Formation of pattern in regenerating tissue pieces of Hydra attenuata

DEVELOPMENTAL

Formation

78, 484-496

BIOLOGY

(1980)

of Pattern in Regenerating I. Head-Body PATRICIA MACAULEY

Department of Developmental

Tissue Pieces of Hydra Menu&a

Proportion

Regulation

BODE AND HANS R. BODE

and Cell Biology and the Developmental Biology Center, University of California at Irvine, Irvine, California 92717

Received November I, 1979; accepted in revised form January 21, 1980 The precision with which an almost uniform sheet of hydra cells develops into a complete animal was measured quantitatively. Pieces of tissue of varying dimensions were cut from the body column of an adult hydra and allowed to regenerate. The regenerated animals were assayed for number of heads (hypostomes plus tentacle rings), head attempts (body tentacles), and basal discs. To ascertain whether the head and body were reformed in normal proportions, the average number of epithelial cells in the heads and bodies was measured. Pieces of tissue, from l/2 to l/20 an adult in size, formed heads that were a constant fraction of the regenerate. Thus, over a IO-fold size range, a proportioning mechanism was operating to divide the tissue into head area and body area quite precisely, but appeared to reach limits at the extremes of the range. However, the regenerates were not all normal miniatures with one hypostome and one basal disc. As the widthlength ratio of the cut piece was increased beyond the circumference-length ratio of the intact body column, the incidence of extra hypostomes in the “head” and body tentacles and extra basal discs in the “body” rose dramatically. A proportioning mechanism based on the Gierer-Meinhardt model for pattern formation is presented to explain the results. INTRODUCTION

However, the accuracy with which such patterns are reproduced has seldom been demonstrated quantitatively. This knowledge is of considerable importance in understanding how patterns are generated. To this end we have quantified the regeneration of hydra tissue pieces. It was found that the head-body proportions of regenerated animals were maintained as the size of the tissue varied from l/2 to l/ 20 of an adult. Deviations in the final pattern occurred at the extremes of the size range where the head proportion changed and in certain-shaped pieces where extra structures developed. The results indicate a simple mode of area-to-area proportion regulation, for which a possible proportioning mechanism is presented.

A variety. of early embryos and a few primitive adult organisms have the ability to regulate morphallactically. Tissue may be removed or added and the resultant cell mass will undergo normal or almost normal development to form a complete organism. The individual cells apparently change their fates in a coordinated fashion to reestablish the correct pattern. For example, normal-appearing pluteus larvae form from the separated blastomeres of the two- and four-celled stages of the sea urchin embryo, as well as from two fused fertilized eggs (Horstadius, 1939). Similarly, various-sized tissue fragments cut from the body column of a hydra regenerate into entire animals (Peebles, 1897). When the surgically altered tissue is repatterned, the new pattern adjusts to fit the tissue available. The final organism, although altered in size, is assumed to have all its parts, and these in proper proportion.

MATERIALS

METHODS

Culture of Animals Hydra

distilled 484

0012-16os/80/1004~-13$02.00/O Copyright 0 1980 by Academic Press, Inc. AU rights of reproduction in any form reserved.

AND

attenuata stock was cultured in water containing 1.25 x lo-” M

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Na*EDTA, low3 M Ca&, 10e4 M MgCL, 10e4 M KCl, and 10F3 M NaHC03 or in deionized water containing lo-” M CaC12, 1O-4 M MgC12, 10e4 M KCl, and 1.25 X 10e4 M NaHC03 (at the European Molecular Biology Laboratory, Heidelberg, West Germany, where a portion of the experiments was carried out). The animals were maintained at 19 + 2°C with a 12-hr alternating dark-light cycle. They were fed daily sufficient Artemia nauplii for continuous asexual reproduction by budding (doubling time, 4 days). The medium was changed 68 hr after each feeding. Preparation

