J. theor. BioL (1976) 58, 365-382
The Cell Surface in Relation to the Growth Cycle C. A. PASTERNAK t
Department of Biochemistry, Universityof Oxford, Oxford OXI 3QU, England (Received 25 June 1975) The cell surface bears an intimate relation to events during the cell cycle. The following postulates are presented as working hypotheses in order to clarify current observations and to stimulate new experimental approaches. (1) Initiation of karyokinesis is a necessary prerequisite for the initiation of cytokinesis; the reverse is not true. (2) In spherical cells that double in volume prior to mitosis, the ratio of surface area ."volume is maintained by the elaboration of microvilli; the extra surface area generated by cytokinesis is provided by an unfolding of microvilli. (3) The state of the cell surface during interphase and in Go is different from that during mitosis; the difference is due to the involvement of intracellular elements that otherwise participate in the formation of the mitotic spindle and cleavage furrow. The association of such elements with the cell surface is greater in normal than in cancer cells.
1. Introduction The cell cycle is a convenient way of defining discrete periods of macromolecular synthesis and assembly that take place between successive cell divisions. What is lacking at present is knowledge of how the various periods, and the operation of the cycle itself, are controlled (Mitchison, 1971a; Padilla, Cameron & Zimmerman, 1974). In this article three postulates are presented which may help to correlate present observations and to stimulate new approaches to the problem. Each concerns the cell surface. The cell surface bears a "special relation" to nuclear events in animal cells. Nuclear division (karyokinesis), for example, is almost always accompanied by cell division (cytokinesis), and exceptions to the reverse situation (cytokinesis without karyokinesis) are rare indeed (see section 2). On the other hand, proliferation o f mitochondria or the endoplasmic retieulum is t Present address: St. George's Hospital Medical School, Blackshaw Road, Tooting, London SWl7 0QT. T.B.
365
24
366
C. A. P A S T E R N A K
not directly related to nuclear division. In embryonic development, for example, cell division (cleavage) occurs without concomitant change in number of mitochondria (Shaver, 1956) or amount of endoplasmic retieulum (Davidson, 1968; Giudice, 1973); in oogenesis, the converse is true. In anaerobically-grown yeast that is exposed to oxygen, mitochondrial assembly (Roodyn & Wilkie, 1968; Getz, 1972) takes place independently of cell division; in the liver of rats exposed to phenobarbital, endoplasmic reticulum proliferates (Orrenius, Ericsson & Ernster, 1965) without an increase in mitotic rate. It is true that during the stimulation of duck salt glands, plasma membrane proliferates without nuclear division (Levine, Higgins & Barnett, 1972), but cytokinesis does not take place. The first hypothesis which is discussed in section 2, concerns this relationship between cytokinesis and karyokinesis. Although the link between the cell surface and nucleus is most obviously expressed during mitosis, there is an increasing number of reports that suggest an influence of the cell surface on nuclear function during interphase also (e.g. Fox, Sheppard & Burger, 1971; Burger, 1973; Inbar & Shinitzky, 1974; reviewed by Pardee, 1971 ; Turner & Burger, 1973; Knox & Pasternak, 1976). In some instances the effect may be more apparent than real, in the sense that the cell surface is merely a transmitter of signals from the outside to the inside of the cell; the stimulation of lymphocytes by agents (Nicolson, 1974) that increase permeability to calcium (Maino, Green & Crumpton, 1974) or the inhibition of cell proliferation by an activation of adenyl cyclase (Sheppard, 1972) are examples. The activation of unfertilized eggs probably fails into the same category. Treatment of sea urchin eggs with dilute ammonia initiates a change in membrane potential which is followed by nuclear activity (DNA synthesis), leading to chromosome condensation (Mazia, 1974). In this instance, formation of the mitotic spindle does not occur, but in parthenogenetic activation by other agents, development right up to a (haploid) free-feeding pluteus can occur (Harvey, 1956a). It is true that this is a rather special case in the sense that the plasma membrane is already preprogrammed to respond to external stimuli in a particular way, but it does illustrate the extent to which apparently minor changes at the cell surface can influence intracellular events. An initial change in membrane potential has also been reported to occur during the serum-stimulated growth of quiescent mammalian cells in vitro (Hulser & Frank, 1971). Recent evidence of surface alterations during the cell cycle points to an involvement of microvilli. In section 3 this role is defined; the implications with regard to interactions between the cell surface and the interior are discussed.
