1. The nucleolus in the nucleus of an Echinus oocyte always orientates itself gravitationally on the floor of the nucleus. When the oocyte is disturbed the nucleolus falls through the fluid contents of the nucleus with an average velocity of 0·4 μ per sec.

  2. Gravity has no direct action on the direction of the cleavage planes in Echinus eggs, but it orientates the whole egg within the fertilisation membrane.

  3. During the first cleavage the mitotic axis can lie in any position in respect to gravity, but if its position deviates appreciably from the horizontal then (as soon as the cell elongates by cleavage) the whole egg moves so as to bring its centre of gravity into equilibrium with gravity and with the frictional forces acting between the egg and the fertilisation membrane.

  4. During the second cleavage the mitotic axis must lie in a plane parallel to the first cleavage furrow in conformity with Hertwig’s Law. If its position deviates from the horizontal, then the egg orientates itself to gravity. In this way the second division gives rise to four blastomeres resting as a flat plate on the floor of the fertilisation membrane, independently of whatever position was occupied by the mitotic axis.

  5. The third cleavage is also in accord with Hertwig’s Law and no gravitational disturbances occur.

  6. The direction of each cleavage plane is determined by the resultant of three factors: (a) the forces underlying Hertwig’s law, (b) gravity, (c) friction between the egg and its fertilisation membrane.

The constant relationship which exists between the first three cleavage planes in a frog’s egg can be regarded as summarized by Hertwig’s Law: “The axis of the spindle lies in the longest axis of the protoplasmic mass”; or, as expressed by Pflüger, “The mitotic figures elongate in the direction of least resistance.” The accumulation of heavy yolk at one pole, with a consequent accumulation of cytoplasm at the other, impresses on the undivided egg a definite visible polarity and a definite orientation in respect to gravity. The egg is only in equilibrium with gravity when the flattened disc of cytoplasm lies vertically over the yolk; two out of the three rectangular axes of the cytoplasm are equal in length and lie horizontally; the third is shorter than the others and is vertical. By dividing the cytoplasm into equal halves at right angles to its longest axis, the first two cleavage planes are naturally meridional and vertical, whereas the third cleavage plane is more or less equatorial and horizontal. Both Hertwig and Pflüger clearly recognised that gravity exerted no direct action on the orientation of the spindle, and inferred that in eggs where the yolk was uniformly distributed throughout the cell not even indirect correlation would exist between the direction of the cleavage planes and the force of gravity.

From a recent study (Gray, 1924) it appears almost certain that the asters rather than the mitotic spindle are the effective agents of cleavage in the eggs of Echinus, and an attempt has therefore been made to analyse the factors which control the orientation of these bodies within the cell. Additional interest was aroused by the views recently expressed by Giglio-Tos (1926):

The asters are known to be areas of comparatively great rigidity lying in a fluid matrix of cytoplasm (Chambers, 1917), and Giglio-Tos stated that (in an unspecified species of echinoderm egg) these bodies orientated themselves under gravity at the lower pole of the egg; as soon as the asters each acquired a diameter equal to half that of the egg, the line joining their centres was inclined at an angle of 45° to the horizontal. At this point the egg divided so that the cleavage plane, being at right angles to the astral axis, was at 45° to the vertical. Giglio-Tos also stated that these positions of equilibria are explicable on the assumption that the two asters represent two rigid spheres free to slide on each other and on the surface of the cell.

The observations here described do not confirm any of the conclusions of this author, but indicate that the effect of gravity on the fertilised eggs of Echinus esculentus and E. miliaris is of an entirely different nature.

In order to obtain a horizontal view of the cells, a culture of eggs was placed in a small drop of water on a slide, a very thin layer of cotton wool superimposed, and a coverslip placed in position; in this way the eggs were encased in a mesh-work of fibres without any pressure being exerted on them by the coverslip. The slide was then placed on the stage of the microscope and the stage fixed in a vertical position with the tube horizontal. An alternative method (that used by Giglio-Tos) consists in enclosing the eggs in a tapered capillary pipette mounted vertically in a water jacket on the stage of the microscope; this method has the advantage that any particular egg can be orientated so as to bring both asters into focus at once, thereby facilitating observation: but for most purposes the first method is simple and effective.

