might be expected in view of the ventral material originally removed. After organiser grafting, the total proportional numbers of cells devoted to each pattern part within the whole embryo, regardless of position, are normal or only slightly overbalanced in the direction of dorsal structures, even though pattern elements are distributed as two normal series, joined ventrally. Since the slightly smaller of the two patterns, that centred round the new organiser, makes one think of a steeper more local gradient, it would be expected on most models for gradient control. This is because the graft, implanted at the onset of gastrulation, has had relatively restricted opportunity for interaction with adjoining tissue in comparison to the embryo's endogenous organiser. The striking feature observed in these double patterns, however, is that presence of the new organiser in the embryo has scaled down significantly the cell numbers incorporated into the dorsal pattern elements formed around the host's original organiser. What does this observation, particularly, suggest about the dynamics of pattern determination? The striking responses of the regulatory mechanism to the experimental challenges are described by the percentage figures for pattern accompanying the diagrams of One of the simpler diffusion-based Figure 2, and by the use of a standard gra- models for gradients carrying positional dient profile to symbolise or represent the information seems to be ruled out for this proportions and scales of patterns in Fig- system. This is the supposition that the or- SCALE AND VERTEBRATE PATTERN FORMATION ganiser region is a source maintaining a set (boundary) concentration, while cells everywhere else in the system are sinks that destroy the morphogen either at a constant rate or at a rate varying simply with the flux of morphogen experienced. Since the field as a whole is the sink, ability to produce complete gradients and hence whole patterns will be sharply dependent on tissue size in relation to the number of organising regions. We would expect failure to restore presumptive ventral parts of patterns following their removal from early embryos (Fig. 3a, version 1) or even "flooding out" to lose specification of more pattern than that corresponding to removed tissue (3a, version 2). In double dorsal, normal-sized mesoderms, similarly, a range of results between versions 1 and 2 of Figure 3b would be expected, due to loss of gradient values specifying more ventral elements and to flooding out. Diffusion gradients could be maintained in complete form, independently of tissue scale, if concentrations were pinned to boundary levels at localised, chemodifferentiated sources and sink regions. The present operations, on this assumption, will have removed one boundary in one case and replaced it by an active boundary of the opposite character in the other case, so that a system would be required with the inherent dynamics to reinstate either source or sink characteristics at appropriate localities following their removal from the system. Furthermore, "upper" and "lower" boundary cells would be expected to manifest complementary organiser properties when used as grafts, due to active modification of the gradient landscape in neighbouring tissue. In fact, only the dorsal lip region gives evidence of organiser properties, for the dorsal midline of pattern, in the primary vertebrate field. The animal-vegetal pattern of the echinoderm blastula (not homologous anatomically with the medio-lateral gastrula pattern) is to my knowledge the only system showing any phenomenological indication of utilising two absolute boundaries (Horstadius, 1973). The reaction diffusion class of model (Gierer and Meinhardt, 1972; Meinhardt, 97 FIG. 3. a. Representation of pattern in terms of gradients profile to scale with Figure lb, but in an experimentally small embryo. Versions 1 and 2 represent results expected from certain simple diffusion models (see text) using the organiser as a fixed source concentration and all other cells as sink. Loss of ventral pattern and even expansion of the remaining pattern parts is expected in small embryos. Version 3 represents the actual results, b. Representation as in Figure la, but after grafting a second organiser ventrally into the blastula (see text). Versions 1 and 2, again involving loss of ventral pattern and expansion of dorsal, represent what would be expected on the simplest models for positional gradients, whereas version 3 represents the observed behaviour. Certain sophisticated gradient mechanisms might be capable of achieving the regulation required by version 3, but an alternative hypothesis (see text) would relieve the gradient of the need for accurate regulation of its profile in relation to scale and the number of organisers. 