of Tissue Pieces

For most experiments adult hydra with two or more buds were used. When the piece of tissue under investigation included the region adjacent to the budding zone, animals with buds in their earliest stages were chosen. These buds served to demarcate the boundary between gastric region and budding zone and, in addition, decreased the possibility of presumptive buds which tend to interfere with regeneration. When a piece of tissue from the budding zone was desired, the corresponding region above the peduncle in nonbudding adults was used. For experiments involving tissue from the peduncle, very heavily budding animals were used because their peduncles tend to be proportionally larger. A few experiments were carried out using young hydra before the onset of budding. These animals were a little more than half the size of the adults used. Pieces of tissue of a specific size and shape were excised with a microscalpel. The number of samples per experiment of any one type ranged from 20 to 60, with an average of 35. The excised pieces were placed in fresh medium and incubated for 7 days under the same conditions as the stock culture. They were washed the day following excision and once more during the course of the experiment. The regenerated animals were not fed.

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Nomenclature

for Excised

Pieces of Tissue

To identify the different types of pieces and thereby give an indication of their size, shape, and original location on the body column, the following notation was used. Horizontal cuts were made at the boundaries between regions as shown in Fig. 1. Thus, the cut piece might include a single region (e.g., 1 or 3), two regions (12 or 34), the entire gastric region (1234), or the whole body column (1234b56). In one case a 3region was cut in half horizontally and is designated 1. Such pieces were left as rings or cylinders in some experiments, and in others were cut open to form rectangular sheets. Other pieces were reduced further in size by vertical cuts, the extent of the reduction given by the number after the slash. For example, 1234/2 indicates a gastric region cut in half and 2/8 is a 2-region cut in eighths. Further examples are presented in Fig. 2. Determination of Size and Width-Length Ratios of Excised Tissue Pieces The number of epithelial cells was used as an indication of tissue size. Whole hydra with buds removed, and some of the initial

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FIG. 1. Scale drawing of the body column of an adult hydra. The body column has been sliced open vertically and is displayed as a sheet. The regions are numbered as described by Wolpert (1969).

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cut pieces from various parts of the body column, were macerated according to the procedure of David (1973). The epithelial cells were then counted in a Neubauer cell counting chamber using phase microscopy. The average cell number per region, together with an estimate of the fraction of the axial length taken up by each region, yielded the approximate scale drawing of the body column sliced open longitudinally shown in Fig. 1. From this the relative dimensions for each type of piece were obtained, and the approximate width-length ratio was calculated. “Width” and “length” were defined operationally as follows. All excised pieces were treated as rectangles and their sides identified according to the regeneration polarity. (See reviews by Webster (1971) and Gierer (1977).) The length of a piece was the dimension originally parallel to the long (polar) axis of the body column in the donor hydra, regardless of whether or not it was the longest dimension in the tissue fragment (see Fig. 2). The width, then, was the dimension perpendicular to it, the edges of which would develop either head structures if originally closer to the head or basal discs if closer to the foot. Analysis

of Regenerated

Structures

After 7 days the regenerated animals were examined under a dissecting microscope for the type of structures formed. The numbers of heads, tentacles per head, body tentacles (not associated with a head), and basal discs were recorded for each regenerate. (Examples of each are shown in Fig. 3.) In experiments in which the fraction of the regenerate forming the head was to be measured, the heads were cut from the bodies of all single-headed regenerates on the seventh or eighth day. The number of samples varied from 5 to 50, depending on the size and/or the number available, with an average of 25. In a few cases doubleheaded regenerates were measured (10-20, with an average of 15). “Head” was the

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clt CZII FIG. 2. Examples of tissue pieces excised from the body column. Using the notation described in Materials and Methods, they are (a) 12/4, (b) 1234b56/8, (c) 4/2, and (d) b. The arrow indicates the apical end where the head will regenerate in the body column or excised piece.

hypostome(s) plus tentacle ring(s), and “body” was the body column including body tentacles (if present) and basal disc(s). Any buds still remaining were excluded. The heads and bodies were macerated and the epithelial cells (including the battery cells of the tentacles) were counted as described previously. RESULTS