RELATION
OF C E L L S U R F A C E
TO G R O W T H
CYCLE
367
The cell surface changes its architecture not only during the cell cycle, but sometimes even more dramatically when cells stop growing, and "opt out" of the ceil cycle into a quiescent phase, designated Go. It is this phase that malignant cells seem unable to reach. In section 4 is presented a hypothesis that defines a difference between the "cycling" and "non-cycling" state, and hence between malignant and normal ceils. 2. Initiation of Cytokinesis The postulate is that Initiation of karyokinesis is a necessary requisite for the initiation of cytokinesis; the reverse is not true. This is largely a restatement of earlier views (e.g. Swann & Mitchison, I958; Wolpert, 1960; Mazia, 1961), revised in the light of recent data. (A) NUCLEAR DUPLICATION WITHOUT CYTOKINESIS
The second part of the postulate, that the initiation of karyokinesis is not dependent on the initiation of cytokinesis, is generally accepted. It has been known for a long time that nuclear division can occur in the absence of cell division. The resulting multinucleate cells may (a) remain so, (b) become mononucleated by a mechanism of cytoplasmic division distinct from normal cytokinesis or (c) become mononucleated, polyploid cells by subsequent fusion of the nuclei; polyploidy may also be achieved by chromosomal duplication without karyokinesis. A clear example of karyokinesis without cytoldnesis is in the development of fertilized insect eggs. A multi-nucleate blastoderm is formed in which the nuclei migrate to the periphery of the cell; mononucleated cells are formed by mechanism (b), in wkich plasma membrane "grows in" from the blastoderm surface (Waddington, 1956a). Another example is in the mammalian liver during early development. Up to 50 ~ of rat liver cells in a month-old rat are binucleate; later, polyploidy develops (Doljanski, 1960). The most striking case of polyploidy is in the mammalian trophoblast (the cells currounding the developing embryo), in which the chromosomal complement (diploid value--2 n) reaches values of 512 ~ or higher (Graham, 1973). Whether polyploidy results from nuclear fusion within a binueleate cell or from chromosomal duplication without karyokinesis is dit~cult to assess. Binuclear ceils certainly can give rise to mononucleate, polyploid cells (Harris, 1970), but whether this occurs by direct fusion of nuclei is not clear. What evidence there is points against intracellular nuclear fusion (Defendi & Stoker, 1973). Polyploid cells such as platelet (Blackett, 1971), trophoblast or liver cell (greater than 4 n) do not normally go on to divide.
368
c.A.
PASTERNAK
Aneuploid cells (chromosomal complement not a multiple of 2 n), on the other hand, have high rates of mitosis and are generally malignant. Indeed, the possession (or lack) of an extra chromosome has been linked to the loss of growth control characteristic of cancer cells (Yamamoto, Rabinowitz & Sachs, 1973). An example of "induced" karyokinesis without cytokinesis is provided by the action of drugs such as cytochalasin B (Carter, 1967), that interfere with the microfilamentous system involved in cytokinesis (Estensen, Rosenberg & Sheridan, 1971; Wessels et al., 1971): binucleate cells result (Carter, 1967). (B) CYTOKINESIS WITHOUT KARYOKINESIS
The first part of the postulate, that the initiation of cytokinesis is dependent on the initiation of karyokinesis, is more contentious. The main point of the hypothesis, and one that has attracted others in the past, is that, by specifying a relationship between the mitotic spindle and the site of cytokinesis, it provides a mechanism for the correct apportioning of chromosomes todaughter cells. A superficial similarity with the attachment of chromosomes to the bacterial membrane during septum formation (Jacob, Ryter & Cuzin, 1966) may be noted. The evidence in favour of the hypothesis is largely circumstantial; it is simply that cytokinesis does not normally occur in the absence of mitosis. Situations in which cytoplasm is naturally (Behnke, 1969) or artificially (Pontecorvo, 1975) pinched off in the absence of mitosis fall outside the definition of cytokinesis. The fact that binucleate and multinucleate cells do not undergo normal cytokinesis supports the hypothesis. Such cells enter another round of the cell cycle, leading to tetraploid nuclei; only when these engage in the formation of another mitotic spindle is cytokinesis achieved (Defendi & Stoker, 1973). The "budding" of multinucleate yeast cells is in a different category; cytokinesis does not divide the cytoplasm in half, and the process is one of membrane growth (Cabib, Ulane & Bowers, 1974), rather than of physical pinching in half (see section 3). The evidence against the hypothesis comes from experiments in which cytokinesis can apparently be initiated in the absence of mitosis. The cleavage of enueleated sea urchin fragments following parthenogenetic activation (Harvey, 1956b) has been cited as a clear-cut example. However, subsequent investigators (Anderson, 1970, and personal communication from others) have failed to detect cleavage under these conditions, despite the fact that the enucleated fragments respond normally in other ways. Membrane elevation, for example, takes place and intracellular protein synthesis is stimulated to the same extent as by fertilization with sperm (Denny &
