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Geometrical relations of the cleavage stimulus in invertebrate eggs
J. Theoret. Biol. (1965) 9, 51-66
Geometrical Relations of the Cleavage Stimulus in Invertebrate Eggs R. RAPPAPORT Department
of Biological Sciences, Union College, Schenectady, New York, U.S.A. and
The Mount Desert Island Biological Laboratory, Maine, U.S. A.
Salisbury Cove,
(Received 22 October 1964) Before cytokinesis, the mitotic apparatus apparently provides a stimulus that affects certain parts of the cell surface and determines the position of the cleavage furrow. An understanding of the pattern of stimulation will help to elucidate other activities involved in the division process. Since different hypothetical physical mechanisms that could accomplish cytokinesis require different stimulus patterns, the form of the stimulus pattern becomes a basis for judgement of alternative physical mechanisms. It is assumed that stimulated surface regions undergo changes in physical properties or activities that culminate in cleavage; unstimulated regions retain qualities characteristic of the entire surface before functional differentiation. The asters are the only parts of the mitotic apparatus required for normal stimulation. Two possible stimulus patterns are considered: polar stimulation in which the position of the furrow is determined by absence of stimulus and the poles are stimulated, and equatorial stimulation in which the presumptive furrow is stimulated and the poles are unstimulated. Experimental results indicate that the position of the furrow is not determined by absence of stimulus, leaving the alternative of positive stimulation in the presumptive furrow region. It is possible that equatorial stimulation may be accomplished by additive activity of the asters which could occur in their zone of confluence. This zone of astral confluence coincides with the future plane of cleavage. Several possibilities concerning the nature of the cleavage stimulus are described.
1. Introduction Classical analyses of the physical mechanisms that accomplish cytoplasmic division in animal cells usually involve operations performed after determination of the position of the cleavage furrow, or measurements of some physical property made at intervals during the division cycle. Study of the 51
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geometrical relations of the cleavage stimulus is a third approach that will yield information useful in the assessment of hypotheses concerning cytokinesis. Although the cytoplasm governs the periodicity of cleavages (Moore, 1933), the stimulus that determines the position of the furrow is released by the mitotic apparatus. Cytokinesis is accomplished by the cell surface or cortex in invertebrate eggs and the purpose of geometrical analysis is to determine which regions of the surface are affected by the stimulus. Cells can divide only if different parts do different things or acquire different physical properties. This functional differentiation (Wolpert, 1960) comes about because some regions are stimulated and others are not. It must be assumed that the activities or properties of stimulated parts are changed while those of unstimulated parts are not. Better understanding of the geometrical relations of the cleavage stimulus could indicate which areas of the surface are stimulated; which parts of the mitotic apparatus furnish the stimulus and may reveal information concerning the nature of the stimulus and the nature of the cytoplasmic activity which brings about division. This paper is primarily intended as a discussion of the geometrical relations of the cleavage stimulus in invertebrate eggs and touches upon other division phenomena only as they relate to that subject. For a review of other aspects of division, the reader is referred to Wolpert’s (1960) excellent summary. 2. Cleavage in Invertebrate Eggs Unadorned observation of dividing animal cells does not permit satisfactory sorting of the division phenomena into active and passive events. The problem requires an experimental approach and its physical nature further requires physical experimentation (Swann & Mitchison, 1958). Speculations and comments in this paper are concerned with and based upon data gained from experiments upon cleaving invertebrate eggs, primarily because they presently constitute the most extensive and coherent body of knowledge concerning cytokinesis. Invertebrate eggs are usually plentiful (in season), durable, reasonably transparent and geometrically regular in shape; their time of division can be suited to the convenience of the investigator, and synchronous division of a large number of cells is easily obtained. Despite the disparate evolutionary backgrounds of the groups whose cells have commonly been used (e.g. Cnidaria, Nemertea, Echinodermata, Mollusca) the form and behavior of the division-related cell structures is similar and responses of the cells to experimentation have fallen in the same pattern. Consistency within this group has satisfied the natural desire to see a fundamental biological event in different organisms accomplished by similar processes. But whether division of echinoderm eggs,
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amphibian eggs, adult vertebrate cells in tissue culture, plant cells, polar bodies and the formation of polar lobes in development of some forms will be reducible to a single universal physical event accomplished by the operation of similar entities in all types of cells remains to be seen. The observation that division in one kind of cell may be accomplished without a particular structure or activity may not always indicate that the structure plays no necessary role in division of another kind of cell where it is normally found. The existence in some species of normal permanent cell division without nuclear division (Rappaport, 1960~) indicates the need for specific information before generalization; despite the long interest in the problem of cytokinesis, good experimental data are still relatively scarce and usually derived from studies on a limited spectrum of cell types. Existing evidence indicates that division of invertebrate eggs is accomplished by activities of the nucleus and the cell surface or cortex. In the living echinoderm egg approaching first division, the first clear visible indication of the initiation of a division cycle is the breakdown of the nuclear membrane and subsequent organization of the mitotic apparatus which consists of the spindle, bearing the chromosomes, and spherical radiate asters located at the poles of the spindle. Evidence from micro-dissection (summarized in Chambers & Chambers, 1961) indicates that the asters are of firmer consistency than interphase cytoplasm. As they wax in the division cycle, they may distort the outline of a spherical cell (Chambers, 1946) and can displace themselves within the cell by pressing against the underside of the surface (Rappaport, 1964). The mitotic apparatus occupies a variable proportion of the total cell volume; in Polychoerus (Costello, 1961) and echinoderm eggs appropriation is nearly complete while in coelenterate eggs it is relatively small and eccentric. Whether the fully developed aster normally contacts the cell surface is not yet fully established. There is no visible barrier separating the two, and some of Harvey’s (1935) and Hiramoto’s (1956) results indicate that shifting of the mitotic apparatus by centrifugation or manipulation causes a stretching of astral fibers on one side, suggesting that the fibers could be anchored to the underside of the surface. Any possible connections must be weak, as asters may be shifted inside the cell without affecting the cell contour (Chambers 8c Chambers, 1961). Before cytoplasmic division begins, mitotic rearrangement of chromosomes into two daughter masses is close to completion (Fig. 1). Where the mitotic apparatus is relatively large, the first indication of cytokinesis is a symmetrical flattening at the equator, resulting in a cylindrical zone capped at both ends by spherical segment of one base (Fig. 2). Indentation at the equator follows and the diameter of the cell is reduced in the restricted area of the furrow. Analyses of surface movements in echinoderm eggs indicate that most of the additional surface
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FIG. 1. Sand dollar egg in anaphase showing the position and relative size of the mitotic apparatus. The position of the cleavage furrow is determined by this time.
t FIG. 2. Echinoderm egg at beginning of cytokinesis showing equatorial flattening. The furrow will form in the plane indicated by the arrows.