1978; Meinhardt and Gierer, 1980) includes systems which in contrast to those just mentioned, show a certain ability to adapt the profile and scale of a morphogen gradient to the available tissue extent. The precise way in which this is achieved may be derived from the above publications (see also Papageorgiou, 1980). Essentially, there may be a steepening of the morphogen profile following a simulation of size reduction in the system, or in systems start- 98 JONATHAN COOKE ing from the condition of possessing too many activated morphogen peaks in relation to their size. This property fits qualitatively with the observations described here, and has been used successfully in quantitative simulations of the Hydra head/ body pattern (Bode and Bode, 1980; MacWilliams, 1982). The hydra pattern, however, as studied by these authors, requires only one sharp boundary between choices made by cells, situated relatively near one end of the system. A gradient profile with a steep local peak at the "upper" end, thus only carrying information utilisable by cells near one end of the system, could suffice, and is indeed the type of profile which reaction/diffusion kinetics can most easily size-regulate {i.e., they reduce the size and extent of a terminal "peak" in proportion to the overall extent of a system). But the sort of profile with which we must deal, if we are to account in this way for patterns such as the vertebrate mediolateral one, contains significantly graded information with precision of slope, at positions far from the boundary. Consider the pronephros, which is (a) centred almost on the 50% point of the system in terms of tissue extent from the organiser, and (b) situated at the right places, and significantly size-regulated in small and doubled patterns. The stringency of the demands that this would place upon a regulating signal gradient can be appreciated from scanning the diagrams of Figure 3, and it must be considered doubtful whether most of the model mechanisms that have been explored could rise to this challenge without being extremely parameter-sensitive and therefore improbable. Meinhardt and Gierer (1980) however discuss other classes of model whose performances might prove relevant. Another possible response when faced with behaviour such as that here described in a pattern-forming system, is to consider that it constitutes a prima facie case against the adequacy of a strictly positional information-based theory, whose criteria were given in the previous section. We are then led to examine other theories, and I present here the outline of one which departs from the positional information idea and looks in part to the work of Rose (e.g., Rose, 1967). The model involves a wavefront organised by a gradient, and a set of logically interconnected, alternative cell states. Let us suppose that the organiser does act as a boundary region controlling a gradient of "morphogen" or some physiological variable in surrounding tissue, but that such a gradient is neither particularly stable in profile over time, nor strictly regulated in profile against scale. All it imparts, in fact, is a reliable, coherent polarity or direction to the time-sequence with which development occurs across the tissue. This is because the level in the gradient acts to set the rate at which embryonic mesoderm cells move towards determination (—considered as a point in developmental progression) but does not itself specify which determinative choices they are going to make. There is much evidence that mechanisms in early development can operate to set the time-schedule with which cells pass through developmental sequences, in intimately graded ways. The result, when we consider the spatio-temporal pattern of the later cellular events that concern us (—in this case the onset of determination or differentiation per se), is a wavefront with respect to the event, sweeping across the tissue in a direction determined by the location of the organiser at its origin. It is as if a population of alarm clocks had been lined up at an earlier time, each one set to ring at a unit interval later than the previous one. The rings will occur as what has been called a kinematic wave. Evidence for the biological occurrence of such organisation has come from experiments explanting small pieces of gastrulae, and from work on the pattern of somites in the longitudinal body dimension (Cooke and Zeeman, 1976; Pearson and Elsdale, 1979). This supposition at once relieves the cell interaction system that sets up the gradient of all demands upon its regulatory powers. It could be quite simple. All that is required is that in any gastrula possessing an organiser, a wavefront with respect to cell maturation sweeps coherently down the medio-lateral dimension of pattern from the dorsal midline, while in a SCALE AND VERTEBRATE PATTERN FORMATION gastrula possessing two organisers, two wavefronts originate from the respective midlines to converge, both setting out and travelling across approximately the same developmental time (—we have seen that patterns around recently implanted organisers tend to be smaller, possibly because more recently produced gradients are local and steep, or wavefronts begin a little later). Switching attention to the intracellular machinery governing the determined state, let us suppose that possible determined states are arranged in a logical sequence as follows. Once activated by the physiological effect due to presence of the organiser, cells progress automatically towards state A (notochord) unless the experience of above-threshold concentrations of an inhibitor specific to A diverts them at an early stage of their progression, whereupon they switch towards state B (somite) until and unless a new inhibitor specific to B builds up enough to divert them again, and so on through pronephros (C) to lateral plate (D). Let us further suppose that an early biosynthetic product