RELATION
OF CELL SURFACE TO GROWTH
CYCLE
369
Tyler, I964). In other cases where cleavage has been observed, mitosis has been first induced and then prevented in some way (e.g. by removal of mitotic spindle (Hiramoto, 1956, 1971), or other microsurgery (Tartar, 1967)). Wolpert (1960) has therefore proposed that it is the "asters", rather than the mitotic apparatus itself, that are the sites for the initiation of cytokinesis, and this seems generally to be accepted (e.g. Hiramoto, 1971; Rappaport, 1971). Since the nature and function of "asters" is still obscure, the wording "initiation of karyokinesis" is here preferred. The effects of high pressure on premature induction of cytokinesis (Marsland, 1970) are in no way inconsistent with the present proposals. What then is the relationship of the mitotic spindle, or precursors thereof, to the initiation of cytokinesis ? At present this is not known. A possible approach is suggested by the finding that cytokinesis is achieved, at least in some cells (section 3, Plate 1) by an unfolding of previously-accumulated microvilli. It might at first sight seem surprising that microvilli disappear from the polar area around the ends of the mitotic spindle, rather than from the cleavage plane itself (Plate 1). But this is exactly what might be expected on the basis of Wolpert's (1960) hypothesis: namely that (in sea urchin eggs) "cleavage is initiated by a relaxation of the membrane in the polar regions which expand in area and allow the furrow to constrict and divide the egg in two". Note that Rappaport (1971) proposes the initial stimulus to act at the equator (cleavage plane), rather than at the poles. In either scheme, the "astral region" appears to be the site both for the establishment of the ends of the mitotic spindle and, at least in some instances (Rappaport & Rappaport, 1974), for the initiation of cytokinesis. An examination of the timing of nuclear events in relation to the first unfolding of microvilli should prove fruitful; for example, the breakdown of the nuclear envelope might release compounds required for the mobilization of microfilaments from microvilli, to participation in "contractile ring" assembly (Schroeder, 1968; Tilney & Marsland, 1969). Of course, it has yet to be established that the mechanism of cytoldnesis is the same in cleaving sea urchin eggs as in mammalian cells in suspension culture. 3. The Role of Microvilli
The postulate is that in spherical cells that double in volume prior to mitosis, the ratio of surface area to volume is maintained by the elaboration of microvilli; the extra surface area generated by cytokinesis is provided by an unfolding of microvilli. During growth of cells without differentiation, all components double between successive mitoses and the daughter cells are exact replicas of their parent. Bacteria and established lines of mammalian ceils in culture
370
c.A.
PASTERNAK
are examples of this mode of growth. The other extreme is growth without a doubling of cell components and without regeneration of the parent cell; cleavage during early embryonic development, in which nuclear material alone doubles between mitoses and in which ceils decrease in size, is an example. Growth in other situations generally falls between these two extremes. It is the first situation (]3, below) in which the relationship between cell division and the cell surface has recently been explored (Graham, Sumner, Curtis & Pasternak, 1973; Knutton, Sumner & Pasternak, 1975). (A) GROWTH WITHOUT DIFFERENTIATION
An exact duplication of parental cells occurs in two ways. In the first, of which bacterial cells are an example, the shape alters during the cell cycle; in the other, of which cloned animal cells in suspension culture are an example, it remains the same while growth takes place. A bacterial rod that grows by elongation, retains an almost constant surface area: volume ratio [Fig. l(a)]. Additional surface area involved in septum formation, at
GI
Case A surface area
()
)
(1
~ G2
~ GI
)
) 'rv'--'~
I
1.9
2x I
0
"0
surface area
I
1.6
2xl
surface area
I
1.6
2x I
o-o surface area
0 I
3
4.8
The Cell Surface in Relation to the Growth Cycle C. A. PASTERNAK t
Department of Biochemistry, Universityof Oxford, Oxford OXI 3QU, England (Received 25 June 1975) The cell surface bears an intimate relation to events during the cell cycle. The following postulates are presented as working hypotheses in order to clarify current observations and to stimulate new experimental approaches. (1) Initiation of karyokinesis is a necessary prerequisite for the initiation of cytokinesis; the reverse is not true. (2) In spherical cells that double in volume prior to mitosis, the ratio of surface area ."volume is maintained by the elaboration of microvilli; the extra surface area generated by cytokinesis is provided by an unfolding of microvilli. (3) The state of the cell surface during interphase and in Go is different from that during mitosis; the difference is due to the involvement of intracellular elements that otherwise participate in the formation of the mitotic spindle and cleavage furrow. The association of such elements with the cell surface is greater in normal than in cancer cells.
