The effect of surface microvilli on the water permeability of single toad oocytes

Conventional methods of estimating the water permeability of cells assume that significant resistance to water flow is confined to the cell membrane and that water diffusion in the cytoplasm is so rapid as to present negligible resistance. However, evidence has been brought forward suggesting that this assumption may not be valid and that water diffusion in the cytoplasm may be slower than was previously supposed (Dick, 1959a, b, c;,1964). In order to test this possibility, a system is required either in which the effects of membrane and cytoplasm can be measured independently or in which their effects vary independently in such as way that the effect of each can be assessed separately. The amphibian oocyte provides a system of the latter type. Owing to the changes in the number and size of the microvilh on the oocyte surface during development, the total area of the cell surface changes strikingly; the cytoplasm also changes, partly by increasing accumulation of yolk during oocyte development, but this change occurs independently of microvillar development. The time relationships of microvillar and yolk development are different since, as will be seen below, the microvilli first enlarge then recede, whereas yolk accumulates continuously. It is thus possible by studying the changes in water permeability throughout oocyte development to relate these to changes in the cell surface independently of the cell interior. In the present experiments water permeability was assessed by observing osmotic shrinkage of the oocytes, while the total area of microvilli at various periods of development was assessed by quantitative analysis of electron micrographs. A preliminary notice of this work has already been published (Bradbury, Dick & Dick, 1967).

Female toads, Bufo bufo, between and in. (5·72 and 6·35 cm) long were obtained in batches of 12 and kept at room temperature for up to 2 months. They were killed by a blow on the head and the ovaries removed immediately and placed in Ringer’s solution (Table 1). Single oocytes were freed from the ovary either by dissection or by gentle shaking after exposure of the ovary for 1 h at 30 °C to a 0·5 % trypsin solution, made up in Ringer’s solution free from calcium ions at pH 8. Isolated oocytes were placed in isotonic Ringer’s solution in separate small glass dishes, 1 in. (2·54 cm) square by in. (1·27 cm) deep

The oocytes ranged in size from 200 μm in diameter to the largest in the ovary, just over 2000 μm in diameter. The water permeability of each oocyte was found from its rate of shrink age in hypertonic Ringer’s solution (⁠ of isotonic osmotic pressure) (Table 1). Diameter measurements were made with an eyepiece filar micrometer in a dissecting microscope at i-min intervals after transfer of the oocyte from isotonic to hypertonic solution

For small and medium sized oocytes (under about 1400 μm) the oocyte was kept in the small glass dish and the oocyte diameter was measured along two axes. Between each pair of readings the oocyte was sucked up into a braking pipette (Holter, 1943) and blown out again so that a random selection of diameters was obtained. For large oocytes, over 1400 μm, which tended to he on their sides (oocyte density is 1 05 g ml⁻¹, Dick & Lea, 1964) the diameter was measured along 3 axes, a horizontally placed microscope being used to measure the vertical diameter (Fig. 1). Each large oocyte was placed in a spectrophotometer cuvette and its position was not changed during shrinkage.

Immediately before and after the shrinkage of most oocytes the diameter was measured of a control oocyte of similar size kept in isotonic solution.

A and ΔΠ both change during the time the oocyte is in an isotonic solution and so A, ΔΠ and dV/dt were all calculated for zero time; that is for the moment when the oocyte was first put into anisotonic solution

A is πD² where D is the diameter of the oocyte at zero time. All is expressed as a difference in water concentration between the cell interior and the external medium. The water concentration inside the cell at zero time is presumed to be equal to that of isotonic Ringer’s solution; that is 55·6 (the number of moles of water per litre in pure water) minus 0·237 (the number of g-ions of salts per litre of Ringer’s solution) which equals 55·363 g-mol of water per litre of Ringer’s solution (see Table 1).. The water concentration of the external medium, i e. the Ringer’s solution, is 55·287 g-mol of water per litre and therefore the difference in water concentration, ΔΠ, across the cell membrane, expressed as a mol. fraction is

