The Blastomere Pattern in Echinoderms: Cleavages One to Four

/. Embryol. exp. Morph. Vol. 40, pp. 23-34, 1977 23 Printed in Great Britain © Company of Biologists Limited 1977

The blastomere pattern in echinoderms: cleavages one to four

By JOHN W. PROTHERO1 AND ARNOLD TAMARIN From the Departments of Biological Structure and Oral Biology, University of Washington

SUMMARY The results of a longitudinal study of the blastomere pattern in six embryos during the first four cleavages are reported. At each cleavage stage optical sections through an embryo, taken at vertical intervals of 5 or 10/*m, were recorded on 35 mm film: digitization of the blastomere contours and computer analysis allow calculation of the center, radius, surface area and volume of each blastomere. The subjective impression of exquisite regularity seen in normal echinoderm blastulae acquires a quantitative dimension from the present study. For example, the individual angles formed by the various quartets of blastomeres depart from right angles by at most a few degrees. The egg volume was found to be conserved up to the fourth cleavage. At the 16-cell stage, unlike the earlier stages, the blastomere positions cannot be ascribed solely to the position and orientation of the respective cleavage planes. Finally, a few features of a formal model of these early cleavages are sketched.

INTRODUCTION Blastula formation, by virtue of its apparent simplicity, may provide a useful model system for the study of morphogenesis. In principle it is possible to provide a relatively complete quantitative description of the process at the cellular level. The transparency of the early blastulae, the ease of cultivation and the exten- sive background information combine to make echinoderm embryos especially inviting material for the study of blastula formation (Horstadius, 1973). A semiquantitative study of blastula formation was the subject of an interesting paper by Wolpert & Gustafson (1961). The present paper seeks to contribute to the construction of a detailed quantitative model of the early blastomere pattern in echinoderms. MATERIALS AND METHODS The procedure employed in this study has been described in some detail in a prior paper, hereafter denoted PTP (Prothero, Tamarin & Pickering, 1974). Essentially, the procedure is to record on film, following each cleavage, a 1 Author's address: Department of Biological Structure SM-20, University of Washington, School of Medicine, Seattle, Washington 98195, U.S.A. 24 J. W. PROTHERO AND A. TAMARIN B

Fig. 1. Blastomere nomenclature at 3rd and 4th cleavages. (A) an and vg refer to animal and vegetable blastomeres at the 8-cell stage. (B) me, ma and mi refer to mesomeres, macromeres and micromeres respectively at the 16-cell stage. In each case, blastomeres are drawn to represent approximately the measured average dimensions. series of optical sections through a developing embryo. Digitization and computer techniques are used to reconstruct the size, shape and position of all the blastomeres, up to and including the 16-cell stage. In the present study, as distinct from the prior one (PTP), the reference co- ordinates on each 35 mm frame are derived from the image of a calibrated reticule inserted at the field diaphragm of the ocular. The animals used in this study {Dendraster excentricus) are maintained in a laboratory tank. For obscure reasons our success in obtaining the classical three-tiered embryo characteristic of the 16-cell stage has been quite variable. (In the previous study (PTP) the blastomeres were shifted with respect to one another.) To circumvent this difficulty the development of several score of embryos was recorded. From the resultant data the film strips for six developing embryos, the 16-cell stages of which seemed normal by inspection, were selected for data processing. The contours for the six embryos were digitized at a total of about 115000 points.

RESULTS The blastomere pattern in six embryos (derived from five pairs of parents) was reconstructed (see Table 1). The data base is incomplete in several respects. Only three embryos had been photographed at the 1-cell stage, and two of these were photographed at the (coarse) vertical interval of 20 /urn. In two cases, the 8-cell stage was not reconstructed because the animal and vegetable quartets ,were not distinguishable in the film (see Fig. 1). Furthermore, the quartet of micromeres could not be discerned in two cases. In consequence of these short- comings, there are only two embryos in this series for which the data are complete (i.e. from the 1-cell to the 16-cell stage). The blastomere pattern in echinoderms 25

Table 1

Cleavage ... 0 1 Micromeres Sample size 3 6 6 4 6 4 Time(min) 80-5±599 139-3±29-9 1933±37-7 229-1 ±33-5 2908±43-4 — Total points 4022 16117 16504 13551 63785 113979 A summary of some features of the data base. Sample size refers to the number of embryos analyzed at each cleavage stage. The last column indicates that in two cases the micromeres could not be distinguished at the 16-cell stage. The time after fertilization at which each embryo was photographed is given in the third row and the total number of digitized points for all embryos in the fourth row. Plus-minus figures in this and other tables represent one standard deviation.