1. Introduction The cell cycle is a convenient way of defining discrete periods of macromolecular synthesis and assembly that take place between successive cell divisions. What is lacking at present is knowledge of how the various periods, and the operation of the cycle itself, are controlled (Mitchison, 1971a; Padilla, Cameron & Zimmerman, 1974). In this article three postulates are presented which may help to correlate present observations and to stimulate new approaches to the problem. Each concerns the cell surface. The cell surface bears a "special relation" to nuclear events in animal cells. Nuclear division (karyokinesis), for example, is almost always accompanied by cell division (cytokinesis), and exceptions to the reverse situation (cytokinesis without karyokinesis) are rare indeed (see section 2). On the other hand, proliferation o f mitochondria or the endoplasmic retieulum is t Present address: St. George's Hospital Medical School, Blackshaw Road, Tooting, London SWl7 0QT. T.B.
365
24
366
C. A. P A S T E R N A K
not directly related to nuclear division. In embryonic development, for example, cell division (cleavage) occurs without concomitant change in number of mitochondria (Shaver, 1956) or amount of endoplasmic retieulum (Davidson, 1968; Giudice, 1973); in oogenesis, the converse is true. In anaerobically-grown yeast that is exposed to oxygen, mitochondrial assembly (Roodyn & Wilkie, 1968; Getz, 1972) takes place independently of cell division; in the liver of rats exposed to phenobarbital, endoplasmic reticulum proliferates (Orrenius, Ericsson & Ernster, 1965) without an increase in mitotic rate. It is true that during the stimulation of duck salt glands, plasma membrane proliferates without nuclear division (Levine, Higgins & Barnett, 1972), but cytokinesis does not take place. The first hypothesis which is discussed in section 2, concerns this relationship between cytokinesis and karyokinesis. Although the link between the cell surface and nucleus is most obviously expressed during mitosis, there is an increasing number of reports that suggest an influence of the cell surface on nuclear function during interphase also (e.g. Fox, Sheppard & Burger, 1971; Burger, 1973; Inbar & Shinitzky, 1974; reviewed by Pardee, 1971 ; Turner & Burger, 1973; Knox & Pasternak, 1976). In some instances the effect may be more apparent than real, in the sense that the cell surface is merely a transmitter of signals from the outside to the inside of the cell; the stimulation of lymphocytes by agents (Nicolson, 1974) that increase permeability to calcium (Maino, Green & Crumpton, 1974) or the inhibition of cell proliferation by an activation of adenyl cyclase (Sheppard, 1972) are examples. The activation of unfertilized eggs probably fails into the same category. Treatment of sea urchin eggs with dilute ammonia initiates a change in membrane potential which is followed by nuclear activity (DNA synthesis), leading to chromosome condensation (Mazia, 1974). In this instance, formation of the mitotic spindle does not occur, but in parthenogenetic activation by other agents, development right up to a (haploid) free-feeding pluteus can occur (Harvey, 1956a). It is true that this is a rather special case in the sense that the plasma membrane is already preprogrammed to respond to external stimuli in a particular way, but it does illustrate the extent to which apparently minor changes at the cell surface can influence intracellular events. An initial change in membrane potential has also been reported to occur during the serum-stimulated growth of quiescent mammalian cells in vitro (Hulser & Frank, 1971). Recent evidence of surface alterations during the cell cycle points to an involvement of microvilli. In section 3 this role is defined; the implications with regard to interactions between the cell surface and the interior are discussed.