The Regeneration

Process

Pieces of tissue of varying dimensions were cut from the body column of hydra. During the first stage of regeneration the largest excised pieces, whole, half, and quarter body columns, simply joined cut surfaces to form closed cylinders. Smaller tissue fragments presented a more complicated situation and will be described in some detail. Almost immediately the pieces began to round up, as if to leave as little surface area exposed as possible. Rectangles rolled in at the long ends. Very thin strips taken from the long axis of the body column formed spirals. Rings came together at top and bottom with the closed edges perpendicular to one another. Early development of the small pieces of tissue was similar to that of aggregates of cells (Gierer et al., 1972). Within hours they were solid balls with the surface cells smoothly

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FIG. 3. Animals regenerated from narrow rectangular pieces of tissue. (a) Adult control hydra starved for a period equivalent to the regeneration time, for comparison. (b) 1234/4 piece: long dimension parallel to axis of polarity. The regenerate is normal. (c-f) S-region piece: long dimension perpendicular to axis of polarity. The regenerate (c) is normal, (d) has an extra head, (e) has a body tentacle, and (f) has an extra basal disc. Notation is described in Materials and Methods. x 10.

joined together. A day later they appeared hollow, as if composed of the double-layered epithelium typical of hydra. Elongation of spheres or short cylinders occurred gradually as the regenerates approached their final shape. A whorl of tentacles pushed out at the head end, with the conical hypostome or mouth forming in the center. At about the same time a disc of cells differentiated at the base, producing the sticky material which functions as a holdfast. In regenerates with additional

structures the basic cylindrical shape was often distorted to a greater or lesser degree as extra heads and sometimes body tentacles or extra basal discs drew out adjacent tissue into secondary axes. Number

of Structures

Regenerated

The majority of regenerates developed at least one head and one basal disc. A very few (1%) failed to develop heads due to small size, inhibition from buds, or partial to complete differentiation into basal disc

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DEVELOPMENTALBIOLOGY

cells. The latter occurred occasionally in upper peduncle pieces and frequently in lower peduncle pieces. The absence of basal disc formation was more frequent and variable, with an overall failure rate of 13% and a range of O-40%. Many types of pieces, regardless of origin in the body column, would show considerable differences in number of regenerates without discs from one experiment to the next. It has been noted previously that hydra sometimes form extra structures during regeneration, which was attributed to the small size of the piece (Weimer, 1928). However, in this series of experiments it became apparent that the number of heads, body tentacles, and basal discs regenerated depended strongly on the shape of the cut piece and its original orientation in the body column. In earlier work the fact that a reduction in size almost always involved a change in shape was not considered. The critical factor in shape changes was found to be the proportion of “width,” i.e., edges which have the potential to form head or basal disc in a polarized piece of tissue. The width-length ratio of cut pieces is used here as a convenient measure of this. (See Materials and Methods.) The body column with just the head and basal disc removed regenerates these missing structures to form a normal animal. The body column cut open lengthwise (1234b56) has a width-length ratio of -0.35 and is the data point labeled C in Fig. 4. Smaller pieces of tissue with roughly the same width-length ratios also regenerated normally most of the time (e.g., Fig. 4, G/2 (1234/2), 12/4, and 34/4). Normal miniatures (Fig. 3b) were also formed from pieces of tissue which were proportionally narrower than the opened body column, such as a and b in Fig. 2. Such pieces, whose width-length ratios ranged from 0.05 to 0.35, developed only occasional extra structures at what might be considered a mistake level (Fig. 4). In sharp contrast, pieces proportionally