required by this distortion derives in echinoderm eggs from stretching at the poles (Dan & Ono, 1954). There is no experimental evidence showing that the cleavage furrow in invertebrate eggs is a local site of new surface formation. In a recent electron microscope study of the cleaving Mytilus edulis egg, Humphreys (1964) described an arrangement of vesicles in the cleavage plane and proposed that the fusion of these vesicles establishes new surface which constitutes the furrow walls in the later stages of cytokinesis. Buck & Tisdale had previously (1962) interpreted similar vesicles observed in certain mammalian cells in much the same way. According to this mechanism, cytokinesis would depend upon a precise array of discontinuous elements which could be profoundly disturbed by cytoplasmic movement. No experimental demonstration of this dependence in MytiZus eggs or in mammalian cells has yet been published, but in Beriie (Ziegler, 1898) and Hydractiniu (Rappaport & Conrad, 1963) natural cytoplasmic currents have been described in the furrow region of normally cleaving eggs while in echinoderm eggs severe agitation
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of the cytoplasm in the cleavage plane before or during division does not stop the process (Hiramoto, 1956; Rappaport, 1961). All existing experimental evidence indicates that the progress of the furrow in cytokinesis is not physically dependent upon the activity or presence of the mitotic apparatus. Beginning with the work of Yatsu (1908, 1912) and culminating in the investigations of Hiramoto (1956) a succession of experiments upon eggs of nemertine worms, ctenophores, coelenterates and echinoderms have shown that egg fragments and enucleated eggs can divide provided the mitotic apparatus and surface are left in their normal relationship until the mitotic events are nearly completed. The correspondence between the plane of cleavage and the former position of the metaphase plate (Conklin, 1917) still strongly suggests a causal relation and the proposal that the mitotic apparatus releases a stimulus that determines the position of the furrow has received much attention. Only relatively recently however have experimental analyses of the nature of geometrical relationship between mitotic apparatus and cell surface been attempted. 3. Geometrical Relations of the Cleavage Stimulus and the Mechanism of Cytokinesis Hypothetical physical mechanisms require the designation of some cell region as a locus of force or changed physical properties. Thus, Lewis (1942) and others considered the furrow a site of active constriction; Swann & Mitchison (1958) designated the poles as areas of active expansion and Wolpert (1960) assembled evidence suggesting that relaxation of the polar surfaces could accomplish division in a cell that preceding cleavage had uniform tension over the entire surface. Widely different hypothetical physical mechanisms require that different areas be denoted as the locus of force. If, for instance, division is accomplished by constriction then constriction must take place in the area of the furrow. On the other hand, relaxation in the furrow area cannot divide a cell, and a relaxation mechanism necessarily involves modification of other areas. In these cases contractility and relaxation are the functionally differentiated states and result from stimulation. Since one mechanism requires stimulation at the furrow and the other at the poles, different stimulation patterns are required. Therefore, a theoretical explanation of cytokinesis can be tested by analysis of the stimulus pattern it requires as well as by direct study of the physical process. 4. Summary of Existing Information Concerning the Cleavage Stimulus The position of the furrow is determined by the position of the mitotic apparatus (Conklin, 1917). The only portions of the mitotic apparatus
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required for production of temporally and morphologically normal and permanent furrows are the asters. Two asters, situated within a critical distance of each other and of the surface, elicit a furrow regardless of the original relation between the opposed astral surfaces and the spindles
(Fig. 3). When the distance between asters is too great, no furrow appears (Rappaport, 1961).
FIG. 3. Establishment of furrow without a spindle or chromosomes. First division of torus-shaped cell results in horseshoe-shaped binucleate cell (see Fig. 6). Mitotic apparatuses for second division appear parallel to the long axis of the cell and cleavagefurrows appear in normal relation to spindles. Non-spindle furrow (shown by arrow) also appears between 2 asters from different mitotic apparatuses. The three furrows produce 4 uninucleate cells and subsequent cleavages are normal. The central circle represents a glass sphere.
Although the ability of asters alone to elicit furrowing activity had been previously shown, Swann in his 1952 review of this earlier work pointed out that a furrow established in response to an incomplete mitotic apparatus was often temporary and delayed, and he suggested that these deficiences were due to lack of spindle and chromosomes. It now seems more likely that previous treatment with parthenogenetic agents or high speed centrifugation which characterized the older work was somewhat deleterious. Wolpert (1960) pointed out the probable sufficiency of the asters alone for furrow stimulation. A single aster cannot produce a furrow. When the mitotic apparatus is sufficiently eccentric, either naturally or following manipulation, the furrow appears on the closest surface and division proceeds from one side of the cell only. In such unilaterally dividing cells, the surface most distant from the mitotic apparatus receives no direct nuclear stimulation (Yatsu, 1908; Rappaport & Conrad, 1963). But if a portion of the distant surface is pushed toward the zone between the asters a furrow will shortly appear in that area (Rappaport & Conrad, 1963). The stimulus pattern must be exceedingly durable or very rapidly established, because cells subjected to repeated kneading and extrusion while the
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position of the furrow is being determined later cleave normally (Rappaport, 1961). Since, in the flattened sand dollar egg, displacement of the mitotic apparatus one spindle diameter off-center results in absence of the furrow on one side, it appears that the limits of the stimulus zone are sharp (Rappaport & Conrad, 1963). At anaphase the asters of the sand dollar egg grow rapidly until they appear to reach into all parts of the cell (Chambers & Chambers, 1961). According to Harvey (1956), the astral rays are most extended in the latter part of anaphase in A&z& punctukzta and Wilson (1895) reports a similar relation between mitotic phase and astral growth in another sea urchin, Toxopneustes variegutus. The fully formed aster appears to have a firmly gelated central zone from which radiate the linear elements that give the structure its name. In the area where the furrow will appear the crossing of fibers from the two asters may be easily observed (Wilson, 1895, sea urchin eggs; Yatsu, 1909, Cerebrutulus eggs). The appearance of crossed fibers indicates that part of one aster can grow into the interstices of the other and that the pair is normally confluent. It is also during anaphase that the position of the furrow appears to be determined, for, from that time onward in the mitotic cycle, fragments of cell containing the presumptive furrow but excluding the mitotic apparatus will divide (Yatsu, 1908), as will the otherwise intact sea urchin egg deprived of its mitotic apparatus (Hiramoto, 1956). Since the establishment of a normal furrow requires neither spindle nor chromosomes, the significance of the correlation between anaphase and furrow determination is unclear. Cells can divide despite extensive modifications of form during the time when the position of the furrow is determined. Normally spherical echinoderm eggs divide without difficulty or delay when stretched into a cylinder of length fivefold the diameter (Rappaport, 1960b); when pressed into a torus shape (Rappaport, 1961); when modified into a hollow cylinder; when flattened and folded upon themselves (Rappaport & Conrad, 1963); and when constricted into dumb-bell shapes (Rappaport, 1964). Only as a result of flattening by compression has cleavage been suppressed by geometrical means (Danielli, 1952; Rappaport & Conrad, 1963). There are a few cases in which the number of furrows exceeds the number of mitotic apparatuses in the dividing cell. Arbuciu and Echinoruchnius eggs centrifuged just before cleavage may divide into three cells at first cleavage. Harvey (1935) suggested that the two furrows produced in this manner corresponded to the original and secondary positions of the mitotic apparatus. When two mitotic apparatuses within a single cell are properly arranged, they will consistently produce three furrows (Fig. 3).