RELATION
OF C E L L S U R F A C E
TO G R O W T H
CYCLE
367
The cell surface changes its architecture not only during the cell cycle, but sometimes even more dramatically when cells stop growing, and "opt out" of the ceil cycle into a quiescent phase, designated Go. It is this phase that malignant cells seem unable to reach. In section 4 is presented a hypothesis that defines a difference between the "cycling" and "non-cycling" state, and hence between malignant and normal ceils. 2. Initiation of Cytokinesis The postulate is that Initiation of karyokinesis is a necessary requisite for the initiation of cytokinesis; the reverse is not true. This is largely a restatement of earlier views (e.g. Swann & Mitchison, I958; Wolpert, 1960; Mazia, 1961), revised in the light of recent data. (A) NUCLEAR DUPLICATION WITHOUT CYTOKINESIS
The second part of the postulate, that the initiation of karyokinesis is not dependent on the initiation of cytokinesis, is generally accepted. It has been known for a long time that nuclear division can occur in the absence of cell division. The resulting multinucleate cells may (a) remain so, (b) become mononucleated by a mechanism of cytoplasmic division distinct from normal cytokinesis or (c) become mononucleated, polyploid cells by subsequent fusion of the nuclei; polyploidy may also be achieved by chromosomal duplication without karyokinesis. A clear example of karyokinesis without cytoldnesis is in the development of fertilized insect eggs. A multi-nucleate blastoderm is formed in which the nuclei migrate to the periphery of the cell; mononucleated cells are formed by mechanism (b), in wkich plasma membrane "grows in" from the blastoderm surface (Waddington, 1956a). Another example is in the mammalian liver during early development. Up to 50 ~ of rat liver cells in a month-old rat are binucleate; later, polyploidy develops (Doljanski, 1960). The most striking case of polyploidy is in the mammalian trophoblast (the cells currounding the developing embryo), in which the chromosomal complement (diploid value--2 n) reaches values of 512 ~ or higher (Graham, 1973). Whether polyploidy results from nuclear fusion within a binueleate cell or from chromosomal duplication without karyokinesis is dit~cult to assess. Binuclear ceils certainly can give rise to mononucleate, polyploid cells (Harris, 1970), but whether this occurs by direct fusion of nuclei is not clear. What evidence there is points against intracellular nuclear fusion (Defendi & Stoker, 1973). Polyploid cells such as platelet (Blackett, 1971), trophoblast or liver cell (greater than 4 n) do not normally go on to divide.
368
c.A.
PASTERNAK
Aneuploid cells (chromosomal complement not a multiple of 2 n), on the other hand, have high rates of mitosis and are generally malignant. Indeed, the possession (or lack) of an extra chromosome has been linked to the loss of growth control characteristic of cancer cells (Yamamoto, Rabinowitz & Sachs, 1973). An example of "induced" karyokinesis without cytokinesis is provided by the action of drugs such as cytochalasin B (Carter, 1967), that interfere with the microfilamentous system involved in cytokinesis (Estensen, Rosenberg & Sheridan, 1971; Wessels et al., 1971): binucleate cells result (Carter, 1967). (B) CYTOKINESIS WITHOUT KARYOKINESIS
The first part of the postulate, that the initiation of cytokinesis is dependent on the initiation of karyokinesis, is more contentious. The main point of the hypothesis, and one that has attracted others in the past, is that, by specifying a relationship between the mitotic spindle and the site of cytokinesis, it provides a mechanism for the correct apportioning of chromosomes todaughter cells. A superficial similarity with the attachment of chromosomes to the bacterial membrane during septum formation (Jacob, Ryter & Cuzin, 1966) may be noted. The evidence in favour of the hypothesis is largely circumstantial; it is simply that cytokinesis does not normally occur in the absence of mitosis. Situations in which cytoplasm is naturally (Behnke, 1969) or artificially (Pontecorvo, 1975) pinched off in the absence of mitosis fall outside the definition of cytokinesis. The fact that binucleate and multinucleate cells do not undergo normal cytokinesis supports the hypothesis. Such cells enter another round of the cell cycle, leading to tetraploid nuclei; only when these engage in the formation of another mitotic spindle is cytokinesis achieved (Defendi & Stoker, 1973). The "budding" of multinucleate yeast cells is in a different category; cytokinesis does not divide the cytoplasm in half, and the process is one of membrane growth (Cabib, Ulane & Bowers, 1974), rather than of physical pinching in half (see section 3). The evidence against the hypothesis comes from experiments in which cytokinesis can apparently be initiated in the absence of mitosis. The cleavage of enueleated sea urchin fragments following parthenogenetic activation (Harvey, 1956b) has been cited as a clear-cut example. However, subsequent investigators (Anderson, 1970, and personal communication from others) have failed to detect cleavage under these conditions, despite the fact that the enucleated fragments respond normally in other ways. Membrane elevation, for example, takes place and intracellular protein synthesis is stimulated to the same extent as by fertilization with sperm (Denny &
