Pattern formation in dictyostelids

Pattern formation in dictyostelids

seminars in DEVELOPMENTAL BIOLOGY, Vol 6, 1995: pp 359-368 Pattern formation in dictyosteUds J. T. Bonner and Edward C. Cox* We make two main points...

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seminars in DEVELOPMENTAL BIOLOGY, Vol 6, 1995: pp 359-368

Pattern formation in dictyosteUds J. T. Bonner and Edward C. Cox*

We make two main points about the present and thefuture of the study of pattern formation, which is perhaps the most interesting problem in modern developmental biology. One is that a complete understanding of a developing organism will require the integration of knowledge from a wide variety of disciplines. Our other main point is the importance of comparing organisms to find universal solutions. Here we compare two dictyostelids that have somewhat different development, to point a way toward understanding how fundamental mechanisms can vary to produce altered shapes. Key words: spatial patterns / polarity / size regulation / proportions / Dic~yostelium/ Polysphondylium 9

Academic Press Ltd

A CENTRALQUESTION of developmental biology continues to be how pattems emerge and are maintained with great regularity from generation to generation. During the past 20 years much of the progress in our understanding of this question has come from combining the tools of genetics and molecular biology. This will continue to be true, especially at the cellular level, as we now begin to understand the interplay of the short range interactions between neighboring cells that lead to larger scale order (see, for example ref 1). This translation of understanding at one level to another can be studied in many ways, but will almost certainly require a combination of different kinds of knowledge gathered at different levels of organization, integrated by models that account for the physics and chemistry of the problem as well as the molecular biology. Our plan here is to use two species of dictyostelids to illustrate this point of view. First we will describe their characteristic life histories, and then the three main aspects of their formation of pattern. This will be followed by two complementary sections: one will discuss our present knowledge of each of the three

developmental problems, and the other will examine how each might be approached in the future.

T h e organisms

Diayostelium discoideum is the cellular slime mold most commonly studied in the laboratory. The amoebae feed as separate individuals, aggregate into a central collection point, and form a multicellular migrating slug that crawls about for varying periods of time. In the slug there are early signs of differentiation where the anterior prestalk cells are separated by a sharp boundary from the posterior prespore cells. When the slug rights itself and 'fruits', or 'culminates', each prespore cell turns into a spore, and the prestalk cells are responsible for lifting the spore mass into the air. As they do so, they progressively turn into large, vacuolate stalk cells (Figure 1). Polysphondylium pallidum is a related cellular slime mold with some very interesting differences in its development. It does not, strictly speaking, have a migrating stage, for the stalk begins to form right at the end of aggregation. Nor does it have a prestalk zone as in Dictyosteliura; instead the whole rising cell mass, or 'sorogen', appears to consist of relatively undifferentiated cells, some of which become committed to the stalk pathway just before they begin to participate in stalk formation. As the sorogen rises, groups of cells are intermittently left behind on the stalk, and each such group then breaks up radially to form a whorl of small fruiting bodies (Figure 1).

The three developmental processes to be examined Polari~

From theDepartment ofEcologyand Evolution and*Department of Molecular Biology, Princeton University, Princeton, N'J 08544, USA 9 AcademicPressLid 1044-5781/95/050359 +10512.00/0

359

It has long been appreciated that one of the first signs of development in any organism is the establishment of polarity: a directional state that is the forerunner of subsequent differentiation. It has also been understood for many years that the basis of polarity is seldom simple, but can be the result of a variety of

j. T. Bonnet and E. C. Cox

Oicfyosfelium discoideum

Polysphondyliumpallidum

Figure 1. Drawings of Dictyosteliurarand Polysphondylium. Note that the stalk cells and the spores are similar in both, and that D. discoideum has a basal disc. (Drawing by Harry William.) different physical and chemical interactions. As we shall see, in the dictyostelids there is already a considerable amount known about the establishment of polarity, all of which provides an important foundation for understanding the differentiation that follows.

control is exerted. The first level of control is aggregation: the n u m b e r of amoebae that enter an aggregate sets an upper limit on the size of the resulting fruiting body. However, aggregates of very large size do not produce giant fruiting bodies; rather, they break up into masses of more normal size, which constitutes the second level of size control. T h e n in Polysphondylium, cell masses released from the base of the sorogen are subdivided into branches o f highly controlled size. In many ways, this third level o f size control in Polysphondylium parallels the second, except that it exhibits a precision and symmetry that is unrivaled.