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wider than the body column (e.g., Fig. 2, c and d), having a width-length ratio > 0.35, produced normal animals (such as Fig. 3c) at much lower frequencies. Instead, many regenerates had additional heads or basal discs, or more frequently body tentacles, or some combination of these (Figs. 3d, e, and f). The distribution of extra structures among the three types was: heads, 17 + 4%; body tentacles, 60 -+ 8%; and basal discs, 24 + 7%. In small pieces (less than l/10 an adult) there was a shift in distribution resulting in a smaller percentage of extra heads and a greater percentage of body tentacles. A shown in Fig. 4, the total number of extra structures increased logarithmically: an average of 0.85 extra structures per doubling of the width with respect to the length. The magnitude of the increase was quite variable, especially in experiments done at widely differing times, but a basic width-length dependence was always discernible. The width-length effect was considerably reduced in tissue derived from the peduncle. The 5-region regenerates formed extra structures only rarely, and the 6-region, when it did regenerate, formed none (Fig. 4, 5, 5/2, and 6). Constancy of Head Fraction in Regenerates If pieces of hydra tissue proportion reg ulate as they regenerate, one would expect the head to form a constant fraction of the whole. To test this, regenerates from pieces of tissue with a variety of initial sizes, shapes, and locations on the body column (except region 6) were assayed for the number of epithelial cells in the head (or heads) and body. The data are presented in Fig. 5, where the number of head epithelial cells is plotted against the number of body epithelial cells for each experiment. Although all the data can be fitted to a single straight line, the points at the extremes of the size range were analyzed separately. Their deviation was too consistent toward larger heads (smallest regenerates) and smaller

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FIG. 4. Number of extra structures formed in regenerates as a function of the width-length ratio of the excised piece. The symbols represent specific horizontal cuts as described in Materials and Methods. (‘I) C = entire body; (m) G = gastric region; (0) double region, e.g., 12; (A) single region, e.g., 3,5, or m (lower half of the 2-region plus upper half of the 3-region). The open symbols are rings of tissue; the closed symbols are rectangles. The numbers after the slash indicate the fraction of a region remaining after vertical cuts. Each point represents l-4 experiments, with an average of 2.5. The two lines were derived separately by linear regression analysis.

heads (largest regenerates) to be considered scatter. It was found that all regenerates over a lo-fold size range from 800 to 8000 total epithelial cells showed regulation of the head proportion. A linear regression analysis indicated that the points of this size range fit the solid line (r = 0.921, P < 0.091). Since the slope is essentially 1.0 (m = 0.94) and the data are plotted on a log-log scale, the head and body are in constant propor-

tion. The data are replotted in Fig. 6 as a histogram which emphasizes that the fraction of tissue forming a head was a constant, an average of 0.32. During the 7-day regeneration period, approximately one-third of the epithelial cells was lost, so that the size range of the initial pieces of tissue undergoing division into head and body was 1300-12,500 epithelial cells. Since the average adult hydra contained 27,000 epithelial cells, the smallest

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DEVELOPMENTAL

BIOLOGY

.4

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6 ceIIs/bo~y

(~10~)

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FIG. 5. Ratio of epithelial cells in head and body of regenerates. (X) Intact adult budding animals starved 7 days; (+) intact young nonbudding animals starved 7 days. The other symbols are described in the legend to Fig. 4. Closed symbols are for tissue pieces from adult budding hydra, while open symbols are for tissue pieces from young budless hydra. The symbols bissected by vertical lines indicate double-headed regenerates. Each point represents a single experiment. The solid and dashed lines are explained in the text.

pieces able to proportion regulate normally were equivalent to l/20 of an adult. Regulation of the head and body proportions was not restricted to regenerates that formed one head and one basal disc. Samples with two heads also fit the relationship (Fig. 5, symbols bisected by lines). Triple heads were too infrequent to measure. Many of the one-headed regenerates had body tentacles and/or extra basal discs in the body fraction. Thus it appears that head tissue and body tissue remain proportional even if divided into multiple structures. Head Fraction at the Upper End of the Size Range One group of samples had a smaller relative head size. These are the regenerates of the whole and half body columns from

adult budding hydra (1234b56 and 1234b56/ 2), as well as the control adults starved for a period equivalent to the regeneration time of 7-8 days. They are represented by the data points around the dotted line in Fig. 5, which was obtained by linear regression analysis (r = 0.969, P < 0.001). Again the head and body are in constant proportion because the slope is close to 1.0 (m = 1.05). However, for these large regenerates, the head represents 0.22 of the total epithelial cells instead of the 0.32 typical of the other regenerates described previously (Fig. 6, dotted line). This indicates that the body is proportionally larger in animals that are budding. This point is further emphasized by examining the proportions of young adult hydra that have not yet begun to bud. The head is the same size as the adult head, but