During the early stages of each mitotic cycle the asters are extremely small, so that it is impossible to determine with any real accuracy the inclination of the line joining their centres. Since they are invariably situated in close proximity to the nucleus, any marked movement effected by gravity must be accompanied by a corresponding movement of the nucleus. Repeated observations failed to detect any gravitational movement of the nucleus of fertilised or unfertilised eggs, but owing to the small size of these nuclei it seemed desirable to investigate the behaviour of the much larger nucleus of the oocytes. Here, again, no movement of the nucleus could be detected through the cytoplasm; but, on the other hand, a definite gravitational effect was observed on the nucleolus. This structure is almost spherical and is about one-fifth the diameter of the nucleus; it can very readily be seen by virtue of its high refractive index. The nucleolus always sinks to the bottom of the nucleus whenever the egg is displaced. The average time required to move from the top to the bottom of the nucleus was found to be 3 minutes, and as the distance moved was approximately 75μ, the velocity of fall was 0·4μ per second or 112 mm. per hour.

These results confirm the conclusions reached by Herrick (1895), who observed that in fixed sections of the ovary of the lobster the nucleoli are always orientated towards the lower side of the nucleus. At the same time there is no evidence which suggests that during the early stages of mitosis the asters orientate themselves at the lower surface of the cell; on the contrary, they are invariably associated with the nucleus near the centre of the egg.

If eggs are fertilised in gently agitated water and are then transferred to a vertical slide, it can be seen that the egg always orientates itself so as to rest on the bottom of the fertilisation membrane as figured by Giglio-Tos. On sudden rotation through 180° the egg begins to fall through the perivitelline fluid at an average velocity of about 2μ, per second (Fig. 2). These facts show that the perivitelline space is filled with a fluid whose viscosity is not materially greater than that of sea-water.

Fig. 1.

Lateral view of oocyte showing in A, the position of equilibrium of the nucleolus; B, the path followed by the nucleolus after rotating the oocyte through 180° on a horizontal axis.

Fig. 1.

Lateral view of oocyte showing in A, the position of equilibrium of the nucleolus; B, the path followed by the nucleolus after rotating the oocyte through 180° on a horizontal axis.

Fig. 2.

Movement of an egg free to move within the fertilisation membrane, the latter being fixed in position and the whole system rotated through 180°. The † indicates the original point of contact between the egg and the fertilisation membrane.

Fig. 2.

Movement of an egg free to move within the fertilisation membrane, the latter being fixed in position and the whole system rotated through 180°. The † indicates the original point of contact between the egg and the fertilisation membrane.

If the eggs of Echinus esculentus are allowed to remain undisturbed for some time, an egg tends to adhere to its fertilisation membrane, so that when rotated it does not detach itself but remains suspended from the top of the membrane. If the whole of such a system (egg and fertilisation membrane) is free to move, it always orientates itself so as to bring the egg to the lower pole (Fig. 3). This secondary adhesion of egg to fertilisation membrane is less frequent in E. miliaris.

Fig 3.

orientation of an egg which is not free to move within the fertilisation membrane.

Fig 3.

orientation of an egg which is not free to move within the fertilisation membrane.

A large number of observations with both Echinus esculentus and E. miliaris leave no doubt that the axis joining the centres of the two asters (mitotic axis) can lie in any plane relative to gravity. The asters having taken up their position at the poles of the nucleus maintain the orientation thus acquired until the egg begins to show signs of cleavage furrows. Further, an egg can be rotated so as to bring the mitotic axis into any desired position, and this position is stable.

It is only when cleavage begins that gravity exerts any effect on the orientation of the system. This is most readily observed in an egg whose mitotic axis is vertical as in Fig. 4. As the egg elongates upwards (Fig. 4,2) it soon becomes unstable and falls on to one side (Fig. 4, 3). This movement is clearly due to gravity, and the egg orientates itself so as to bring its centre of gravity to the lowest possible position. In this way the mitotic axis becomes more or less horizontal (Fig. 4, 3). Having reached this position the egg continues to elongate, and its long axis may either continue to remain horizontal or it may tilt upwards as in Fig. 4 (4-6). Both types of movement are obviously induced by the accommodation of the egg to the confines of the fertilisation membrane; as the egg elongates, the two points of contact (Fig. 4, x and y) move apart forming a longer and longer arc.