S/ze In both genera, the size of the multicellular mass that will become a fruiting body is regulated at two levels initially; then in Polysphondylium a third level of size 360

Pattern formation in diayostelids Pmp~

U-turn rather than back up. 9 [It is'worthy of note that these observations are consistent with the ancient (and often maligned) ideas of C.M. Child on the importance of metabolic gradients in development. Indeed, Child 1~ illustrated some of his ideas by appeal to the regularity of whorl spacing in P pallidura.]

From the first observations of Raper 2 we know that for D. discoideum the proportion of stalk cells to spores is roughly constant, regardless of the overall size of the cell mass. Although the early stages of differentiation seem to be quite different in Polysphondylium, it also exerts close control over the final stalk-to-spore ratio, a

S/ze The size of the aggregation territory is controlled, n'12 It has been shown that for Diclyostelium one external factor that affects this size is the concentration of gaseous ammonia, lsA4 Since each center concentrates cells, it becomes a rising source of NH 3 that may serve to space aggregates roughly equidistant from one another. It is also likely that the cAMP pacemakers in adjacent centers compete for the amoebae between them, and that this is a n o t h e r factor influencing size. However, these mechanisms are relatively crude, and there is considerable variability in the size of the aggregating masses in any culture dish. If the carpet of amoebae in a dish is thick, then often a large aggregation center will form, but later break up into smaller masses of roughly equal size. This second level of size control is quite different from the first, because (among other things) it occurs in a contiguous mass of amoebae. In an interesting study in which he compacted amoebae in different size holes in agar, Kopachik 15 was able to show that each tip gives off a substance that inhibits surrounding cells from producing another tip, and that the size of the resulting bodies is a combination of the strength of this inhibitor and the degree to which the surrounding amoebae are susceptible to its influence. He also did experiments in which he examined the ability of this inhibitor to cross various barriers, and showed that it must be a small molecule; perhaps he was dealing with competition between cAMP pacemakers. Polysphondylium differs from Dictyostelium in a number of respects. In the first place, as Shaffer showed long ago, 4 the focal point for aggregation is a single cell, the 'founder cell', that inhibits other cells from becoming founders during early aggregation. He showed that if he killed a f o u n d e r cell, a n u m b e r of nearby cells became founders. A second difference is that the chemoattractant of Polysphondylium is not cAMP, but a dipeptide called 'glorin '16 (although it is clear that at the multicellular stage glorin wanes, a n d cAMP takes over as the internal chemoattractant17). The most distinctive feature of Polysphondylium, however, is its ability to give offwhorls of branches. As

A summary o f what w e k n o w about the three processes

Po~r/~ The polarity of the cell mass appears to be closely connected with chemotaxis. In Dictyostelium, aggregation is initiated by a group of cells that emit pulses of the chemoattractant cAMP, and the initial pulse stimulates surrounding cells to move towards the source and, in their turn, secrete cAME By such a relay method, amoebae move into the central collection points from considerable distances. 4'5 In aggregating streams, the amoebae are elongate and exhibit strict morphological polarity, and this polarity is retained within the slug, even when cells become compressed antero-posteriorly, as they do in the front end of the-slug. 4 There is clear evidence that the cAMP relay continues to operate in the slug, 6 supporting the idea that the overall polarity of a slug is due to the collective polarities of its individual cells, which are in turn controlled by the chemotactic relay system. Oxygen influences the pacemaker-relay system, and hence polarity. There appears to be a metabolic gradient of oxygen that controls the orientation of the chemotaxis field, 7 such that if the top of a slug is shielded from the inward diffusion of oxygen, overall polarity can be modified or reversed. This is best illustrated in some elegant experiments ofYamamoto s in which he persuaded vitally stained slugs to enter agar tunnels. W h e n a slug reached a dead end in the t u n n e l - - the region with least access to oxygen m the slug reversed and came back out. But because cells were vitally stained, he could see that this reversal was the result of the anterior, rapidly moving prestalk cells turning a r o u n d and percolating through the posterior prespore cells to once again take up the lead position during the retreat. Similarly, it has long been known that aggregating cells suddenly subjected to a reversed gradient of chemoattractant will make a 361