within cells, of the entry to each determined or differentiating state, is the specific inhibitor of access to that state by less mature cells. We assume these inhibitors to be so diffusible that their concentration builds up widely in the tissue sheet, within a short time relative to the progress of the slow wavefront of determination. We then see that as the wavefront progresses the determination produced will change, to give the successive zones of different character corresponding to each pattern element. Each inhibitor, synthesized in increasing amounts as more cells progressively enter the state that produces it, has only the available tissue as a diffusive sink, so that its rate of build-up in concentration acts in effect as a size-sensor of the system as a whole. The smaller the field, the more rapidly will entry to each successive state become prohibited to further cells, which will thereby be switched towards development of the next determined state leading to global build-up of the next inhibitor. As the wavefront of development progresses, the width of the 99 zone occupied by each determined state may be adapted to the size of the whole tissue, in a way that is formally equivalent to the operation of a temporal series of regulating reaction-diffusion systems, each specifying one boundary. If the inhibitors are sufficiently diffusible, relative to the developmental rate, for inhibitor contributed from two similar developing zones to be summated in the territory between them, we have an explanation for the crucial result in Figure 3b, version 3, that the presence of an extra organiser scales down the pattern parts controlled by the original one as well as leading to a new pattern of its own. In its most general form this might be termed a serial switch model rather than a serial inhibition model, since by symmetry, the logical sequence of cell states might be implemented by a series of positive, diffusible activators for succeeding states (i.e., A —» B) as opposed to self-inhibition by each state. Certain details of the results (Cooke, in preparation) such as a lesser degree of size regulation by the earliest-determined notochord, correspond to weak predictions of the model. A strong prediction, which has not yet been tested, concerns the effect of large pieces of already-determined somite or pronephric zone, transplanted from older gastrulae to the ventral region of younger, undetermined hosts. Specific suppressant effects upon the size of homologous elements in the host pattern should be observed. On the positional information theory only the organiser itself, implanted from a young donor, should be able to cause such effects, and they must be accompanied by a whole new pattern sequence in ventral opposition to the host sequence. The serial switch model also relieves cellular interpretative mechanisms of the demands generally imposed by the positional information concept, in that each interpretative "decision" is essentially binary, the final multiplicity being achieved because of cellular history (i.e., in a combinatorial fashion), rather than by exact perception of many levels of a continuous positional variable. We lack information that makes us confident that cells could accomplish the latter task. 100 JONATHAN COOKE The chick limb antero-posterior pattern growth on normal schedule Vf' FIG. 4. Model which best fits the current data relating limb pattern specification to early growth control. Pattern-controlling and growth-promoting signals in the system are seen as distinct entities, only loosely correlated in profile, though both organised from the ZPA at the posterior edge of the field. The process of setting up a complete gradient and founding all the digit rudiments is one that intrinsically occupies a particular space, perhaps because a pre-pattern as well as a simple "diffusion" gradient system is involved. On this view, anterior graft of a new ZPA, as well as causing mirror duplication of pattern, leads initially to "flooding out" of pattern corresponding to digit 2. Widespread enhanced growth due to the extra ZPA however allows both pattern specification systems to be once again complete by stages of determination. The first three levels of the diagram represent the normal situation, and the two timepoints within the first, say, 24 hr after an anterior ZPA graft. The bottom line gives the proportions (—the scale is by then much greater, and irrelevant) in the later limb cross-section. Ordinate is the signal value for each location, abscissa the anterior (left) to posterior (right) tissue extent at each stage. Profile of pattern-determining signal, . Profile of a signal influencing the cell cylce, . Levels of signal associated with particular digits, but with cell fate still undetermined, 2, 3, 4. Tissue determined as or actually forming particular digits, (5 © ©. Note that growth is greatest for more posterior elements in the pattern. The vertebrate limb-bud is an example of a secondary field, in that the limb pattern is regulated as a whole, but has derived its location in the body and its overall orientation from the primary embryonic field during axial patterning. Subject to the lively argumentation that attended the limb presentations at this symposium, an organiser region for the antero-posterior pattern dimension, which is initially expressed in the skeleton and