Non-ideality of the solution is ignored in this calculation of ΔΠ. Since the osmotic coefficient of NaCl, the major solute, is approximately 0·93 in 0·1 M solution, the ‘effective’ mol-fraction difference in water concentration may be up to 7 % less than that calculated above, and the oocyte permeability coefficients up to 7 % higher from this cause A further possible correction might be made for the difference between the partial molal volumes in solution of the ions of solute on the one hand and H₂O molecules on the other. As shown by Dick (1964), the solute ion may be taken as having, on average, approximately 63 % of the volume of water molecule. The present estimates of water permeability might have to be increased by 59 % on this account so as to be comparable with those calculated by Dick (1964). A total increase of 66 % is therefore possible in the present figures if these corrections are adopted.

Knowing A, ΔΠ and dV/dt, the permeability coefficient, k, was found for each oocyte from equation (1)

After shrinkage in hypertonic solution each oocyte, and its control, which had been kept in isotonic Ringer’s solution, were fixed for electron microscopy. Fixation, which took place usually within 4 h of the death of the toad, was carried out in 3 % glutaraldehyde solution at pH 7 0–7·3 f°r between 3 and 24 h at 4 °C. The oocytes were given 4 washes of 30 min each in 0·1 M phosphate buffer, pH 7·3 at 4 °C; then put in 1 % osmium tetroxide at 4 °C overnight; dehydrated in alcohol, placed for 30 min in epoxypropane; left overnight in a 50/50 mixture of epoxypropane and Araldite, and embedded in Araldite which was hardened at 60 °C for 24-48 h.

The Araldite blocks were trimmed with a razor blade, almost half the oocyte being sliced away so that sections would be cut approximately through the equator of the oocyte, thus maximizing the chance of the microvilli being cut longitudinally. Large oocytes over 1000 μm in diameter were halved or quartered in the block The sections, which showed gold or silver-gold interference colours, were stained with uranyl acetate or lead citrate or both these stains used in sequence. Electron micrographs of different parts of the surface of each oocyte were made, using a Siemens Elmiskop I or a Philips 200 electron microscope.

About 6 electron micrographs were made for each oocyte, and from these a quantitative estimation was made of the factor by which the microvilli of the oocyte increased its surface area beyond that of a smooth sphere of the same diameter.

The diameter and linear density of the microvilli appearing in each electron micrograph were estimated by means of a perspex grid laid over the micrograph (Fig. 3 A). The grid consisted of a series of lines drawn to be equivalent to a length of 10 μm with a separation of 0·5 μm (most micrographs were printed at a magnification of × 18000 and for these the grid used had lines 18 cm long and 9 mm apart) The number of microvilli and their average diameter was esti mated separately for each strip, because generally the microvilli were narrower and sparser at their periphery than at their base.

The catchment area of cell surface for microvilli appearing in each strip was found not just from the thickness, t, of the section but from (t + d), the section thickness plus a distance on either side of it equal to half the average diameter of the microvilh (Floderus, 1944; Abercrombie, 1946) For the shaded area in Fig. 3 A, the catchment area is (t + d) × 1 μm², the length of the shaded area being 1 μm. The catchment area for the whole strip, of which the shaded area is a part, is (t + d) × 10 μm³, the strip being io/(m long. The thickness, t, of this and all other sections was taken to be 100 nm, although probably the sections, which showed gold or silver-gold interference colours, varied in thickness from 80–120 nm (Williams & Meek, 1966).

Table 2 shows the calculation made from the electron micrograph which was used as a guide in drawing Fig 3 A. The cylindrical surface area of the parts of the microvilli lying across one strip is (nΠdh) μm², where h is the height, 0·5 μm, of one strip, d is the average diameter of the microvilli, and n is the number of microvilli appearing in the strip (Table 2, column 6). The catchment area for the microvilli appearing in one strip is 10 × (t + d) μm² (column 7), and therefore the equivalent cylindrical surface of microvilli for each strip over 1 μm² of cell surface is [nΠd (0·5)]/[10 (t + d)] μm² (column 8). Adding together the cylindrical surface areas for the microvilli in all the strips gives the total cylindrical surface, C, in μm² of the microvilli over 1 μm² of cell surface. If the area of cell membrane in between the bases of the microvilh plus the area of the tips of the microvilli themselves occupy 1 μm² over 1 μm² of cell surface then the total membrane area will be the cylindrical surface area of the microvilli, C, plus 1 μm², i.e. (C+1) μm²