J. T. Bonner and E. C. Cox

of basic mechanisms are involved in p r o p o r t i o n regulation. It has been known since the early work of Raper 2 that it is possible for prestalk cells to convert to prespore cells and vice versa. T h e position o f a cell in the slug will strongly influence its ultimate fate: anterior cells tend to b e c o m e stalk cells, whereas m o r e posterior ones b e c o m e spores (except for those at the very back o f a slug, which make up a basal disc c o m p o s e d o f stalk-like cells). In o t h e r words, the e n v i r o n m e n t o f the front e n d of the slug encourages cells to turn into prestalk (and later stalk) cells, while the posterior e n v i r o n m e n t favors formation o f prespore cells that turn into spores. This raises the question o f what distinguishes these two regions biochemically, such that cells are not only guided into two different pathways, but that the proportions between the two cell types are essentially i n d e p e n d e n t o f the size of the cell mass. We are far from the final solution to this problem, but we know that there are at least four substances (and probably others) that influence cell fate: a lipophilic m o r p h o gen called DIF ('differentiation inducing factor') is particularly i m p o r t a n t in inducing stalk cell differentiation; N H 3 (possibly t h r o u g h its effect on intracellular pH) seems to influence differentiation in the spore direction; cAMP can influence the formation o f both spores and stalk cells; and adenosine may in some way be involved in the action o f cAMP. 2~ In addition, it has b e e n shown by Sternfeld 21 that oxygen affects the proportions o f the prestalk and prespore zones. T h e second set o f mechanisms that contribute to the regulation o f proportions has to do with the fact that a m o e b a e at the threshold o f aggregation are not identical: some have certain prespore characteristics, while others have those o f prestalk cells. 22 These preaggregation differences are not fixed, but are best described as tendencies towards one of the two fates. T h e first clue to the source o f these differences came from the work o f Leach et al, 2s who mixed cells that had b e e n fed differently. T h e well-fed cells moved to the prespore zone, while the cells fed a minimal diet moved to the anterior, prestalk zone. T h e next major advance came from work o f McDonald and Durston 24 who showed that the point in the cell cycle at which a m o e b a e e n t e r e d the p e r i o d o f preaggregation st,amd o n was correlated with the ultimate fate. Perhaps because different m e t h o d s have b e e n used to synchronize cell populadons, there is some disagreement a b o u t just when d u r i n g the cell cycle prestalk and prespore tendencies are established, 2s-2s although

the sorogen culminates, it releases basal masses of cells that are spherically symmetric, clumped about the central stalk. Within 10 minutes or so, radially oriented tips form at the equator o f a whorl. These tips act as organizing centers that attract cells from the rest of the whorl mass, soon p r o d u c i n g a radial array o f secondary sorogens, which then go on to culminate, eventually forming tiny secondary fruiting bodies. T h e precision with which the tips form a r o u n d the equator o f a recently f o r m e d whorl is impressive, as is the spacing between them (Figure 1). T h e n u m b e r o f secondary fruiting bodies that form on a whorl is not fixed, but can vary from one to a dozen or so. This variation arises because the n u m b e r of cells released periodically at the base of the sorogen varies quite w i d e l y - - f o r reasons that are not u n d e r s t o o d - - a n d , as McNally ~s was able to show, it is the surface area o f a whorl that determines the n u m b e r o f secondary fruiting bodies that it will form. This relationship is the key to the patterning process, as we describe later. T h e reason that cell masses separate from the base o f the ascending sorogen at all is not understood. It is clear, however, that branching is normally suppressed everywhere on the surface o f the primary sorogen, probably because the primary sorogen tip is the source of an inhibitor which suppresses secondary tip formation. Evidence for this model comes from experiments of Byme et a/, 19 who showed that extremely large sorogens divide along their length to form large basal portions that rapidly break up into a forest o f poorly organized secondary branches, whereas the r e m a i n d e r of the primary sorogen - - now r e d u c e d to a length and diameter m o r e characteristic of the s t r a i n - - g o e s on to subdivide and f r u i t m o r e normally. These results, apart from d o c u m e n t i n g that size is also regulated within the sorogen o f P. paUidum, suggest that the primary sorogen tip exhibits apical dominance, an idea consistent with the observation that secondary fruiting bodies form over the entire surface o f a primary sorogen if its tip is removed with a hair loop. 19

