/ . Embryol. exp. Morph. Vol. 40, pp. 23-34, 1977 2 3Printed in Great Britain © Company of Biologists Limited 1977

The blastomere pattern in echinoderms:cleavages one to four

By JOHN W. PROTHERO1 AND ARNOLD TAMARINFrom 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 thefirst 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 theblastomere contours and computer analysis allow calculation of the center, radius, surfacearea and volume of each blastomere.

The subjective impression of exquisite regularity seen in normal echinoderm blastulaeacquires a quantitative dimension from the present study. For example, the individual anglesformed by the various quartets of blastomeres depart from right angles by at most a fewdegrees. The egg volume was found to be conserved up to the fourth cleavage. At the 16-cellstage, unlike the earlier stages, the blastomere positions cannot be ascribed solely to theposition and orientation of the respective cleavage planes. Finally, a few features of aformal model of these early cleavages are sketched.

INTRODUCTION

Blastula formation, by virtue of its apparent simplicity, may provide a usefulmodel system for the study of morphogenesis. In principle it is possible toprovide a relatively complete quantitative description of the process at thecellular level.

The transparency of the early blastulae, the ease of cultivation and the exten-sive background information combine to make echinoderm embryos especiallyinviting material for the study of blastula formation (Horstadius, 1973). Asemiquantitative study of blastula formation was the subject of an interestingpaper by Wolpert & Gustafson (1961). The present paper seeks to contributeto the construction of a detailed quantitative model of the early blastomerepattern in echinoderms.

MATERIALS AND METHODS

The procedure employed in this study has been described in some detailin 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 toanimal and vegetable blastomeres at the 8-cell stage. (B) me, ma and mi refer to meso-meres, 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 com-puter techniques are used to reconstruct the size, shape and position of all theblastomeres, 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 calibratedreticule inserted at the field diaphragm of the ocular.

The animals used in this study {Dendraster excentricus) are maintained in alaboratory tank. For obscure reasons our success in obtaining the classicalthree-tiered embryo characteristic of the 16-cell stage has been quite variable.(In the previous study (PTP) the blastomeres were shifted with respect to oneanother.) To circumvent this difficulty the development of several score ofembryos was recorded. From the resultant data the film strips for six developingembryos, the 16-cell stages of which seemed normal by inspection, were selectedfor data processing. The contours for the six embryos were digitized at a totalof 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 ofthese 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 ofmicromeres 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 com-plete (i.e. from the 1-cell to the 16-cell stage).

The blastomere pattern in echinoderms

Table 1

25

Cleavage ... 0 1 Micromeres

Sample size 3 6 6 4 6 4Time(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 embryosanalyzed at each cleavage stage. The last column indicates that in two cases the micromerescould not be distinguished at the 16-cell stage. The time after fertilization at which eachembryo was photographed is given in the third row and the total number of digitized pointsfor all embryos in the fourth row. Plus-minus figures in this and other tables represent onestandard deviation.

Cleavage ...

Horizontalradius (/*m)

Verticalradius (/*m)

Surface area(/*m2 x 10-3)

VolumeOm3 x 10-4)

4th cleavageHorizontalradius (/*m)

Verticalradius (/*m)

Surface areaOm2 x 10-3)

VolumeOm3xl0-4)

0

66±5

78±2

63 ±10

136±30

Meso meres26±4

36±5

18±11

10±3

Mean values of the horizontalvolume (V)at each cleavage stage.

Table

1

51±3

66±8

41 ±6

69 ±14

Macromeres32±2

33±6

22 ±14

13-5±4

radius (Rs),

2

2

39±3

544+11

28±5

37±8

Micromeres12-5±2

20±4

5±4

l-3±O-5

vertical radius

3

an

30-5±l-5

33-O±2-5

14±2

13±2

Blastocoel—

—

—

11 ±6

veg

33 ±1

36±5

16±2

17±4

Totalvolume

—

—

—

147 ±34-5

(Rv), surface area (S) and

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 largestcross-section of the blastomere, which need not coincide with an equatorialplane.

For each blastomere one may compute a hypothetical surface area (Sc) anda hypothetical volume (Vc) from the radii (RH, Rv), assuming that the blasto-

26 J. W. PROTHERO AND A. TAMARIN

120

110

"5 100

90

80 L

2 4 8 16Number of blastomeres

Fig. 2. The conservation of total cellular volume. The volume (V) of each embryo isnormalized 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:

Sc = 1-00S+1-55 x 103 Om2), (1)Vc = 1 -05 V+1 -00 x 104 Om3). (2)

For both equations the correlation coefficient is 0-98.The total blastomeric volume is simply the sum of the volumes of the blasto-

meres. To facilitate the comparison of total volumes at successive cleavages wehave normalized the volume (V) to that at the 1-cell stage (three cases) or the2-cell stage (three cases). The comparison, expressed in percent, is shown inFig. 2.