If it is presumed that the microvilli are evenly distributed over the cell surface, then the factor by which the microvilli increase the surface area is (C + 1). For small oocytes sections included the whole circumference of the oocyte, and for large oocytes of the circumference. When selecting areas of cell surface to photograph an attempt was made to choose representative areas including places where the microvilli were sparse and irregular as well as where they were denser and more regular. The variation in the values of (C + 1) obtained from different micrographs of the same oocyte was approximately ± 25 % from the mean and the average value of (C+ 1) was taken to be the factor by which the microvilli of that oocyte increased its surface area. For example the value of (C+ 1) for the micrograph analysed in Table 2 is 9·5, and the values obtained from other micrographs of the same oocyte were 7·5, 8·2, 8·7, 88, 10·0 and 11·4, the average being 9·3 μm².

The surface of a normal toad oocyte dissected from the ovary and kept until fixation in isotonic Ringer’s solution is shown in Fig. 13. Its features are similar to those which have been described for the oocytes of other amphibian species (Wischnitzer, 1966). Microvilli project from the oocyte through the zona pellucida. In the outer part of the zona pellucida is a layer of homogeneous material, probably consisting of mucopolysaccharide, which appears to be organized into bands running parallel to the oocyte surface (Fig. 19). After ovulation this material forms the vitelhne membrane (known after fertilization as the fertilization membrane) and it is referred to here as the previtelline membrane. Peripheral to the zona pellucida are 3 cellular layers surrounding the oocyte; the follicular epithelium which consists of elongated follicle cells oriented with their long axes parallel to the oocyte surface; the theca which consists mainly of collagenous fibres; and the surface epithelium, the outermost layer of which is derived from the inner ovarian epithelium (Wischnitzer, 1966).

Oocytes, isolated by exposure of the ovary to a 0·5% trypsin solution, usually had their cellular coverings (i.e. their surface epithelium, theca and follicular epithelium) loosened or removed (Fig. 14). The previtelline membrane was either removed or elevated but the oocyte membrane appeared undamaged.

A more complete removal of the cellular coverings and of the previtelline membrane was found in oocytes which were exposed to both trypsin and hypertonic Ringer’s solution. In medium sized oocytes (600–1200 μm diameter) the oocyte membrane remained intact but in large (over 1200 μm) cells it was lost (Fig. 15) and in one of the 3 small (under 600 μm) oocytes examined it was damaged. Eleven out of 14 small trypsinized oocytes which were shrunk in Ringer’s solution burst before fixation suggesting that their membranes too had been damaged.

Exposure of dissected (i.e. untrypsinized) oocytes to hypertonic (⁠ of isotonic osmotic pressure) Ringer’s solution caused no damage to the cellular coverings, pre vitelline membrane or oocyte membrane. In medium sized oocytes (600–1200 μm in diameter), however, in which the microvilli are normally maximally developed, the microvilli were shorter than those of oocytes kept in isotonic Ringer’s solution.

As the toad oocyte grows the microvilli at first increase in size and then recede. Qualitatively this observation is in agreement with observations made on other amphibian oocytes by Kemp (1956), Wartenburg & Schmidt (1961), Hope, Humphreys & Bourne (1963), Balinsky & Devis (1963) and Wischnitzer (1964). Figures 16–19, which are all at the same magnification, illustrate how the microvilli change as the oocyte grows. Figure 16, of a very small oocyte, 246 μm in diameter, shows the microvilli beginning to project from the oocyte surface, while in places the oocyte membrane is still smooth and in contact with the membrane of the follicular cell. (In the smallest amphibian oocytes, under 100 μm in diameter and not included in the present study, there are no microvilli and the smooth oocyte membrane adjoins the follicular cell membrane (Wischnitzer, 1964).)