RELATION
OF CELL SURFACE TO GROWTH
CYCLE
369
Tyler, I964). In other cases where cleavage has been observed, mitosis has been first induced and then prevented in some way (e.g. by removal of mitotic spindle (Hiramoto, 1956, 1971), or other microsurgery (Tartar, 1967)). Wolpert (1960) has therefore proposed that it is the "asters", rather than the mitotic apparatus itself, that are the sites for the initiation of cytokinesis, and this seems generally to be accepted (e.g. Hiramoto, 1971; Rappaport, 1971). Since the nature and function of "asters" is still obscure, the wording "initiation of karyokinesis" is here preferred. The effects of high pressure on premature induction of cytokinesis (Marsland, 1970) are in no way inconsistent with the present proposals. What then is the relationship of the mitotic spindle, or precursors thereof, to the initiation of cytokinesis ? At present this is not known. A possible approach is suggested by the finding that cytokinesis is achieved, at least in some cells (section 3, Plate 1) by an unfolding of previously-accumulated microvilli. It might at first sight seem surprising that microvilli disappear from the polar area around the ends of the mitotic spindle, rather than from the cleavage plane itself (Plate 1). But this is exactly what might be expected on the basis of Wolpert's (1960) hypothesis: namely that (in sea urchin eggs) "cleavage is initiated by a relaxation of the membrane in the polar regions which expand in area and allow the furrow to constrict and divide the egg in two". Note that Rappaport (1971) proposes the initial stimulus to act at the equator (cleavage plane), rather than at the poles. In either scheme, the "astral region" appears to be the site both for the establishment of the ends of the mitotic spindle and, at least in some instances (Rappaport & Rappaport, 1974), for the initiation of cytokinesis. An examination of the timing of nuclear events in relation to the first unfolding of microvilli should prove fruitful; for example, the breakdown of the nuclear envelope might release compounds required for the mobilization of microfilaments from microvilli, to participation in "contractile ring" assembly (Schroeder, 1968; Tilney & Marsland, 1969). Of course, it has yet to be established that the mechanism of cytoldnesis is the same in cleaving sea urchin eggs as in mammalian cells in suspension culture. 3. The Role of Microvilli
The postulate is that in spherical cells that double in volume prior to mitosis, the ratio of surface area to volume is maintained by the elaboration of microvilli; the extra surface area generated by cytokinesis is provided by an unfolding of microvilli. During growth of cells without differentiation, all components double between successive mitoses and the daughter cells are exact replicas of their parent. Bacteria and established lines of mammalian ceils in culture
370
c.A.
PASTERNAK
are examples of this mode of growth. The other extreme is growth without a doubling of cell components and without regeneration of the parent cell; cleavage during early embryonic development, in which nuclear material alone doubles between mitoses and in which ceils decrease in size, is an example. Growth in other situations generally falls between these two extremes. It is the first situation (]3, below) in which the relationship between cell division and the cell surface has recently been explored (Graham, Sumner, Curtis & Pasternak, 1973; Knutton, Sumner & Pasternak, 1975). (A) GROWTH WITHOUT DIFFERENTIATION
An exact duplication of parental cells occurs in two ways. In the first, of which bacterial cells are an example, the shape alters during the cell cycle; in the other, of which cloned animal cells in suspension culture are an example, it remains the same while growth takes place. A bacterial rod that grows by elongation, retains an almost constant surface area: volume ratio [Fig. l(a)]. Additional surface area involved in septum formation, at
GI
Case A surface area
()
)
(1
~ G2
~ GI
)
) 'rv'--'~
I
1.9
2x I
0
"0
surface area
I
1.6
2xl
surface area
I
1.6
2x I
o-o surface area
0 I
3
4.8