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5. Hypothetical Stimulus Patterns Theoretical discussions of surface activity during division have assumed that there are only two states to be considered: active or passive. Correspondingly, it is assumed that there are only two conditions of cleavage stimulus : stimulated or unstimulated. It must also be assumed that stimulated and unstimulated regions manifest their respective physical properties and activities whether or not they are normally arranged. The number of arrangements, consistent with reliable information, that may be proposed is very limited and at this time the most pressing question to be settled is whether the portion of the cell surface that becomes furrow does so because it is stimulated or because it is not stimulated. (A)
POLAR
STIMULATION
In a polar stimulation pattern the position of the furrow is determined by the absence of stimulus. In this scheme first proposed by Swann & Mitchison (1958), a substance derived from the telophase nuclei moved to the polar surfaces but failed to reach the surface in the presumptive furrow region. Wolpert (1960) suggested a basically similar pattern except that the asters were considered the source of the stimulus. This is the only stimulus pattern that has been adequately discussed in the literature and related to a physical cleavage mechanism. Its theoretical possibility derives from the fact that in a spherical cell, the astral centers may be closer to the polar surface than to the presumptive furrow surface (Fig. 4). A substance diffusing from the astral
l-4
FIG. 4. Geometrical relations in a polar stimulus pattern, after Wolpert (1960). Dotted line indicates limits of the stimulus zone. A, astral center; F, furrow (equatorial) region; P, polar region.
center would therefore reach the polar surface first and elicit polar stimulation, or a nearly spherical aster that contacts the polar surface would not contact the presumptive furrow surface. In either case functional differentia-
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tion takes place at the poles and the furrow retains the properties that characterized the entire surface before regional functional differentiation. (B)
EQUATORIAL
STIMULATION
Stimulation of the presumptive furrow area or equatorial surface is the alternative to polar stimulation. The existence of this pattern would imply that functional differentiation takes place at the equator and that the polar regions retain the properties that previously characterized the entire surface. Polar behavior would therefore be passive. Kawamura (1960) suggested that the surface at the equator responds to some substance derived from the anaphase spindle. Nakahara (1952) attributed stimulatory function to a concentration of mitochondria peripheral to the spindle. Mazia (1961, p. 330) briefly alluded to the possibility that the plane of division might be defined by “expanding spheres of influence” that meet at the equator. The hypothesis that astral interaction may produce a stimulus has been briefly discussed (Rappaport, 1961) and will be further considered in the final section of this paper. 6. Choice of Hypothetical (A)
POLAR
Stimulus Pattern
PATTERN
If the position of the furrow were determined by absence of stimulus (polar pattern) then any unstimulated portion of the cell surface should take on normal furrow properties. Where the pattern is incomplete or abnormal, unstimulated areas would be expected to produce surface irregularities or constrictions which may be termed furrowing activity even though a normal furrow is not established. In cleaving eggs, the distance from the astral center to the early furrow would have to exceed the effective stimulus radius of the aster. Therefore, any part of the surface beyond this radius in any direction should show furrowing activity. Conversely, if the distance from the astral centers to the entire surface can be equalized then the surface would be uniformly stimulated and the regional functional differentiation necessary for cleavage could not occur. In sand dollar eggs subjected to constant tensile stress within 20 minutes of fertilization (Rappaport, 196Ob) the asters lie close to the furrow. The marked alteration of form of these cells places an estimated one-half of the surface farther from the astral center than the furrow (Fig. 5). Yet in this circumstance the poles exhibit no consistent tendency to constrict or change form and a furrow only appears between the asters. In the first cleavage of a torus-shaped cell there are two areas situated beyond the effective stimulus radius; one is in the presumptive furrow adjacent to the spindle and the other is between the “backs” of the asters (Fig. 6). The surface adjacent to the
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FIG. 5. Geometrical relations of the asters and surface in a cleaving sand dollar egg subjected to constant tensile stress. The circle represents a glass bead.
FIG. 6. Geometrical relations of the asters and surface in a torus-shaped sand dollar egg at fist cleavage. Completion of division results in a horseshoe-shaped, binucleate cell.
spindle produces a normal furrow, but the surface between the backs of the asters shows no signs of furrowing activity during first cleavage although much of it is farther from the asters than is the furrow. The capacity of all sides of the aster to elicit furrowing has been demonstrated (Rappaport, 1961). When the normally central mitotic apparatus of an echinoderm egg is shifted to a sufficiently eccentric position, the furrow is formed on the side closest to the mitotic apparatus (Harvey, 1935; Rappaport & Conrad, 1963). In such cells the distance from the mitotic apparatus to the surface that fails to cleave exceeds the distance from the same point to the beginning furrow and the geometrical relation between the asters and polar surfaces is (Fig. 7)
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FIG. 7. Geometrical relations in a sand dollar egg with an artificially displaced mitotic apparatus. This degree of eccentricity results in furrowing only on the cell margin closest to the mitotic apparatus.
not drastically different from normal. Further, the side farthest from the mitotic apparatus will form a furrow if it is pushed inward and held close to the zone between the asters (Rappaport & Conrad, 1963). These results indicate that in cleaving cells furrowing activity does not take place where astral influence would be minimal or absent. In the sand dollar egg, the distance between the astral centers or surfaces and the cell surface can be approximately equalized by artificially constricting the egg so that it appears half divided before and during the time when the position of the furrow is determined (Rappaport, 1964). When one aster lies in each cell half, the distance from the astral center to the presumptive furrow surface is no greater than the distance to any other part of the surface (Fig. 8). Were the difference between stimulated and unstimulated surface
FIG. 8. Geometrical relations of the asters and surface in a constricted sand dollar egg where the mitotic apparatus straddles the constriction. Bars outside cell indicate plane of artificial constriction.