In oocytes from 200–600 μm in diameter the microvilli develop rapidly. Figure 17 shows an oocyte 445 μm in diameter. The microvilli are longer and more numerous than those of the smaller oocyte illustrated in Fig. 16 and they are seen to contain filaments, which sometimes extend into the cortical cytoplasm in a manner analogous to that described for filaments in mammalian microvilli (Threadgold, 1967). The follicular cell has receded further from the oocyte and follicular cell processes, or macrovilli, interdigitate with the narrower microvilli from the oocyte. The pre vitelline membrane is seen in an early stage of development.

The microvilli reach their peak when the diameter of the oocyte is about 800-900 μm. Figure 18 shows an oocyte 848 μm in diameter. The microvilli are longer, and branching, and they penetrate right through the previtelline membrane. The basal unbranched parts of the microvilli are about 0·5 μm wide and contain cytoplasm similar to that of the oocyte cortex. These basal portions have been described (Kemp, 1956) as cytoplasmic protrusions of the cell cortex from which the microvilli proper project; in the present work, however, which aims at finding the increase in area of cell mem brane resulting from microvillar development, these basal portions are treated as part of the microvilli. The peripheral parts of the microvilli, about 0·08 μm in diameter, contain filaments like those of the unbranched microvilli of smaller oocytes. The total length of the microvilli at their maximum is about 3·5 μm.

As the oocyte diameter increases above 900 /6m the microvilli slowly recede. Figure 19 shows a large oocyte 1763 μm in diameter. The microvilli are shorter and sparser than those in Fig. 18 and no longer penetrate right through the previtelline membrane.

The development of the microvilli with oocyte growth is summarized in the diagram shown in Fig. 4. The 4 drawings are all on the same scale and correspond roughly to the stages of development shown in Figs. 16–19.

Figure 5 shows the factor by which the microvilli of an oocyte increases its surface area plotted against cell size. The broken line at 1 on the x axis represents the base line, i.e. the surface area of an oocyte if it were a smooth sphere without microvilli. In the smallest oocytes used, about 200 μm in diameter, the microvilli approximately double the surface area; in oocytes of about 800–900 μm, when the microvilli are at their peak, the surface area is increased about 11 times, and in the largest oocytes, when the microvilli are receding, the area is increased about 5 times. Figure 5 confirms quantitatively the qualitative observation that the microvilli at first increase with cell size and then recede.

The probable main sources of error in the present method of calculation are, first, variation in section thickness introducing an error of about 20%; and secondly, variation in size and density of the microvilli between different parts of the oocyte surface, involving a probable error of up to about 50%; and thirdly a possible change in size and shape of the microvilli during fixation, embedding and sectioning, intro ducing an error which, while difficult to estimate, is probably not great, for the dia meter of the oocyte, when measured in the Araldite block or in 0·5-μm sections cut through the equator of the egg, is not significantly bigger or smaller than the diameter of the oocyte immediately before fixation. As the method of calculation was the same for all oocytes, these errors do not affect relative estimates of microvillar area for different eggs, nor the conclusion that the factor by which the microvilli extend the oocyte surface area at first increases with cell size and then decreases.

The water permeability of the oocytes was calculated from their rate of shrinkage in hypertonic solution. The membrane permeability coefficients for the 39 oocytes ex amined ranged from 1 to 50 μm s⁻¹. The coefficients were calculated on the assumptions (i) that each oocyte was a smooth sphere and (ii) that only the membrane and not the cytoplasm resisted the flow of water. Plotted against cell diameter, in Fig. 6, these coefficients show an increase with cell size up to about 800 μm diameter and thereafter a decline. The rising regression line shown was calculated from cells up to 900 μm in diameter, and the falling line from cells more than 800 μm in diameter; cells between 800 and 900 μm were thus included in both regressions. The regression coefficient for the rising line was 0·025+0·013 (0·1 > P > 0·05) and for the falling line — 0·024 ±0·004 (P < 0·001). The regression coefficients were significantly different (P = 0·001).