Table 2

Cleavage ... 0 1 2 an veg Horizontal 66±5 51±3 39±3 30-5±l-5 33 ±1 radius (/*m) Vertical 78±2 66±8 544+11 33-O±2-5 36±5 radius (/*m) Surface area 63 ±10 41 ±6 28±5 14±2 16±2 (/*m2 x 10-3) Volume 136±30 69 ±14 37±8 13±2 17±4 Om3 x 10-4) Total 4th cleavage Meso meres Macromeres Micromeres Blastocoel volume Horizontal 26±4 32±2 12-5±2 — — radius (/*m) Vertical 36±5 33±6 20±4 — — radius (/*m) Surface area 18±11 22 ±14 5±4 — — Om2 x 10-3) Volume 10±3 13-5±4 l-3±O-5 11 ±6 147 ±34-5 Om3xl0-4)

Mean values of the horizontal radius (Rs), vertical radius (Rv), surface area (S) and volume (V)at each cleavage stage.

The parameters which have been computed for each blastomere include: the center, horizontal (RH) and vertical (Rv) radii, surface area (S) and volume (V) (see Table 2). Note that the horizontal radius is computed at the largest cross-section of the blastomere, which need not coincide with an equatorial plane.

For each blastomere one may compute a hypothetical surface area (Sc) and a hypothetical volume (Vc) from the radii (RH, Rv), assuming that the blasto- 26 J. W. PROTHERO AND A. TAMARIN

120

110

"5 100

80 L

2 4 8 16 Number of blastomeres Fig. 2. The conservation of total cellular volume. The volume (V) of each embryo is normalized to 100 % at the 1-cell or 2-cell stage (whichever was recorded initially). The vertical bars represent one standard deviation. meres are simply prolate spheroids. The regression lines fitted to (Sc, S) and (Vc, K)are given by: 3 2 Sc = 1-00S+1-55 x 10 Om ), (1) 4 3 Vc = 1 -05 V+1 -00 x 10 Om ). (2) For both equations the correlation coefficient is 0-98. The total blastomeric volume is simply the sum of the volumes of the blastomeres. To facilitate the comparison of total volumes at successive cleavages we have normalized the volume (V) to that at the 1-cell stage (three cases) or the 2-cell stage (three cases). The comparison, expressed in percent, is shown in Fig. 2. Another approach to the question of the conservation of cellular volume entails a comparison of the volume of each pair of daughter cells with that of the mother cell. Taking the volume of each mother cell as 100 %, we find (for 60 cases) that the mean volume of the daughter cells is 101 ±22 %. (Throughout this paper plus-minus figures denote one standard deviation from the mean.)

It proves useful to compute the regression of Rv on RH. The result (see Fig. 3) is given by: Rv = l-16RH + 3-36(jim) (3) with a correlation coefficient of 0-92. As a corollary we find that the axial ratio (RHIRV) varies systematically from 0-67 for the micromeres to 0-82 for the egg. This fact may be important in understanding the control of blastomere packing (see Discussion). Study of the pattern formed by the array of blastomere centers provides some insight into the organization of the embryo as a whole. To this end we need to The blastomere pattern in echinoderms 27 80 1 cell

60 2 cell

on Mesomeres / 1 40 4 cell

Micromeres

20 40 60 80 Horizontal radius (j.im)

Fig. 3. Mean values of Kv are plotted against mean values of R# at each cleavage stage. The bars represent one standard deviation. The solid line is the regression line fitted to all the data. The point for the macromeres is omitted for reasons of clarity (see Table 2).