related to the distance from aster to surface then all parts should be equally stimulated; the necessary functional differentiation could not occur and the cell could not divide. However, constricted sand dollar eggs divide normally and the furrow lies at the zone between the asters even when that zone coincides with the plane of the constriction. In these complementary experiments
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the concept of determination of the furrow by absence of stimulus has been tested and found wanting. Geometrical re-arrangements that should have produced extra furrows failed to do so and other re-arrangements that should have suppressed division did not. (B)
EQUATORIAL
PATTERN
Since the cell does not behave as though the furrow is an unstimulated or undifferentiated area, the simplest alternative is to suggest the oppositenamely, that the presumptive furrow surface is stimulated to a greater extent than is the surface in any other portion of the cell. First, the source of the stimulus must be identified. One of the oldest correlations in the study of cytokinesis is the observation that the furrow cuts through the spindle at the site earlier occupied by the metaphase plate. Recently, Kawamura (1960) confirmed the existence of this relationship in the grasshopper neuroblast following relocation and rotation of the intact mitotic apparatus by micromanipulation. He further speculated that the position of the furrow was determined by some substance derived from the anaphase spindle but his results do not strongly support the designation of any specific region of the mitotic apparatus as the source, since usually neither the fundamental form of the apparatus nor its relation to the surface were altered. At any rate the spindle cannot be the source of the stimulus in sand dollar eggs since temporally and morphologically normal and permanent furrows appear between pairs of asters that lack an intervening spindle (Rappaport, 1961). Establishment of a furrow requires a geometrical arrangement in which two critical (and unmeasured) distances are not exceeded. First, the surface must be close enough to the mitotic apparatus to receive the stimulus; when the mitotic apparatus is eccentric the unilateral furrow begins from the surface closest to the mitotic apparatus (Yatsu, 1908; Harvey, 193.5; Rappaport & Conrad, 1963). Second, the asters cannot be too far apart; when two asters are within normal distance of the surface, but abnormally distant from each other, no furrow is formed (Fig. 6) (Rappaport, 1961). The absence of furrowing when the distance between asters is abnormally great leads to the conjecture that stimulation is a consequence of joint astral activity. Observations of cleavage in eggs where the mitotic apparatus lies on one side of a median constriction lends support to this idea (Rappaport, 1964). In such experimentally modified cells, one aster lies with its center nearly in the plane of the constriction while the other aster lies at the other end of the spindle against the polar cell surface (see Fig. 9). The spindle and its contents have previously been eliminated as a possible stimulus source (Rappaport, 1961) and the aster at the constriction projects nearly as far into the empty side of the cell as into the side containing the balance of the mitotic apparatus.
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FIG. 9. Geometrical relations of the asters and surfaces in a constricted sand dollar egg where the mitotic apparatus lies on one side of the constriction. Bars outside cell indicate plane of artificial constriction.
Functionally, the only difference between the two halves of the constricted cell is the presence of a second aster in one of them. The furrow, however, only appears on the side containing the second aster and eventually separates the asters. Were the position of the furrow established by absence of stimulus, both halves of the cell would have manifested furrowing activity. The results strongly suggest that establishment of the furrow requires two asters working in concert. One explanation of the fact that a pair of asters can accomplish something that neither can accomplish singly is that somehow their activity is additive. The necessity for proximity and the appearance of crossing astral fibers in the presumptive furrow or equatorial region (Wilson, 1895 ; Yatsu, 1909) suggests that when stimulation is accomplished the asters are normally confluent in the zone lying peripheral to the spindle. In this arrangement the stimulatory activity of the aster could be evenly distributed over its surface and the polar surfaces would be subject to some stimulation. In the zone of confluence the equatorial cell surface would be exposed to both asters and therefore to a higher level of stimulatory activity. The stimulus zone would be shaped like a torus with its inner limit peripheral to the spindle and its outer limit at the cell surface. Thus the difference between a stimulated and an unstimulated zone would be quantitative. It may be that some of the physical cytoplasmic changes that take place outside the equatorial zone in the cleavage cycle result from the lower level of astral stimulation although some appear to take place independently of the nuclear cycle (Bell, 1962). It is also possible that the internal rearrangement which must occur as the asters grow may yield a redistribution of cytoplasmic elements that could serve as a stimulus. Mazia (1961, section IX, A) discussed the capacity of the mitotic apparatus to exclude foreign particles. Although astral fibers cross under the equatorial surface, the cytoplasm in this zone is not SO firmly gelated (Rappaport, 1964) and may be fluid (Chambers & Chambers, 1961).
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Where the mitotic apparatus expands close to the surface some particles would be displaced from areas adjacent to the lateral and polar regions of the asters to the zone between the asters, and non-homogenous distribution would be achieved. Invertebrate eggs do not present the clear picture of mitochondrial concentration in the presumptive furrow plane demonstrated by Nakahara (1952) in the grasshopper spermatocyte; further, the identification of particulate stimulating elements may be complicated by Harvey’s (1951) observation that the clear quarter of centrifuged Arbacia eggs cleaves and develops normally. 7. The Nature of the Cleavage Stimulus Evidence in section 2 suggests that division is a consequence of physical activities of the surface and information discussed in section 6(~) points to the probability that the changes are localized in the equatorial region. Such changes could result directly from modification of the surface itself or indirectly from modification of the underlying cytoplasm to which the surface would respond. The asters may cause the changes by one of the following basic processes: addition of something to the surface; removal of something from the surface or infection of the surface with some propagable change in molecular structure accomplished without moving specific substances. There is so little information bearing upon the nature of the stimulus that discussion aimed at selection of the most likely of these alternatives is now futile. However, the following speculations may eventually prove useful. If stimulation is accomplished by adding to or removing something from the presumptive furrow surface, the system involved is probably not a simple one involving a freely diffusable substance in a fluid underlying a membrane. Such a system would be more easily disrupted by kneading and extrusion during the time of furrow determination than is the case. The substance would have to be fixed to some structure that is not disrupted by cytoplasmic flow. The aster appears to be very conveniently constructed and located for this type of activity. Astral growth in part occurs at the expense of cytoplasmic components and as the volume of aster increases, the concentration of free astral precursor must fall. This relationship could constitute a triggering mechanism for furrowing and since the zone of confluence of the asters might be expected to be most depleted of astral precursor, one event would accomplish several ends. Anything that can be trapped by the asters. whether or not it becomes an integral part of the aster, would be more thoroughly removed from the fluid cytoplasm in the zone of confluence. In this connection, Mazia’s (1959) observations concerning the marked chelating capacity of the isolated mitotic apparatus are very pertinent. A trigger operating by the sequestering of a
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common substance is a more attractive working hypothesis than one involving the periodic synthesis of a special stimulatory entity. On the other hand, it is possible that cleavage is the culmination of a single process that begins with the growth of the asters. Astral fibers appear to elongate by terminal accretion of precursor; in this mechanism the reactions responsible for elongation must be located at the tips of the fibers. Therefore, each new increment in addition to contributing additional length is itself changed to become the active site that binds free precursor from the cytoplasm. The period of activity must be brief; free precursor must lack the capacity to bind or else astral growth would be forestalled by random aggregations of precursor in the cytoplasm, and an increment must lose its binding capacity when it is no longer terminal, else the astral elements would not appear as unbranched radiating fibers. There is implied a propagable molecular reorganization at the tip of the eIongating fiber. When the tip of the fiber reaches the continuum of the surface (Harvey, 1935), it could lead to physical changes in the part contacted. The number of surface-fiber contacts should be greater where the asters are confluent and quantitative requirements would be satisfied. After the furrow has been established, it appears to be self-propagating and can pass through unstimulated areas (Rappaport & Conrad, 1963). This interpretation endows the cleavage process with a certain unity for which Dan (1963) has expressed desire. This work was supported by grant GB-2% from the National Foundation.