Figure 6 shows only dissected oocytes. Oocytes which were isolated by trypsiniza tion are not included, because of the morphological damage observed to the membranes of some of the oocytes which were exposed both to trypsin and Ringer’s solutions. The trypsinized cells, omitting those known to have damaged membranes, do, nevertheless, show a similar rise and fall in permeability with increasing cell size (Fig. 7).

Small oocytes reached a constant volume in Ringer’s solution after about 0·5 h and large oocytes after about 1 h. Small oocytes shrank to about 75 % and large oocytes to about 85 % of their original volume (Fig. 8). The small degree of shrinkage of large oocytes is probably due to the yolk in their cytoplasm. Yolk platelets begin to form in the peripheral part of the cytoplasm of oocytes of about 350 μm diameter and gradually move inwards until in oocytes of 1000 μm diameter and over they fill the whole cytoplasm. These yolk platelets probably consist mainly of protein and lipid (Ohno, Karaski & Takata, 1964: Honjin, Nakamura & Shimasaki, 1965; Bahnsky & Devis, 1963; Karaski, 1963) and therefore contribute to the cells non-solvent volume which probably does not change during osmotic swelling or shrinkage.

During the shrinkage of some oocytes a control oocyte of similar size was taken from the same ovary and kept in isotonic Ringer’s solution. The volume of these oocytes should remain constant and generally does so as is shown by the triangles in Fig. 8. The mean final volume of the control oocytes is 100·75% (S.D. 4·97) of their original volume.

As a check that the oocyte membrane did not suffer physiological damage and allow leakage of salts while in Ringer’s solution, 8 shrunken oocytes of various sizes were returned to isotonic solution for about i h before fixation. Seven out of the 8 oocytes returned to an equilibrium volume that was within 3% of their original volume, which indicates that generally the oocyte membrane remained in good condition and did not become leaky during the time it was in Ringer’s solution.

Figure 8 shows only oocytes which were removed from the ovary by dissection. The equilibrium volume of oocytes which were isolated by exposure of the ovary to trypsin is shown in Fig. 9. The failure of large trypsinized oocytes to shrink in Ringer’s solution is probably due to damage to the cell membrane caused by exposure first to a trypsin and then to hypertonic solution. Three of these large trypsinized oocytes (over 1200 μm) which failed to shrink in Ringer’s solution were examined in the electron microscope and all showed that the cell membrane had disintegrated (Fig. 15). Such cells were excluded from Fig. 7.

It has been suggested by Merriam (1966) that in the late Spring frog ovarian oocytes show less response to’ osmotic shocks’ than at other seasons. The present experiments were carried out during various months (from 1965 to 1968), but no correlation could be found between oocyte water permeability and the season of the year.

The water permeability of oocytes appeared to rise with increasing oocyte size in cells up to about 800 μm in diameter and then to fall (Fig. 6). The change in surface area of the oocyte due to microvillar development showed a similar rise and fall with a similar peak for oocytes around 800 /an in diameter (Fig. 5). The membrane water permeabihty coefficients of oocytes were therefore plotted against the factor by which the microvilli of each oocyte increased its surface area beyond that of a smooth sphere (Fig. 10); the correlation was significant, the correlation coefficient being 0·474

It was hoped originally to find f for each oocyte by an analysis of electron micro graphs of its own microvilli. It was found, however, that in medium-sized oocytes (600–1200 μm diameter) shrunk in Ringer’s solution, the basal parts of the micro villi were much shorter than those of the control oocytes which had been kept in isotonic solution. Since the oocyte was fixed for electron microscopy only after 1 h exposure to hypertonic solution, it was thought that the original state of the microvilli would more closely resemble that seen in electron micrographs of a control non shrunken oocyte of similar size, than the state of its own microvilli after shrinkage. The factor, f, for each experimental oocyte was therefore estimated according to its diameter from the line drawn through the data for non-shrunken cells shown in Fig. 5. This was in any case an appropriate figure for comparison with the water permeability, since the latter was calculated from the rate of shrinkage extrapolated to zero time (i.e. the time of transfer from isotonic to hypertonic solution) before significant shrinkage had occurred.