distinguish between center-to-center spacings in the horizontal (DH) and vertical (Dv) planes. In addition, we require, for an adequate description, a specification of the angle (a) enclosed by lines joining those blastomere centers lying in a horizontal plane. In this regard note that for a (planar) polygon having n sides (generally of unequal length) the average angle (a) subtended at the vertices is given by: a = 180 (n-2)jn degrees. (4) Thus the mean angle is 90° for a quadrilateral and 135° for an octagon (individual angles may, of course, deviate widely from these values for a given arbitrary polygon). At the 2-cell stage the horizontal center-to-center spacing (DH) is 84 ± 5 jum. For the 4-cell stage we find a DH of 70 + 2-5 /an and an average a of 90 ± 3°. The average values of DH, Dv and a for the 8-cell stage are given in Table 3. The computation of DH, Dv and

Table 3 O H X m Cleavage ... an/an veg/veg an/veg meso/meso meso/macro macro/macro macro/micro micro/micro Horizontal spacing 61 ±4 56±4 — 42±3 — 61 ±5 — 23±2 (/tin) Vertical spacingCwm) — — 58±8 — 59±6 — 15±6 — Angle (degrees) 90±5 90±3 — 131 ±23 — 90±5 — 90±10

Center-to-center spacings (DH, Dv) and enclosed angles (a) at the third and fourth cleavages (see text). The blastomere pattern in echinoderms 29

o o

74 nm

61-5 //m

T 23 /

Fig. 4. A plan view of each tier of blastomeres was constructed for each 16-cell embryo by joining blastomere centers. Five of the plan views were superimposed successively on the sixth by bringing a homologous point into register at the origin (circle, upper left of octagon) and aligning the plan views along a common axis (arrow). From all the plan views a (somewhat idealized) mean plan view was constructed. The mean is shown as a solid line and the original centers for each case by points. (A) Mesomeres (O); (B) macromeres (O), (C) micromeres (A, •, •)• fit. An average plan view of the mesomeres, macromeres and micromeres (in the same respective orientations) and the scatter of the empirical centers about the average is shown in Fig. 4. The average plan view of the mesomeres (Fig. 4 A) exhibits two distinct angles (a, /?) having the (idealized) values of 110° and 160°. The average measured values for (a, ft) are 110-0° ± 17-3 and 152-7° ± 14-3, respectively. The average angle (a) for all the embryos (i.e. 48 values) is 131 ± EMB 40 30 J. W. PROTHERO AND A. TAMARIN 23°. The value of 131° differs from the ideal value of 135° for an octagon because of slight departures from planarity in the computed positions of the mesomere centers. The values of DHi Dv and a for the 16-cell stage are given in Table 3. Finally, we note that the volume of the blastocoel (see Table 2) at the 16-cell stage constitutes 8 ± 6 % of the total volume (i.e. blastocoel plus blastomeres). This volume is equivalent to that of a sphere having a diameter of about 30 /on. Our study, both of growing embryos and of several time-lapse movies, is consistent with the hypothesis that the interior space between blastomeres is not simply a gap between otherwise close-packed blastomeres (it seems too large for that), but represents, indeed, the initial appearance of the definitive blastocoel.

DISCUSSION Equations (1) and (2) confirm our previous finding (PTP) that the blastomeric surface area and volume may be calculated with reasonable accuracy from (RH, Rv). The total blastomeric volume at each cleavage stage (see Fig. 2 and above) is consistent with the hypothesis that the initial egg volume is conserved up to the 16-cell stage. Thus our earlier conjecture (PTP) that total blastomeric volume decreases somewhat during early cleavage is not supported by the present results. Examination of Fig. 3 shows that, with the exception of the 1-cell stage, the standard deviation of RH is larger (and usually much larger) than that in Rv. We take this to mean that the vertical interval between contours (usually 5 jam at the 16-cell stage and 10 [im. otherwise) is too large relative to the effective digitization interval (about 1 jum). The appreciable standard deviations in the volume and surface area determinations (see Table 2) are explicable on the same basis. It may be of interest to compare some of the measured parameters from a statistical standpoint. Thus-we find that the values of RH and Rv (see Table 2) are significantly different (i.e. P < 0-01) in five cases and not in three cases (i.e. animal (an) and vegetable (veg) blastomeres at 8-cell stage and macromeres an at 16-cell stage). When we compare (RH)an with (RH)veg d (RH)meso vvith we nnc no (^ir)macro - significant differences. The same is true when values of Rv are compared. Our a priori expectation is that twice the value of RH would give a reasonable estimate of the horizontal center-to-center spacing (DH) (see Tables 2 and 3). In five of the six cases 2 RH is, in fact, greater than DH) and in four of the cases the difference is statistically significant (i.e. for the mesomeres, veg and an, at the 2- and 4-cell stages). This may be a reflexion of the fact mentioned above that the plane of largest diameter is often not in the equatorial plane. We have not, however, examined this question carefully as yet. Table 4