Another approach to the question of the conservation of cellular volumeentails a comparison of the volume of each pair of daughter cells with that of themother cell. Taking the volume of each mother cell as 100 %, we find (for 60cases) that the mean volume of the daughter cells is 101 ±22 %. (Throughoutthis 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 someinsight into the organization of the embryo as a whole. To this end we need to

The blastomere pattern in echinoderms 2780

60

on

1 40

20

Mesomeres /

Micromeres

1 cell

2 cell

4 cell

20 40 60Horizontal radius (j.im)

80

Fig. 3. Mean values of Kv are plotted against mean values of R# at each cleavagestage. The bars represent one standard deviation. The solid line is the regression linefitted 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) andvertical (Dv) planes. In addition, we require, for an adequate description, aspecification of the angle (a) enclosed by lines joining those blastomere centerslying in a horizontal plane. In this regard note that for a (planar) polygonhaving n sides (generally of unequal length) the average angle (a) subtended atthe 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 (in-dividual angles may, of course, deviate widely from these values for a givenarbitrary 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 <x is straightforward at the 2-, 4- and 8-cellstages because the embryos are approximately symmetric (making it reasonabletherefore to average all the values). At the 16-cell stage the disposition of themesomeres is clearly asymmetric, thus precluding, in the first instance, a simpleaveraging of values of either DH or a. In order to compare the pattern of meso-meres in the different embryos we have rotated and translated the plan views ofthe mesomere center-to-center diagrams so as to give the best (visually estimated)

to oo

Cle

avag

e ...

Tab

le 3

an/a

n ve

g/ve

g an

/veg

m

eso/

mes

o m

eso/

mac

ro

mac

ro/m

acro

m

acro

/mic

ro

mic

ro/m

icro

Hor

izon

tal

spac

ing

61 ±

4 56

±4

—

42

±3

—

61 ±

5 —

23

±2

(/ti

n)

Ver

tical

spa

cing

Cw

m)

—

—

58±

8 —

5

9±

6 —

15

±6

—A

ngle

(de

gree

s)

90

±5

90±

3 —

13

1 ±

23

—

90±

5 —

90

±10

Cen

ter-

to-c

ente

r sp

acin

gs (

DH,

Dv)

and

enc

lose

d an

gles

(a)

at

the

thir

d an

d fo

urth

cle

avag

es (

see

text

).

O H X m

The blastomere pattern in echinoderms 29

o o

74 nm

61-5 //m

T23 /<m

1

Fig. 4. A plan view of each tier of blastomeres was constructed for each 16-cellembryo by joining blastomere centers. Five of the plan views were superimposedsuccessively 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 con-structed. The mean is shown as a solid line and the original centers for each case bypoints. (A) Mesomeres (O); (B) macromeres (O), (C) micromeres (A, • , • ) •

fit. An average plan view of the mesomeres, macromeres and micromeres (inthe same respective orientations) and the scatter of the empirical centers aboutthe average is shown in Fig. 4.

The average plan view of the mesomeres (Fig. 4 A) exhibits two distinctangles (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 octagonbecause of slight departures from planarity in the computed positions of themesomere centers. The values of DHi Dv and a for the 16-cell stage are givenin Table 3.

Finally, we note that the volume of the blastocoel (see Table 2) at the 16-cellstage 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 con-sistent with the hypothesis that the interior space between blastomeres is notsimply a gap between otherwise close-packed blastomeres (it seems too largefor that), but represents, indeed, the initial appearance of the definitive blasto-coel.

DISCUSSION

Equations (1) and (2) confirm our previous finding (PTP) that the blastomericsurface 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 tothe 16-cell stage. Thus our earlier conjecture (PTP) that total blastomericvolume decreases somewhat during early cleavage is not supported by thepresent results.

Examination of Fig. 3 shows that, with the exception of the 1-cell stage, thestandard 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 jamat the 16-cell stage and 10 [im. otherwise) is too large relative to the effectivedigitization interval (about 1 jum). The appreciable standard deviations in thevolume and surface area determinations (see Table 2) are explicable on thesame basis.

It may be of interest to compare some of the measured parameters from astatistical 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 macromeresat 16-cell stage). When we compare (RH)an with (RH)veg

a n d (RH)meso vvith(^ir)macro w e n n c- n o 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 casesthe difference is statistically significant (i.e. for the mesomeres, veg and an, atthe 2- and 4-cell stages). This may be a reflexion of the fact mentioned abovethat the plane of largest diameter is often not in the equatorial plane. We havenot, however, examined this question carefully as yet.

Cle

avag

e ..

.

Tab

le 4

0 61 74 1400

1

48 59 700

2

38 47 350

an 28 36 15 3

veg

31 39 19-7

Mes

omer

esM

acro

mer

esM

icro

mer

es

Ho

rizo

nta

l ra

dius

(/*

m)

Ver

tica

l ra

diu

s (/*

m)

Vol

ume

(/im

3 x 1

0"4 )

22 29 7-7

30 38 18-2

12 17 1-5

Val

ues

of t

he h

oriz

onta

l ra

dius

(/?