The corrected permeabilities, k’ thus obtained were plotted against cell size (Fig. 11). There was a significant downward trend (regression coefficient, —0·0022+ 0·00036, P < 0·001). This implied that some other factor in addition to the area of the cell membrane was influencing the overall water permeability of the cell.

The quantitative estimate of the microvillar increase in oocyte surface area made in this study was lower than that made by Kemp (1956) for the oocytes of the frog Rana pipiens. Kemp estimated that for a frog oocyte with a diameter of 400 μm, the micro villi, which had not yet reached their peak, increased the oocyte surface to about 35 times that of a simple sphere of the same diameter. Kemp’s method of calculation was based on the assumption that half the cell surface was covered with the bases of microvilh, which were all regular cylinders 0·08 μm wide and 1·67 μm long. The method of calculation used in the present study, when applied to Kemp’s micrograph of a frog oocyte with microvilli at their peak (oocyte diameter between 600 and 900 μm, (figure 8, Kemp, 1956)) gave a figure of 10·1 times for the increase in oocyte surface area by the microvilli. This assumed a section thickness of 0 ·1 μm. When a section thickness of 25 nm was assumed a figure of 16·2 was obtained. Kemp used a micro tome set at 25 nm, but did not state what interference colours the sections showed. Early estimates of section thickness tended to be too low (Williams & Meek, 1966) and an attempt in the present study to cut sections as Kemp did, with the knife set at 25 nm, resulted in silver (70-nm) or silver-gold (80-nm) sections alternating with the knife missing or scraping the block. Presuming Kemp’s sections to be 75 nm thick, a figure of 11·9 times was obtained. This was close to the figure of 11 times obtained for the equivalent toad oocytes with maximally developed microvilli, and was probably more accurate than Kemp’s own estimate of over 35 times.

The finding that the microvilli increased and then declined as the oocyte grew agrees with the findings of Kemp (1956), Wartenberg & Gusek (1960), Wartenberg & Schmidt (1961), Wartenberg (1962), Hope et al. (1963) and Wischnitzer (1964). It seemed, moreover, that the total area of the oocyte surface (including microvilli) had an effect on oocyte water permeability, since these two quantities were significantly correlated (Fig. 10). When the calculated membrane permeability coefficients were corrected for the increase in area due to microvilli, the previous rise and fall with cell size disappeared. However, the microvillar correction did not eliminate all trend from the size-permeability graph; for there was a significant decrease of corrected permeabi lity with increasing oocyte size (Fig. 11). This decrease was similar to that previously found on comparison of permeability coefficients for a wide variety of cells (Dick, 1959 a, b, c). Dick estimated that water permeability apparently decreased approxi mately to one seventh for a 10 times increase in cell size; this decrease may be com pared with the present finding that the apparent water permeability of 2000-m oocytes was approximately one quarter of that of 200-μm oocytes. It must be concluded either that the intrinsic water permeability of the cell membrane was greatly reduced with increasing cell size or that some other factor was to some extent rate limiting to water flow.

Consider, first, possible changes in the intrinsic water permeability of the cell membrane. Prescott & Zeuthen (1953) explained the fact that the membrane water permeability which they found for frog ovarian eggs (89 μm s⁻¹) was much higher than for frog body-cavity eggs (1·3–1·6 μm. s⁻¹) by suggesting that the cell membrane of the ovarian egg had unusually large pores. High-power electron micrographs made by the present authors of the toad ovarian egg membrane showed it to be a typical 3-layered structure about 7 nm wide and no change in it was observed with increasing cell size. Nevertheless the existence of large pores in the membrane and the possibility of changes in them could not be excluded, since the resolution of the electron micro graphs was not adequate to reveal them if they existed.