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FIG. 6. Fraction of regenerate forming the head. The data are the same as presented in Fig. 5. The solid and dashed bars represent data fit to the solid and dashed lines, respectively, in Fig. 5. The error bars represent the standard deviation.

the body is 40% smaller, giving a head fraction of 0.34. The data for these budless animals, represented by the + symbol in Fig. 5, and regenerates of pieces of such animals, represented by open symbols, fit very well with the other regenerates. Unlimited increase in size of head and body is prevented by budding, which begins when the young hydra reach a certain size. Further growth results in additional buds (Otto and Campbell, 1977), thereby enlarging the budding region and usually the peduncle or stalk area below it. Thus it is not unexpected that budding hydra have a proportionally smaller head since size increases are occurring preferentially in the lower portion of the body column. Lower Size Limits in Proportion Regulation and Regeneration Regenerates containing 800 epithelial cells (from tissue pieces l/20 of an adult) still showed proportion regulation. In smaller regenerates the head seemed to be composed of a fiied number of cells and consequently the head fraction increased

(Figs. 5 and 6). The smallest regenerates, in which cell number determinations of the head were no longer feasible, appeared to be mostly hypostome and basal disc. The data suggest that there may be a minimumsized head which can form, consisting of -150 epithelial cells. Further, this minimum head size can be related to the minimum-sized piece which undergoes regeneration. The smallest tissue fragments which can regenerate successfully, i.e., make a head and basal disc, contain about 500 cells when initially cut (Fig. 7). Pieces smaller than 400 cells show a sharp drop in their ability to regenerate; the majority of these pieces either disintegrates, forms into odd-shaped hollow vesicles, or differentiates into one or two tentacles. Two hundred to four hundred cells may be an approximate minimum size for regeneration. Since about one-third of the cells is lost during the regeneration period, the smallest complete regenerates might have 150-300 cells at the end. If J-50 cells is the minimum head size, the lower limit for regeneration may be the least amount of

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DEVELOPMENTALBIOLOGY

.2

4 Epithalial

6 cells

/initial

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FIG. 7. Percentage of small pieces regenerating both heads and basal discs. The symbols are the same as used in Fig. 4. Each point represents a single experiment.

tissue from which a complete form, head plus basal disc, can be fashioned. DISCUSSION

The final pattern of structures which forms in a morphallactically regulating organism is reputed to be proportionally correct. However, the evidence for this in multicellular organisms is mainly of a descriptive nature. Hydra, with its impressive ability to regenerate, is a very convenient system for exploring this problem. The tissue can be cut so as to provide a whole spectrum of size and shape changes to the morphogenetic field which must regulate. The animal which develops can then be subjected to quantitative analysis. Precision and Range of Proportion Regulation The approach in the experiments presented here was to cut pieces of a variety of initial sizes and shapes out of the body column and allow them to regenerate.