Proport/om Because there has b e e n considerable interest in how the prespore-prestalk ratio is maintained, there have b e e n several reviews o f the topic, of which the o n e by Nanjundiah and Saran 2~ is especially r e c o m m e n d e d . H e r e we will briefly summarize evidence that two sets 362

Pattern formation in dictyostelids Arald et al make a persuasive case that both are determined during G2, with prestalk determination preceding prestalk. 25 Even though differences in cell cycle status influence the tendencies of cells to become prestalk or prespore, it has been known for some time that Dictyostelium need not progress through the cell cycle for the prestalk-prespore ratio to be correctly determined. It has frequendy been observed that spores of D. discoideum can germinate in the absence of food, reaggregate, and form correcdy proportioned fruiting bodies in the absence of cell division. An even more striking example of proportioning in the absence of division comes from experiments with a variety of D. mucoroides (var. stoloniferum) in which spores have been carried through the entire life cycle for seven generations in the absence of food. 29 Even though there is considerable decrease in spore size during this extensive fast, slugs and fruiting bodies continue to form, strongly suggesting that the prestalk-prespore ratio can be regulated wholly independently of position in the cell cycle. An important advance in the study of proportioning and morphogenesis in Dictyostelium has come from the use of reporter genes to examine temporal and

spatial regulation of the genes encoding two extracellular matrix proteins (EcmA and EcmB) that are markers of prestalk and stalk cell differentiation (reviewed by Williams and Morrisona~ A much deeper insight into the anatomy of differentiation developed when Williams and his co-workers used this technique to show that the prestalk region is not uniform, but is made up of three sub-regions that express these two genes differently, and that appear to play distinctive roles in stalk differentiation. The upstream regulatory regions governing spatial and temporal expression of these genes have been analysed in a beautiful series of papers by this group (reviewed in ref 30). They have shown, for example, that a 1.6-kb region upstream of the ecmB gene contains binding sites for both positive and negative regulators of transcription, and that the temporal and spatial expression pattern of this gene (which, among other things, is expressed just as cells undergo the prestalk-to-stalk cell transition; Figure 2, left) is controlled by a complex interplay of cAMP and DIE which act by modulating the affinities of these regulators for their upstream binding sites. Although our understanding of stalk cell differentiation in other dictyostelids is far more primitive, a

Upper cup Stalk tube Lower cup Basal disc

Figure 2. Left: a culminating D. discoideum fruiting body showing the expression pattern of an extracellular matrix protein, EcmB. Redrawn from ref 35. Right: the expression of ~galactosidase in apex-proximal cells of P. pallidum (C. Vocke, unpublished). These sorogens had been stably transformed with a D. discoideum vector carrying the ecmBpromoter fused to the ~-galactosidase gene from E. coli. The stained cells reveal a region where expression is analogous to EcmB expression in D. discoideum. 363

j. T. Bonner and E. C. Cox

variety of observations suggest that at least some of these regulatory molecules are conserved. For example, when P pallidum was transformed with a construct in which the promoter region of the D. discoideum ecmB gene had been fused to a [$-galactosidase reporter gene, it expressed the reporter gene in a very limited region (Figure 2, right). Indeed, additional studies have demonstrated that a P pallidum strain transformed with such a fusion vector expresses [3-galactosidase in stalk and pre-stalk c e l l s - - o f both the primary and secondary sorogens - - in a pattern very similar to ecmB expression in Dictyostelium discoideum, ss These results suggest that P pallidum possesses regulatory factors similar to those governing ecmB expression in D. discoideum. A similar conclusion can now be extended to D. minutim (which is thought to be a primitive dictyostelid because it neither establishes an oscillating cAMP system during aggregation nor forms a migrating slug), since van Es et al have recently isolated a D. minutim homologue of ecmB that is responsive to DIE s~ It seems likely, then, that stalk cell differentiation in the dictyostelids is universally u n d e r the control of upstream response elements sensitive to cAMP and DIF or DIF-like molecules, sl It is also known now that the prespore region, like the prestalk region, is not uniform in D. discoideum. Sternfeld and David 34 showed that cells with staining properties like those of prestalk cells are scattered through the prespore region. They called these 'anterior-like' cells, and found that normally they are u n d e r constraint and do not move significantly as a group; but should the anterior prestalk region be removed by amputation, the anterior-like cells rush forward to form a new prestalk region. By using various [$-galactosidase fusions of the kind described above, anterior-like cells have been marked, and Sternfield and David's earlier observation~ that these cells move forward and backward to form cups on both ends of the prespore-spore zone during culmination have been confirmed, s~ These results also show that the n u m b e r of anterior-like cells is regulated: amputated slugs increase their numbers, and migrating slugs continuously replenish them when forced to migrate for extended periods of real time. Studies by Vocke s6 with reporter constructs in P pallidum have revealed an unexpected aspect of cell fate that has yet to be incorporated into our understanding of cell determination and morphogenesis in other dictyostelids. She showed with a [?Hgalactosidase construct that cells committed to become apical or basal cells in the sorogen are committed very early to this fate. As soon as amoebae begin to starve, a 364