Another explanation for the decrease in water permeability with cell size might be the development of mechanical resistance to osmotic volume changes by the cell surface. Physiological evidence has been put forward to suggest that there is a cortical tension at the surface of amphibian and some invertebrate eggs (see, for example, Holtfreter, 1943; Mitchison & Swann, 1954; Schechter, 1956; Løvtrup, 1960), possibly to give protection from the low osmotic pressure of pond water.

Three morphological features of the cell surface might be responsible for a mechani cal resistance to osmotic volume changes; the cell cortex, the previtelline membrane, or the cellular coverings of the oocyte. The cortex may be discounted for the present experiments, for although Holtfreter (1943) described an ‘elastic intracellular surface coat’ for amphibian eggs, there is no electron-microscopic evidence for this before ovulation (Wartenberg & Schmidt, 1961; Balinsky & Devis, 1963). The previtelline membrane (after ovulation called the vitelline membrane, and after fertilization the fertilization membrane), was present, on the other hand, in ovarian oocytes, but probably did not account for the permeability changes observed in toad ovarian oocytes in the present studies for three reasons. First, there is evidence that changes take place in the amphibian vitelline membrane at ovulation and fertilization which make it more contractile and less permeable (DettlafF, Nikitina & Stroeva, 1964; Maeno, 1959; Holtfreter, 1943; Morrill, Rosenthal & Watson, 1966), so that significant resistance to osmotic changes probably does not occur in the previtelline membrane of ovarian eggs. An increase in contractility of the vitelline membrane at ovulation (rather than a change in the nature of the pores in the cell membrane) may explain why Prescott & Zeuthen (1953) found frog ovarian eggs more permeable than body-cavity eggs. A second reason why the vitelline membrane probably does not seriously affect the permeability coefficients found in the present experiments is that these coefficients were calculated from the rate of cell shrinkage, to which a contractile vitelline mem brane might be expected to offer less resistance than to cell swelling. Thirdly, no electron-microscopic change was observed in the previtelline membrane in eggs over about 1000 /*m, whereas the downward trend in permeability continued throughout the whole of cell growth.

A third possible site of surface resistance is in the cellular coverings around the oocyte; the surface epithelium, the theca and the follicular epithelium (see Fig. 13). It was in order to remove these layers that in early experiments trypsin was used to isolate oocytes from the ovary. The permeability coefficients of these trypsinized oocytes, whose cellular layers were removed (Fig. 14) were not significantly different (provided their cell membrane was not damaged) from the coefficients of dissected oocytes which retained their cellular coverings.

It was concluded therefore that some factor other than mechanical resistance of the cell surface must have been involved to explain the downward trend in membrane permeability coefficients with cell size. One possible explanation is that the cytoplasm offers significant resistance to water flow which varies with the relative amount of cytoplasm present, i.e. with the volume: surface ratio. For a spherical cell such as the oocyte this ratio is equal to r/3 where r is the radius so that an increase in volume: surface ratio occurs with increasing cell size.

In order to explore this last possibility more fully, it is possible to calculate an associated membrane permeability coefficient (α) from the rate of osmotic volume change, provided a value for the diffusion coefficient (D) for water in the cell interior is assumed. This diffusion coefficient is taken as infinitely large in conventional permeability calculations, but if lower values of the diffusion coefficient are assumed, higher values of the corresponding permeability coefficient are calculated. Pairs of possible values of the diffusion and permeability coefficients are thus obtained and may be represented by a continuous line on a graph of α against D. (The method of calculation is described in the Appendix.) Graphs for 6 oocytes of varying size are shown in Fig. 12. The associated membrane permeability coefficients given have been corrected for the effects of the microvilli. Interpretation of these curves may be based on two considerations, (i) Since the overall rate of water flow depends on the extent of the microvilli, the membrane permeability cannot be so high as to have no effect on water flow, (ii) Since the corrected apparent membrane permeability coefficient still varies with oocyte size, the diffusion coefficient for water in the cytoplasm is not so high as to have no effect on water flow.