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Then, by measuring the relative size of the major differentiated structure, the head, it was possible to determine if the proportions of the head and the body were regulated during regeneration. The cell count data obtained clearly show that there is regulation of proportion and establish the limits within which it occurs. Pieces of tissue, ranging in size from 1300 to 12,500 epithelial cells, representing l/20 to l/2 of an adult hydra, respectively, regenerate a head which is a constant fraction, 0.32, of the whole animal. (Due to cell loss during the regeneration period, this corresponds to a size range of BOO-8000 epithelial cells in the regenerates.) The initial shape of the piece does not affect the proportion of the head. The pieces included rectangles whose width-length ratio varied from 0.05 to 4.0. The mode of proportion regulation is a simple one because it guarantees only that the total amount of tissue which becomes incorporated into the head be a fixed fraction of the whole, i.e., the process simply divides the tissue into head area and body area. The resulting regenerates are not necessarily normal miniatures with one hypostome and one basal disc. “Head” may include two or even three hypostomes plus tentacle rings. The “body” can have up to four basal discs and many body tentacles. The proportioning mechanism is precise, but not in the sense that a perfect animal is the inevitable result. Proportion regulation has been measured in one other system, the cellular slime mold, and some similarity to the process in hydra can be seen. (See review by MacWilliams and Bonner (1979).) It involves volume-tovolume proportioning over a comparable lo-fold size range; e.g., in Dictyostelium discoideum the stalk (analogous organizing area to head in hydra) was found to be an almost constant fraction in fruiting bodies ranging from 1000 to 10,000 cells. In very small and very large fruiting bodies the relative size of the stalk increased (Stenhouse and Williams, 1977).

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Deviations in the Final Pattern at the Extremes of the Size Range

Effect of Field Shape on the Number of Structures Formed

At the upper end of the size range, the head portion appears to reach a maximum. The full-length adult body column with just the head and foot removed regenerates a head which comprises 0.22 instead of 0.32 of the whole. If the cell numbers are examined it can be seen that such regenerates have heads which are similar in absolute size to those of corresponding regenerates of young budless hydra (head fraction = 0.34). The young animals just before budding begins may represent the largest piece of tissue which can regulate as a unit. As the animal’s size increases the first bud appears, which marks the end of the gastric region as the limit to that field of organization. One hundred cells has been estimated to be the maximum field dimension (Wolpert, 1969), and the gastric region in the adults used for these experiments was about 95 cells long. Thus the head of the mature budding adult may be regulating with respect to the gastric region alone, and not the complete body which would be beyond its sphere of influence. The isolated adult gastric region also regenerates the same size head as does the complete body column (head fraction = 0.33), which supports this idea. At the lower extreme of the size range the cell count data point toward a minimum head size. Thus, as the excised tissue mass is decreased to the equivalent of l/30 of an adult, the regenerated head and basal disc begin to take up an increasing portion of the animal. If the head fraction does reach a constant value, it would suggest that some limit in the patterning process has been reached. Otherwise, if the underlying pattern continued to proportion regulate, one would expect the head size to decrease until the tissue could no longer respond with the head form. The latter interpretive failure is the point at which regeneration is no longer possible. This occurs in tissue pieces less than l/80, whose total number of cells is below the minimum head size.

While the geometry of the initial cut piece has little effect on the head fraction, it profoundly affects the number of structures regenerated. Pieces of hydra tissue are polarized; i.e., head structures develop at the apical cut end, originally closest to the head, and basal discs at the opposite or basal end. These two edges with the potential to form head or foot will be termed “boundaries” to distinguish them from the two perpendicular edges in a rectangular piece. Depending on how the cuts are made, more or less boundary tissue is exposed, and when the relative extent of boundary tissue exceeds a critical value, the incidence of extra structures begins to rise in the regenerates. The width-length ratio was adopted as an index of the relative amount of boundary tissue (width = boundary). The opened body column with just the head and foot removed has the critical ratio, -0.35, and regenerates a single structure at each end, as do smaller pieces with similar ratios. Normal miniatures are also formed from long narrow pieces (width-length, <0.35) which have proportionally less boundary tissue than the complete body column. However, in short wide pieces, where the relative amount of boundary exceeds that of the body column, the probability of producing multiple differentiated structures rises dramatically. Although there is considerable variation the number of extra structures per regenerate increases logarithmically at an average of 0.85 per doubling of the width-length ratio. Patterning in hydra has long been thought of in terms of gradients of one kind or another, which confer on the apical boundary an advantage in headforming potential (Webster, 1971; Wolpert, 1971). In these terms long narrow pieces would have only a small area with high potential and thus might be expected to develop only one head-forming site. On the other head, wider pieces would have a considerable stretch of