Science
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Geometrical Relations of the Cleavage Stimulus in Invertebrate Eggs R. RAPPAPORT Department
of Biological Sciences, Union College, Schenectady, New York, U.S.A. and
The Mount Desert Island Biological Laboratory, Maine, U.S. A.
Salisbury Cove,
(Received 22 October 1964) Before cytokinesis, the mitotic apparatus apparently provides a stimulus that affects certain parts of the cell surface and determines the position of the cleavage furrow. An understanding of the pattern of stimulation will help to elucidate other activities involved in the division process. Since different hypothetical physical mechanisms that could accomplish cytokinesis require different stimulus patterns, the form of the stimulus pattern becomes a basis for judgement of alternative physical mechanisms. It is assumed that stimulated surface regions undergo changes in physical properties or activities that culminate in cleavage; unstimulated regions retain qualities characteristic of the entire surface before functional differentiation. The asters are the only parts of the mitotic apparatus required for normal stimulation. Two possible stimulus patterns are considered: polar stimulation in which the position of the furrow is determined by absence of stimulus and the poles are stimulated, and equatorial stimulation in which the presumptive furrow is stimulated and the poles are unstimulated. Experimental results indicate that the position of the furrow is not determined by absence of stimulus, leaving the alternative of positive stimulation in the presumptive furrow region. It is possible that equatorial stimulation may be accomplished by additive activity of the asters which could occur in their zone of confluence. This zone of astral confluence coincides with the future plane of cleavage. Several possibilities concerning the nature of the cleavage stimulus are described.
1. Introduction Classical analyses of the physical mechanisms that accomplish cytoplasmic division in animal cells usually involve operations performed after determination of the position of the cleavage furrow, or measurements of some physical property made at intervals during the division cycle. Study of the 51
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geometrical relations of the cleavage stimulus is a third approach that will yield information useful in the assessment of hypotheses concerning cytokinesis. Although the cytoplasm governs the periodicity of cleavages (Moore, 1933), the stimulus that determines the position of the furrow is released by the mitotic apparatus. Cytokinesis is accomplished by the cell surface or cortex in invertebrate eggs and the purpose of geometrical analysis is to determine which regions of the surface are affected by the stimulus. Cells can divide only if different parts do different things or acquire different physical properties. This functional differentiation (Wolpert, 1960) comes about because some regions are stimulated and others are not. It must be assumed that the activities or properties of stimulated parts are changed while those of unstimulated parts are not. Better understanding of the geometrical relations of the cleavage stimulus could indicate which areas of the surface are stimulated; which parts of the mitotic apparatus furnish the stimulus and may reveal information concerning the nature of the stimulus and the nature of the cytoplasmic activity which brings about division. This paper is primarily intended as a discussion of the geometrical relations of the cleavage stimulus in invertebrate eggs and touches upon other division phenomena only as they relate to that subject. For a review of other aspects of division, the reader is referred to Wolpert’s (1960) excellent summary. 2. Cleavage in Invertebrate Eggs Unadorned observation of dividing animal cells does not permit satisfactory sorting of the division phenomena into active and passive events. The problem requires an experimental approach and its physical nature further requires physical experimentation (Swann & Mitchison, 1958). Speculations and comments in this paper are concerned with and based upon data gained from experiments upon cleaving invertebrate eggs, primarily because they presently constitute the most extensive and coherent body of knowledge concerning cytokinesis. Invertebrate eggs are usually plentiful (in season), durable, reasonably transparent and geometrically regular in shape; their time of division can be suited to the convenience of the investigator, and synchronous division of a large number of cells is easily obtained. Despite the disparate evolutionary backgrounds of the groups whose cells have commonly been used (e.g. Cnidaria, Nemertea, Echinodermata, Mollusca) the form and behavior of the division-related cell structures is similar and responses of the cells to experimentation have fallen in the same pattern. Consistency within this group has satisfied the natural desire to see a fundamental biological event in different organisms accomplished by similar processes. But whether division of echinoderm eggs,
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amphibian eggs, adult vertebrate cells in tissue culture, plant cells, polar bodies and the formation of polar lobes in development of some forms will be reducible to a single universal physical event accomplished by the operation of similar entities in all types of cells remains to be seen. The observation that division in one kind of cell may be accomplished without a particular structure or activity may not always indicate that the structure plays no necessary role in division of another kind of cell where it is normally found. The existence in some species of normal permanent cell division without nuclear division (Rappaport, 1960~) indicates the need for specific information before generalization; despite the long interest in the problem of cytokinesis, good experimental data are still relatively scarce and usually derived from studies on a limited spectrum of cell types. Existing evidence indicates that division of invertebrate eggs is accomplished by activities of the nucleus and the cell surface or cortex. In the living echinoderm egg approaching first division, the first clear visible indication of the initiation of a division cycle is the breakdown of the nuclear membrane and subsequent organization of the mitotic apparatus which consists of the spindle, bearing the chromosomes, and spherical radiate asters located at the poles of the spindle. Evidence from micro-dissection (summarized in Chambers & Chambers, 1961) indicates that the asters are of firmer consistency than interphase cytoplasm. As they wax in the division cycle, they may distort the outline of a spherical cell (Chambers, 1946) and can displace themselves within the cell by pressing against the underside of the surface (Rappaport, 1964). The mitotic apparatus occupies a variable proportion of the total cell volume; in Polychoerus (Costello, 1961) and echinoderm eggs appropriation is nearly complete while in coelenterate eggs it is relatively small and eccentric. Whether the fully developed aster normally contacts the cell surface is not yet fully established. There is no visible barrier separating the two, and some of Harvey’s (1935) and Hiramoto’s (1956) results indicate that shifting of the mitotic apparatus by centrifugation or manipulation causes a stretching of astral fibers on one side, suggesting that the fibers could be anchored to the underside of the surface. Any possible connections must be weak, as asters may be shifted inside the cell without affecting the cell contour (Chambers 8c Chambers, 1961). Before cytoplasmic division begins, mitotic rearrangement of chromosomes into two daughter masses is close to completion (Fig. 1). Where the mitotic apparatus is relatively large, the first indication of cytokinesis is a symmetrical flattening at the equator, resulting in a cylindrical zone capped at both ends by spherical segment of one base (Fig. 2). Indentation at the equator follows and the diameter of the cell is reduced in the restricted area of the furrow. Analyses of surface movements in echinoderm eggs indicate that most of the additional surface
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FIG. 1. Sand dollar egg in anaphase showing the position and relative size of the mitotic apparatus. The position of the cleavage furrow is determined by this time.
t FIG. 2. Echinoderm egg at beginning of cytokinesis showing equatorial flattening. The furrow will form in the plane indicated by the arrows.