Fig. 4.

Orientation of a cleaving egg in which the astral axis is originally vertical. The changes in inclination to the vertical of the mitotic axis at stages 1—6 are shown in 7.

Fig. 4.

Orientation of a cleaving egg in which the astral axis is originally vertical. The changes in inclination to the vertical of the mitotic axis at stages 1—6 are shown in 7.

When the first cleavage is completed, the long axis of egg may therefore lie in any position from the horizontal (Fig. 5,2) up to a maximum inclination of about 35° (Fig. 5,3), The first cleavage plane is eventually therefore either vertical or deviates from the vertical by an angle not exceeding 35°. It is clear that these phenomena are due to the fact that on the initiation of cleavage the egg ceases to be spherical, and were it not for the presence of the fertilisation membrane, the egg would only be in equilibrium with gravity when its long axis was horizontal, and the cleavage furrow vertical. As the egg must accommodate itself to the confines of the fertilisation membrane, the egg can be in equilibrium as long as the inclination of its long axis does not exceed a value which depends on the forces exerted at the points of contact with the membrane (see p. 110).

Fig. 5.

Photographs of living eggs of Echinus esculentus viewed horizontally. 1. Undivided egg resting on the floor of the fertilisation membrane. 2. Two-celled stage with mitotic axis horizontal. 3. Two-celled stage with mitotic axis in position of maximum inclination. 4. Four-celled stage resting on floor of fertilisation membrane.

Fig. 5.

Photographs of living eggs of Echinus esculentus viewed horizontally. 1. Undivided egg resting on the floor of the fertilisation membrane. 2. Two-celled stage with mitotic axis horizontal. 3. Two-celled stage with mitotic axis in position of maximum inclination. 4. Four-celled stage resting on floor of fertilisation membrane.

When an egg is firmly attached to the fertilisation membrane, and the mitotic axis is more or less horizontal, cleavage not infrequently causes a distortion of the fertilisation membrane, causing it to become elliptical.

During the early stages of the cleavage cycle it is not uncommon to find that the mitotic axis does not lie along a diameter of the egg but is displaced to one side owing to the acentric position of the nucleus. As the asters enlarge, however, the mitotic axis gradually moves towards the diameter of the egg, thereby causing symmetrical division (Fig. 6). This movement appears to be due to the mechanical effect of the cell periphery on the aster; it is obvious that if both rigid asters are of the same size and growing at equal rates, as soon as each of their diameters equals one-half that of the egg, the mitotic axis must lie along the egg diameter.

Fig. 6.

Movement of two assymmetrically situated asters. In 1, the centres of the asters are at a, a1; in 2 they lie at b, b1; in 3 they lie at c, c1; in 4 the diameter of each aster is equal to the radius of the egg so that the centres of the asters must lie on a diameter of the egg and produce symmetrical cleavage.

Fig. 6.

Movement of two assymmetrically situated asters. In 1, the centres of the asters are at a, a1; in 2 they lie at b, b1; in 3 they lie at c, c1; in 4 the diameter of each aster is equal to the radius of the egg so that the centres of the asters must lie on a diameter of the egg and produce symmetrical cleavage.

When the first division is completed, the three main axes of each cell are no longer equal since each blastomere is compressed along the original mitotic axis. Each blastomere has in fact one short axis (αβ), which is < 0·8 times the original diameter of the undivided egg, and two other equal and longer axes (γδ, ϵθ) which are > 0·8 times the original diameter. Average values for these axes as fractions of the original diameter are αβ = 0·71, and γδ = ϵθ = 0·87.

The three rectangular views of the egg are seen in Fig. 7. Fig. 7,1 shows the egg when viewed along the vertical axis ϵθ; Fig. 7, 2 shows the same egg viewed horizontally along γδ, while Fig. 7,3 shows the view along the axis αβ; in the last figure of course only one blastomere is seen in the diagram, in the living object the outline of the second blastomere can usually be detected.

Fig. 7.

Two-celled stage: 1, viewed vertically along axis ϵθ; 2, viewed horizontally along axis γδ; 3, viewed horizontally along axis αβ.