Cleavage ... 0 1 2 an veg Mesomeres Macromeres Micromeres Horizontal radius (/*m) 61 48 38 28 31 22 30 12 Vertical radius (/*m) 74 59 47 36 39 29 38 17 Volume (/im 3 x 10" 4) 1400 700 350 15 3 19-7 7-7 18-2 1-5

Values of the horizontal radius (/?«), vertical radius (R v) and volume (V) for each blastomere calculated for the idealize d model. (Compare with Table 2.)

Table 5

Cleavage ... an/an veg/veg an/veg meso/meso meso/macro macro/macr o macro/micro micro/micro © Horizontal spacing 54 62 44 60 24 Vertical spacing (/*m) — — 75 — 6 6 — 50

Values of the center-to-center spacings (D H, £>,,) for the idealized model. (Compare with Table 3.) 32 J. W. PROTHERO AND A. TAMARIN

A similar argument to the above applies to the sum of the vertical radii (Rv) vis-a-vis the vertical spacing (Dv) (compare Tables 2 and 3). The sum of the vertical radii is not significantly greater than the vertical spacing except in the case of the macromere-micromere separation. We should also note that the two angles (i.e. 110-0° and 153°) describing the disposition of the mesomeres are significantly different.

Toward a formal model It may prove helpful, in the interests of making the data of Tables 1-3 and and Figs. 2-4 intelligible, to initiate the construction of a model of the blastomere dispositions. A satisfactory model should (ultimately) mimic the normal disposition of blastomeres, perhaps as set forth in Tables 4 and 5, as well as pre- dicting the effects of at least modest perturbations. Indeed, it is the requirement for quantitative data in the construction of such a model which provided the rationale for the present study. For the time being such a model is of necessity rather formal and chiefly illustrative (see also Bezem & Raven, 1975). The suggestive model of Wolpert & Gustafson (1961) has been called into question on quantitative grounds (Prothero, 1975). We suppose that early blastula formation is governed, partially, by four rules: (1) Total blastomeric volume is conserved; (2) Rv = 1-16 RH + 3-36 (/*m), cf. equation (3); (3) DH = 2 RH (jum); (4) Dv = 2Rv{fixn). The vertical spacing (Dv) is expected to be slightly less than 2 Rv because the blastomeres overlap (in fact, the effect is significant only for the macromere/micromere separation). The rules are compatible with the following general picture. We start with a single cell, the volume of which is conserved during successive cleavages. We may suppose that prior to cleavage the blastomeres 'round up' and then go through cleavage at constant volume. Subsequent to cleavage the spherical daughter cells may be presumed to deform continuously into prolate spheroids. The packing of the blastomeres (i.e. DH, Dv) is here considered to be controlled essentially by RH and Rv. But Rv is determined by RH (equation (3)). We can, therefore, perhaps think of the disposition of blastomeres as the consequence of a cellular 'program' which is 'played out', mathematically speaking, in the (RH, Rv) plane (see Fig. 3). To obtain a reasonable fit to the data we arbitrarily choose a set of values of RH, from which the values of Rv, DH and Dv may be calculated. The packing of the blastomeres is determined, largely, by the values of DH and Dv. The angles 110° and 160° for the mesomere packing are likewise assumed as are the right angles and the symmetrical position of the micromeres. The parameters for this formal model are given in Tables 4 and 5. The horizontal spacings (DH) are 96 and 76 ^m at the 2-cell and 4-cell stages, respectively. A plan view of the model at the 16-cell stage is compared with the empirical plan in Figure 5 A.