required by this distortion derives in echinoderm eggs from stretching at the poles (Dan & Ono, 1954). There is no experimental evidence showing that the cleavage furrow in invertebrate eggs is a local site of new surface formation. In a recent electron microscope study of the cleaving Mytilus edulis egg, Humphreys (1964) described an arrangement of vesicles in the cleavage plane and proposed that the fusion of these vesicles establishes new surface which constitutes the furrow walls in the later stages of cytokinesis. Buck & Tisdale had previously (1962) interpreted similar vesicles observed in certain mammalian cells in much the same way. According to this mechanism, cytokinesis would depend upon a precise array of discontinuous elements which could be profoundly disturbed by cytoplasmic movement. No experimental demonstration of this dependence in MytiZus eggs or in mammalian cells has yet been published, but in Beriie (Ziegler, 1898) and Hydractiniu (Rappaport & Conrad, 1963) natural cytoplasmic currents have been described in the furrow region of normally cleaving eggs while in echinoderm eggs severe agitation
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of the cytoplasm in the cleavage plane before or during division does not stop the process (Hiramoto, 1956; Rappaport, 1961). All existing experimental evidence indicates that the progress of the furrow in cytokinesis is not physically dependent upon the activity or presence of the mitotic apparatus. Beginning with the work of Yatsu (1908, 1912) and culminating in the investigations of Hiramoto (1956) a succession of experiments upon eggs of nemertine worms, ctenophores, coelenterates and echinoderms have shown that egg fragments and enucleated eggs can divide provided the mitotic apparatus and surface are left in their normal relationship until the mitotic events are nearly completed. The correspondence between the plane of cleavage and the former position of the metaphase plate (Conklin, 1917) still strongly suggests a causal relation and the proposal that the mitotic apparatus releases a stimulus that determines the position of the furrow has received much attention. Only relatively recently however have experimental analyses of the nature of geometrical relationship between mitotic apparatus and cell surface been attempted. 3. Geometrical Relations of the Cleavage Stimulus and the Mechanism of Cytokinesis Hypothetical physical mechanisms require the designation of some cell region as a locus of force or changed physical properties. Thus, Lewis (1942) and others considered the furrow a site of active constriction; Swann & Mitchison (1958) designated the poles as areas of active expansion and Wolpert (1960) assembled evidence suggesting that relaxation of the polar surfaces could accomplish division in a cell that preceding cleavage had uniform tension over the entire surface. Widely different hypothetical physical mechanisms require that different areas be denoted as the locus of force. If, for instance, division is accomplished by constriction then constriction must take place in the area of the furrow. On the other hand, relaxation in the furrow area cannot divide a cell, and a relaxation mechanism necessarily involves modification of other areas. In these cases contractility and relaxation are the functionally differentiated states and result from stimulation. Since one mechanism requires stimulation at the furrow and the other at the poles, different stimulation patterns are required. Therefore, a theoretical explanation of cytokinesis can be tested by analysis of the stimulus pattern it requires as well as by direct study of the physical process. 4. Summary of Existing Information Concerning the Cleavage Stimulus The position of the furrow is determined by the position of the mitotic apparatus (Conklin, 1917). The only portions of the mitotic apparatus
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required for production of temporally and morphologically normal and permanent furrows are the asters. Two asters, situated within a critical distance of each other and of the surface, elicit a furrow regardless of the original relation between the opposed astral surfaces and the spindles
(Fig. 3). When the distance between asters is too great, no furrow appears (Rappaport, 1961).
FIG. 3. Establishment of furrow without a spindle or chromosomes. First division of torus-shaped cell results in horseshoe-shaped binucleate cell (see Fig. 6). Mitotic apparatuses for second division appear parallel to the long axis of the cell and cleavagefurrows appear in normal relation to spindles. Non-spindle furrow (shown by arrow) also appears between 2 asters from different mitotic apparatuses. The three furrows produce 4 uninucleate cells and subsequent cleavages are normal. The central circle represents a glass sphere.
Although the ability of asters alone to elicit furrowing activity had been previously shown, Swann in his 1952 review of this earlier work pointed out that a furrow established in response to an incomplete mitotic apparatus was often temporary and delayed, and he suggested that these deficiences were due to lack of spindle and chromosomes. It now seems more likely that previous treatment with parthenogenetic agents or high speed centrifugation which characterized the older work was somewhat deleterious. Wolpert (1960) pointed out the probable sufficiency of the asters alone for furrow stimulation. A single aster cannot produce a furrow. When the mitotic apparatus is sufficiently eccentric, either naturally or following manipulation, the furrow appears on the closest surface and division proceeds from one side of the cell only. In such unilaterally dividing cells, the surface most distant from the mitotic apparatus receives no direct nuclear stimulation (Yatsu, 1908; Rappaport & Conrad, 1963). But if a portion of the distant surface is pushed toward the zone between the asters a furrow will shortly appear in that area (Rappaport & Conrad, 1963). The stimulus pattern must be exceedingly durable or very rapidly established, because cells subjected to repeated kneading and extrusion while the
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position of the furrow is being determined later cleave normally (Rappaport, 1961). Since, in the flattened sand dollar egg, displacement of the mitotic apparatus one spindle diameter off-center results in absence of the furrow on one side, it appears that the limits of the stimulus zone are sharp (Rappaport & Conrad, 1963). At anaphase the asters of the sand dollar egg grow rapidly until they appear to reach into all parts of the cell (Chambers & Chambers, 1961). According to Harvey (1956), the astral rays are most extended in the latter part of anaphase in A&z& punctukzta and Wilson (1895) reports a similar relation between mitotic phase and astral growth in another sea urchin, Toxopneustes variegutus. The fully formed aster appears to have a firmly gelated central zone from which radiate the linear elements that give the structure its name. In the area where the furrow will appear the crossing of fibers from the two asters may be easily observed (Wilson, 1895, sea urchin eggs; Yatsu, 1909, Cerebrutulus eggs). The appearance of crossed fibers indicates that part of one aster can grow into the interstices of the other and that the pair is normally confluent. It is also during anaphase that the position of the furrow appears to be determined, for, from that time onward in the mitotic cycle, fragments of cell containing the presumptive furrow but excluding the mitotic apparatus will divide (Yatsu, 1908), as will the otherwise intact sea urchin egg deprived of its mitotic apparatus (Hiramoto, 1956). Since the establishment of a normal furrow requires neither spindle nor chromosomes, the significance of the correlation between anaphase and furrow determination is unclear. Cells can divide despite extensive modifications of form during the time when the position of the furrow is determined. Normally spherical echinoderm eggs divide without difficulty or delay when stretched into a cylinder of length fivefold the diameter (Rappaport, 1960b); when pressed into a torus shape (Rappaport, 1961); when modified into a hollow cylinder; when flattened and folded upon themselves (Rappaport & Conrad, 1963); and when constricted into dumb-bell shapes (Rappaport, 1964). Only as a result of flattening by compression has cleavage been suppressed by geometrical means (Danielli, 1952; Rappaport & Conrad, 1963). There are a few cases in which the number of furrows exceeds the number of mitotic apparatuses in the dividing cell. Arbuciu and Echinoruchnius eggs centrifuged just before cleavage may divide into three cells at first cleavage. Harvey (1935) suggested that the two furrows produced in this manner corresponded to the original and secondary positions of the mitotic apparatus. When two mitotic apparatuses within a single cell are properly arranged, they will consistently produce three furrows (Fig. 3).