skin, can be defined at the posterior edge of the undifferentiated chick wingbud. This appears to control pattern according to a gradient formalism such as in the case of the primary medio-lateral pattern just discussed, although the system is complicated by the rapid growth that is undergone while pattern is actually being determined. Transplantation of this "zone of polarising activity" as a graft to the anterior border of a bud at stages around 19 (Hamburger and Hamilton, 1951) results with high reliability in the ultimate formation of a wing digit and forearm pattern mirror-imaged around the normal anterior border. When presenting their model for "Pattern formation in epimorphic fields," French et al. (1976) suggested that development in all seconary fields might be found to show an intimate relationship between growth control and the control of pattern, whereas primary pattern formation in fact shows no such inter-relationship or dependency. A shape change that includes a widening has been noted as an early accompaniment of successful pattern duplication in limb buds following ZPA grafting. Summerbell and 1 therefore decided to look in detail at the cell cycle in host wingbud mesenchyme during the 17 hr following the anterior graft of a (normally posterior) ZPA mesenchymal region that results in symmetric double pattern formation. Anterior-to-anterior grafting, with little or no positional disparity, served as a control for any effect of operation per se upon thymidine uptake; this turns out to be localised and transitory at most. The results have been presented in de- SCALE AND VERTEBRATE PATTERN FORMATION tail elsewhere (Cooke and Summerbell, 1980; see also Summerbell and Honig, 1982). Though very striking, they are not consistent either with the idea that the new pattern is produced by intercalation in tissue specifically grown at the host/graft junction, or with the idea of a cell cycle schedule in wingbud mesenchyme that is independent of pattern specification, as in primary fields. Between 9 and 17 hr after a positional disparity has been imposed by the anterior graft, a cell cycle response that will in due course increase the rate of growth has been instigated in the tissue of more than half the bud, and often extending to parts of the original posterior border. The response is certainly concentrated in the anterior half, which fits with the finding (Honig, in preparation) that the anterior duplicated limb structure, although it usually ends up equal to the normal structure in size, is derived from an initially small (25%) sector of the original bud width. But even tissue that is undoubtedly to contribute to the posterior limb pattern, of normal polarity, experiences significant stimulation of the cell cycle just after anterior ZPA grafting. We believe that by the time the duplicated, mirror symmetrical digit pattern in these limbs is actually being laid down, the width of tissue in the handplate will have approached a doubling relative to what it would normally be. Determination of pattern probably only occurs when the tissue has expanded throughout, and the growth schedule is once again receding towards that normal for the stage concerned. The signalling mechanism whereby this is achieved remains to be elucidated, but it seems most likely that each ZPA is a source for some growth control agent as well as a specifically pattern-specifying signal, and that the growth stimulation "diffuses" much more rapidly than does the signal respecifying pattern around that source if it is placed ectopically as a graft. This model (Fig. 4) contrasts with the idea of a tight linkage between position values in pattern formation and the control of growth, as in epimorphic intercalation of pattern (French elal., 1976). 101 French flags, repeating patterns and pre-patterns The above observations on the behaviour of the limb bud are particularly interesting because we already have evidence, from primary embryonic pattern formation such as that described earlier, that biological machinery exists for the control of pattern in a way that is independent of spatial scale over a considerable range. Why then, when we come to the setting up of a pattern like that of the limb, do we see behaviour which seems to indicate that the mechanism requires a certain amount of tissue in order to specify completely, and has acquired additional features to make sure that tissue mass indeed coincides with the number of pattern elements to be laid down? Feedback mechanisms that adapt the final sizes of growing limbs to their hosts must exist, after all, so that by analogy with the primary body pattern's behaviour, we might expect twin, complete but miniature limb patterns to be founded in one normal-sized bud after ZPA grafting, with each structure perhaps going on to grow up to normal size over a period when, in any case, an enormous amount of growth occurs. In conclusion, I should like to speculate, and to suggest there may be a difference, in principle, between the tasks of specifying on the one hand a "French Flag" pattern of stripes or zones (Wolpert, 1969), each showing a unique cellular activity as in the medio-lateral body pattern, and on the other hand a pattern exhibiting repetitions of an obviously similar group of cellular activities, such as we see across the vertebrate limb rudiment. Both pattern types are