The model generates 26 values of RH, Rv, DH and Dr. We find that 14 values The blastomere pattern in echinoderms 33

74 ^m (71 urn)

117/im (*• (121 nm) -H

89 nm

152/itn Fig. 5(A) The plan view for the 16-cell stage derived from Fig. 4 A. The values for the idealized model are given in parentheses. 5(B) A plan view for the idealized model representing the transition from spherical 8-cell animal blastomeres to the spherical mesomeres. The dimensions are center-to-center spacings, calculated on the assumption that the blastomeres are spheres having the volumes given in Table 4. The hypothesis is ventured that the animal blastomeres may form a 'fixed' contact at A and a 'sliding' contact at B. This might account for the substantial departure from the pattern to be expected if cleavage occurred without an asymmetric dis- placement of the mesomeres. Following cleavage the spherical blastomeres are assumed to deform back to the prolate spheroid form which is the basis of the plan views shown in Fig. 5 A. lie within one and 8 values within two standard deviations of the observed value. In three cases, namely the horizontal spacings (DH) at the 2-cell and 4- cell stages, and the vertical spacing (Dv) at the 8-cell stage, the values differ by three standard deviations. Finally, the macromere/micromere vertical spacing differs from the observed value by six standard deviations. This latter disparity also arises when the sum of the empirical radii (Rv) is compared with the 34 J. W. PROTHERO AND A. TAMARIN empirical spacing (Dv) (see above). The reason seems to be that the micromeres sit in little concavities in the macromeres. The above discrepancies show that the treatment of the blastomeres as regular solids breaks down chiefly in the calculation of the center-to-center spacings. This is attributed primarily to the fact that the (real) blastomeres, as opposed to the ideal ones, overlap in the vertical plane and do not necessarily exhibit side-to-side contact in the equatorial plane. The total volume of the blastomeres in the idealized model at each cleavage stage is 140x 10~4/tm3. This value differs by 3 % from the mean empirical value (136 ± 31 x 10~4 /mi3) for all the embryos at all stages (n = 26). (By coin- cidence, the mean volume happens to be the same as the mean for the three embryos at the 1-cell stage; see Table 2.) At the 2-, 4- and 8-cell stages the position of the blastomeres can be accounted for, to a first approximation, by assuming that successive cleavage planes are mutually perpendicular. In effect, the form of the embryo at these stages may be viewed as the result of the autonomous determination of the position and orientation of the cleavage planes by each individual blastomere. At the 16-cell stage the cleavage planes are oblique (see fig. 10 a, Horstadius, 1973), but the obliquity is insufficient to account for the average positions of the mesomeres. A possible hypothesis is that the 8-cell animal quartet of blastomeres maintain a fixed contact along one interface (see A, Fig. 5B) and a sliding contact (see B, Fig. 5B) along the orthogonal interface during cleavage. Coupled with an oblique orientation of the cleavage plane, this hypothesis could account for the mesomere pattern. (Implicitly one is assuming that the blastomeres are constrained, as by the hyaline layer.) The position taken up by the mesomeres is especially interesting as it represents the first step we see in blastula formation at which autonomous activity (in the above sense) of blastomeres is clearly inadequate to account for their spatial relations. The above formal model also does not take into account the formation of the blastocoel. The mechanism of blastula inflation in echinoderms has yet to be determined (Prothero, 1975). It is a pleasure to acknowledge the excellent technical assistance of James Walker in carry- ing out this project. This work was supported in part by the Health Sciences Computer Fund, in part by a grant from N1DR, DE-01701-10 and DE-02329-07. REFERENCES BEZEM, J. J. & RAVEN, CHR. P. (1975). Computer simulation of early embryonic development. J.Theor.Biol. 54,47-61. HORSTADIUS, S. (1973). Experimental Embryology of Echinoderms. Oxford: Clarendon Press. PROTHERO, J. W. (1975). Concerning the mechanics of blastula formation in echinoderms. Can. J. Zool. 53, 285-289. PROTHERO, J. W., TAMARIN, A. & PICKERING, R. (1974). Morphometrics of living specimens. A methodology for the quantitative three-dimensional study of growing microscopic embryos. /. Microscop. 101, 31-58. WOLPERT, L. & GUSTAFSON, T. (1961). Studies on the cellular basis of morphogenesis of the sea urchin embryo. The formation of the blastula. Expl Cell Res. 25, 374-382. {Received 28 September 1976, revised 10 December 1976)