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high potential boundary where many head beginnings could be initiated. With an increasing amount of tissue behind the boundary, the tendency is for these sites to coalesce into a single appropriately large head. For example, one head forms from the l-region when it is the apical boundary of the entire body column with only the head removed. If, however, all the tissue below the l-region is also cut away, doubleheads and body-tentacles develop quite frequently in the regenerates. Apparently in wide pieces which are short, the head-forming sites fail to coalesce completely as a proportionally smaller amount of head tissue is differentiated. An additional factor in isolating high potential spots might be the folding and annealing of such tissue strips. During the process boundary tissue could become interspersed with nonboundary tissue. A Possible Proportioning

Mechanism

A mechanism is needed to explain the area-to-area proportioning which is limited to a lo-fold range in field size and which occurs regardless of field shape. In addition, it must account for the appearance of extra structures, which clearly is related to the shape of the initial field. Such a proportioning mechanism was devised using concepts derived from the model for pattern formation presented by Gierer and Meinhardt (Gierer and Meinhardt, 1972; Meinhardt and Gierer, 1974). Our’version of this, however, is purely qualitative and its validity remains to be tested quantitatively. The patterning system consists of an activator whose production is autocatalytic and whose diffusion range is very short, perhaps only a few cells in extent. The activator also stimulates the production of its antagonist, the inhibitor, whose diffusion range is long and may extend throughout the tissue. Wherever the inhibitor level is greater than the activator level, activation does not occur. When the activator reaches a threshold concentration in a particular

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region of tissue, that region is committed to head formation. The remainder or inhibited area then becomes the body. The polarity of the tissue is maintained by a stable gradient of activator and inhibitor sources which is highest apically. Immediately after excision, activation increases all along the apical boundary. Because diffusion is minimal, the activator remains essentially in place. Due to local tissue inhomogeneities the concentration of activator would be uneven and, during the early stages, might be visualized as a series of peaks of varying heights. Inhibitor is produced in conjunction with the activation process and diffuses away rapidly. As activation increases and gradually spreads, the concentration of inhibitor rises throughout the tissue, its accumulation depending on the amount of activator and the size of the total tissue area. When the inhibition level near the activating region reaches a critical concentration, activation ceases. Since the inhibitor concentration is dependent on the relative size of the activated region, the process would always stop when the activated region reaches a particular fraction of the total tissue. Thus, the inhibitor has a rough sizesensing property. The whole process which starts in the rectangular pieces should be pictured as finishing with a hollow sphere or cylinder divided into activated area (head) and inhibited area (body). Although such a scheme should, in principle, regulate proportion in any size tissue, limits were found at the extremes of a lofold size range. At the lower end the head fraction increased as the absolute size of the head reached a minimum at 150-200 epithelial cells. This restriction may reflect the diffusion range of the activator. Consider the cells to be in the form of a twolayered sphere. Then activator diffusing from an activated spot of 10 cells need traverse a linear distance of only 6 or 7 cells to cover (that is, commit to head formation) a surface area of 90 cells, 2 cells thick. An effective distance of 6 or 7 cells is consistent