fraction of them will sort to specific locations in the early mound. Thereafter, they maintain their positions with great fidelity, so that even spores in a mature primary or secondary sorogen retain the apical-basal positions first established early in aggregation. These observations argue that cell surface adhesive molecules expressed very early on are maintained and used for sorting t h r o u g h o u t morphogenesis. What these putative molecules may be is unknown, although many possible candidates in the dictyostelids are known. Whether a similar system is active in D. discoideum is not known, since these very early cell-sorting events have not been studied by Vocke's method. The fate of the majority of the anterior and posterior cells during culmination needs to be studied with lineage specific markers in real time, something now possible with cells tagged with the green fluorescent protein (GFP) isolated from the jelly fish Aequorea victoria. 37 We have f o u n d that it is possible to follow living cells over many hours during developm e n t in P pallidum and D. discoideum with GFP fused to a variety of different promoters (Figure 3). With further tinkering, we can look forward to engineered variants of GFP with different half-lives, and even different emission ss and adsorption maxima, so that two- and three-color experiments over the entire lifecycle will become possible. This will profoundly influence our understanding of morphogenesis in the Dictyostelids and will allow us ultimately to model the formation of radial branches in the P. pallidum whorl, and to follow most if not all of the cells in a migrating slug. Even though GFP has been available for only a short time, it has already allowed us to establish that cells within a whorl begin their transition toward ordered m o v e m e n t into secondary whorls by moving randomly. In migrating slugs, there is a great deal of ordered cell movement, at least a m o n g the cells near the surface. 39 How results of this kind might turn into a greater understanding of development will be discussed in the next section.

How future progress might involve a combination of different approaches A satisfactory description of any physical system is an abstraction. To be satisfying, it must be both more and less than the sum of the experimental observation: more, because it should reveal truths about the real world that are not evident from the data alone; less,

Pattern formation in dictyostelids because it must be powerful enough to subsume much of the experimental detail. To ask this much of any science is asking a lot. Many simple physical systems resist description at the level we are talking about, and a developing organism of any size is much more complex than all but a few physical systems. Nonetheless, there have been striking insights into slime mold morphogenesis, in the sense that we mean, particularly in the modeling of aggregation, the earliest signs of polarity in these organisms.

Shaffer4 pointed out that the beauty of aggregation is that it is development in two dimensions, rather than the usual three. As a result it has been possible to visualize and analyse it effectively (Figure 4). Because cAMP is central to signaling and gene regulation, it is not surprising that there is a very large body of excellent biochemistry and cell biology in this area, and it can be analysed in the context of equally good descriptive data on cell motion, cell-cell contact, and signal relay, all of which now can be easily recorded in real time. The essential features of aggregation have been realistically modeled by Martiel and Goldbeter. 4~They incorporated known rate constants for cAMP synthesis, excretion, degradation, and binding-site occupancy into a 'stirred reactor' model which, when perturbed, oscillates with respect to cAMP concentration. By adding a spatial component in the form of diffusion to this basic model, Tyson and co-workers41 found that the emergence of spiral and target patterns in the aggregating field (Figure 4) could also be understood, although it is not yet clear why some kinds of spatial patterns dominate others. Nonetheless, the work we have just described comes close to satisfying our criteria for successful modeling because it generalizes from the experimental facts, shows that one aspect of aggregation, signal propagation, is an example of the very widely studied phenomenon of