Combination of these two considerations means that probable values of a. and D must he on the bends of the curves and not on the straight parts at either end. The variations between the curves in Fig. 12 are due first of all to differences of cell size but probably also to variations between oocytes or to experimental error. Reasonable limits for a and D have therefore been estimated by drawing a rectangle so as to include at least some part of all the curves but not to transgress on the straight parts of any of them; α is thus estimated to lie between 2 × 10⁻⁴ and 3 × 10⁻³ cm s⁻¹ and D between 6×10⁻⁸ and 10⁻⁶ cm² s⁻¹. These estimates depend, of course, on the assumption that the variations between the curves are due to experimental error or to random differences between cells. If, on the other hand, it is assumed that a systematic change of either α or D occurs during development (although there is no evidence of this) then a slightly wider range of values for individual cells might be adopted; in view of the lack of evidence, it seems safer to assume that variations between cells occur at random.

Wang, Anfinsen & Polestra (1954) obtained a value of 8·7 10⁻⁸ cm² s⁻¹ for the self-diffusion coefficient of ovalbumin in 24·4% solution. As pointed out by Dick (1964) this probably represents the rate of mutual diffusion of water and protein in a concentrated solution, which is governed largely by the slow movement of the protein and thus makes a proper comparison with D in the present experiments; at lower concentrations mutual diffusion coefficients for protein-water systems lie between 10⁻⁷ and 10⁻⁶ cm² s¹ (Edsall, 1953). Thus the present range of values of D between 6 × 10⁻⁸ and 10⁻⁶ cm² s⁻¹ is consistent with slow mutual diffusion in a protein solution.

It may be noted that two authors have obtained values for the diffusion coefficient of tracer water in amphibian oocyte cytoplasm. In cells in which he had reason to believe that the cell membrane had been destroyed Lovtrup (1962, 1963) obtained a value of 4·76 × 10⁻⁶ cm² s⁻¹; while by a kinetic study involving ‘influx profile analysis’ Ling, Ochsenfelt & Karreman (1967) calculated values ranging between 7·2 ×10⁻⁶ and 1·5 ×10⁻⁵ cm² s⁻¹. Since the self-diffusion of tracer water involves an entirely different mechanism from that of osmotic water movement (see Dick, 1964), these figures are not, of course, comparable to the values of D, calculated in the present experiments, which involves mutual diffusion. Nevertheless, the values of Løvtrup and Ling et al. (1967) are significantly less than the self-diffusion coefficient of water in pure water, 2·35 × 10 ⁻⁵ cm² s⁻¹ (for H2O18 at 18 °C (Kohn, 1965)). This suggests that the oocyte cytoplasm retards tracer water exchange as well as osmotic water flow though to a much less extent.

Cass & Finkelstein (1967) obtained a value of 1 × 10⁻³ cm² s⁻¹ and Everitt, Redwood & Hay don (1969) a value of 2 × 10 ⁻³ cm² s⁻¹ for the osmotic water permeability of bimolecular phospholipid membranes. Such values are at least consistent with the approximate estimate of a between 2 × 10⁴ and 3 × 10⁻³ cm² s⁻¹ obtained for the cell membrane from the present data. However, it must be noted that all the above values are much lower than recent values of osmotic water permeability of mammalian erythrocytes which range from 1 × 10² to 4 × 10⁻³ cm² s⁻¹ (see Dick, 1966). Since internal diffusion is not taken into account in computing the latter values they must represent the minimum water permeability of the erythrocyte membrane and are thus significantly higher than the present estimate of α.

A correction was applied to this value to take account of the approximations involved in the derivation of (2’). a Calculated for L →0 (i.e. D→∞) was compared with k obtained by equation (1) for the same oocyte. All values of α obtained from (2’) were corrected by multiplying by the factor k/α. so as to obtain values of a comparable with the k values obtained from equation (1). Values of α were further corrected for the effects of microvilli by dividing by/(see p. 464).

This work was supported by a grant from the Medical Research Council to D. A. T. D. We wish to thank Mr Derek Coldham and Miss Linda McFarlane for their skilled and careful assistance with this work. Thanks are also due to Mrs J. Hornby of the Computing Laboratory, University of Dundee for assistance with designing the computer programme used.