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5. Hypothetical Stimulus Patterns Theoretical discussions of surface activity during division have assumed that there are only two states to be considered: active or passive. Correspondingly, it is assumed that there are only two conditions of cleavage stimulus : stimulated or unstimulated. It must also be assumed that stimulated and unstimulated regions manifest their respective physical properties and activities whether or not they are normally arranged. The number of arrangements, consistent with reliable information, that may be proposed is very limited and at this time the most pressing question to be settled is whether the portion of the cell surface that becomes furrow does so because it is stimulated or because it is not stimulated. (A)
POLAR
STIMULATION
In a polar stimulation pattern the position of the furrow is determined by the absence of stimulus. In this scheme first proposed by Swann & Mitchison (1958), a substance derived from the telophase nuclei moved to the polar surfaces but failed to reach the surface in the presumptive furrow region. Wolpert (1960) suggested a basically similar pattern except that the asters were considered the source of the stimulus. This is the only stimulus pattern that has been adequately discussed in the literature and related to a physical cleavage mechanism. Its theoretical possibility derives from the fact that in a spherical cell, the astral centers may be closer to the polar surface than to the presumptive furrow surface (Fig. 4). A substance diffusing from the astral
l-4
FIG. 4. Geometrical relations in a polar stimulus pattern, after Wolpert (1960). Dotted line indicates limits of the stimulus zone. A, astral center; F, furrow (equatorial) region; P, polar region.
center would therefore reach the polar surface first and elicit polar stimulation, or a nearly spherical aster that contacts the polar surface would not contact the presumptive furrow surface. In either case functional differentia-
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tion takes place at the poles and the furrow retains the properties that characterized the entire surface before regional functional differentiation. (B)
EQUATORIAL
STIMULATION
Stimulation of the presumptive furrow area or equatorial surface is the alternative to polar stimulation. The existence of this pattern would imply that functional differentiation takes place at the equator and that the polar regions retain the properties that previously characterized the entire surface. Polar behavior would therefore be passive. Kawamura (1960) suggested that the surface at the equator responds to some substance derived from the anaphase spindle. Nakahara (1952) attributed stimulatory function to a concentration of mitochondria peripheral to the spindle. Mazia (1961, p. 330) briefly alluded to the possibility that the plane of division might be defined by “expanding spheres of influence” that meet at the equator. The hypothesis that astral interaction may produce a stimulus has been briefly discussed (Rappaport, 1961) and will be further considered in the final section of this paper. 6. Choice of Hypothetical (A)
POLAR
Stimulus Pattern
PATTERN
If the position of the furrow were determined by absence of stimulus (polar pattern) then any unstimulated portion of the cell surface should take on normal furrow properties. Where the pattern is incomplete or abnormal, unstimulated areas would be expected to produce surface irregularities or constrictions which may be termed furrowing activity even though a normal furrow is not established. In cleaving eggs, the distance from the astral center to the early furrow would have to exceed the effective stimulus radius of the aster. Therefore, any part of the surface beyond this radius in any direction should show furrowing activity. Conversely, if the distance from the astral centers to the entire surface can be equalized then the surface would be uniformly stimulated and the regional functional differentiation necessary for cleavage could not occur. In sand dollar eggs subjected to constant tensile stress within 20 minutes of fertilization (Rappaport, 196Ob) the asters lie close to the furrow. The marked alteration of form of these cells places an estimated one-half of the surface farther from the astral center than the furrow (Fig. 5). Yet in this circumstance the poles exhibit no consistent tendency to constrict or change form and a furrow only appears between the asters. In the first cleavage of a torus-shaped cell there are two areas situated beyond the effective stimulus radius; one is in the presumptive furrow adjacent to the spindle and the other is between the “backs” of the asters (Fig. 6). The surface adjacent to the
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FIG. 5. Geometrical relations of the asters and surface in a cleaving sand dollar egg subjected to constant tensile stress. The circle represents a glass bead.
FIG. 6. Geometrical relations of the asters and surface in a torus-shaped sand dollar egg at fist cleavage. Completion of division results in a horseshoe-shaped, binucleate cell.
spindle produces a normal furrow, but the surface between the backs of the asters shows no signs of furrowing activity during first cleavage although much of it is farther from the asters than is the furrow. The capacity of all sides of the aster to elicit furrowing has been demonstrated (Rappaport, 1961). When the normally central mitotic apparatus of an echinoderm egg is shifted to a sufficiently eccentric position, the furrow is formed on the side closest to the mitotic apparatus (Harvey, 1935; Rappaport & Conrad, 1963). In such cells the distance from the mitotic apparatus to the surface that fails to cleave exceeds the distance from the same point to the beginning furrow and the geometrical relation between the asters and polar surfaces is (Fig. 7)
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FIG. 7. Geometrical relations in a sand dollar egg with an artificially displaced mitotic apparatus. This degree of eccentricity results in furrowing only on the cell margin closest to the mitotic apparatus.
not drastically different from normal. Further, the side farthest from the mitotic apparatus will form a furrow if it is pushed inward and held close to the zone between the asters (Rappaport & Conrad, 1963). These results indicate that in cleaving cells furrowing activity does not take place where astral influence would be minimal or absent. In the sand dollar egg, the distance between the astral centers or surfaces and the cell surface can be approximately equalized by artificially constricting the egg so that it appears half divided before and during the time when the position of the furrow is determined (Rappaport, 1964). When one aster lies in each cell half, the distance from the astral center to the presumptive furrow surface is no greater than the distance to any other part of the surface (Fig. 8). Were the difference between stimulated and unstimulated surface
FIG. 8. Geometrical relations of the asters and surface in a constricted sand dollar egg where the mitotic apparatus straddles the constriction. Bars outside cell indicate plane of artificial constriction.