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Figure $. Negative images of green fluorescent protein expression in living specimens of P. paUidum (left) and D. discoidtum (right). Strains were transformed with standard vectors carrying GFP regulated by the aain-6 (a.-c.) or ecmB (d.) promoters. The P. pallidum images were gathered by confocal microscopy of sorogens containing approximately 1% GFP expressing cells. Panels a~, b. and c. are from the same sorogen and illustrate the morphology of the sorogen just before (a.), during (b.) and after (c.) the release of a whorl. Scale bar = 50 lun. (P. Fey,K. Compton and E.C. Cox, unpublished.) 365

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lr~mre 4. An aggregating field of D. discoidtum illustrating the distinctive waves of cell shape change accompanying cyclic AMP signaling. Scale bar= 5 mm. (I~ Lee, unpublished.)

f T. Bonner and E. C. Cox wave propagation in an excitable medium, and suggests fruitful areas for further research. It holds the promise of greater progress, once cell-cell interactions are incorporated into the overall scheme. This last step, since it involves the incorporation of changes in cell shape, cell-cell signaling, and the regulation of cell-cell adhesion, may be some way off. Nonetheless, the relative simplicity of the system, and the richness of the molecular, cellular and biochemical data, augers well for future progress. The question of polarity in the migrating slug, and its consequences for the differentiation that follows, is less well resolved, but of great interest. We know that the tip continues to be the pacemaker for cAMP relay, and that those cells that have prestalk tendencies will move more rapidly and go to the anterior end, while those that are to become prespore cells will lag behind. Furthermore, at this stage of development, these properties are intrinsic to the cells, for if some cells are removed from one region and plugged into a n o t h e r they will return to their original positions. 42 To put the matter another way, slug polarity is the result of chemotaxis and signal relay, and the response of the individual amoebae within the slug to cAMP gradients. It is known that prestalk amoebae have more surface cAMP receptors than prespore cells, which would account for the differences in their response to the chemotactic stimulus. 4s Furthermore, it is known that anterior cells are more adhesive than posterior ones, opening the further possibility that the antero-posterior sorting out could involve differential a d h e s i o n : 4 Finally, anterior cells move more rapidly towards a cAMP pulse, and provide the main engine for forward movement of the slug. 45'~ As we have noted, the ratio of prestalk to prespore cells is relatively constant in a D. discoideum slug, despite the fact that the n u m b e r of cells ~n the slug can range over more than two orders of magnitude. Simple-minded ideas about diffusion-controlled gradients whose source is at the tip of the slug cannot account for these data, since the diffusion range of a m o r p h o g e n such as cAMP produces a fixed concentration profile if the concentration at the source is constant, and this should lead to a constant n u m b e r of prestalk cells. And yet slugs vary in length by at least an order of magnitude. One way out of this problem is to model the prespore-prestalk boundary by a reaction-diffusion system in which two morphogens are made everywhere. One of them is an activator whose concentration is higher at the slug tip, the second is an inhibitor whose synthesis also depends on activator concentration, and whose concentration

is also higher at the tip. With a suitable choice of p a r a m e t e r s - - r a t e constants, nonlinearities, and diffusion coefficients4 7 - a very plausible reaction-diffusion system which will both maintain tip dominance and produce a proportion regulating gradient can be designed. 4s What these morphogens might be is conjectural. Three obvious candidates are cAMP, NHs and DIE The question of polarity in Polysphondylium has some extra features of particular interest connected with the formation of whorls of branches. As the sorogen rises and pinches off a cell mass that will form a whorl, the cells at the base of the sorogen appear to lose their orientation toward the tip. It is as though the cells at the rear e n d of the sorogen suddenly lost their ability to respond to the dominance of the tip, a p h e n o m e n o n well illustrated in the tip excision experiments m e n t i o n e d above. Just as the whorl mass is released, a remarkable series of changes in cell movement and gene expression begins, leading to the establishment of a prepattern whose ultimate function is the specification of radially oriented tips about the equator of the whorl. 49 The very first step is the synthesis of prestalk antigens over the entire surface of the nascent whorl. The next step in developing a prepattern is the restriction of further synthesis to a band a r o u n d the equator. Next, this band breaks up into randomly ordered patches. Eventually, some of these p a t c h e s - - t h o s e that are radially o r d e r e d - win out to become organizing centers for secondary tips, presumably recapitulating some of the early events in aggregation. All of this occurs before visible tips can be seen. The two interesting features of this process, apart from the striking change in symmetry of the nascent whorl, is that a true pre-pattern is established by a series of restrictions from a global to a radial distribution of patterning elements, and that the main events occur on the surface of the nascent whorl. Thus the a r r a n g e m e n t of the fruiting bodies in the whorl begins in two dimensions, the surface, but is quickly reduced to one dimension, the equator. This restriction from a higher to a lower dimension during the establishment of a prepattern is one way in which a pattern can be made robust and reproducible, as pointed out by Harrison. s~ Clearly, for new tips to form at the sites of the radial prepatteru, cells must move. A qualitative model for how this might h a p p e n assumes that cells first stop moving towards the apex of the sorogen, then begin to move randomly, finally heading towards the centers of the radial prepattern. By using GFP-tagged cells 366