Fig. 7.

Two-celled stage: 1, viewed vertically along axis ϵθ; 2, viewed horizontally along axis γδ; 3, viewed horizontally along axis αβ.

The behaviour of the asters during the second cleavage cycle is essentially the same as during the first cycle. During the opening phases the mitotic axis may lie in any plane whatsoever, but an orientation along the plane αβis uncommon. As soon as the asters are of considerable size, however, their axis begins to accommodate itself to the plane in which lie the two longer axes γδ and ϵθ, and having reached this plane it remains there. It is obvious that the mitotic axis can come to lie anywhere in the plane between two extreme positions. In one of these positions the mitotic axis is horizontal and lies along γδ; in the other position it is vertical and lies along ϵθ. In the first of these two cases cleavage is perfectly simple and when viewed vertically (i.e. along the e0 axis) the egg acquires the form seen in Fig. 8 (1-3) and forms a flat plate of four equal cells lying on the floor of the fertilisation membrane.

Fig. 8.

Second division with mitotic axis horizontal along γδ. In 1, 2, 3 the egg is viewed vertically along the axes ϵθ. In 4, 5, 6 the egg is viewed horizontally along αβ.

Fig. 8.

Second division with mitotic axis horizontal along γδ. In 1, 2, 3 the egg is viewed vertically along the axes ϵθ. In 4, 5, 6 the egg is viewed horizontally along αβ.

If, however, the second mitotic axis lies in the plane ϵθ, the blastomeres begin to elongate vertically upwards, but before this process has advanced very far the system becomes gravitationally unstable and the whole egg falls on to its side just as was the case during the first division (Fig. 9). The net result of the second cleavage is therefore independent of the particular position occupied by the mitotic axis, for elongation along any axis lying in the γδ-ϵθ plane results in a flat plate of four cells resting on the floor of the fertilisation membrane. Again, the plane containing the αβ axis may either be horizontal or deviate from the horizontal to a finite extent.

Fig. 9.

Second division (viewed horizontally along αβ) with mitotic axis vertical along ϵθ. Note gravitational movement of the egg.

Fig. 9.

Second division (viewed horizontally along αβ) with mitotic axis vertical along ϵθ. Note gravitational movement of the egg.

The second cleavage leaves each blastomere with one long axis and two equal shorter axes. The single long axis is directed at right angles to the plane in which the four cells are themselves lying and points upwards into the cavity of the fertilisation membrane. The third mitotic axes accommodate themselves to this direction, so that at the eight-cell stage the egg consists of four cells above and four cells below. No gravitational effects were observed, and the planes of cleavage obey the Hertwig-Pflüger Law.

If the two contiguous blastomeres of the two-celled stage were able to slide on the surface of the fertilisation membrane without frictional resistance, then the line joining their centres would invariably be horizontal unless the diameter of each blastomere was exactly one-half of that of the fertilisation membrane; in the latter case the blastomeres would be in equilibrium in any position since their common centre of gravity would coincide with the centre of the membrane. The fact that the two-celled stage can remain tilted at an angle to the horizontal when confined within a membrane whose diameter is greater than the longest axis of the egg shows that frictional forces must exist when the egg slides on the surface of the membrane. By observation the maximum angle of inclination was found to be about 35°, and since the diameter of the fertilisation membrane is about 1·25 times the diameter of each cell, it follows that the coefficient of friction between the egg and the membrane is of the order of 0·2 or approximately that between two oak planks lubricated with dry soap.

For the following deduction of this value I am indebted to Mr R. A. Hayes, Trinity Hall, Cambridge.

The two blastomeres may be regarded as spheres of equal size and radius, attached to each other at a point P (Fig. 10), but free to move with friction at A and B over the surface of the fertilisation membrane whose radius is R. The three forces holding the blastomeres in equilibrium are (i) the weight of the blastomeres at P, and (ii) the reactions F1 and F2 at A and B which will both be inclined at an angle λ (= angle of friction between the blastomeres and the membrane) to the same side of the normals at A and B. These three forces must meet in a point, let it be Q.

This analysis will only be applicable to the living egg if the distortion of the blastomeres along the αβ axis does not materially affect the expression PC2= CA. CA′.

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