related to the distance from aster to surface then all parts should be equally stimulated; the necessary functional differentiation could not occur and the cell could not divide. However, constricted sand dollar eggs divide normally and the furrow lies at the zone between the asters even when that zone coincides with the plane of the constriction. In these complementary experiments
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the concept of determination of the furrow by absence of stimulus has been tested and found wanting. Geometrical re-arrangements that should have produced extra furrows failed to do so and other re-arrangements that should have suppressed division did not. (B)
EQUATORIAL
PATTERN
Since the cell does not behave as though the furrow is an unstimulated or undifferentiated area, the simplest alternative is to suggest the oppositenamely, that the presumptive furrow surface is stimulated to a greater extent than is the surface in any other portion of the cell. First, the source of the stimulus must be identified. One of the oldest correlations in the study of cytokinesis is the observation that the furrow cuts through the spindle at the site earlier occupied by the metaphase plate. Recently, Kawamura (1960) confirmed the existence of this relationship in the grasshopper neuroblast following relocation and rotation of the intact mitotic apparatus by micromanipulation. He further speculated that the position of the furrow was determined by some substance derived from the anaphase spindle but his results do not strongly support the designation of any specific region of the mitotic apparatus as the source, since usually neither the fundamental form of the apparatus nor its relation to the surface were altered. At any rate the spindle cannot be the source of the stimulus in sand dollar eggs since temporally and morphologically normal and permanent furrows appear between pairs of asters that lack an intervening spindle (Rappaport, 1961). Establishment of a furrow requires a geometrical arrangement in which two critical (and unmeasured) distances are not exceeded. First, the surface must be close enough to the mitotic apparatus to receive the stimulus; when the mitotic apparatus is eccentric the unilateral furrow begins from the surface closest to the mitotic apparatus (Yatsu, 1908; Harvey, 193.5; Rappaport & Conrad, 1963). Second, the asters cannot be too far apart; when two asters are within normal distance of the surface, but abnormally distant from each other, no furrow is formed (Fig. 6) (Rappaport, 1961). The absence of furrowing when the distance between asters is abnormally great leads to the conjecture that stimulation is a consequence of joint astral activity. Observations of cleavage in eggs where the mitotic apparatus lies on one side of a median constriction lends support to this idea (Rappaport, 1964). In such experimentally modified cells, one aster lies with its center nearly in the plane of the constriction while the other aster lies at the other end of the spindle against the polar cell surface (see Fig. 9). The spindle and its contents have previously been eliminated as a possible stimulus source (Rappaport, 1961) and the aster at the constriction projects nearly as far into the empty side of the cell as into the side containing the balance of the mitotic apparatus.
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FIG. 9. Geometrical relations of the asters and surfaces in a constricted sand dollar egg where the mitotic apparatus lies on one side of the constriction. Bars outside cell indicate plane of artificial constriction.
Functionally, the only difference between the two halves of the constricted cell is the presence of a second aster in one of them. The furrow, however, only appears on the side containing the second aster and eventually separates the asters. Were the position of the furrow established by absence of stimulus, both halves of the cell would have manifested furrowing activity. The results strongly suggest that establishment of the furrow requires two asters working in concert. One explanation of the fact that a pair of asters can accomplish something that neither can accomplish singly is that somehow their activity is additive. The necessity for proximity and the appearance of crossing astral fibers in the presumptive furrow or equatorial region (Wilson, 1895 ; Yatsu, 1909) suggests that when stimulation is accomplished the asters are normally confluent in the zone lying peripheral to the spindle. In this arrangement the stimulatory activity of the aster could be evenly distributed over its surface and the polar surfaces would be subject to some stimulation. In the zone of confluence the equatorial cell surface would be exposed to both asters and therefore to a higher level of stimulatory activity. The stimulus zone would be shaped like a torus with its inner limit peripheral to the spindle and its outer limit at the cell surface. Thus the difference between a stimulated and an unstimulated zone would be quantitative. It may be that some of the physical cytoplasmic changes that take place outside the equatorial zone in the cleavage cycle result from the lower level of astral stimulation although some appear to take place independently of the nuclear cycle (Bell, 1962). It is also possible that the internal rearrangement which must occur as the asters grow may yield a redistribution of cytoplasmic elements that could serve as a stimulus. Mazia (1961, section IX, A) discussed the capacity of the mitotic apparatus to exclude foreign particles. Although astral fibers cross under the equatorial surface, the cytoplasm in this zone is not SO firmly gelated (Rappaport, 1964) and may be fluid (Chambers & Chambers, 1961).
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Where the mitotic apparatus expands close to the surface some particles would be displaced from areas adjacent to the lateral and polar regions of the asters to the zone between the asters, and non-homogenous distribution would be achieved. Invertebrate eggs do not present the clear picture of mitochondrial concentration in the presumptive furrow plane demonstrated by Nakahara (1952) in the grasshopper spermatocyte; further, the identification of particulate stimulating elements may be complicated by Harvey’s (1951) observation that the clear quarter of centrifuged Arbacia eggs cleaves and develops normally. 7. The Nature of the Cleavage Stimulus Evidence in section 2 suggests that division is a consequence of physical activities of the surface and information discussed in section 6(~) points to the probability that the changes are localized in the equatorial region. Such changes could result directly from modification of the surface itself or indirectly from modification of the underlying cytoplasm to which the surface would respond. The asters may cause the changes by one of the following basic processes: addition of something to the surface; removal of something from the surface or infection of the surface with some propagable change in molecular structure accomplished without moving specific substances. There is so little information bearing upon the nature of the stimulus that discussion aimed at selection of the most likely of these alternatives is now futile. However, the following speculations may eventually prove useful. If stimulation is accomplished by adding to or removing something from the presumptive furrow surface, the system involved is probably not a simple one involving a freely diffusable substance in a fluid underlying a membrane. Such a system would be more easily disrupted by kneading and extrusion during the time of furrow determination than is the case. The substance would have to be fixed to some structure that is not disrupted by cytoplasmic flow. The aster appears to be very conveniently constructed and located for this type of activity. Astral growth in part occurs at the expense of cytoplasmic components and as the volume of aster increases, the concentration of free astral precursor must fall. This relationship could constitute a triggering mechanism for furrowing and since the zone of confluence of the asters might be expected to be most depleted of astral precursor, one event would accomplish several ends. Anything that can be trapped by the asters. whether or not it becomes an integral part of the aster, would be more thoroughly removed from the fluid cytoplasm in the zone of confluence. In this connection, Mazia’s (1959) observations concerning the marked chelating capacity of the isolated mitotic apparatus are very pertinent. A trigger operating by the sequestering of a
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common substance is a more attractive working hypothesis than one involving the periodic synthesis of a special stimulatory entity. On the other hand, it is possible that cleavage is the culmination of a single process that begins with the growth of the asters. Astral fibers appear to elongate by terminal accretion of precursor; in this mechanism the reactions responsible for elongation must be located at the tips of the fibers. Therefore, each new increment in addition to contributing additional length is itself changed to become the active site that binds free precursor from the cytoplasm. The period of activity must be brief; free precursor must lack the capacity to bind or else astral growth would be forestalled by random aggregations of precursor in the cytoplasm, and an increment must lose its binding capacity when it is no longer terminal, else the astral elements would not appear as unbranched radiating fibers. There is implied a propagable molecular reorganization at the tip of the eIongating fiber. When the tip of the fiber reaches the continuum of the surface (Harvey, 1935), it could lead to physical changes in the part contacted. The number of surface-fiber contacts should be greater where the asters are confluent and quantitative requirements would be satisfied. After the furrow has been established, it appears to be self-propagating and can pass through unstimulated areas (Rappaport & Conrad, 1963). This interpretation endows the cleavage process with a certain unity for which Dan (1963) has expressed desire. This work was supported by grant GB-2% from the National Foundation.
Science
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