Pattern formation in dictyostelids Proport/ons

(Figure 3) and time lapse confocal microscopy, we have now been able to show that this is likely to be the case. 39

S/ze The problem of size can be approached in exactly the same manner as polarity. Ideally one must identify the morphogens responsible for regulating size, and hopefully get at their genetic foundations. At the same time, it is equally important to see how the morphogens respond to the environment, affect one another, and affect cellular processes so that size can be delimited. The identification of the morphogens involved in size regulation is still at a rather rudimentary state. As we indicated earlier, NH a, DIF, and cAMP clearly play a role. It is difficult to understand the developmental genetic regulation of small molecules like NH a. There are undoubtedly numerous biochemical cascades that could lead to the production of N H s - - t h e real question is whether there is some enzyme that ultimately controls deamination and release of NH3 in a way that is connected with territory size. By contrast, cAMP production and elimination is quite well understood. The adenyl cyclases which produce, and the phosphodiesterases which degrade, cAMP have been identified, and much is known about the genes that produce these enzymes at the appropriate time in development. 51 Yet this knowledge has not yet led to an understanding of how cAMP and the relay system might affect size. Size control in Polysphondylium is an interesting combination of regulated and stochastic events. The number of branches in a whorl is highly variable, ranging from one to at least a dozen, a Why whorls contain a 10-fold variation in total cell number is a mystery. The variability of spacing between fruiting bodies in a whorl, however, can be plausibly explained and has been modeled by a reaction diffusion mechanism.49,52, 5s It has been known for some time that cAMP and cGMP are synthesized in the culminating Polysphondylium sorogen 54 and, as discussed above, DIF (or DIFlike molecules) are also synthesized in Polysphondylium~ species. P pallidum also regulates DIF responsive upstream sequences derived from D. discoideum in a spatially specific way. These molecules and NHs are therefore logical candidates for the morphogens likely to be involved.

We have just discussed the usefulness of reactiondiffusion models for Dictyostelium spore-stalk proportions, and how this might involve morphogens such as DIF, cAMP, adenosine, NH s (plus compounds associated with the first two) affecting proportions. But then there is the interesting difference in Polysphondylium where there are no proportioned prestalk and prespore zones initially, yet the end result is an equally precise ratio of spores to stalk cells, even in each small branch. 3'55 So even though similar morphogens appear to be functioning in the two species, they must be exerting their influences in different ways. How will we achieve an ultimate explanation of how such morphogens establish a balance between spore and stalk cells? Obviously, various workers will continue to analyse the activities of the known morphogens; this is already a complex story, but may become more so, and more morphogens may be identified, as the matter is probed further. At the same time we can expect increasingly realistic mathematical modeling to keep pace with biochemical advances. Eventually, as we have noted, such models will have to encompass cell locomotion and polar movement as well as cell adhesion, and perhaps other physical properties of the amoebae. Already we can see that the control of proportions is the result of a complex of factors, and sorting it all out in the dictyostelids will be a difficult task, but one that will undoubtedly be of importance for developmental biology, because solutions found here will certainly have application to the problems of pattern formation in other organisms.

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Acknowledgements

Our work has been supported in part by the National Science Foundation.

References

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