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with the assumed short diffusion range of the activator. Tissue pieces just below the minimal head size regenerate incompletely, often forming nothing but a tentacle or two, no hypostome (or basal disc). Further reduction of tissue size results in complete failure of regeneration. It is possible that there is a minimal activation area or concentration which can still be interpreted as “make hypostome.” Below this threshold there would be an activation level just sufficient to initiate tentacle formation alone. The body tentacles which frequently arise in regenerates could also be explained in this manner. A similar idea has been presented by Berking (1979) in terms of “source density.” At the other extreme the maximum size piece which can be organized may represent the diffusion range of the inhibitor, which leads indirectly to a reduced head fraction. The bud may be initiated at the effective limit of the inhibitor range in a large enough animal (see reviews by Burnett, 1961; Webster, 1971; Gierer, 1977). Since the gastric region contains the presumptive bud at its basal end, this would mean a diffusion range of somewhat less than 95 cells, the length of the gastric region. During head regeneration in budding adults the hollow cylinder would then become divided into an activated area (head) which is proportioned relative to the inhibited area (gastric region). The budding zone and peduncle, which are out of range, are extra tissue and can vary in size. This results in a head which is a smaller fraction of the total. To help explain how the shape and orientation of a polarized piece of tissue affect the number of structures regenerated, a long narrow rectangle will be used as an example. Its patterning can be considered in two situations: first, if the long dimension were parallel to the direction of polarity in the donor animal (e.g., 1234/4) and, second, if it were originally perpendicular to that axis (e.g., 2-region). In the former case it is the short edge which is boundary tissue,

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making regulation straightforward. The initial activated region is relatively small and the produced inhibitor will diffuse into a relatively large area. Therefore, the inhibitor concentration would rise quite slowly. Consequently, the early localized peaks of activation continue to expand, coalescing across the boundary and extending proximally before the inhibitor concentration reaches the critical level which brings activation to a halt. A normally proportioned hydra with a single head should result (Fig. 3b). In the second case the long edge is the boundary. This means activation is occurring over a large part of the balled up piece of tissue. Concomitantly inhibitor would be produced in quantities with little room to diffuse. Accumulated inhibitor would reach the critical concentration relatively fast, preventing peaks of activation from fusing. This might leave the maximum activated area divided into two, even three parts, each of which would form a head (Fig. 3~). A number of smaller activated spots could be halted below the level for a complete head but sufficient to initiate tentacle formation (Fig. 3d). An increasing number of body tentacles should then arise with more boundary tissue and less total area, as was observed. Isolation of activated peaks would be compounded if, during the healing process of the cut pieces, nonboundary tissue becomes mixed with boundary tissue. The patterning of the basal discs, which was not discussed, is an interesting problem, bringing up the question of whether one or two gradient systems are involved. This will be dealt with in a subsequent paper. Conclusion

The formation of pattern during regeneration of hydra appears to be a dynamic process involving two dimensions. Considering it to be a static one-dimensional problem as implied by a gradient of positional information (Wolpert, 1969) may not be appropriate. A simple scaling-down of the

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pattern, characteristic of these models (Crick, 1970; Wolpert, 1971), implies a greater degree of exactness than was found and does not explain the failure of proportioning in very large and very small regenerates. A Turing system where adjacent regions have either high or low concentrations of morphogen is perhaps sufficient to explain the formation of hydra’s simple pattern (Turing, 1952). In addition, such a system provides the element of chance clearly operating in the variable appearance of extra structures with certain field shape changes. While the original Turing model could not adjust to an altered field size, the Turing-derived Gierer-Meinhardt model (1972) did include a limited regulating version. This has been expanded by MacWilliams to explain proportioning in Dictyostelium (MacWilliams and Bonner, 1979) and in hydra (personal communication) . The proportion regulation described here is primitive, dealing as it does with a pattern of only two elements and having an inherent capacity for mistakes. In broad outline it is quite precise, providing head and body at constant proportion. In detail it can result in many types of imperfect animals: squat ones with incorrect length to diameter, those with extra structures which may distort the cylindrical body column, even monsters whose basic body plan is unrecognizable. However such a mechanism is surprisingly adequate. Because of the plastic embryonic quality of the tissue, the regenerate is not set in a final state. A secondary regulatory process continually pushes the form of the animal toward normality, which may be attained in a matter of weeks. We are grateful to H. Chica Schaller and the European Molecular Biology Laboratory for their generous hospitality during a portion of this work. We are deeply indebted to Harry K. MacWilliams for his helpful comments throughout. We would also like to thank Susan G. Cummings, Kristine M. Flick, and David I. Rubin for their critical reading of the manuscript, and Margaret Chow for her painstaking photography. The research was supported by the National

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