fundamental to animal form. In repeating patterns, successive collections of cells undertake the same, obviously homologous or similar set of activities, then differentiations, while cells in between do something different or else simply aggregate towards the centres of the developing structures. The deepest problem is to get the number of centres correct, while superimposed on this is a gradation in unique properties—the "little finger-to- 102 JONATHAN COOKE thumb" character in the present case, that exhibits the phenomenology of organiser boundaries, polarity and continuity in response to experiments on the embryo and so draws the mind towards the idea of the positional information gradient. The available gradation between boundaries is expressed primitively in five repetitions of the structure in the tetrapod hand, whereas bird hands express it in three (—the rudiment for a fourth is laid down but lost embryonically). In French Flag patterns only the unique series of features behaving according to gradient phenomenology is seen, and it is fundamental to them. Populations of cells embark on unique programmes of activity and differentiation, showing almost no homology with those elsewhere in the system, according to their positions relative to the boundaries of pattern. The concept of "pre-patterns," together with a family of models as to how these might be set up during early development (see Turing, 1952; Gierer and Meinhardt, 1972) was evolved in attempts to explain the control of certain types of repetitive pattern in morphogenesis, where number of structures is kept constant within the species. The skeletal pattern of the limb rudiment is a good example of such repetitiveness in two dimensions. By a prepattern, we mean a spatial distribution in concentration of unknown "morphogens" or some quantifiable cell state as in the positional information idea, but this time the distribution is in some important way isomorphic with the pattern that can finally be seen to develop as a result of the (hypothetical) pre-pattern. Thus if we could view the undifferentiated tissue through some appropriate microscope or spectroscope, we should recognise the form of the pattern already in the landscape of the spatial variable that was to control cellular activity. The task of pre-pattern machinery is to control by cell biosynthetic interaction and diffusion the non-monotonic distribution {i.e., a particular number of peaks separated by troughs or valleys) of morphogen in order to control the pattern produced. This notion contrasts sharply with positional information in the expla- nation of morphologically repetitive patterns, in that the latter postulates a very simple, monotonic distribution of signal and, necessarily, a complex set of cellular perceptions and responses to this, rather than a complex signal distribution and a simple, on-off cellular response (see MacWilliams and Papageorgiou, 1978, for further discussion). One effect of the more recent ascendancy of positional information theory, indeed one of its assertions, is that the concept of pre-patterns is largely unnecessary and redundant. To air a difference in viewpoint which, I imagine, will not be resolved until it is replaced by real knowledge of cells and the apparatus at their disposal, I find it implausible to imagine that the pattern of, say, the wrist and hand cartilage condensations could initially be produced only by cellular interpretation of one or two variables, simply graded between boundaries. The mapping function from the spatial variables onto cellular activity would seem to present too complex a task to intracellular interpretative machinery. Each element of such a pattern is obviously comparable with others in terms of cell activity and differentiation, even though they may go on to exhibit nonequivalence in subsequent development (Summerbell and Lewis, 1975) so that a positional grid system is also indicated. Thus it seems to me more parsimonious to assume that a set of spatially distributed, locally equivalent situations of the pre-pattern type is being responded to in parallel with a range of unique readings for some other variable to give the graded properties. It is intriguing to note that all models for generating pre-patterns thus far described and explored by simulation, have at most a very limited capacity to adjust the spatial "wavelength" at which they specify pattern units, to differences in overall field size (though see Papageorgiou, 1980). Prepattern models are essentially reaction-diffusion gradient models (see earlier discussion) with the effective inhibitor range adjusted downwards to allow development of multiple activation peaks. Each set of biosynthetic and diffusion parameters pro- SCALE AND VERTEBRATE PATTERN FORMATION grammed into such models gives rise to peaks separated by a particular "chemical wavelength" which it is hard, in principle, to have adjusted according to the tissue size that individual embryos of a species might have available. In practical, and especially biological, terms this means that the number of elements produced in repetitive patterns set up by pre-patterns would be a function of the extent of tissue available at the time. Quantitatively and qualitatively normal pattern would tend strongly to require normal size initially. 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