«),

vert

ical

rad

ius

(Rv)

an

d vo

lum

e (V

) fo

r ea

ch b

last

omer

e ca

lcul

ated

for

the

ide

aliz

ed m

odel

.(C

om

par

e w

ith

Tab

le 2

.)

Tab

le 5

Cle

avag

e ..

.an

/an

veg/

veg

an/v

eg

mes

o/m

eso

mes

o/m

acro

m

acro

/mac

ro

mac

ro/m

icro

m

icro

/mic

ro©

5462

4460

Ho

rizo

nta

l sp

acin

g

Ver

tica

l sp

acin

g (/*

m)

—

—

75

—

66

—

50

Val

ues

of t

he c

ente

r-to

-cen

ter

spac

ings

(D

H,

£>,,)

for

the

idea

lized

mod

el.

(Com

pare

wit

h T

able

3.)

24

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 thevertical radii is not significantly greater than the vertical spacing except in thecase of the macromere-micromere separation.

We should also note that the two angles (i.e. 110-0° and 153°) describingthe 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 andand Figs. 2-4 intelligible, to initiate the construction of a model of the blastomeredispositions. A satisfactory model should (ultimately) mimic the normal dis-position 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 requirementfor quantitative data in the construction of such a model which provided therationale for the present study. For the time being such a model is of necessityrather formal and chiefly illustrative (see also Bezem & Raven, 1975). Thesuggestive model of Wolpert & Gustafson (1961) has been called into questionon 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 asingle cell, the volume of which is conserved during successive cleavages. Wemay suppose that prior to cleavage the blastomeres 'round up' and then gothrough cleavage at constant volume. Subsequent to cleavage the sphericaldaughter cells may be presumed to deform continuously into prolate spheroids.The packing of the blastomeres (i.e. DH, Dv) is here considered to be controlledessentially by RH and Rv. But Rv is determined by RH (equation (3)). We can,therefore, perhaps think of the disposition of blastomeres as the consequenceof 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 ofRH, from which the values of Rv, DH and Dv may be calculated. The packingof the blastomeres is determined, largely, by the values of DH and Dv. Theangles 110° and 160° for the mesomere packing are likewise assumed as are theright angles and the symmetrical position of the micromeres.

The parameters for this formal model are given in Tables 4 and 5. Thehorizontal spacings (DH) are 96 and 76 ̂ m at the 2-cell and 4-cell stages, res-pectively. A plan view of the model at the 16-cell stage is compared with theempirical 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 forthe idealized model are given in parentheses. 5(B) A plan view for the idealizedmodel representing the transition from spherical 8-cell animal blastomeres to thespherical mesomeres. The dimensions are center-to-center spacings, calculated onthe assumption that the blastomeres are spheres having the volumes given in Table4. The hypothesis is ventured that the animal blastomeres may form a 'fixed' contactat A and a 'sliding' contact at B. This might account for the substantial departurefrom the pattern to be expected if cleavage occurred without an asymmetric dis-placement of the mesomeres. Following cleavage the spherical blastomeres areassumed to deform back to the prolate spheroid form which is the basis of the planviews shown in Fig. 5 A.

lie within one and 8 values within two standard deviations of the observedvalue. 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 bythree standard deviations. Finally, the macromere/micromere vertical spacingdiffers from the observed value by six standard deviations. This latter disparityalso 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 micromeressit in little concavities in the macromeres. The above discrepancies show thatthe treatment of the blastomeres as regular solids breaks down chiefly in thecalculation of the center-to-center spacings. This is attributed primarily to the factthat the (real) blastomeres, as opposed to the ideal ones, overlap in the verticalplane 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 cleavagestage is 140x 10~4/tm3. This value differs by 3 % from the mean empiricalvalue (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 threeembryos at the 1-cell stage; see Table 2.)

At the 2-, 4- and 8-cell stages the position of the blastomeres can be accountedfor, to a first approximation, by assuming that successive cleavage planes aremutually perpendicular. In effect, the form of the embryo at these stages maybe viewed as the result of the autonomous determination of the position andorientation 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 themesomeres. A possible hypothesis is that the 8-cell animal quartet of blasto-meres maintain a fixed contact along one interface (see A, Fig. 5B) and a slidingcontact (see B, Fig. 5B) along the orthogonal interface during cleavage. Coupledwith an oblique orientation of the cleavage plane, this hypothesis could accountfor the mesomere pattern. (Implicitly one is assuming that the blastomeres areconstrained, as by the hyaline layer.) The position taken up by the mesomeresis especially interesting as it represents the first step we see in blastula formationat which autonomous activity (in the above sense) of blastomeres is clearlyinadequate to account for their spatial relations.

The above formal model also does not take into account the formation ofthe blastocoel. The mechanism of blastula inflation in echinoderms has yetto 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 agrant 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 microscopicembryos. / . Microscop. 101, 31-58.

WOLPERT, L. & GUSTAFSON, T. (1961). Studies on the cellular basis of morphogenesis of thesea urchin embryo. The formation of the blastula. Expl Cell Res. 25, 374-382.

{Received 28 September 1976, revised 10 December 1976)